A method and system for detecting spline engagement clearance in a drive shaft assembly

Abstract

The application relates to the technical field of mechanical component detection, and discloses a driving shaft assembly spline meshing gap detection method and system, wherein the driving shaft assembly spline meshing gap detection method comprises the following steps: determining an axial micro-loading peak value and a micro-loading position window; collecting axial forces and proximal differential displacement coordinates under each detection speed; obtaining a corrected branch load, identifying a forward contact area and a reverse contact area, respectively extrapolating a forward contact boundary and a reverse contact boundary, and calculating an axial equivalent assembly play; forming a measurement effectiveness gating result; weighting and fusing the axial equivalent assembly plays to obtain a final axial equivalent assembly play and outputting the final axial equivalent assembly play; and the application can avoid distortion data in an abnormal contact state from participating in final result calculation by fusing effective multiple measurement results, so that the accuracy, repeatability and online quality judgment reliability of driving shaft assembly spline meshing gap detection are improved.

Description

Technical Field

[0001] This application relates to the field of mechanical component testing technology, and more specifically, it relates to a method and system for detecting the spline meshing clearance of a drive shaft assembly. Background Technology

[0002] The drive shaft assembly is a crucial component of a vehicle's transmission system. Its ends typically engage with the internal splines of the wheel hub, differential gear, or other connecting components via external splines to transmit torque. The spline clearance directly affects the assembly quality and transmission performance of the assembly. Excessive clearance can easily cause impacts, backlash, vibrations, and abnormal noises during start-up, reversing, and load changes. Insufficient clearance or the presence of localized interference can lead to assembly difficulties, increased insertion and extraction forces, and abnormal wear. Therefore, accurate detection of the spline meshing clearance of the drive shaft assembly in its assembled state is of great importance.

[0003] Existing inspection methods include indirectly calculating clearance based on the individual dimensions of internal and external splines, using go / no-go gauges for dimensional judgment, manual push-pull combined with dial indicators or displacement sensors for measurement, and collecting force-displacement data under axial loading conditions to determine the spline fit status. Among these, dimensional calculation and go / no-go gauge inspection are difficult to reflect the actual contact state after assembly; manual inspection is significantly affected by the applied force and readings. While axial loading inspection facilitates online automation, the force and displacement obtained during the inspection process are not solely determined by the spline meshing clearance.

[0004] However, during axial loading, the drive shaft, connecting parts, fixtures, and detection mechanism may undergo elastic deformation; the friction and lubrication conditions of the spline teeth and the detection speed will change the force-displacement response; the end retaining ring may cause sudden changes in local load when compressed, overcoming obstacles, or entering the groove; and when there is radial eccentricity or axial tilt between the drive shaft and the mating parts, some tooth surfaces may make premature contact or local jamming. These factors, coupled with the axial response caused by the spline clearance, result in different detection curves for the same geometric fit under different assembly postures, speeds, or friction conditions.

[0005] Therefore, the main problem with existing drive shaft assembly spline clearance detection technology is that it is difficult to reliably identify the effective boundary that can truly characterize the axial free displacement range of the spline connection structure from axial force and displacement data that includes the effects of structural deformation, friction and speed effects, snap ring action and abnormal posture, and thus obtain the assembly state spline meshing clearance with good accuracy and repeatability; when there is abnormal contact or the measurement conditions do not meet the requirements, the detection results are also prone to distortion, thereby affecting the reliability of online quality judgment. Summary of the Invention

[0006] The purpose of this application is to solve the problem that in the existing process of detecting spline meshing clearance of drive shaft assembly, factors such as structural elastic deformation, friction and speed effects, snap ring action and assembly posture changes are coupled with the spline clearance detection signal, making it difficult to accurately identify the axial equivalent assembly clearance of the spline, thus affecting the accuracy, repeatability and reliability of the detection results. Therefore, this application provides a method and system for detecting spline meshing clearance of drive shaft assembly.

[0007] This application provides a method for detecting the spline meshing clearance of a drive shaft assembly, including the following steps:

[0008] Insert the external spline into the internal spline to the preset engagement position, identify the snap ring action position range, and determine the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position range;

[0009] A proximal differential measurement benchmark is established. Within the micro-loading position window, a symmetrical micro-loading cycle of forward and reverse micro-loading is performed at different detection speeds with the axial micro-loading peak value. Based on the proximal differential measurement benchmark, the axial force and proximal differential displacement coordinates at each detection speed are collected.

[0010] The axial force at each detection speed is corrected by speed-related load correction and friction baseline subtraction to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the negative contact area are identified and extrapolated to obtain the positive contact boundary and the negative contact boundary respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the negative contact boundary is used as the axial equivalent assembly clearance.

[0011] The effectiveness of the axial equivalent assembly clearance is assessed to generate measurement effectiveness gating results.

[0012] When the measurement validity gating result is valid, the weighted fusion of each axial equivalent assembly clearance is used to obtain the final axial equivalent assembly clearance and output it.

[0013] Furthermore, methods for identifying the operating position range of the snap ring include:

[0014] Insert the external spline into the internal spline at a preset insertion speed, and collect the axial force and axial position.

[0015] The axial force signal is smoothed and filtered, and then resampled to equal displacement intervals according to the axial position;

[0016] A dimensionless load mutation index is constructed based on the first and second rates of change of the filtered axial force with respect to the axial position.

[0017] When the dimensionless load mutation index exceeds the preset load mutation index threshold, and the preset peak width criterion, preset peak fall amplitude criterion, and preset displacement span criterion are triggered, the axial start position to axial end position of the corresponding segment is recorded as the snap ring action position range.

[0018] Furthermore, methods for determining the axial micro-load peak value and the micro-load location window include:

[0019] Determine the force measurement noise and load fluctuation margin based on the current sensor noise level;

[0020] Calculate the limiting load for circlip state changes based on the circlip's obstacle crossing peak value within the circlip's operating position range;

[0021] The minimum value of the sum of the preset maximum axial friction force, force measurement noise, and loading fluctuation margin is used as the lower limit, and the minimum value of the load limiting the change of the snap ring state and the preset snap ring disengagement load is used as the upper limit, thus forming a micro-load safety load window.

[0022] Determine the peak value of axial micro-load within the micro-load safety load window;

[0023] The maximum displacement under unidirectional micro-loading is determined based on the preset meshing position;

[0024] With the preset meshing position as the center, the positions offset by the maximum displacement of unidirectional micro-loading along two opposite axial directions are used as the two boundaries of the micro-loading position window, and the micro-loading position window does not include the snap ring action position interval.

[0025] Furthermore, methods for establishing proximal differential measurement benchmarks include:

[0026] Axial displacement detection units with the same positive coordinate direction are set at the rigid reference position near the outer spline side and the rigid reference position near the inner spline side, respectively.

[0027] Preload stabilization is achieved by performing a symmetrical micro-loading cycle of forward and reverse micro-loading at a preset engagement position and a preset number of preload stabilization cycles.

[0028] After preloading stabilization is completed, the reference establishment time is determined based on the axial displacement detection unit;

[0029] At the time of reference establishment, the initial proximal differential value is obtained by subtracting the displacement of the proximal rigid reference position on the inner spline side from the displacement of the proximal rigid reference position on the outer spline side.

[0030] The proximal differential measurement reference is composed of the external spline side proximal rigid reference position, the internal spline side proximal rigid reference position, and the initial proximal differential value.

[0031] Furthermore, methods for acquiring axial force and proximal differential displacement coordinates include:

[0032] At each detection speed, a positive peak load is applied from a preset engagement position along the first axial direction and held for a preset holding time, then a negative peak load is applied along the second axial direction and held for the same preset holding time, and finally the initial load state is returned. The absolute values ​​of the positive peak load and the negative peak load are both axial micro-load peak values.

[0033] For any data sampling time after the reference establishment time, the current proximal differential value is obtained by subtracting the displacement of the rigid reference position of the inner spline side from the displacement of the rigid reference position of the proximal end of the outer spline side.

[0034] The proximal differential displacement coordinates are obtained by subtracting the initial proximal differential value from the current proximal differential value. The axial force and proximal differential displacement coordinates at each detection speed are collected using the same proximal differential measurement benchmark.

[0035] Furthermore, methods for obtaining the corrected branch load include:

[0036] For each data point at each detection speed, the corrected load at that detection speed is calculated based on the axial force collected at that detection speed.

[0037] Based on the detection speed and the corrected load, the quasi-static load estimate is calculated;

[0038] In the free micro-motion zone where the connection structure only bears frictional load, the median of the quasi-static load estimates of continuous data points with local stiffness less than a preset local stiffness threshold is used as the friction baseline estimate.

[0039] The corrected branch load is obtained by subtracting the friction baseline estimate from the quasi-static load estimate.

[0040] Furthermore, methods for obtaining the positive contact boundary and the negative contact boundary include:

[0041] Robust fitting of the modified branch load and the near-end differential displacement coordinates is performed to obtain the fitted straight line, and the residual robustness scale of the fitted residuals is determined.

[0042] When the absolute value of the modified branch load is greater than the preset minimum contact load, the modified branch load changes in the same direction as the near-end differential displacement coordinate, and the residual robustness scale is less than or equal to the preset upper limit of the contact area fitting error, it is identified as a stable contact area. The stable contact areas located in the positive micro-loading branch and the reverse micro-loading branch are respectively regarded as the positive contact area and the reverse contact area.

[0043] The fitted straight lines of the positive and negative contact areas are extrapolated to the point where the corrected branch load is zero, and the resulting intersection points are taken as the positive and negative contact boundaries, respectively.

[0044] Furthermore, methods for generating measurement validity gating results include:

[0045] The absolute values ​​of the slopes of the fitted straight lines in the forward and reverse contact areas are used as the equivalent stiffness of the forward and reverse contact areas, respectively. The stiffness asymmetry coefficient of the forward and reverse contact is calculated based on the equivalent stiffness of the forward and reverse contact areas.

[0046] Detect the radial offset at the end of the drive shaft and the tilt of the drive shaft axis during micro-loading;

[0047] When the asymmetry coefficient of positive and negative contact stiffness, the maximum radial offset and the maximum drive shaft axis tilt are less than or equal to the corresponding preset upper limit, and the equivalent stiffness of positive contact and the equivalent stiffness of negative contact are both greater than or equal to the preset minimum equivalent stiffness of contact, the attitude effective condition is triggered.

[0048] Execute multiple micro-loading loops and check if the repeatability pass condition is triggered;

[0049] If the attitude validity condition and repeatability pass condition are triggered, the measurement validity gating result will be valid; otherwise, it will be invalid.

[0050] Furthermore, by performing micro-loading cycles multiple times at the same detection location, multiple axial equivalent assembly clearance measurement results were obtained.

[0051] The repeatability range, repeatability robustness standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift are calculated based on the results of multiple axial equivalent assembly clearance measurements.

[0052] When the repeatability range, repeatability robust standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift are all less than or equal to the preset allowable upper limit, the repeatability pass condition is triggered, and the measurement results are retained.

[0053] The weighted sum of the axial equivalent assembly clearances from each retained measurement is calculated to obtain the final axial equivalent assembly clearance.

[0054] This application provides a drive shaft assembly spline meshing clearance detection system for performing the aforementioned drive shaft assembly spline meshing clearance detection method; the system includes:

[0055] The position interval module inserts the external spline into the internal spline to a preset engagement position, identifies the snap ring action position interval, and determines the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position interval.

[0056] The loading loop module establishes a proximal differential measurement benchmark. Within the micro-loading position window, with the axial micro-loading peak value, a symmetrical micro-loading loop of forward and reverse micro-loading is executed at different detection speeds. Based on the proximal differential measurement benchmark, the axial force and proximal differential displacement coordinates at each detection speed are collected.

[0057] The equivalent assembly module performs speed-related load correction and friction baseline subtraction on the axial force at each detection speed to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the reverse contact area are identified and extrapolated to obtain the positive contact boundary and the reverse contact boundary respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the reverse contact boundary is used as the axial equivalent assembly clearance.

[0058] The effective gating module determines the effectiveness of the axial equivalent assembly clearance and generates a measurement effectiveness gating result.

[0059] The clearance output module, when the measurement validity gating result is valid, weights and fuses the axial equivalent assembly clearance of each measurement to obtain the final axial equivalent assembly clearance and outputs it.

[0060] The beneficial effects of this application are as follows: By identifying the working position range of the snap ring and performing detection within a separate micro-loading position window, the interference of non-spline clearance factors such as snap ring compression and obstacle crossing on the detection results is reduced. By establishing a near-end differential measurement benchmark and combining symmetrical micro-loading data at different detection speeds, the speed-related load and friction baseline are corrected. The relative displacement between the positive and negative contact boundaries characterizes the axial equivalent assembly clearance, thereby improving the ability to identify the true axial free displacement range of the spline and reducing measurement deviations caused by structural deformation, friction, and changes in detection speed. By validating the radial offset, axial tilt, and other attitude states during the detection process and fusing valid multiple measurement results, this application avoids distorted data under abnormal contact states from participating in the final result calculation, improving the accuracy, repeatability, and reliability of online quality judgment in the detection of spline meshing clearance of the drive shaft assembly. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating a method for detecting the spline meshing clearance of a drive shaft assembly according to this application;

[0062] Figure 2 This is a flowchart of the acquisition of axial force and proximal differential displacement coordinates in this application;

[0063] Figure 3 This is a module example diagram of a drive shaft assembly spline meshing clearance detection system according to this application. Detailed Implementation

[0064] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0065] A method and system for detecting spline meshing clearance in a drive shaft assembly, comprising the following embodiments:

[0066] Example 1:

[0067] A method for detecting the spline meshing clearance of a drive shaft assembly is provided to obtain the axial equivalent assembly clearance between the external spline and the mating internal spline of the drive shaft at a preset meshing position without disassembling the drive shaft assembly. When the detection data is affected by factors such as snap ring overcoming obstacles, radial offset, axis tilting, abnormal friction or nonlinear contact, or when the repeatability condition is not triggered, the method outputs an invalid measurement result and the corresponding cause of the abnormality.

[0068] In this embodiment, the spline meshing clearance specifically refers to the equivalent free displacement between two repeatable axial contact boundaries formed by the spline connection structure, retaining structures such as snap rings or shoulders, and adjacent connecting components when the external spline of the drive shaft and the mating internal spline are in the preset meshing position. In this embodiment, it is uniformly referred to as the axial equivalent assembly clearance. This axial equivalent assembly clearance is different from the spline circumferential tooth side clearance measured under positive torsional load and reverse torsional load conditions.

[0069] In this embodiment, the repeatable axial contact boundary refers to the critical point of axial displacement that can be stably reproduced in multiple loading operations when the connection structure transitions from a free micro-motion state to a bearing contact state under axial load applied along the spline axis. The first axial direction is the positive direction of the axial coordinate, and the second axial direction is the negative direction of the axial coordinate. The contact boundary formed when loading along the first axial direction is uniformly referred to as the positive contact boundary, and the contact boundary formed when loading along the second axial direction is uniformly referred to as the reverse contact boundary.

[0070] In an optional embodiment, the inspection system for implementing the method is located on an automated assembly line for drive shaft assemblies, an online final inspection station, or a rework inspection station; the inspection system includes an axial servo driver, which is used to drive the external spline to insert, hold, perform forward micro-loading, and reverse micro-loading relative to the internal spline; forward micro-loading refers to applying an axial load along a first axial direction, and reverse micro-loading refers to applying an axial load along a second axial direction.

[0071] In an optional embodiment, the detection system includes a drive shaft positioning fixture and an internal spline positioning fixture; the drive shaft positioning fixture is used to fix the drive shaft assembly and allow controlled micro-displacement along the axial direction at the end of the drive shaft; the internal spline positioning fixture is used to fix the actual mating parts or simulate the internal spline detection parts; when the axial displacement detection unit can be arranged at the proximal rigid reference position of the external spline and internal spline, the actual mating parts are used, and the resulting axial equivalent assembly clearance characterizes the assembly state of the actual assembly; when the external spline and internal spline are located inside a closed housing and the axial displacement detection unit cannot be arranged at the proximal rigid reference position... When a simulated internal spline test piece is used, the axial equivalent assembly clearance obtained under simulated conditions represents the assembly state. Only when the spline tooth profile, snap ring groove position, mating inner diameter, surface condition, lubrication conditions, and manufacturing tolerances of the simulated internal spline test piece have established a correspondence with the actual mating parts through equivalent type testing can the axial equivalent assembly clearance under simulated conditions be converted into the axial equivalent assembly clearance of the actual assembly. If this correspondence is not established, the testing system marks the results of the actual mating parts and the results of the simulated internal spline test piece separately, and does not treat the two as results of the same assembly state.

[0072] The detection system includes a floating centering mechanism. The floating centering mechanism is used to release the preset radial degree of freedom during the initial insertion stage, so that the external spline and internal spline can complete self-centering, and lock the current position after entering the detection stage. The preset radial degree of freedom is determined according to the coaxiality tolerance of the external spline and internal spline, the movable range of the floating centering mechanism, and the range of the radial displacement detection unit. Specifically, the initial radial offset is changed step by step through the eccentric assembly type test to select a radial movement range that can cover the allowable coaxiality tolerance, enable the external spline and internal spline to complete self-centering, and whose upper boundary of the radial movement range is less than or equal to the upper limit of the range of the radial displacement detection unit.

[0073] The detection system includes an axial force sensor; the axial force sensor is used to collect axial force during positive and reverse micro-loading processes; using axial force as input, it can distinguish between free micro-motion state and bearing contact state, and provide load basis for inertial load correction, friction baseline subtraction and contact boundary extrapolation.

[0074] The detection system includes a dual-reference axial displacement detector. The dual-reference axial displacement detector comprises two axial displacement detection units respectively positioned at the proximal rigid reference positions on the external spline side and the internal spline side. The two axial displacement detection units use the same positive coordinate direction to synchronously obtain the axial displacements on both sides of the spline connection structure. "Proximal" refers to the rigid reference position closest to the spline meshing area axially. The difference in axial displacement between the two axial displacement detection units at the moment the reference is established is called the initial proximal differential value. The proximal rigid reference positions on the external spline side, the internal spline side, and the initial proximal differential value together constitute the proximal differential measurement reference, where the two proximal rigid reference positions constitute a spatial reference, and the initial proximal differential value constitutes a numerical zero point. Using this proximal differential measurement reference, the relative axial displacements on both sides of the spline connection structure can be obtained, and the common-mode effects of elastic deformation of the drive shaft assembly, fixture deformation, and deformation of the detection equipment frame can be suppressed.

[0075] The detection system includes radial offset and tilt detectors; the radial offset and tilt detectors include orthogonal radial displacement detection units respectively set on the first and second measurement sections, with the first and second measurement sections spaced at a preset axial distance along the spline axis; the preset allowable measurement error of the drive shaft axis tilt is determined according to the error budget allocated to the axis attitude measurement based on the product measurement requirements; the preset axial distance is determined based on the measurement sections that can be arranged on the drive shaft, the resolution of the radial displacement detection units, and the preset allowable measurement error of the drive shaft axis tilt. Specifically, by calibrating the tilt measurement error under different axial intervals, an axial interval is selected that can distinguish between overall radial translation and axis tilt, both measurement sections are located in rigid measurement positions, and the tilt measurement error is less than or equal to the preset allowable measurement error of the drive shaft axis tilt; two mutually orthogonal radial displacement detection directions are set on each measurement section, referred to as the first radial detection direction and the second radial detection direction, respectively, to detect the radial offset and drive shaft axis tilt at the end of the drive shaft during micro-loading.

[0076] In this embodiment, the drive shaft axis tilt is the ratio of the radial offset vector difference between two measurement sections to the axial distance between the two measurement sections. It is a dimensionless slope, equal to the tangent of the tilt angle of the drive shaft axis relative to the spline axis. Within the small tilt range involved in this embodiment, this dimensionless slope is close to the tilt angle expressed in radians and can be used as an approximate representation of the tilt angle. In this embodiment, all thresholds and allowable upper limits related to the drive shaft axis tilt and the absolute axis tilt are based on this dimensionless slope. They are directly calibrated and judged according to the slope through type testing, and the output is a dimensionless slope, which is no longer converted into an angle.

[0077] In an optional embodiment, each radial displacement detection unit is calibrated relative to the absolute reference axis of the detection system. The absolute reference axis is either the mechanical rotation axis of the drive shaft positioning fixture or a calibrated laser reference axis. After calibration, each radial displacement detection unit can output the absolute radial position relative to the absolute reference axis to determine the absolute radial eccentricity and absolute axis tilt of the drive shaft axis relative to the absolute reference axis. It can also output the radial displacement change relative to the reference establishment time to determine the radial offset and drive shaft axis tilt caused by micro-loading. The absolute radial eccentricity and absolute axis tilt are used to characterize the static eccentricity and static tilt that already exist when clamping is completed and will not be zeroed even if they remain unchanged during micro-loading. The radial offset and drive shaft axis tilt are used to characterize the attitude change caused by micro-loading. The above-mentioned absolute attitude index and attitude index caused by micro-loading are two independent sets of indexes participating in the attitude judgment in step 400, so that both the static eccentricity and static tilt at the completion of clamping and the attitude change caused by micro-loading can be identified.

[0078] The detection system includes a data acquisition controller; the data acquisition controller is used to synchronously acquire axial force, axial displacement, radial displacement, velocity, acceleration, and temperature data; synchronous acquisition ensures that the motion state, axis attitude, and environmental state correspond to the force and displacement data at the same data sampling time, avoiding mismatch between the correction amount and the corrected data caused by inconsistent sampling times; the detection system includes a curve segmentation processor; the curve segmentation processor is used to identify the snap ring action position range, free micro-motion zone, forward contact zone, and reverse contact zone; the detection system includes a clearance calculation processor; the clearance calculation processor is used to perform velocity-related load correction, friction baseline estimation, contact zone fitting, and contact boundary extrapolation; the detection system includes a measurement validity judge; the measurement validity judge is used to determine the measurement validity gating result.

[0079] A method for detecting the spline meshing clearance of a drive shaft assembly, such as Figure 1 As shown, it includes the following steps:

[0080] Step 100: Insert the external spline into the internal spline to the preset engagement position, identify the snap ring action position range, and determine the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position range; this step is used to isolate the snap ring obstacle-crossing load from the spline contact load before formal measurement, and at the same time limit the micro-load range that can identify the contact boundary without changing the snap ring state.

[0081] The detection start conditions are set as follows: the detection system confirms that the drive shaft assembly is installed on the drive shaft positioning fixture; the axial servo driver can apply positive and negative micro-loading along the spline axis; the drive shaft assembly is stationary or its rotational speed is less than a preset static measurement threshold; the tested connection structure has been confirmed by type verification to have two repeatably identifiable axial contact boundaries; and the drive shaft assembly model, detection fixture number, temperature near the spline, and sensor status have all been acquired. This embodiment's detection method is applicable only if the tested connection structure has two repeatably identifiable axial contact boundaries. This method is applicable to spline pairs without axial restraint that can slide continuously axially; connection structures where the axial free travel is greater than the available travel of the detection mechanism; connection structures where snap rings or elastic components form continuous gradual loads without forming identifiable contact boundaries; connection structures where friction loads mask the characteristics of contact stiffness changes; and other related conditions. Connection structures where multiple limiting components contact sequentially, making it impossible to determine a unique contact boundary, lack identifiable axial equivalent assembly clearance and are not applicable to this method. For such connection structures, the testing system determines they are unsuitable during the type verification stage and does not proceed to subsequent testing in this step. The preset static measurement threshold is determined based on the speed detection resolution during the drive shaft assembly's stoppage, the axial inertial load caused by residual rotation, and the repeatability of the contact boundary. Specifically, the residual speed is gradually changed through type testing to select the speed boundary corresponding to when the axial inertial load can be compensated and the repeatability of the contact boundary meets the product measurement requirements. The testing system simultaneously acquires the drive shaft assembly model, testing fixture number, temperature near the spline, and sensor status. When all criteria in the testing start condition are met, the testing system triggers the testing start condition and executes subsequent testing; if any criterion is not met, the testing start condition is not triggered, and the testing system does not execute subsequent testing.

[0082] The data acquisition controller reads the number of external spline teeth and effective meshing length, the type of mating internal spline, drive shaft length, drive shaft diameter, clamping position, type of snap ring or other axial limiting structure, and preset meshing position. The above structural and geometric inputs are used to match the meshing position, axial limiting method, and micro-load stroke constraint of the corresponding product model, avoiding the use of assembly boundaries from other models for the current drive shaft assembly. The preset meshing position is the preset axial position of the external and internal splines during micro-load testing. It is determined based on the effective meshing length of the corresponding product model, the assembly position of the snap ring or shoulder, and the product assembly technical requirements. Type testing verifies that this position is not within the snap ring's active position range and can repeatedly identify positive and negative contact boundaries. The data acquisition controller also reads the displacement sensor calibration coefficient, current sensor noise level, and... The number of historical qualified product benchmark curves is equal to the preset number of historical benchmark curves, used for displacement data calibration, load mutation identification, and micro-loading parameter determination in this step; the displacement sensor calibration coefficient is obtained by applying a traceable standard displacement within the sensor range and fitting the sensor output with the standard displacement; the preset allowable lubrication range is determined according to the product lubrication material specifications and assembly process requirements, and the preset allowable temperature range is determined according to the product testing environment requirements, the applicable temperature range of the lubrication material, and the intersection of the compensation temperature ranges of the displacement sensor and the axial force sensor; the number of preset historical benchmark curves is determined according to the operating condition coverage requirements of the corresponding product model within the preset allowable lubrication range and preset allowable temperature range, specifically selecting the number of curves that cover all allowable operating conditions and whose load mutation index statistical boundary remains unchanged after continuing to add historical qualified product benchmark curves.

[0083] The axial servo drive drives the external spline into the internal spline at a preset insertion speed. The data acquisition controller synchronously acquires the axial load, the control displacement of the axial servo drive, and the insertion speed according to the data sampling time. The preset insertion speed is obtained through the insertion type test of the corresponding product model. Specifically, within the speed range that does not cause impact on the spline tooth surface or abnormal deformation of the snap ring, and the lubrication temperature after detection is greater than or equal to the lower limit of the preset allowable temperature range and less than or equal to the upper limit of the preset allowable temperature range, the insertion speed is selected that can completely acquire the snap ring compression, obstacle crossing and groove entry process, and the snap ring action position interval repeated identification results meet the requirements.

[0084] In an optional embodiment, the curve segmentation processor first processes the axial force signal using a zero-phase low-pass filter with a preset cutoff frequency or local polynomial smoothing to obtain a filtered axial force signal. Zero-phase low-pass filtering refers to filtering the axial force signal in the forward direction first and then in the reverse direction, ensuring that the filtering result does not introduce phase delay. When using local polynomial smoothing, the curve segmentation processor compensates for the filtering delay introduced by the smoothing, ensuring that the position of the smoothed load abrupt change peak corresponds to the position of the original load abrupt change peak. Local polynomial smoothing refers to fitting a polynomial of a preset order using the least squares method within a preset sliding window centered on the current sampling point, and using the value of this polynomial at the current sampling point. As a smoothing result, high-frequency noise is suppressed while retaining load mutation characteristics. The preset cutoff frequency, preset sliding window, and preset order are determined by the historical insertion force curve with the snap ring action interval marked. Specifically, the noise residue, load mutation peak distortion, and snap ring action position interval boundary deviation are compared after different parameter combinations. The parameter combination that can retain the snap ring load mutation characteristics, make the peak attenuation less than or equal to the upper limit of the peak attenuation corresponding to the snap ring action position interval boundary repetition recognition requirement, make the axial position deviation less than or equal to the upper limit of the axial position deviation corresponding to the snap ring action position interval boundary repetition recognition requirement, and make the interval boundary repetition recognition result meet the requirements is selected.

[0085] The curve segmentation processor first resamples the filtered axial force signal to equal displacement intervals according to the axial position. Then, it constructs a dimensionless load mutation index based on the first and second rate of change of the filtered axial force signal with respect to the axial position. Using the axial position as the independent variable can eliminate the influence of insertion speed fluctuations on the first and second rate of change, ensuring that the spatial force-displacement characteristics of the snap ring compression, obstacle crossing, and slot insertion do not change with the insertion speed. The first rate of change reflects the change in load slope, and the second rate of change reflects the change in load curvature and peak edge. Combining the two allows for the simultaneous utilization of the slope and peak characteristics of the snap ring's action range. In this step, the first and second rate of change refer to the first and second rate of change of the filtered axial force signal with respect to the axial position. At each data sampling moment, the curve segmentation processor first takes the absolute value of the first rate of change, and then divides this absolute value by the robustness scale of the first rate of change and the preset first rate of change. The sum of the rate regularization constants is multiplied by the quotient and a preset first-order rate of change term weight to obtain the first-order rate of change component. The curve segmentation processor also takes the absolute value of the second-order rate of change, divides this absolute value by the sum of the robustness scale of the second-order rate of change and the preset second-order rate of change regularization constant, and multiplies the quotient by the preset second-order rate of change term weight to obtain the second-order rate of change component. The dimensionless load mutation index is the sum of the first-order rate of change component and the second-order rate of change component. The sum of the preset first-order rate of change term weight and the preset second-order rate of change term weight is one. The two preset rate of change term weights are determined according to the ability of the first-order rate of change component and the second-order rate of change component to distinguish between the snap ring action area and the non-snap ring action area. Specifically, historical insertion force curves with interval labels are used for cross-validation. Candidate weight combinations with a sum of weights of one are traversed, and the weight combination with the fewest interval identification errors and the interval boundary repetition identification results meet the requirements is selected.

[0086] For example, for the first digit after equal displacement resampling For each location point, the dimensionless load mutation index can be expressed as:

[0087] and satisfy The first-order rate of change and the second-order rate of change can be expressed as follows: and .

[0088] in, For the first Dimensionless load mutation index at each location point This represents the sequence number of the resampling location point with equal displacement. This refers to the axial position. For the first The axial position of each location point Axial position axial force after filtering at the location, For the first The first-order rate of change at each location point For the first The second-order rate of change at each location point It is a robust measure of the first-order rate of change. It is a robust measure of the second-order rate of change. To pre-determine the first-order rate of change regularization constant, To pre-set the second-order rate of change regularization constant, To pre-determine the weights of the first-order rate of change term, The weights are preset for the second-order rate of change term.

[0089] Both the preset first-order rate of change regularization constant and the preset second-order rate of change regularization constant are positive numbers to avoid the corresponding division by zero. The two preset rate of change regularization constants are determined according to the noise scale of the corresponding rate of change channel in the steady-state insertion section. Specifically, they are determined by the sensor resolution of the channel and the steady-state noise scale in the historical qualified product benchmark curve, and the stability of the noise disturbance is verified by the load mutation index.

[0090] Both the robust scales for the first-order and second-order rates of change are determined using the median absolute deviation. For any signal sequence, the curve segmentation processor first determines the median of all sampled values, then calculates the absolute value of the difference between each sampled value and the median, then determines the median of all absolute differences, and finally multiplies the median of the absolute differences by a preset scale uniformity coefficient. The result is the robust scale of the signal sequence. The preset scale uniformity coefficient is determined based on the conversion relationship between the median absolute deviation and the standard deviation of the reference distribution used. In this embodiment, a normal distribution is used as the reference distribution, so that the converted median absolute deviation and the standard deviation have a consistent scale. By processing the first-order and second-order rate of change sequences of the filtered axial force signal in the above manner, the corresponding robust scales can be obtained. Using the median absolute deviation can limit the influence of isolated load pulses on scale estimation. The dimensionless load mutation index normalizes the first-order and second-order rates of change through the robust scale, and is therefore unaffected by the load dimension.

[0091] The identification conditions for the snap ring's action position interval include four criteria: the dimensionless load mutation index is greater than a preset load mutation index threshold, the corresponding load change meets a preset peak width criterion, the corresponding load change meets a preset post-peak drop amplitude criterion, and the corresponding load change meets a preset displacement span criterion. When all four criteria are met simultaneously, the curve segmentation processor triggers the snap ring action position interval identification conditions, marking the corresponding segment as the snap ring compression, obstacle crossing, or slot insertion action interval, and recording the axial start position to axial end position covered by this interval as the snap ring action position interval. By combining mutation intensity, peak width, post-peak drop amplitude, and displacement span, it is possible to exclude... Only instantaneous noise or ordinary friction fluctuations that meet the single mutation characteristic are considered. The preset load mutation index threshold, preset peak width criterion, preset peak fall amplitude criterion, and preset displacement span criterion are obtained through type test curves with markings for snap ring compression, obstacle crossing, and slot insertion intervals. Specifically, candidate criteria are generated based on the index distribution boundary between the snap ring action interval and the normal insertion interval, and independent verification curves are used to select the criterion combination that can identify all marked snap ring action intervals and has the fewest misidentified intervals. The snap ring obstacle crossing peak value identified in this step is used to determine the upper limit of the axial micro-load peak value, and the snap ring action position interval recorded in this step is used to determine the micro-load position window.

[0092] Within the identified circlip obstacle-crossing range, the curve segmentation processor determines the maximum load value of the filtered axial force signal along the insertion direction and identifies this maximum load value as the circlip obstacle-crossing peak value for this insertion process. The axial position corresponding to this maximum load value is identified as the circlip obstacle-crossing peak position. When multiple local load peaks exist within the circlip obstacle-crossing range, only the local load peaks that meet the preset peak width criterion, the preset peak fall-off amplitude criterion, and the preset displacement span criterion are retained, and the maximum load value along the insertion direction is taken as the circlip obstacle-crossing peak value. Using the maximum load value that satisfies all peak shape criteria can avoid using secondary local peaks as the main peak of circlip obstacle-crossing. If no local load peak that meets the above criteria is identified, the current circlip obstacle-crossing peak value is determined to be invalid, and subsequent micro-load detection is not performed.

[0093] The axial servo driver continues to drive the external spline insertion until the external spline moves to the preset engagement position with the actual mating internal spline or the simulated internal spline detection part, and then stops continuous insertion. The detection system confirms that the actual effective engagement length between the external spline and the internal spline is greater than or equal to the specified effective engagement length based on the number of external spline teeth, effective engagement length, and axial position information. When a snap ring is provided at the end of the drive shaft, the detection system also confirms that the snap ring has passed the mating part inlet or entered the specified assembly position based on the snap ring's active position range and axial position information. If the actual effective engagement length criterion or the snap ring assembly position criterion is not met, the micro-load execution condition is not triggered, and the detection system does not perform micro-load detection.

[0094] Before formal micro-loading, the testing system reads the preset maximum axial friction force and the preset minimum circlip release load obtained through type testing for the corresponding model within the preset allowable lubrication range and preset allowable temperature range. The preset maximum axial friction force is obtained by performing reciprocating axial micro-movements under various test conditions covered by the preset allowable lubrication range and preset allowable temperature range, and taking the maximum absolute value of the friction load in the stable micro-movement zone of each condition. The preset minimum circlip release load is obtained by performing axial release tests on circlip and circlip combinations within the allowable tolerance range, and taking the minimum axial load when each combination of circlips releases. The testing system also determines the force measurement noise and loading fluctuation margin based on the current sensor noise level. The method for obtaining the data is as follows: during the calibration process of the axial servo drive maintaining the load and performing repeated micro-loading, the deviation envelope of the axial force sensor output relative to the stable load and the deviation envelope of the actual peak load of the axial servo drive relative to the commanded peak load are obtained respectively. The sum of the upper boundaries of the two deviation envelopes is then used as the force measurement noise and load fluctuation margin. The axial micro-loading peak value is not used as the initial preset parameter. The detection system dynamically determines the axial micro-loading peak value based on the preset maximum axial friction force, force measurement noise and load fluctuation margin applicable to this detection, and the snap ring load boundary. The dynamically determined axial micro-loading peak value can adapt to the friction, noise and snap ring load boundary of the current model, so that the contact boundary has identifiable load characteristics, while not changing the snap ring state.

[0095] The lower limit of the micro-load safety load window is set as the sum of the preset maximum axial friction force, force measurement noise, and load fluctuation margin. The peak value of the axial micro-load must be greater than the sum of the preset maximum axial friction force, force measurement noise, and load fluctuation margin. This lower limit allows the load to exceed the force value range formed by friction and noise in order to identify the contact boundary.

[0096] The detection system multiplies the peak value of the retaining ring crossing obstacle identified during the insertion process by a preset auxiliary limit coefficient to obtain the retaining ring state change limit load; the preset auxiliary limit coefficient is greater than zero and less than one; the detection system also divides the preset minimum retaining ring disengagement load by a preset safety factor to obtain the preset retaining ring disengagement limit load, the preset safety factor is greater than one; the preset auxiliary limit coefficient is determined based on the ratio of the peak value of the retaining ring crossing obstacle to the axial load when the retaining ring state begins to change in the micro-loading direction; since the direction, contact geometry, and friction state corresponding to the insertion obstacle crossing are different from the direction, contact geometry, and friction state when the retaining ring begins to change state in the positive and negative directions of micro-loading after it has entered the slot, the peak value of the obstacle crossing obstacle and the retaining ring state change load in the micro-loading direction are not assumed to be a fixed proportional relationship; the preset auxiliary limit coefficient is determined through type tests with direction differentiation, specifically for retaining ring and retaining ring combinations within the allowable tolerance range, in the positive and negative directions of micro-loading respectively. The axial load at the start of the circlip state change is measured, and a coefficient is selected to ensure that the circlip state change limiting load is less than or equal to the circlip state change load of each combination in the forward and reverse directions of micro-loading. The preset safety factor is determined based on the test discrete range of the preset minimum circlip release load, the measurement error of the axial force sensor, and the loading error of the axial servo drive. Specifically, a coefficient is selected to ensure that the actual axial load after the preset circlip release limiting load and each error are superimposed is still less than the preset minimum circlip release load. The detection system takes the minimum value between the circlip state change limiting load and the preset circlip release limiting load as the upper limit of the micro-loading safety load window. The peak value of the axial micro-loading must be less than this upper limit, so that the loading process does not trigger the circlip state change and does not cause the circlip to release. If there is no micro-loading safety load window that simultaneously meets the above lower and upper limits, the detection system will not perform subsequent micro-loading detection and will output "Micro-loading safety load window does not exist".

[0097] The detection system dynamically determines the maximum displacement under unidirectional micro-loading simultaneously. The method for obtaining the maximum displacement under unidirectional micro-loading is as follows: Calculate the available axial distance from the preset engagement position to the boundary of the snap ring's working position, the available axial distance from the preset engagement position to the spline disengagement position, and the available axial distance allowed for the snap ring to remain within the slot. For each available axial distance, subtract the displacement margin caused by the axial displacement measurement error and the axial servo drive positioning error to obtain the available axial distance after deducting the margin. Take the minimum value among the available axial distances after deducting the margin as the maximum displacement under unidirectional micro-loading. This system enables the micro-loading stroke to simultaneously satisfy three constraints: the snap ring's operating position range, the spline's exit position, and the snap ring's retaining position. The detection system uses a preset engagement position as the center, and takes the position after offsetting the maximum unidirectional micro-loading displacement along the second axial direction as one boundary of the micro-loading position window, and the position after offsetting the maximum unidirectional micro-loading displacement along the first axial direction as the other boundary of the micro-loading position window. The micro-loading position window defined by the two boundaries must not include any position within the snap ring's operating position range. The maximum unidirectional micro-loading displacement must also be less than the spline's exit stroke, and the snap ring must remain in the slot throughout the micro-loading process.

[0098] After the micro-loading parameters are determined, the measurement validity judge determines whether the micro-loading position window is separated from the snap ring action position interval. If the two intervals have a common position, the detection position is adjusted until the two intervals no longer have a common position, provided that the actual effective engagement length is greater than or equal to the specified effective engagement length. Interval separation can prevent snap ring compression, obstacle crossing, or slot load from entering the spline contact boundary fitting data. If the two intervals cannot be separated by adjustment, the micro-loading execution condition is not triggered, the detection system outputs "Measurement invalid - snap ring action position interval interference" and terminates the current detection.

[0099] After completing spline insertion and confirming the separation of the micro-loading position window from the snap ring's operating position range, the detection system confirms that the near-end rigid reference position on the external spline side, the near-end rigid reference position on the internal spline side, and the four radial displacement detection directions are all within the effective range of the corresponding detection unit. The micro-loading execution conditions include: the actual effective meshing length between the external and internal splines being greater than or equal to the specified effective meshing length; the snap ring having passed the mating part inlet or entered the specified assembly position; the existence of the micro-loading safety load window; the axial micro-loading peak value being within the micro-loading safety load window; the separation of the micro-loading position window from the snap ring's operating position range; and the two near-end rigid reference positions and the four radial displacement detection directions being within the effective range of the corresponding detection unit. When all the criteria in the micro-loading execution conditions are met, the detection system triggers the micro-loading execution conditions and uses the preset meshing position as the position reference for establishing the measurement reference later. The values ​​of the near-end differential measurement reference and the radial incremental measurement reference are read after the pre-loading stabilization in step 200, so as to avoid changes in the initial measurement state caused by snap ring positioning, lubrication redistribution, clamping slippage, and structural adjustment due to pre-loading.

[0100] Before establishing the radial increment measurement reference, the radial offset and tilt detectors determine the absolute radial eccentricity and absolute axial tilt of the first and second measurement sections based on the absolute radial positions of each radial displacement detection unit relative to the absolute reference axis. The absolute radial eccentricity of any measurement section is equal to the square of the absolute radial positions of the first and second radial detection directions of that measurement section relative to the absolute reference axis, the sum of the two squares, and the square root of the sum. The absolute axial tilt is obtained by calculating the absolute radial position of the first radial detection direction of the second measurement section and the absolute radial position of the first radial detection direction of the first measurement section. The difference in absolute radial position, and the difference between the absolute radial position of the second radial detection direction of the second measuring section and the absolute radial position of the second radial detection direction of the first measuring section; the two differences are squared and added together, the square root of the sum is taken, and then divided by the axial interval distance between the first and second measuring sections; the absolute radial eccentricity and the absolute axial tilt are measured before and after the floating centering mechanism is locked, respectively, to characterize the static eccentricity and static tilt that already exist when the clamping is completed; since the absolute radial eccentricity and the absolute axial tilt are referenced to the absolute reference axis, even if the static eccentricity and static tilt remain unchanged during the micro-loading process, they will not be zeroed by the radial increment measurement reference.

[0101] Step 200: Establish a proximal differential measurement benchmark. Within the micro-loading position window, at the axial micro-loading peak value, perform symmetrical micro-loading cycles of forward and reverse micro-loading at different detection speeds. Based on the proximal differential measurement benchmark, collect the axial force and proximal differential displacement coordinates at each detection speed, specifically as follows: Figure 2 As shown.

[0102] At the start of step 200, the data acquisition controller obtains the preset first detection speed, preset second detection speed, and preset preload stabilization cycle number for the corresponding product model. The preset first detection speed and preset second detection speed are both expressed as absolute speed values. Subsequent processing always categorizes the data into the preset first detection speed data or the preset second detection speed data according to the detection speed to which the data belongs.

[0103] Before performing the symmetrical micro-loading for measurement, the axial servo drive first performs a symmetrical micro-loading cycle of forward and reverse micro-loading at the same detection position with a preset number of pre-loading stabilization cycles, as pre-loading stabilization. Pre-loading stabilization is used to stabilize the snap ring positioning, lubrication redistribution, clamping slip, and structural plastic adjustment before the formal measurement, thereby avoiding position jumps caused by the first loading from entering the measurement data. The data collected in the pre-loading stabilization cycle is only used to confirm whether stabilization is completed and is not used as the measurement result of axial equivalent assembly clearance.

[0104] After preloading stabilization is completed, the axial servo drive returns to the preset engagement position and initial load state. The measurement reference establishment conditions include that the micro-loading execution condition has been triggered, the preloading stabilization has been completed, the axial servo drive has returned to the preset engagement position and initial load state, the axial load fluctuation is less than or equal to the loading control calibration error, and the reading changes of the two axial displacement detection units are both less than or equal to the resolution of the corresponding axial displacement detection unit. When all the aforementioned criteria are met, the detection system triggers the measurement reference establishment conditions, determines the current data sampling time as the reference establishment time, and the reference establishment time is also used as the initial time of the formal micro-loading. The two preset detection speed data and the repeated measurement data in step 400 in this detection all use this reference establishment time and do not reset to zero at the beginning of each micro-loading cycle. The shared reference establishment time can retain the true position changes between different detection speeds and different measurement sequences, and avoid eliminating position drift by resetting to zero in each cycle.

[0105] The dual-reference axial displacement detector reads the displacements of the proximal rigid reference positions on the external spline side and the internal spline side at the reference establishment time, respectively. The axial displacement difference obtained by subtracting the internal spline side proximal rigid reference position displacement from the external spline side proximal rigid reference position displacement is used as the initial proximal differential value. The proximal rigid reference position on the external spline side, the internal spline side proximal rigid reference position, and the initial proximal differential value together constitute the proximal differential measurement reference. For any data sampling time after the reference establishment time, the detection system first subtracts the internal spline side proximal rigid reference position displacement from the external spline side proximal rigid reference position displacement at that data sampling time to obtain the current proximal differential value. Then, it subtracts the initial proximal differential value from the current proximal differential value to obtain the proximal differential displacement coordinate at that data sampling time. The proximal differential displacement coordinate at the reference establishment time is zero.

[0106] The proximal differential displacement coordinate serves as the unified axial coordinate for dual-velocity data position registration, free micro-motion zone identification, stable contact zone fitting, and contact boundary extrapolation in step 300. The positive and negative contact boundaries obtained in step 300 are both located on this coordinate system. Steps 300 and 500 calculate the axial equivalent assembly clearance using the difference between the proximal differential displacement coordinates of the two contact boundaries. Therefore, the initial proximal differential value, as a shared zero point for both contact boundaries, cancels out during the difference calculation and does not reappear as an independent calculation item. Its function is not to directly form the clearance value, but rather to enable the two... The load data, positive micro-loading branch, reverse micro-loading branch, and repeated measurement data at the detection speed are all in the same relative axial coordinate. The two axial displacement detection units use the same positive coordinate direction and are respectively associated with two near-end rigid reference positions. This enables the near-end differential displacement coordinate to characterize the relative axial displacement between the near-end rigid reference positions on both sides of the spline connection structure and suppresses the common mode influence of elastic deformation of the drive shaft assembly, fixture deformation, and deformation of the detection equipment frame. The total stroke of the axial servo drive is only used for motion control and is not directly used as the measurement value of the axial equivalent assembly clearance.

[0107] The radial offset and tilt detector reads four initial radial displacement values ​​in the first and second radial detection directions on the first and second measurement sections at the same reference establishment time. The four initial radial displacement values ​​together constitute the radial increment measurement reference. For any data sampling time and any measurement section after the reference establishment time, the detection system subtracts the corresponding initial radial displacement value from the current radial displacement in the first radial detection direction of the measurement section to obtain the first radial detection direction offset component, and subtracts the corresponding initial radial displacement value from the current radial displacement in the second radial detection direction of the measurement section to obtain the second radial detection direction offset component. The initial radial displacement value is not directly used as the judgment index in step 400, but continues to participate in the calculation of the radial offset component at each data sampling time. The obtained radial offset component further forms the radial offset amount and the drive shaft axis tilt amount.

[0108] The axial servo drive performs a symmetrical micro-loading cycle of forward and reverse micro-loading at a preset first detection speed. Starting from a preset engagement position, the axial servo drive loads a forward peak load along the first axial direction at a preset first detection speed, holds the forward peak load for a preset holding time, then moves along the second axial direction and passes through the free micro-motion zone, continues to load a reverse peak load along the second axial direction, holds the reverse peak load for the same preset holding time, and finally returns to the initial load state. The preset holding time is determined based on the stabilization time of the axial servo drive after loading to the peak load, the synchronous acquisition time of the axial force sensor and the axial displacement detection unit, and the load relaxation time of the spline connection structure. Specifically, it is selected through a holding test where the peak load fluctuation is less than or equal to the loading control calibration error, the change in the near-end differential displacement coordinate during the holding phase is less than or equal to the resolution of the axial displacement detection unit, and synchronous sampling can be completed. The absolute values ​​of the forward peak load and the reverse peak load are both the axial micro-loading peak values ​​determined in step 100. The free micro-motion zone refers to the displacement range where the connection structure is free from the contact constraints of the two axial contact boundaries and only bears friction loads.

[0109] During the aforementioned micro-loading cycle, the data acquisition controller synchronously acquires the axial force of the forward micro-loading branch, the axial force of the reverse micro-loading branch, the near-end differential displacement coordinates, the radial offset of the first measurement section, the radial offset of the second measurement section, the drive shaft axis tilt, the absolute radial eccentricity of the first measurement section, the absolute radial eccentricity of the second measurement section, the absolute axis tilt, and the instantaneous acceleration of the axial servo drive. The above inputs are used to form the force-displacement relationship, verify the axis attitude, and calculate the inertial load, respectively, and the synchronous acquisition maintains the correspondence between the three types of data at the same data sampling time.

[0110] For any of the first and second measurement sections, the radial offset and tilt detectors obtain the first radial detection direction offset component and the second radial detection direction offset component by subtracting the corresponding initial value of the radial displacement from the current radial displacement. The radial offset of the measurement section is equal to the value obtained by first squaring the first and second radial detection direction offset components, then adding the two squared values, and finally taking the square root of the sum.

[0111] The drive shaft axis tilt is determined based on the difference in radial offset components between the first and second measuring sections. The detection system first subtracts the first radial offset component of the first measuring section from the first radial offset component of the second measuring section to obtain the first radial offset difference. Then, it subtracts the second radial offset component of the first measuring section from the second radial offset component of the second measuring section to obtain the second radial offset difference. Subsequently, the detection system adds the square of the first radial offset difference to the square of the second radial offset difference, takes the square root of the sum, and divides the resulting value by the axial distance between the first and second measuring sections to obtain the drive shaft axis tilt at the data sampling time. This drive shaft axis tilt is the ratio of the radial offset vector difference between the two measuring sections to the axial distance, and is a dimensionless slope. It is equal to the tangent of the tilt angle of the drive shaft axis relative to the spline axis, and can be used as an approximate representation of the tilt angle within the small tilt range involved in this embodiment. The absolute axis tilt is determined by subtracting the absolute radial position components in step 100, and is also a dimensionless slope.

[0112] When the radial offset components of the two measurement sections in the two radial detection directions are the same, the detection result represents the overall radial translation; the difference between the radial offset components of the two measurement sections in the two radial detection directions jointly represents the axis tilt; the radial offset of the first measurement section, the radial offset of the second measurement section and the tilt of the drive shaft axis, which are calculated hourly from the initial value of the radial displacement, are passed to steps 300 and 400, respectively, for the stable contact area screening in step 300 and the attitude judgment in step 400.

[0113] During the micro-loading process, the measurement validity judge continuously judges whether the load and displacement have entered the snap ring action position range; if they have entered the snap ring action position range, the current detection is stopped immediately to prevent the snap ring state from continuing to change and to prevent the snap ring load from being used for contact boundary extrapolation.

[0114] After completing the symmetrical micro-loading at the preset first detection speed, the axial servo drive keeps the axial micro-loading peak value and micro-loading stroke unchanged, adjusts the detection speed to the preset second detection speed, and repeats the aforementioned symmetrical micro-loading cycle of forward and reverse micro-loading. The data acquisition controller uses the same proximal differential measurement reference and the same radial incremental measurement reference to synchronously acquire the axial force of the forward micro-loading branch, the axial force of the reverse micro-loading branch, the proximal differential displacement coordinate, the radial offset of the first measurement section, the radial offset of the second measurement section, the drive shaft axis tilt, the absolute radial eccentricity of the first measurement section, the absolute radial eccentricity of the second measurement section, the absolute axis tilt, and the instantaneous acceleration at the preset second detection speed. Keeping the axial micro-loading peak value, micro-loading stroke, and the two measurement references unchanged, the only controlled variable between the two sets of data is the detection speed, thereby enabling the determination of the speed-related load.

[0115] The preset first detection speed and the preset second detection speed are determined by the type test of the corresponding product model, and the preset first detection speed and the preset second detection speed are different; specifically, among the candidate speeds where the snap ring remains unchanged, the lubrication temperature after the test is within the preset allowable temperature range, and the repeated identification results of the axial contact boundary meet the requirements, two speeds are selected where the speed response difference of the correction load can be distinguished by the detection system, and the corresponding inertial load is within the compensation capability range; the axial contact boundary identified under the two preset detection speeds remains consistent.

[0116] Since two detection speeds can only determine one velocity-load straight line, the data from these two detection speeds alone cannot determine whether the velocity-related load is linear within that velocity range, whether the velocity-related load can be represented by a linear relationship, or whether the velocity model fitting residuals meet the requirements. These are all determined by type tests covering multiple candidate detection speeds, not by the data from these two detection speeds. To limit the amplification of force measurement errors by zero-velocity extrapolation, the ratio of the absolute value of the difference between the preset second detection speed and the preset first detection speed to the maximum value of the two is set to be greater than or equal to a preset lower limit for the detection speed ratio. The preset lower limit for the detection speed ratio is based on the measurement error of the axial force sensor and inertia. The upper limit of the allowable uncertainty of the load correction error and the preset zero-velocity extrapolation uncertainty are determined. Specifically, the speed ratio boundary corresponding to the load error is selected such that the extrapolation uncertainty of the zero-velocity branch load obtained by extrapolation according to the preset first detection speed and the preset second detection speed is less than or equal to the upper limit of the allowable uncertainty of the preset zero-velocity extrapolation uncertainty. The speed nonlinearity caused by Coulomb friction, viscous friction, lubricating film speed effect, starting load, direction-related hysteresis, and position history and holding time effect are all checked within the candidate detection speed range of the above type test. The detection speed interval in which the speed model fitting residual caused by speed nonlinearity is less than or equal to the upper limit of the preset speed model fitting error is selected.

[0117] After two sets of symmetrical micro-loading in this step, the detection system obtains two sets of force-displacement data corresponding to the preset first detection speed and the preset second detection speed at the same detection position, the same axial micro-loading peak value, and the same micro-loading stroke. The force-displacement data includes axial force and proximal differential displacement coordinates, which are used for speed-related load correction in step 300.

[0118] Step 300: The axial force at each detection speed is corrected by speed-related load correction and friction baseline subtraction to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the negative contact area are identified and extrapolated to obtain the positive contact boundary and the negative contact boundary respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the negative contact boundary is used as the axial equivalent assembly clearance.

[0119] At the start of step 300, the clearance calculation processor acquires the preset force sensor zero-point offset, equivalent moving mass under forward loading, equivalent moving mass under reverse loading, calibration models for other dynamic loads under forward loading, and calibration models for other dynamic loads under reverse loading. It also acquires the preset upper limit of the contact area fitting error, the preset upper limit of the velocity model fitting error, the preset upper limit of the axial equivalent assembly clearance measurement error, the preset upper limit of the radial offset, the preset upper limit of the drive shaft axis tilt, the preset local stiffness threshold, the preset minimum contact load, the preset number of continuous valid data points, the preset upper limit of the dual-velocity response difference index, the preset upper limit of the zero-velocity extrapolation uncertainty, and the preset positive load regularization constant. The preset force sensor zero-point offset is used to correct the zero-point drift of the force sensor. The calibration models for equivalent kinematic mass under forward loading, equivalent kinematic mass under reverse loading, other dynamic loads under forward loading, and other dynamic loads under reverse loading are used to correct inertial loads and other dynamic loads related to the loading direction. The preset upper limit of the contact area fitting error is used to screen stable contact areas. The preset upper limit of the radial offset and the preset upper limit of the drive shaft axis tilt are used to exclude data that cannot trigger the stable contact area identification condition due to the failure of the axis attitude criterion. The preset upper limit of the zero velocity extrapolation uncertainty is used to limit the amplification of force measurement error by zero velocity extrapolation. Using the above calibration input, the equipment load unrelated to spline contact can be deducted from the axial force. Using the above upper limit and threshold, the data entering the contact boundary fitting can simultaneously meet the requirements of error, attitude, and identifiability.

[0120] The preset force sensor zero-point offset is obtained by continuously acquiring the zero-point output of the axial force sensor when it is in a state of no axial load, and taking the median of each zero-point output. Since the force path, friction direction, and mass involved in motion of components such as the servo screw, cable chain, seals, and floating mechanism are not necessarily the same under forward and reverse loading, the equivalent motion mass and other dynamic loads related to the loading direction are calibrated separately. The equivalent motion mass under forward and reverse loading is obtained through calibration tests. Specifically, multiple sets of known instantaneous accelerations are applied to the detection mechanism in the forward and reverse loading directions, and the corresponding inertial loads are acquired. The inertial loads in each direction are compared with the instantaneous accelerations. The fitted slope is used as the equivalent motion mass of the load in that direction, and the inertial load correction error is checked using calibration data not involved in the fitting. The calibration models for other dynamic loads under forward and reverse loading are obtained by performing no-load reciprocating motion in the corresponding loading directions. These models are used to characterize the dynamic loads generated by the servo screw, cable chain, seals, and floating mechanism in that loading direction, which vary with position and motion state. The calibration process also determines the sign of the inertial load relative to the loading direction, so that the inertial load correction for forward and reverse loading adopts the same sign as the loading direction, thereby ensuring that the definitions of the positive direction of the axial force sensor, the positive direction of acceleration, and the positive direction of loading are consistent.

[0121] The upper limit of the preset contact zone fitting error is determined based on the robust scale distribution of residuals in the stable contact zone of historical qualified products and the repeatability requirements of the contact boundary. Specifically, the robust scale boundary of residuals is selected to retain the data segment that meets the repeatability requirements of the contact boundary and excludes the data segment where the contact state changes. The upper limit of the preset velocity model fitting error is determined based on the measurement error of the axial force sensor, the correction error of the inertial load, and the allowable extrapolation error of the zero velocity branch load. Specifically, the velocity model is fitted using type test data of multiple candidate detection velocities, and the model is selected to make the extrapolation error of the zero velocity branch load less than or equal to the preset axial equivalent. The model residual boundary of the load error corresponding to the allowable measurement error of assembly clearance; the preset allowable measurement error of axial equivalent assembly clearance is determined according to the product tolerance zone width and the measurement capability requirements for product release, and is verified by measurement system analysis and testing; the preset upper limit of zero velocity extrapolation uncertainty is determined according to the transmission relationship of the preset allowable measurement error of axial equivalent assembly clearance and the contact boundary fitting to the load uncertainty, and specifically, the load uncertainty boundary is selected such that the boundary deviation caused by the extrapolation uncertainty of the zero velocity branch load after being transmitted to the contact boundary is less than or equal to the boundary deviation corresponding to the preset allowable measurement error of axial equivalent assembly clearance.

[0122] The upper limit of the preset radial offset and the upper limit of the preset drive shaft axis tilt are determined based on the product coaxiality requirements and the preset axial equivalent assembly clearance allowable measurement error. Specifically, the correspondence between the axis posture and the contact boundary deviation is established through radial offset and axis tilt calibration tests. The radial offset and drive shaft axis tilt corresponding to the contact boundary deviation being equal to the preset axial equivalent assembly clearance allowable measurement error are used as candidate upper limits. The candidate upper limits are then verified in conjunction with the measurement error of the radial displacement detection unit.

[0123] The preset local stiffness threshold and preset minimum contact load are determined using type test data labeled with free fretting area and stable contact area. Specifically, the local stiffness boundary that can separate the free fretting area and stable contact area is selected based on the local stiffness distribution of the two intervals, and the contact load boundary that can exclude friction load and noise load is selected based on the friction baseline fluctuation envelope of the free fretting area, the noise envelope of the axial force sensor, and the load distribution of the stable contact area. The preset number of continuous effective data points is determined based on the identifiability requirements of the linear fitting parameters, the actual data sampling interval, and the repeatability requirements of the contact boundary. Specifically, the number of continuous effective data points participating in the fitting is changed step by step, and the number of data points required when the fitting slope, fitting intercept, and extrapolated contact boundary all meet the repeatability requirements is selected.

[0124] In this embodiment, a valid data point refers to a force-displacement data point that is synchronously acquired by the data acquisition controller at the same data sampling time, and whose readings from the axial force sensor, the two axial displacement detection units, and the four radial displacement detection units are all within their respective valid ranges without saturation or exceeding the range. A valid data point at the data sampling time simultaneously possesses axial force, proximal differential displacement coordinates, instantaneous acceleration, and radial offset of the first measurement section, radial offset of the second measurement section, and drive shaft axis tilt, and can participate in velocity-related load correction, friction baseline estimation, and contact boundary fitting. Data points that do not meet the above requirements are invalid data points and will not be included in friction baseline estimation and contact boundary fitting.

[0125] In this embodiment, the number of consecutive valid data points refers to the number of valid data points arranged adjacent to each other along the proximal differential displacement coordinate direction in the same micro-loaded branch, without being interrupted by invalid data points. The method for determining the number of consecutive valid data points is as follows: the gap calculation processor first sorts the data points of the same micro-loaded branch from smallest to largest according to the proximal differential displacement coordinate, and then checks each data point along the proximal differential displacement coordinate direction to determine whether it is a valid data point. When adjacent data points are all valid data points, they are grouped into the same continuous data segment, and the number of consecutive valid data points in that continuous data segment is increased by one. When an invalid data point is encountered... When valid data points are obtained, the current continuous data segment ends and the number of consecutive valid data points is counted again from zero, thus obtaining the number of consecutive valid data points for each continuous data segment. When the number of consecutive valid data points in the free micro-motion zone or candidate continuous data segment is greater than or equal to the preset number of consecutive valid data points, the data points in this segment meet the requirements for the identifiable linear fitting parameters and can be used for friction baseline estimation or contact boundary fitting. When the number of consecutive valid data points is less than the preset number of consecutive valid data points, the data points in this segment do not meet the requirements for the identifiable linear fitting parameters and are not used for friction baseline estimation or contact boundary fitting.

[0126] The upper limit of the preset dual-speed response difference index is determined by historical qualified product data within the preset allowable lubrication range and preset allowable temperature range, as well as verification data of lubrication abnormalities or dynamic response abnormalities. Specifically, the index boundary is selected that can retain historical qualified product data and exclude confirmed abnormal data. The preset positive load regularization constant is determined based on the resolution of the axial force sensor and the noise envelope of the no-load state, and is checked by changing the peak value of axial micro-load, so that the regularization process can avoid division by zero and does not change the judgment result of the dual-speed response difference index on abnormal states.

[0127] In an optional embodiment, the calibration models for other dynamic loads under forward and reverse loading are established during the offline calibration phase and are not updated during the single-piece online inspection process. The establishment process is as follows: first, perform no-load reciprocating motion covering the detection stroke, a preset first detection speed, a preset second detection speed, and a preset holding time in the forward and reverse loading directions, respectively, and collect axial position, absolute velocity value, holding state, and axial force; then, divide the data in each direction into model establishment data and independent verification data, using axial position, absolute velocity value, and holding state as model inputs, and the no-load axial force after deducting the preset force sensor zero-point offset and inertial load as the model... The model output is used to fit candidate piecewise linear or polynomial models. Then, the load correction error of each candidate model is calculated using independent validation data. The model with the load correction error less than or equal to the corresponding allowable upper limit and the fewest parameters is selected. Finally, the model parameters are associated with the product model, testing tooling number, and calibration version and then fixed. The above input can characterize the changes of dynamic loads in other directions with axial position, absolute velocity, and holding state. Independent validation and version fixing can prevent unvalidated model parameters from entering online load correction. In this embodiment, the iterative reweighted least squares and block resampling are solved on the current measurement data according to predetermined rules, without the need for pre-training of model parameters.

[0128] The gap calculation processor uses the near-end differential measurement benchmark established in step 200 to perform position registration on the positive micro-loading branch and the reverse micro-loading branch according to the near-end differential displacement coordinates. The position registration uses the near-end differential displacement coordinates as the independent variable to align the axial force of the same micro-loading branch at two preset detection speeds to the same near-end differential displacement coordinates, without directly averaging or subtracting the positive and reverse micro-loading branches. Processing the two micro-loading branches separately can preserve the differences in the friction direction and the bearing contact direction, avoiding the averaging process from changing the positive or reverse contact boundary. Therefore, the near-end differential measurement benchmark established in step 200 is specifically manifested in this step as the axial coordinate benchmark shared by all force and displacement data.

[0129] For any micro-loading branch in either the forward or reverse micro-loading branch, the gap calculation processor performs force sensor zero-point correction, inertial load correction, and other directional dynamic load correction for each registration data point. The gap calculation processor first selects the corresponding equivalent motion mass based on the loading direction of the micro-loading branch, multiplies this equivalent motion mass by the instantaneous acceleration corresponding to the registration data point, and then multiplies it by the calibrated loading direction sign to obtain the inertial load of the registration data point. Then, based on the other dynamic load calibration model corresponding to the loading direction, it obtains the other directional dynamic loads of the registration data point. The gap calculation processor then subtracts the preset force sensor zero-point offset and inertial load from the axial force of the registration data point acquired in step 200. The dynamic loads related to other directions are used to obtain the load of the micro-loading branch at the corresponding detection speed after zero-point correction, inertial load correction, and other direction-related dynamic load correction. The above corrections are used to separate the sensor zero point, mechanism inertia, and equipment motion resistance from the acquired axial force, so that the load processed by the subsequent velocity model corresponds to the spline connection structure and its friction state. The inertial load is the inertial force component that needs to be subtracted from the axial force acquired in step 200, which is determined according to Newton's second law. Its magnitude is determined by the equivalent motion mass and instantaneous acceleration corresponding to the loading direction, and its sign is determined by the loading direction. The positive micro-loading branch and the negative micro-loading branch respectively adopt the equivalent motion mass, loading direction sign, and other dynamic load calibration models calibrated in their respective loading directions.

[0130] When the type test confirms that the velocity-related load can be represented by a linear relationship within the range of the preset first detection speed to the preset second detection speed, and the velocity model fitting residual is less than or equal to the upper limit of the preset velocity model fitting error, the gap calculation processor applies a velocity model to each micro-loaded branch. For the same micro-loaded branch and the same near-end differential displacement coordinate, the load after zero-point correction, inertial load correction, and other directional dynamic load correction consists of zero-velocity branch load and velocity-related load. The zero-velocity branch load is the branch load when the detection speed approaches zero. The velocity-related load is equal to the velocity-related load coefficient of the micro-loaded branch at the near-end differential displacement coordinate multiplied by the absolute value of the detection speed. The velocity-related load coefficient represents the slope of the load after zero-point correction, inertial load correction, and other directional dynamic load correction as the absolute value of the detection speed changes linearly. It is obtained by subtracting the correction load at the preset first detection speed from the correction load at the preset second detection speed, and then dividing the resulting load difference by the difference between the preset second detection speed and the preset first detection speed.

[0131] In an optional implementation, for the same micro-loaded branch, the preset first detection velocity data and the preset second detection velocity data are sorted according to the near-end differential displacement coordinates, and the intersection of the two sets of near-end differential displacement coordinate ranges is determined as a common registration interval. A common position coordinate sequence is established within the common registration interval. The loads corresponding to each common position coordinate are determined according to the two sets of force-displacement data, resulting in a dual-velocity load pair with the same near-end differential displacement coordinates. The loads corresponding to the common position coordinates can be obtained by linear interpolation, piecewise polynomial interpolation, or neighbor point resampling.

[0132] The gap calculation processor substitutes the corrected loads under the preset first detection speed and the preset second detection speed into the velocity model and performs linear extrapolation to eliminate velocity-dependent load components. For any micro-loaded branch and any co-registered proximal differential displacement coordinate, the gap calculation processor first multiplies the preset second detection speed by the corrected load of the micro-loaded branch under the preset first detection speed to obtain a first product; then multiplies the preset first detection speed by the corrected load of the micro-loaded branch under the preset second detection speed to obtain a second product; subsequently, the first product is subtracted from the second product, and the resulting difference is divided by the velocity difference obtained by subtracting the preset first detection speed from the preset second detection speed; this quotient is the quasi-static load estimate of the micro-loaded branch at the proximal differential displacement coordinate under the condition of zero velocity extrapolation.

[0133] For example, for branch road signs The micro-loaded branch, in the near-end differential displacement coordinate The estimated quasi-static load at the location can be expressed as:

[0134] ,in .

[0135] in, The branch road is marked as The micro-loaded branch in the near-end differential displacement coordinate The quasi-static load estimate is extrapolated to the zero velocity condition. Indicates a forward micro-loading branch. Indicates the reverse micro-loading branch. For proximal differential displacement coordinates, The speed amplitude of the preset first detection speed, The speed amplitude of the preset second detection speed, The branch road is marked as After the micro-loading branch completes the force sensor zero-point correction, inertial load correction, and other directional dynamic load correction at the preset first detection speed, it is located at the coordinate... Corrected load at the location, For the same micro-loaded branch, after the above correction is completed at the preset second detection speed, the coordinates are located... Corrected load at the location.

[0136] The gap calculation processor simultaneously determines the extrapolation uncertainty of the zero-velocity branch load. For any micro-loaded branch and any near-end differential displacement coordinate, the gap calculation processor first adds the square of the preset first detection velocity and the square of the preset second detection velocity, takes the square root of the sum, multiplies it by the measurement error of the corrected load, and finally divides it by the absolute value of the difference between the preset second detection velocity and the preset first detection velocity. The resulting value is the extrapolation uncertainty of the zero-velocity branch load at that point. When the absolute value of the difference between the preset first detection velocity and the preset second detection velocity decreases, the above divisor decreases. The extrapolation uncertainty increases; a preset detection speed ratio lower limit is used to ensure that the extrapolation uncertainty is less than or equal to the preset zero-velocity extrapolation uncertainty upper limit; the gap calculation processor transfers the zero-velocity branch load extrapolation uncertainty of each stable contact area data point to step 500 as a component of the standard uncertainty introduced by the contact boundary fitting; if the zero-velocity branch load extrapolation uncertainty of any micro-loaded branch stable contact area is greater than the preset zero-velocity extrapolation uncertainty upper limit, the detection system outputs "Measurement invalid - zero-velocity extrapolation uncertainty is greater than the upper limit" and terminates the current detection.

[0137] The gap calculation processor identifies the free fretting zone on the near-end differential displacement coordinates and estimates the friction baseline of each micro-loaded branch using continuous data points within the free fretting zone where the local stiffness is less than a preset local stiffness threshold. Local stiffness is the rate of change of the quasi-static load estimate relative to the near-end differential displacement coordinates. The free fretting zone is not subject to the bearing constraints of the positive or negative contact boundary, so the quasi-static load estimate of this zone can be used to extract the friction load of the corresponding micro-loaded branch. For any micro-loaded branch, the gap calculation processor collects the quasi-static load estimates of each valid data point within the free fretting zone and takes the median of all quasi-static load estimates as the friction baseline estimate of that micro-loaded branch. Using the median can limit the influence of individual abnormal data points on the friction baseline estimation results.

[0138] For any micro-loaded branch and any co-registered proximal differential displacement coordinate, the gap calculation processor subtracts the friction baseline estimate of the micro-loaded branch from the quasi-static load estimate at the proximal differential displacement coordinate to obtain the corrected branch load after velocity correlation correction and friction baseline subtraction; the corrected branch load is used for subsequent contact area identification and contact boundary extrapolation.

[0139] In an optional embodiment, if there is no free micro-motion zone with a number of consecutive valid data points greater than or equal to the preset number of consecutive valid data points, or if the data at two preset detection speeds do not conform to the above speed model, the gap calculation processor will not perform friction correction, and the detection system will output "Measurement invalid - friction state unidentifiable" and terminate the current detection.

[0140] The gap calculation processor simultaneously calculates the dual-velocity response difference index for both the forward and reverse micro-loading branches. For any micro-loading branch, the gap calculation processor, in all sampling points jointly registered with the preset first and second detection speeds, subtracts the correction load at the preset first detection speed from the correction load at the preset second detection speed for each sampling point, and squares each load difference. The gap calculation processor sums the squares of all load differences, divides them by the number of jointly registered sampling points, and then takes the square root of the average value to obtain the root mean square of the difference between the correction loads at the two preset detection speeds. The gap calculation processor divides this root mean square by the sum of the axial micro-loading peak value and the preset positive load regularization constant, and the quotient is the dual-velocity response difference index for that micro-loading branch. The preset positive load regularization constant is used to avoid division by zero. The dual-velocity response difference index is normalized by the root mean square of the difference between the correction loads at the axial micro-loading peak value to characterize the sensitivity of the load of the micro-loading branch to the detection speed.

[0141] For example, the branch road sign is The difference in dual-velocity response of the micro-loaded branch can be expressed as:

[0142] ;

[0143] in, The branch road is marked as The dual-speed response difference index of the micro-loaded branch, The number of sampling points to be registered together with the preset first detection speed and the preset second detection speed. The serial number of the sampling points to be jointly registered. For the first Proximal differential displacement coordinates of common registered sampling points and The aforementioned modified load symbols are used to represent the first load. Corrected loads for common registration sampling points at preset first and second detection speeds. The peak value is due to axial micro-loading. This is the preset positive load regularization constant.

[0144] When the difference index of the dual speed response of the forward micro-loading branch or the reverse micro-loading branch exceeds the upper limit of the preset dual speed response difference index of the corresponding model, the measurement validity judge determines that the lubrication state or dynamic response is abnormal.

[0145] After completing the speed-related load correction and friction baseline subtraction, the gap calculation processor identifies the positive and negative contact areas and extrapolates the positive and negative contact boundaries.

[0146] The gap calculation processor identifies stable contact regions in the modified branch loads of the positive micro-loading branch and the reverse micro-loading branch, respectively. The stable contact region refers to a continuous data segment in which the modified branch load exhibits a unidirectional bearing contact characteristic with the near-end differential displacement coordinate, and is used for contact boundary extrapolation. The stable contact region identified in the modified branch load of the positive micro-loading branch is called the positive contact region, and the stable contact region identified in the modified branch load of the reverse micro-loading branch is called the reverse contact region. The positive contact region and the reverse contact region are the specific manifestations of the stable contact region in the positive micro-loading branch and the reverse micro-loading branch, respectively. Both adopt the same stable contact region identification conditions and the same identification method, only the micro-loading branch and the bearing contact direction are different.

[0147] The stable contact zone identification criteria are applied segment by segment to candidate continuous data segments. For any candidate continuous data segment, the gap calculation processor first uses the modified branch load of the candidate continuous data segment as the dependent variable and the near-end differential displacement coordinate as the independent variable to robustly fit and determine a fitting straight line. Then, the modified branch load of each data point in the candidate continuous data segment is subtracted from the value of the fitting straight line at the near-end differential displacement coordinate of that data point to obtain the fitting residual of that data point. Then, according to the median absolute deviation method, the robustness scale of the residuals of all data points in the candidate continuous data segment is determined. In this embodiment, the robust fitting residual is the fitting residual of each data point obtained by subtracting the modified branch load from the value of the fitting straight line, and the robustness scale of the residual is the robustness scale determined by the robust fitting residual according to the median absolute deviation method, which is used to characterize the degree to which the candidate continuous data segment deviates from the straight contact feature.

[0148] The stable contact zone identification conditions include: the absolute value of the corrected branch load is greater than the preset minimum contact load; the direction of the corrected branch load changing with the near-end differential displacement coordinate remains consistent; the robustness scale of the robust fitting residual is less than or equal to the preset upper limit of the contact zone fitting error; the corresponding position does not belong to the snap ring action position range; the radial offset of the first measurement section and the radial offset of the second measurement section are both less than or equal to the preset upper limit of the radial offset; and the tilt of the drive shaft axis is less than or equal to the preset upper limit of the drive shaft axis tilt. When all of the aforementioned criteria are met within the same continuous data segment, the gap calculation processor triggers stable contact. The system identifies the stable contact zone based on the conditions for identifying the continuous data segment. Specifically, the continuous data segment located in the positive micro-loading branch is the positive contact zone, and the continuous data segment located in the reverse micro-loading branch is the reverse contact zone. By jointly using load, change direction, fitting residual, snap ring position, and axis attitude criteria, it is possible to prevent free micro-motion data, snap ring action data, or abnormal attitude data from entering the contact boundary fitting. Thus, the initial value of radial displacement participates in the stable contact zone identification through radial offset and drive shaft axis tilt. Data that does not trigger the stable contact zone identification condition due to the attitude change criterion not being met will not enter the contact boundary fitting.

[0149] For a positive contact zone that triggers the stable contact zone identification condition, the gap calculation processor uses the fitted straight line obtained by robustly fitting the corrected branch load when identifying the positive contact zone as the fitted straight line for the positive contact zone; the corrected branch load of the positive micro-loaded branch at any near-end differential displacement coordinate is equal to the product of the positive contact equivalent stiffness and the displacement difference obtained by subtracting the positive contact boundary from the near-end differential displacement coordinate; the positive contact equivalent stiffness is a positive number.

[0150] For the reverse contact zone that triggers the stable contact zone identification condition, the gap calculation processor uses the fitted straight line obtained by robustly fitting the corrected branch load when identifying the reverse contact zone as the fitted straight line of the reverse contact zone; the corrected branch load of the reverse micro-loaded branch at any near-end differential displacement coordinate is equal to the product of the negative value of the reverse contact equivalent stiffness and the displacement difference obtained by subtracting the near-end differential displacement coordinate from the reverse contact boundary; the reverse contact equivalent stiffness is a positive number.

[0151] This embodiment of robust fitting is a regression method that is insensitive to outlier data points. Robust fitting limits the impact of individual outlier data points on the fitting result by determining the slope and intercept of the fitted line. The implementation of robust fitting is iterative reweighted least squares. The gap calculation processor first determines the initial slope and intercept of the fitted line using least squares. Then, it subtracts the value of the current fitted line at the near-end differential displacement coordinate of the data point from the corrected branch load of each data point to obtain the fitting residual of each data point. Then, it determines the robustness scale of the residual of each data point according to the median absolute deviation method. Then, it determines the weight of each data point according to the ratio of the fitting residual to the robustness scale. The weight of data points whose absolute value of the fitting residual is greater than the product of the preset robust weighting threshold and the robustness scale is reduced. Then, the weighted least squares fitting is re-performed with the updated weights. The above process of calculating the fitting residual, determining the robustness scale, updating the weights and weighted fitting is repeated until the fitting slope and the weighted least squares fitting are both obtained. The change in the sum of the intercepts between two adjacent iterations is less than or equal to the preset fitting convergence criterion, thus obtaining the slope and intercept of the robust fit; the robust fitting residuals and their robust residual scales in the stable contact zone identification conditions are obtained from the converged robust fitting lines according to the above subtraction method and the median absolute deviation method; the preset robust weighting threshold is determined based on the residual distribution range of normal data points under the adopted reference distribution, specifically selecting the residual multiple that can retain normal data points and reduce the weight of deviating data points; the preset fitting convergence criterion is determined based on the identification and resolution of the fitting slope and fitting intercept, specifically selecting the boundary of the change in the fitting slope and fitting intercept when they no longer change after further iterations; the gap calculation processor extrapolates the fitting lines of the positive contact zone and the negative contact zone to the position where the corrected branch load is zero; the intersection of the fitting line of the positive contact zone and the coordinate axis of the zero corrected branch load is the positive contact boundary, and the intersection of the fitting line of the negative contact zone and the coordinate axis of the zero corrected branch load is the negative contact boundary.

[0152] The forward and reverse contact boundaries represent the critical displacement points at which the connection structure transitions from a free micro-motion state to a load-bearing contact state under forward and reverse micro-loading, respectively. The equivalent stiffness of the forward and reverse contact boundaries are the absolute values ​​of the slopes of the corresponding fitted lines, used for the elastic asymmetry judgment in step 400. The gap calculation processor also determines the relative standard error of the fitted slopes for the forward and reverse contact areas based on the robust fitting results. The relative standard error of the fitted slope is the ratio of the standard error of the fitted slope to the absolute value of the fitted slope, used for the connection... The identifiability of the contact stiffness is determined; the standard error of the fitting slope is determined based on the robustness scale of the robust fitting residuals and the dispersion of the data points involved in the fitting on the near-end differential displacement coordinates. Specifically, the robustness scale of the robust fitting residuals is first determined according to the median absolute deviation method. Then, the difference between the near-end differential displacement coordinates of each data point involved in the fitting and the mean of the near-end differential displacement coordinates of all data points involved in the fitting is calculated. The squares of each difference are then added together, and the square root of the sum is calculated. Finally, the robustness scale of the residuals is divided by the square root, and the resulting value is the standard error of the fitting slope.

[0153] When the proximal differential displacement coordinate of the positive contact boundary is greater than that of the negative contact boundary, the clearance calculation processor subtracts the proximal differential displacement coordinate of the negative contact boundary from the proximal differential displacement coordinate of the positive contact boundary. The difference is the axial equivalent assembly clearance measured for the first time. The two contact boundaries share the proximal differential measurement reference established in step 200. The initial proximal differential values ​​cancel each other out when the coordinates of the two boundaries are subtracted. Therefore, the proximal differential measurement reference participates in the clearance calculation by determining the unified coordinates of the two boundaries, and does not appear as an independent addition or subtraction item.

[0154] If the proximal differential displacement coordinate of the positive contact boundary is less than or equal to the proximal differential displacement coordinate of the negative contact boundary, or if any micro-loaded branch does not trigger the stable contact area identification condition, the clearance calculation processor will not calculate the axial equivalent assembly clearance, the detection system will output "Measurement invalid - contact boundary unidentifiable" and terminate the current detection.

[0155] Step 400: The validity of the axial equivalent assembly clearance is determined to generate a measurement validity gating result.

[0156] At the start of step 400, the measurement validity determiner acquires the following preset limits: lower limit of axial equivalent assembly clearance, upper limit of axial equivalent assembly clearance, upper limit of positive and negative contact stiffness asymmetry coefficient, minimum contact equivalent stiffness, upper limit of relative standard error of fitting slope, upper limit of absolute repeatability error, upper limit of relative repeatability index, upper limit of repeatability robust standard deviation, upper limit of repeatability monotonic drift, number of preload stabilization cycles, upper limit of absolute radial eccentricity, upper limit of absolute axial tilt, and normalization constant of positive stiffness. It also uses the preset allowable measurement error of axial equivalent assembly clearance and the preset upper limit of radial offset acquired in step 300. The preset upper limit of drive shaft axis tilt; the preset lower limit of axial equivalent assembly clearance and the preset upper limit of axial equivalent assembly clearance together limit the range of allowable axial equivalent assembly clearance; the preset upper limit of positive and negative contact stiffness asymmetry coefficient, the preset minimum contact equivalent stiffness, the preset upper limit of relative standard error of fitting slope, the preset upper limit of radial offset, the preset upper limit of drive shaft axis tilt, the preset upper limit of absolute radial eccentricity and the preset upper limit of absolute axis tilt are used to determine the force path and axis attitude; the preset upper limit of absolute repeatability error, the preset upper limit of relative repeatability index, the preset upper limit of repeatability robust standard deviation and the preset upper limit of repeatability monotonic drift are used to determine the repeatability of measurement results.

[0157] The preset lower and upper limits of the axial equivalent assembly clearance are obtained based on the design tolerances, assembly technical requirements, and functional verification results of the corresponding product model. Specifically, the lower and upper boundaries of the allowable range are determined after verifying the consistency between the axial equivalent assembly clearance range corresponding to the functionally verified assembly state and the design tolerance. The preset upper limit of the asymmetric coefficient of positive and negative contact stiffness is obtained through centering type tests and eccentricity, tilting, or local interference verification tests of the same model product. Specifically, the coefficient boundary is selected based on the asymmetric coefficient distribution corresponding to the normal and abnormal force paths, which can retain the normal force path and exclude the confirmed abnormal force path. The preset lower limit of the minimum contact equivalent stiffness and the preset upper limit of the relative standard error of the fitting slope are determined through type test data with stable contact area markings. The minimum contact equivalent stiffness is selected as the contact equivalent stiffness boundary that distinguishes the fitting slope of the stable contact area from the stiffness estimation fluctuation in the non-contact state. The upper limit of the relative standard error of the preset fitting slope is selected as the fitting slope relative standard error boundary that ensures the contact boundary extrapolation and repeated identification results meet the requirements. The upper limit of the preset absolute radial eccentricity and the upper limit of the preset absolute axial tilt are determined based on the product coaxiality requirements and the preset axial equivalent assembly clearance allowable measurement error. Specifically, the correspondence between the axial attitude and the contact boundary deviation is established by the radial offset and axial tilt calibration test. The absolute radial eccentricity and absolute axial tilt corresponding to the contact boundary deviation being equal to the preset axial equivalent assembly clearance allowable measurement error are used as candidate upper limits. The candidate upper limits are then verified by combining the measurement error of the radial displacement detection unit relative to the absolute reference axis.

[0158] The preset upper limits for absolute repeatability error, relative repeatability index, robustness standard deviation, and monotonic drift are obtained through repeatability tests of the measurement system. Specifically, under the same tooling, inspection position, and environmental conditions, the same drive shaft assembly undergoes a preset number of preload stabilization cycles, followed by multiple repeated measurements. The range of the repeated measurement results, the repeatability index relative to the allowable tolerance zone, the robustness standard deviation, and the monotonic drift of the measurement results as a function of the measurement sequence are calculated. These parameters are then combined with the preset allowable measurement error for axial equivalent assembly clearance to determine the repeatability parameters. Boundary; The preset preload stabilization cycle number is determined based on the number of cycles required for the snap ring to stabilize during repeated loading, including snap ring placement, lubrication redistribution, clamping slippage, and structural plastic adjustment. Specifically, the number of preload cycles is increased sequentially, and the cycle number corresponding to the point where the range and monotonic drift of repeated measurements no longer change after further increasing the number of preload cycles is selected; The preset positive stiffness regularization constant is determined based on the contact equivalent stiffness identification resolution and the stiffness estimation fluctuation envelope in the non-contact state, and is verified by the combination of positive contact equivalent stiffness and reverse contact equivalent stiffness, so that the regularization process can avoid the judgment results of abnormal samples with division by zero and without changing the force path.

[0159] The measurement validity judge calculates the forward and reverse contact stiffness asymmetry coefficient based on the forward and reverse contact equivalent stiffness obtained in step 300. The measurement validity judge first subtracts the reverse contact equivalent stiffness from the forward contact equivalent stiffness and takes the absolute value of the difference as the dividend. Then, it adds the forward contact equivalent stiffness, the reverse contact equivalent stiffness, and the preset forward stiffness regularization constant as the divisor. Finally, it divides the dividend by the divisor, and the quotient is the forward and reverse contact stiffness asymmetry coefficient. The preset forward stiffness regularization constant is used to avoid a divisor of zero. The forward and reverse contact stiffness asymmetry coefficient ranges from zero to one, representing the relative difference between the forward and reverse contact equivalent stiffness. Using a dimensionless relative difference eliminates the influence of the dimensions of the contact equivalent stiffness on the comparison results and allows different drive shaft assemblies of the same product model to use the same preset upper limit for the forward and reverse contact stiffness asymmetry coefficient.

[0160] The measurement validity determiner also assesses the identifiability of the forward and reverse contact equivalent stiffness. When both the forward and reverse contact equivalent stiffness are greater than or equal to the preset minimum contact equivalent stiffness, and the relative standard error of the forward contact area fitting slope and the relative standard error of the reverse contact area fitting slope obtained in step 300 are both less than or equal to the preset upper limit of the relative standard error of the fitting slope, the measurement validity determiner considers the forward and reverse contact equivalent stiffness identifiable, and the forward and reverse contact stiffness asymmetry coefficient can represent... The actual force path difference is not reflected. When the equivalent stiffness of the positive contact or the equivalent stiffness of the negative contact is less than the preset minimum equivalent stiffness of the contact, or when the relative standard error of the fitting slope of the positive contact area or the relative standard error of the fitting slope of the negative contact area is greater than the upper limit of the preset relative standard error of the fitting slope, the asymmetry coefficient of the positive and negative contact stiffness will be lowered by the preset positive stiffness regularization constant when the equivalent stiffness of the contact on both sides is less than the preset minimum equivalent stiffness of the contact, and thus cannot characterize the actual force path difference. The measurement validity judge determines that the contact stiffness is unidentifiable.

[0161] The measurement validity judge determines the maximum radial offset during the detection process based on the radial offset calculated in step 200 with the initial radial displacement as the radial increment measurement reference. The measurement validity judge collects the first and second radial offsets of the measurement section at each data sampling time during the entire detection process, and takes the maximum value from all collected radial offsets as the maximum radial offset during the detection process.

[0162] The measurement validity judge also collects the drive shaft axis tilt amount calculated hourly from four initial radial displacement values ​​and the corresponding current radial displacement throughout the entire detection process, and takes the maximum value from all drive shaft axis tilt amounts as the maximum drive shaft axis tilt amount during the detection process. Taking the maximum radial offset and the maximum drive shaft axis tilt amount during the entire detection process can identify attitude changes that only occur in some micro-load sections, avoiding missing midway offsets or tilts by only checking the end of the cycle. The above-mentioned maximum radial offset and maximum drive shaft axis tilt amount are both determined by the radial displacement increment relative to the reference establishment time, and are used to characterize the attitude changes caused by micro-load. In this step, the initial radial displacement value is not directly compared with the allowable upper limit; instead, the maximum radial offset and the maximum drive shaft axis tilt amount calculated from the initial radial displacement value are compared with the allowable upper limit.

[0163] The measurement validity judge also determines the maximum absolute radial eccentricity and the maximum absolute axis tilt based on the absolute radial eccentricity and the absolute axis tilt measured in steps 100 and 200. The measurement validity judge collects the absolute radial eccentricity of the first measurement section and the absolute radial eccentricity of the second measurement section at each data sampling moment before and after the floating centering mechanism is locked and throughout the entire detection process, and takes the maximum value as the maximum absolute radial eccentricity. It also collects the absolute axis tilt at the corresponding moment and takes the maximum value as the maximum absolute axis tilt. Since the absolute radial eccentricity and the absolute axis tilt are referenced to the absolute reference axis, even if the eccentricity and tilt that already exist when clamping is completed remain unchanged during the micro-loading process, the maximum absolute radial eccentricity and the maximum absolute axis tilt can still reflect the static eccentricity and static tilt when clamping is completed, thus complementing the maximum radial offset and the maximum drive shaft axis tilt that characterize the attitude change caused by micro-loading.

[0164] When the asymmetry coefficient of the positive and negative contact stiffness, the maximum radial offset, and the maximum drive shaft axis tilt are less than or equal to the corresponding preset upper limits, and the equivalent stiffness of the positive contact and the equivalent stiffness of the negative contact are both greater than or equal to the preset minimum equivalent contact stiffness, the preset upper limits include the preset upper limits for the asymmetry coefficient of the positive and negative contact stiffness, the preset upper limits for the radial offset, and the preset upper limits for the drive shaft axis tilt. Specifically, the effective attitude conditions include the asymmetry coefficient of the positive and negative contact stiffness being less than or equal to the preset upper limits for the asymmetry coefficient of the positive and negative contact stiffness, and the equivalent stiffness of the positive contact and the equivalent stiffness of the negative contact being both greater than or equal to the preset minimum equivalent contact stiffness. When the stiffness and maximum radial offset are less than or equal to the preset allowable upper limit of radial offset, and the maximum drive shaft axis tilt is less than or equal to the preset allowable upper limit of drive shaft axis tilt, the measurement validity judge triggers the attitude validity condition and considers the force path and axis attitude of this test to be valid. The joint judgment of contact stiffness, stiffness asymmetry degree and axis attitude can avoid mistaking displacement caused by unilateral contact, local interference or attitude change as axial equivalent assembly clearance. The positive and negative contact stiffness asymmetry coefficient is only one of the constituent criteria of the attitude validity condition and is not used alone as the basis for determining eccentricity or local interference.

[0165] In this embodiment, the effective attitude conditions also include the maximum absolute radial eccentricity being less than or equal to the preset upper limit of absolute radial eccentricity, and the maximum absolute axial tilt being less than or equal to the preset upper limit of absolute axial tilt. The absolute attitude criterion can identify static eccentricity and static tilt that remain unchanged during micro-loading and therefore do not manifest as radial displacement increments.

[0166] The realignment conditions include four criteria: the maximum radial offset is greater than the preset upper limit of radial offset, the maximum drive shaft axis tilt is greater than the preset upper limit of drive shaft axis tilt, the maximum absolute radial eccentricity is greater than the preset upper limit of absolute radial eccentricity, or the maximum absolute axis tilt is greater than the preset upper limit of absolute axis tilt. The realignment conditions are triggered when any one of these criteria is met. When the realignment conditions are triggered, the detection system controls the floating alignment mechanism to release the radial constraint and performs a realignment action with an axial load less than or equal to the preset upper limit of the realignment load. Then, the fixture is locked, and the absolute radial eccentricity and absolute axis tilt measurements in step 100 are re-executed to re-determine the micro-load execution conditions. After the micro-load execution conditions are triggered, the detection system performs pre-load stabilization in step 200. When all the criteria included in the measurement reference establishment conditions are met, the detection system triggers the measurement reference establishment conditions and re-establishes the proximal differential measurement reference and the radial incremental measurement reference. Subsequently, step 300 and the aforementioned attitude judgment processing are executed.

[0167] All pre-alignment proximal differential measurement references, initial radial displacement values, and measurement data are discarded and not used in calculations with post-alignment data. Two new measurement references are established and the pre-alignment data is discarded to avoid the use of coordinate zero points and measurement data corresponding to different clamping postures in calculations. The preset realignment load upper limit is obtained through floating alignment type tests. Specifically, axial loads are applied step by step, and radial offset, drive shaft axis tilt, and snap ring status are recorded. The upper boundary of the axial load is selected to drive the external and internal splines to complete self-alignment without causing changes in snap ring status, spline disengagement, or contact boundary offset. If the attitude validity condition is not triggered after realignment, the measurement validity gating result is set to invalid, and "Measurement invalid - suspected eccentricity, tilt, or local interference" is output, and the test is terminated.

[0168] After completing the attitude judgment, the detection system performs repeated micro-loading and judges the stability of the axial equivalent assembly clearance measurement results. Since the pre-loading stabilization was completed in step 200 before the formal measurement, the repeated measurement in this step and the first measurement obtained in step 300 are both in the state after pre-loading stabilization.

[0169] At the same detection position, the axial servo drive performs two more symmetrical micro-loading cycles at preset first and second detection speeds, one forward and one reverse. The second and third measurements both use the proximal differential measurement reference and the radial incremental measurement reference established in step 200. At each data sampling time, the proximal differential displacement coordinates are calculated using the same initial proximal differential value, and the radial offset and drive shaft axis tilt are calculated using the same set of initial radial displacement values. Using the two measurement references ensures that the three axial equivalent assembly clearance measurement results are under the same axial coordinate and radial attitude reference, and retains the positional drift between measurement numbers. The clearance calculation processor obtains the axial equivalent assembly clearance for the second and third measurements according to the speed-related load correction, other direction-related dynamic load correction, friction baseline subtraction, contact area identification, and contact boundary extrapolation processing methods specified in step 300. The detection system thus obtains the three axial equivalent assembly clearance measurement results: the first measurement, the second measurement, and the third measurement.

[0170] After completing the second and third measurements, the measurement validity judge adds the radial offset of the first measurement section, the radial offset of the second measurement section, the drive shaft axis tilt, the absolute radial eccentricity of the first measurement section, the absolute radial eccentricity of the second measurement section, and the absolute axis tilt at each sampling time of the two repeated measurements to the aforementioned attitude data set. It then redetermines the maximum radial offset, the maximum drive shaft axis tilt, the maximum absolute radial eccentricity, and the maximum absolute axis tilt, and re-executes the aforementioned attitude judgment. If any of the re-determined attitude indicators triggers the re-alignment condition, the aforementioned re-alignment process is executed. The new set of detection data formed after re-alignment is re-measured three times, and the results of the three measurements before re-alignment are not included in the repeatability judgment. Only when none of the four re-determined attitude indicators trigger the re-alignment condition and the aforementioned force path criterion remains valid, does the measurement validity judge trigger the attitude validity condition, and the detection system uses the three axial equivalent assembly clearance measurement results for subsequent repeatability judgment.

[0171] The measurement validity assessor calculates the repeatability range, repeatability robust standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift based on the results of three axial equivalent assembly clearance measurements. The repeatability range characterizes the absolute fluctuation range covered by the three measurement results; the repeatability robust standard deviation characterizes the degree of dispersion not dominated by a single deviation; the repeatability index relative to the allowable tolerance zone converts absolute fluctuation into a percentage of product tolerance; and the repeatability monotonic drift identifies measurement states that continuously change with measurement sequence numbers. The repeatability range is the difference between the maximum and minimum values ​​of the three measurement results; in this embodiment, this repeatability range is used as the absolute repeatability error. The repeatability robust standard deviation is determined using the median absolute deviation method, specifically by first determining the median of the three measurement results. Then, calculate the absolute value of the difference between each measurement result and the median, determine the median of each absolute difference, and finally multiply the median by the preset scaling coefficient. The result is the repeatability robust standard deviation. The repeatability index relative to the allowable tolerance zone is the quotient obtained by dividing the repeatability range by the tolerance zone width of the allowable axial equivalent assembly clearance range. The tolerance zone width is the preset upper limit of the axial equivalent assembly clearance minus the preset lower limit of the axial equivalent assembly clearance. The repeatability monotonic drift is determined by fitting a straight line with the measurement sequence number as the independent variable and the corresponding measurement result as the dependent variable. The absolute value of the difference between the value of the fitted line at the first measurement sequence number and the value at the third measurement sequence number is taken as the repeatability monotonic drift, which is used to characterize the monotonic drift of the measurement result with the measurement sequence number.

[0172] When the repeatability range, repeatability robustness standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift are all less than or equal to the preset allowable upper limit, the repeatability pass condition is triggered. The preset allowable upper limit includes the preset absolute repeatability error allowable upper limit, the preset relative repeatability index allowable upper limit, the preset repeatability robustness standard deviation allowable upper limit, and the preset repeatability monotonic drift allowable upper limit. Specifically, the repeatability pass condition includes four criteria: the repeatability range is less than or equal to the preset absolute repeatability error allowable upper limit, the repeatability index relative to the allowable tolerance zone is less than or equal to the preset relative repeatability index allowable upper limit, the repeatability robustness standard deviation is less than or equal to the preset repeatability robustness standard deviation allowable upper limit, and the repeatability monotonic drift is less than or equal to the preset repeatability monotonic drift allowable upper limit. When all four criteria are met, the measurement validity judge triggers the repeatability pass condition and retains all three measurement results. By using repeatability range, repeatability robustness standard deviation, and repeatability monotonic drift that cover all three measurement results, it is possible to avoid the situation where the proximity of individual measurement results masks the abrupt changes in other measurement results.

[0173] The outlier detection condition is based on the criterion that the repeatability pass condition has not been triggered. When the repeatability pass condition is not triggered, the measurement validity judge triggers the outlier detection condition and performs a preset outlier detection. The preset outlier detection judges whether there is a unique outlier measurement result among the three measurement results according to the criteria determined by the type test of the corresponding model. The criterion for the preset outlier detection is a preset outlier deviation boundary. The implementation method is as follows: for each measurement result participating in the test, the measurement validity judge uses the absolute value of the difference between the measurement result and the median of the other measurement results as the dividend, and uses the robust standard deviation of the other measurement results determined according to the absolute deviation of the median as the divisor. The quotient is the deviation of the measurement result. When the determined robust standard deviation is within the threshold range, the deviation is determined. When the standard deviation is less than the preset repeatability regularization constant, the preset repeatability regularization constant is used as the divisor. The preset repeatability regularization constant is determined based on the measurement resolution or the lower limit of repeatability noise of historical qualified products. When only one measurement result among the measurement results participating in the inspection has a deviation greater than the preset abnormal deviation boundary, it is determined that there is a unique abnormal measurement result, and this measurement result is the unique abnormal measurement result. Each group of three measurement results is only allowed to perform one abnormal measurement result rejection and one supplementary measurement. After adding the supplementary measurement result to the retained measurement results, the repeatability pass condition is re-evaluated. If the repeatability pass condition is still not triggered, the abnormal result rejection or supplementary measurement will not be performed again, and the measurement validity gating result will be determined as invalid.

[0174] The preset abnormal deviation boundary is determined through repeatability type testing of the corresponding model. Specifically, among multiple sets of repeated measurement results and confirmed abnormal measurement results of the same drive shaft assembly, the deviation distribution between normal repeated measurement results and confirmed abnormal measurement results is compared, and the deviation boundary that prevents normal repeated measurement results from being misjudged as abnormal and can identify confirmed abnormal measurement results is selected. When there is a unique abnormal measurement result, it is allowed to be removed. Subsequently, the axial servo drive performs a symmetrical micro-load test at a preset first detection speed and a preset second detection speed. The gap calculation processor obtains the supplementary measurement results, and then the repeatability range and repeatability stability are recalculated using the retained measurement results after removal and the supplementary measurement results. The repeatability index and repeatability monotonic drift are reassessed based on the standard deviation, repeatability index relative to the allowable tolerance zone, and the number of measurement results removed in each assessment is less than or equal to one. Only the unique abnormal measurement result is allowed to be removed, and a supplementary measurement is required to pass the repeatability assessment again. This can prevent systematic drift or repeatability anomalies from being masked by continuously deleting measurement results. When there is no unique abnormal measurement result, or the repeatability pass condition is not triggered after supplementary measurement, the measurement validity gating result is set to invalid, "Measurement invalid - detection repeatability does not meet requirements" is output, and the current inspection is terminated. The repeatability assessment result and the retained measurement results and their measurement sequence numbers are used for subsequent repeatability validity assessment and the final axial equivalent assembly clearance calculation in step 500.

[0175] The aforementioned supplementary measurements use the proximal differential measurement reference and radial incremental measurement reference established in step 200, and calculate the proximal differential displacement coordinates, radial offset, drive shaft axis tilt, absolute radial eccentricity, and absolute axis tilt in the same manner as the first, second, and third measurements. Before recalculating the repeatability parameters, the measurement validity judge adds the attitude data from the supplementary measurements to the attitude dataset and re-executes the attitude judgment. When any attitude index triggers the realignment condition, the aforementioned realignment process is executed, and all measurement results formed before the supplementary measurements are invalidated.

[0176] After completing the measurement repeatability judgment, the measurement validity judge generates a measurement validity gating result. If the attitude validity condition and the repeatability pass condition are triggered, the measurement validity gating result is set to valid, the detection system enters step 500 and outputs the axial equivalent assembly clearance that can be used for product judgment; otherwise, the measurement validity gating result is set to invalid. When the measurement validity gating result is invalid, the detection system does not output the determined clearance value for product release, and outputs the measurement invalidation reason corresponding to the trigger criterion.

[0177] Step 500: When the measurement validity gating result is valid, the weighted fusion of each axial equivalent assembly clearance is used to obtain the final axial equivalent assembly clearance and output it.

[0178] For each measurement result that has been validated through measurement validity and retained through repeatability determination in step 400, the gap calculation processor determines the random standard uncertainty of the measurement and the common system standard uncertainty of the detection system. The random standard uncertainty of the measurement is determined by the standard uncertainty introduced by the fitting of the positive contact boundary, the standard uncertainty introduced by the fitting of the negative contact boundary, and the covariance between the positive and negative contact boundaries. Since the axial equivalent assembly clearance of the measurement is equal to the near-end differential displacement coordinate of the positive contact boundary minus the near-end differential displacement coordinate of the negative contact boundary, and since the positive and negative contact boundaries share the near-end differential measurement reference established in step 200, the same displacement sensor calibration coefficient, the same temperature environment, and the same clamping state, there is a correlation between the fitting results of the two contact boundaries, and their covariance is not ignored. The gap calculation processor first determines the standard uncertainty introduced by the fitting of the positive contact boundary. The standard uncertainty is squared, and then the standard uncertainty introduced by fitting the reverse contact boundary is squared. The two squared values ​​are added together and then subtracted by twice the covariance between the forward and reverse contact boundaries. Finally, the square root of the subtraction result is taken. The result is the random standard uncertainty of this measurement. When the value within the square root is less than zero due to the value of the covariance, the detection system determines that the random standard uncertainty of this measurement is invalid and outputs that the measurement is invalid. The common system standard uncertainty is determined by the standard uncertainty introduced by calibration and the standard uncertainty introduced by the centering error. The gap calculation processor squares the standard uncertainty introduced by calibration and the standard uncertainty introduced by the centering error respectively. The square root of the two squared values ​​is taken. The result is the common system standard uncertainty. The calibration and clamping states are shared among all retained measurements and belong to the source of systematic error. Therefore, the common system standard uncertainty takes the same value for all retained measurements.

[0179] The standard uncertainty introduced by the positive contact boundary fitting, the standard uncertainty introduced by the negative contact boundary fitting, and the covariance between the positive and negative contact boundaries are determined by the residuals of the robust fitting of the corresponding contact boundaries in step 300 and the extrapolation uncertainty of the zero-velocity branch load. Since the continuous force displacement residuals have positional correlation and autocorrelation along the near-end differential displacement coordinates, the gap calculation processor uses a block resampling method to repeatedly resample the fitted residuals. This involves dividing the residuals into continuous data blocks according to the near-end differential displacement coordinates and resampling in units of these blocks, thereby preserving the positional correlation and autocorrelation of the residuals. The data block length and resampling frequency used in the block resampling are specified. The preset data block length and preset resampling count are used. The preset data block length is determined based on the autocorrelation range of the fitting residuals along the proximal differential displacement coordinates. Specifically, it is selected as the data block length corresponding to the coordinate interval when the autocorrelation of the fitting residuals tends to zero as the proximal differential displacement coordinate interval increases, so that the residual correlation between each data block tends to zero while the positional correlation and autocorrelation within each data block are preserved. The preset resampling count is determined based on the convergence requirements of the standard deviation and covariance of the contact boundary fitting results. Specifically, it is selected as the count corresponding to the standard deviation of the positive contact boundary fitting results, the standard deviation of the negative contact boundary fitting results, and the covariance of both no longer change after further increasing the resampling count.

[0180] During each resampling, the gap calculation processor adds the load disturbance corresponding to the extrapolation uncertainty of the zero-velocity branch load at each contact zone data point to the fitted load. It then performs joint resampling on both the forward and reverse contact zones using the same near-end differential measurement reference and the same displacement sensor calibration coefficients. Subsequently, it refits the forward and reverse contact boundaries. The gap calculation processor uses the standard deviation of each forward contact boundary fitting result as the standard uncertainty introduced by the forward contact boundary fitting, and the standard deviation of each reverse contact boundary fitting result as the standard uncertainty introduced by the reverse contact boundary fitting. Finally, it uses the covariance between the forward and reverse contact boundary fitting results as the covariance between the forward and reverse contact boundaries. This preserves the correlation between the two contact boundaries under the condition that they share the same near-end differential measurement reference and calibration coefficients. The standard uncertainty introduced by the centering error is determined by the maximum radial offset, maximum drive shaft axis tilt, maximum absolute radial eccentricity, and maximum absolute axis tilt in step 400. Specifically, the correspondence between the axis attitude and the contact boundary deviation established by the radial offset and axis tilt calibration test is used to convert the above attitude quantities into contact boundary deviation components, and then the square root is calculated according to the sum of the squares of the independent uncertainty components. The standard uncertainty introduced by calibration is determined by the displacement sensor calibration coefficients. Specifically, the standard uncertainty introduced by the standard uncertainty given by the displacement sensor calibration certificate and the standard uncertainty introduced by the fitting residual of the calibration coefficients are calculated according to the sum of the squares.

[0181] The fusion weights are not used as initial preset weights. The gap calculation processor dynamically determines the fusion weights based on the random standard uncertainty of each retained measurement. For any retained measurement, the gap calculation processor first calculates the reciprocal of the square of the random standard uncertainty of that measurement, then calculates the sum of the reciprocals of the squares of the random standard uncertainty of all retained measurements. The former is then divided by the latter, and the quotient is the fusion weight for that retained measurement. The sum of all fusion weights determined in this way is one, and the fusion weight is inversely proportional to the square of the random standard uncertainty of the corresponding measurement. Before calculating the fusion weights, it is determined whether the random standard uncertainty corresponding to each retained measurement is greater than zero. When the random standard uncertainty of any measurement is less than zero... When the value is less than or equal to zero, the corresponding uncertainty calculation result is marked as invalid, and the uncertainty estimation is re-executed. If the value is still less than or equal to zero after re-estimation, the corresponding measurement result is not included in the weighted fusion as a retained measurement result. The fusion weight is determined by using the inverse of the random variance normalization, which can allocate the contribution of the random uncertainty of each measurement to the final axial equivalent assembly clearance according to its random uncertainty. Since the systematic errors such as calibration and clamping status are shared among the retained measurements, the weighted fusion of repeated measurements only reduces the independent random uncertainty components, and does not reduce the above common system standard uncertainty. Therefore, the common system standard uncertainty is included separately in the final standard uncertainty and is not eliminated by the weighted fusion of repeated measurements.

[0182] The clearance calculation processor multiplies the axial equivalent assembly clearance of each retained measurement by the fusion weight of that retained measurement, and then adds all the products together. The resulting weighted sum is the final axial equivalent assembly clearance.

[0183] The clearance calculation processor further determines the combined standard uncertainty of the final axial equivalent assembly clearance. The clearance calculation processor first squares the product of the fusion weight of each retained measurement and its random standard uncertainty, and then adds the squares of each product to obtain the weighted fusion random variance component. Subsequently, the random variance component is added to the square of the common system standard uncertainty. Finally, the square root of the sum is taken, and the result is the combined standard uncertainty of the final axial equivalent assembly clearance. This combined standard uncertainty includes both the random uncertainty component reduced by weighted fusion and the common system uncertainty component that was not eliminated by repeated measurements.

[0184] The clearance calculation processor compares the final axial equivalent assembly clearance with the preset lower limit and upper limit of the axial equivalent assembly clearance. When the final axial equivalent assembly clearance is greater than or equal to the preset lower limit of the axial equivalent assembly clearance and less than or equal to the preset upper limit of the axial equivalent assembly clearance, the detection system determines that the axial equivalent assembly clearance is qualified.

[0185] When the final axial equivalent assembly clearance is less than the preset lower limit of the axial equivalent assembly clearance, the detection system determines that the axial equivalent assembly clearance is unqualified because it is less than the lower limit of the allowable clearance.

[0186] When the final axial equivalent assembly clearance is greater than the preset upper limit of the axial equivalent assembly clearance, the detection system determines that the axial equivalent assembly clearance is greater than the upper limit and is unqualified; this determination is used to prevent drive shaft assemblies with equivalent free displacement between two repeatable axial contact boundaries that exceed the design limit from entering the product release process.

[0187] Finally, the testing system saves the drive shaft assembly number, product model, testing time, original force and displacement data, snap ring action position range, micro-load safety load window, near-end differential measurement benchmark, initial near-end differential value, initial values ​​of four radial displacements, branch data under two preset testing speeds, dual-speed response difference index, zero-speed branch load extrapolation uncertainty, positive contact equivalent stiffness, negative contact equivalent stiffness, relative standard error of the fitting slope of the positive contact area, relative standard error of the fitting slope of the negative contact area, positive contact boundary, negative contact boundary, radial offset of the first measurement section, radial offset of the second measurement section, drive shaft axis tilt, absolute radial eccentricity, absolute axis tilt, measurement results of each axial equivalent assembly clearance and its random standard uncertainty, common system standard uncertainty, measurement validity gating results, final axial equivalent assembly clearance and its combined standard uncertainty, as well as qualified, unqualified, or invalid measurement results, as testing traceability information; it saves the original input, intermediate parameters, validity criteria, and output results, and can reproduce the calculation path of the axial equivalent assembly clearance and locate the cause of measurement invalidity.

[0188] Thus, this embodiment completes the entire inspection process from spline insertion, snap ring action position interval identification, preload stabilization, establishment of near-end differential measurement benchmark and radial incremental measurement benchmark, dual-velocity symmetrical micro-loading, velocity-related load correction, contact boundary extrapolation, attitude judgment, repeatability judgment, measurement validity gating, to final axial equivalent assembly clearance calculation and product judgment. The near-end differential measurement benchmark uses near-end differential displacement coordinates to pass through dual-velocity data registration, contact boundary extrapolation, and axial equivalent assembly clearance calculation. The initial radial displacement value uses radial offset and drive shaft axis tilt to pass through stable contact area screening, attitude judgment, and centering error uncertainty calculation. Thus, the axial equivalent assembly clearance is obtained without disassembling the drive shaft assembly, and invalid measurement results and corresponding abnormal reasons are output when the inspection data is interfered with.

[0189] Example 2:

[0190] See Figure 3As shown, a drive shaft assembly spline meshing clearance detection system is provided for performing the aforementioned drive shaft assembly spline meshing clearance detection method. The system includes:

[0191] The position interval module 101 inserts the external spline into the internal spline to a preset engagement position, identifies the snap ring action position interval, and determines the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position interval.

[0192] The loading loop module 102 establishes a proximal differential measurement benchmark. Within the micro-loading position window, with the axial micro-loading peak value, a symmetrical micro-loading loop of forward micro-loading and reverse micro-loading is executed at different detection speeds. Based on the proximal differential measurement benchmark, the axial force and proximal differential displacement coordinates at each detection speed are collected.

[0193] The equivalent assembly module 103 performs speed-related load correction and friction baseline subtraction on the axial force at each detection speed to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the reverse contact area are identified and the positive contact boundary and the reverse contact boundary are extrapolated respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the reverse contact boundary is used as the axial equivalent assembly clearance.

[0194] The effective gating module 104 performs an effectiveness judgment on the axial equivalent assembly clearance and generates a measurement effectiveness gating result.

[0195] The clearance output module 105, when the measurement validity gating result is valid, weights and fuses the axial equivalent assembly clearance of each measurement to obtain the final axial equivalent assembly clearance and outputs it.

[0196] The embodiments of this application have been described above, but these embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments based on the guidance of these embodiments, and all of them are within the protection scope of these embodiments.

Claims

1. A method for detecting the spline meshing clearance of a drive shaft assembly, characterized in that, Includes the following steps: Insert the external spline into the internal spline to the preset engagement position, identify the snap ring action position range, and determine the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position range; A proximal differential measurement benchmark is established. Within the micro-loading position window, a symmetrical micro-loading cycle of forward and reverse micro-loading is performed at different detection speeds with the axial micro-loading peak value. Based on the proximal differential measurement benchmark, the axial force and proximal differential displacement coordinates at each detection speed are collected. The axial force at each detection speed is corrected by speed-related load correction and friction baseline subtraction to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the negative contact area are identified and extrapolated to obtain the positive contact boundary and the negative contact boundary respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the negative contact boundary is used as the axial equivalent assembly clearance. The effectiveness of the axial equivalent assembly clearance is assessed to generate measurement effectiveness gating results. When the measurement validity gating result is valid, the weighted fusion of each axial equivalent assembly clearance is used to obtain the final axial equivalent assembly clearance and output it.

2. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 1, characterized in that, Methods for identifying the operating position range of a snap ring include: Insert the external spline into the internal spline at a preset insertion speed, and collect the axial force and axial position. The axial force signal is smoothed and filtered, and then resampled to equal displacement intervals according to the axial position; A dimensionless load mutation index is constructed based on the first and second rates of change of the filtered axial force with respect to the axial position. When the dimensionless load mutation index exceeds the preset load mutation index threshold and triggers the preset peak width criterion, the preset peak fall amplitude criterion, and the preset displacement span criterion, the axial start position to axial end position of the corresponding section is recorded as the snap ring action position range.

3. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 2, characterized in that, Methods for determining the peak value of axial micro-load and the micro-load location window include: Determine the force measurement noise and load fluctuation margin based on the current sensor noise level; Calculate the limiting load for circlip state changes based on the circlip's obstacle crossing peak value within the circlip's operating position range; The minimum value of the sum of the preset maximum axial friction force, force measurement noise, and loading fluctuation margin is used as the lower limit, and the minimum value of the load limiting the change of the snap ring state and the preset snap ring disengagement load is used as the upper limit, thus forming a micro-load safety load window. Determine the peak value of axial micro-load within the micro-load safety load window; The maximum displacement under unidirectional micro-loading is determined based on the preset meshing position; With the preset meshing position as the center, the positions offset by the maximum displacement of unidirectional micro-loading along two opposite axial directions are used as the two boundaries of the micro-loading position window, and the micro-loading position window does not include the snap ring action position interval.

4. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 1, characterized in that, Methods for establishing proximal differential measurement benchmarks include: Axial displacement detection units with the same positive coordinate direction are set at the rigid reference position near the outer spline side and the rigid reference position near the inner spline side, respectively. Preload stabilization is achieved by performing a symmetrical micro-loading cycle of forward and reverse micro-loading at a preset engagement position and a preset number of preload stabilization cycles. After preloading stabilization is completed, the reference establishment time is determined based on the axial displacement detection unit; At the time of reference establishment, the initial proximal differential value is obtained by subtracting the displacement of the proximal rigid reference position on the inner spline side from the displacement of the proximal rigid reference position on the outer spline side. The proximal differential measurement reference is composed of the external spline side proximal rigid reference position, the internal spline side proximal rigid reference position, and the initial proximal differential value.

5. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 4, characterized in that, Methods for acquiring axial force and proximal differential displacement coordinates include: At each detection speed, a positive peak load is applied from a preset engagement position along the first axial direction and held for a preset holding time, then a negative peak load is applied along the second axial direction and held for the same preset holding time, and finally the initial load state is returned. The absolute values ​​of the positive peak load and the negative peak load are both axial micro-load peak values. For any data sampling time after the reference establishment time, the current proximal differential value is obtained by subtracting the displacement of the rigid reference position of the inner spline side from the displacement of the rigid reference position of the proximal end of the outer spline side. The proximal differential displacement coordinates are obtained by subtracting the initial proximal differential value from the current proximal differential value. The axial force and proximal differential displacement coordinates at each detection speed are collected using the same proximal differential measurement benchmark.

6. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 5, characterized in that, Methods for obtaining corrected branch loads include: For each data point at each detection speed, the corrected load at that detection speed is calculated based on the axial force collected at that detection speed. Based on the detection speed and the corrected load, the quasi-static load estimate is calculated; In the free micro-motion zone where the connection structure only bears frictional load, the median of the quasi-static load estimates of continuous data points with local stiffness less than a preset local stiffness threshold is used as the friction baseline estimate. The corrected branch load is obtained by subtracting the friction baseline estimate from the quasi-static load estimate.

7. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 6, characterized in that, Methods for obtaining positive and negative contact boundaries include: Robust fitting of the modified branch load and the near-end differential displacement coordinates is performed to obtain the fitted straight line, and the residual robustness scale of the fitted residuals is determined. When the absolute value of the modified branch load is greater than the preset minimum contact load, the modified branch load changes in the same direction as the near-end differential displacement coordinate, and the residual robustness scale is less than or equal to the preset upper limit of the contact area fitting error, it is identified as a stable contact area. The stable contact areas located in the positive micro-loading branch and the reverse micro-loading branch are respectively regarded as the positive contact area and the reverse contact area. The fitted straight lines of the positive and negative contact areas are extrapolated to the point where the corrected branch load is zero, and the resulting intersection points are taken as the positive and negative contact boundaries, respectively.

8. The method for detecting spline meshing clearance in a drive shaft assembly according to claim 7, characterized in that, Methods for generating measurement validity gating results include: The absolute values ​​of the slopes of the fitted straight lines in the forward and reverse contact areas are used as the equivalent stiffness of the forward and reverse contact areas, respectively. The stiffness asymmetry coefficient of the forward and reverse contact is calculated based on the equivalent stiffness of the forward and reverse contact areas. Detect the radial offset at the end of the drive shaft and the tilt of the drive shaft axis during micro-loading; When the asymmetry coefficient of positive and negative contact stiffness, the maximum radial offset and the maximum drive shaft axis tilt are less than or equal to the corresponding preset upper limit, and the equivalent stiffness of positive contact and the equivalent stiffness of negative contact are both greater than or equal to the preset minimum equivalent stiffness of contact, the attitude effective condition is triggered. Execute multiple micro-loading loops and check if the repeatability pass condition is triggered; If the attitude validity condition and repeatability pass condition are triggered, the measurement validity gating result will be valid; otherwise, the measurement validity gating result will be invalid.

9. A method for detecting the spline meshing clearance of a drive shaft assembly according to claim 8, characterized in that, Methods for obtaining the final axial equivalent assembly clearance include: By performing micro-loading cycles multiple times at the same detection location, multiple axial equivalent assembly clearance measurement results were obtained. The repeatability range, repeatability robustness standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift are calculated based on the results of multiple axial equivalent assembly clearance measurements. When the repeatability range, repeatability robust standard deviation, repeatability index relative to the allowable tolerance zone, and repeatability monotonic drift are all less than or equal to the preset allowable upper limit, the repeatability pass condition is triggered, and the measurement results are retained. The weighted sum of the axial equivalent assembly clearances from each retained measurement is calculated to obtain the final axial equivalent assembly clearance.

10. A system for detecting the spline meshing clearance of a drive shaft assembly, characterized in that, A system for performing a method for detecting spline meshing clearance of a drive shaft assembly as described in any one of claims 1-9; the system comprises: The position interval module inserts the external spline into the internal spline to a preset engagement position, identifies the snap ring action position interval, and determines the axial micro-load peak value and the micro-load position window that is separated from the snap ring action position interval. The loading loop module establishes a proximal differential measurement benchmark. Within the micro-loading position window, with the axial micro-loading peak value, a symmetrical micro-loading loop of forward and reverse micro-loading is executed at different detection speeds. Based on the proximal differential measurement benchmark, the axial force and proximal differential displacement coordinates at each detection speed are collected. The equivalent assembly module performs speed-related load correction and friction baseline subtraction on the axial force at each detection speed to obtain the corrected branch load. Based on the corrected branch load, the positive contact area and the reverse contact area are identified and extrapolated to obtain the positive contact boundary and the reverse contact boundary respectively. The difference between the near-end differential displacement coordinates of the positive contact boundary and the reverse contact boundary is used as the axial equivalent assembly clearance. The effective gating module determines the effectiveness of the axial equivalent assembly clearance and generates measurement effectiveness gating results. The clearance output module, when the measurement validity gating result is valid, weights and fuses the axial equivalent assembly clearance of each measurement to obtain the final axial equivalent assembly clearance and outputs it.

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