Coaxiality measuring device and method for cmg shaft end unit

Abstract

This invention belongs to the field of coaxiality detection technology, specifically relating to a device and method for measuring the coaxiality of CMG shaft end units. It can simultaneously detect the displacement changes of the shaft end units to obtain the coaxiality of the shaft systems at both ends. By constructing a spatial measurement benchmark with a high-precision negative-pressure air-bearing one-dimensional platform as its core, this invention fundamentally ensures the straightness accuracy of the measurement system itself, making sub-micron level coaxiality detection possible. By employing a scheme of mounting sensors at both ends of the rotor shaft system and combining them with equal-angle trigger sampling, it successfully solves the problem that traditional cylindricity gauges cannot be directly applied due to the special structure of the CMG rotor. This achieves synchronous, accurate, and non-contact measurement of the radial runout of the shaft end units at both ends of a long shaft system, and the measurement results truly reflect the form and position errors of the shaft system in its assembled state.

Description

Technical Field

[0001] This invention belongs to the field of coaxiality detection technology, specifically relating to a device and method for measuring the coaxiality of CMG shaft end units. Background Technology

[0002] As a core actuator in a spacecraft's attitude control system, the control moment gyroscope (CMG) directly impacts the spacecraft's on-orbit maneuverability and lifespan. The CMG's core lies in its high-speed rotating rotor shaft system, which typically employs a symmetrically supported structure with precision end-units mounted at both ends. The coaxiality of these end-units is a critical geometric tolerance for ensuring smooth rotor operation, reducing vibration and noise, and extending bearing life. Excessive coaxiality error will lead to significant unbalanced forces during high-speed rotor operation, causing not only overall vibration and affecting the CMG's control accuracy, but also drastically shortening the lifespan of the supporting bearings and potentially causing the entire CMG system to fail.

[0003] In traditional mechanical manufacturing, cylindricity gauges are commonly used high-precision measuring tools for measuring the coaxiality of shaft parts. However, the rotor shaft system of CMG has a unique structure, with a relatively long overall dimension and the shaft end units at both ends separated by the large rotor body. This structure prevents the measuring arm or probe of a standard cylindricity gauge from crossing the rotor body to simultaneously and uniformly measure the reference surfaces (such as the cylindrical surface or end face of the journal) of both shaft end units. If a method of measuring in stages and then fitting the data through reference conversion is used, secondary clamping errors and reference misalignment errors will be introduced. These accumulated errors may approach or even exceed the coaxiality tolerance itself, leading to distorted measurement results that cannot accurately reflect the actual coaxiality of the rotor shaft system in the assembled state.

[0004] Therefore, existing cylindricity gauges, limited by their physical structure and measurement principles, are difficult to directly apply to the accurate and efficient detection of coaxiality of the shaft end units on both sides of the CMG rotor shaft system. To overcome this technical bottleneck, there is an urgent need to develop a dedicated shaft coaxiality detection system. The core idea of ​​this system is to abandon the traditional single-center measurement mode and instead set up independent data acquisition devices at the shaft end units on both sides of the rotor shaft system. By establishing a unified measurement benchmark and a precise data synchronization and fusion algorithm, data reflecting the true form and position error of the overall shaft system can be obtained, thereby achieving accurate evaluation of the coaxiality of the shaft end units on both sides. Summary of the Invention

[0005] In view of this, the present invention provides a device and method for measuring the coaxiality of CMG shaft end units, which can simultaneously detect the displacement change data of the shaft end units and obtain the coaxiality of the shaft systems at both ends.

[0006] To achieve the objectives of this invention, the following technical solutions are provided. A device for measuring the coaxiality of CMG shaft end units, comprising: A one-dimensional air-floating platform serves as a measurement reference, and its mover can move along a straight line. A multi-degree-of-freedom adjustment module is installed on the mover of the air flotation platform and is used to clamp and adjust the position and orientation of the CMG rotor shaft system. A drive module is used to drive the stator of the shaft end unit of the CMG rotor shaft system to rotate via a friction wheel; The data acquisition module includes at least two displacement sensors fixed to the mover of the air-bearing platform, used to measure the radial displacement of the two end shaft units respectively; the processing and analysis module is used to receive and process the data from the data acquisition module and calculate the coaxiality; wherein, the data acquisition module further includes an encoder and a programmable logic controller (PLC), the encoder is used to detect the rotation angle of the friction wheel, and the PLC is used to trigger the displacement sensors to perform synchronous data acquisition at equal angular intervals according to the signal from the encoder.

[0007] The one-dimensional air flotation platform is a negative pressure static pressure air flotation platform with a straightness ≤0.5μm, a range ≥250mm, and a load ≥300kg.

[0008] The multi-degree-of-freedom adjustment module includes: The combination of worm gear and linear guide rail is used to achieve height adjustment; A combination of servo motor, ball screw and rotary bearing used to achieve orientation adjustment; A servo motor combined with a threaded lifting pin is used to achieve pitch adjustment.

[0009] The friction wheel in the drive module is pressed against the stator of the shaft end unit by a spring hinge mechanism to provide constant contact pressure.

[0010] The processing and analysis module is configured to perform the following operations: The collected displacement data are unified into a spatial rectangular coordinate system based on the air-floating platform; The nonlinear least squares method is used to fit all the effective data points of the shaft end element as a whole, and the ideal axis equation of the cylindrical surface of the shaft end element is solved by the Gauss-Newton iteration method. The coaxiality error value is calculated based on the ideal axis equation.

[0011] When the processing and analysis module calculates the coaxiality error, it merges all the valid data points of the two end shaft units and performs overall fitting to obtain a common ideal reference axis. The coaxiality error value is taken as twice the maximum distance from the feature points of the two end shafts to the common axis.

[0012] This invention also proposes a method for measuring the coaxiality of CMG shaft end units, implemented using the device described in this invention, characterized by comprising the following steps: System assembly and benchmark establishment: Adjust the CMG rotor shaft system to make its axis parallel to the motion axis of the air flotation platform; Equal-angle data acquisition: Drive the shaft end unit to rotate, and the PLC triggers the displacement sensor at equal angular intervals according to the encoder signal to synchronously acquire the radial displacement data of the two shaft end units on multiple axial sections; Unified data coordinates: Transform all data points to a unified spatial rectangular coordinate system; Axis fitting: The nonlinear least squares method is used to fit all data points of each end unit of the axis as a whole, and the Gauss-Newton iteration method is used to solve the ideal axis equation for each. Coaxiality calculation: Based on the ideal axis equation, calculate the coaxiality error with a single axis as the reference or a common axis as the reference.

[0013] Beneficial effects 1. This invention, by constructing a spatial measurement benchmark with a high-precision negative pressure air-float one-dimensional platform as its core, fundamentally guarantees the straightness accuracy (≤0.5μm) of the measurement system itself, making sub-micron level coaxiality detection possible. By employing a scheme of mounting sensors at both ends of the rotor shaft system and combining it with equal-angle trigger sampling, it successfully solves the problem that traditional cylindricity gauges cannot be directly applied due to the special structure of the CMG rotor. This achieves synchronous, accurate, and non-contact measurement of the radial runout of the shaft end units at both ends of a long shaft system, and the measurement results truly reflect the form and position errors of the shaft system in its assembled state.

[0014] 2. The friction wheel drive combined with the spring hinge constant pressure mechanism designed in this invention effectively drives the large inertia rotor to rotate smoothly while avoiding the introduction of additional radial interference forces, thus ensuring the accuracy and reliability of the measurement data. The multi-degree-of-freedom adjustment module ensures rapid and accurate alignment and positioning of rotor shaft systems of different specifications, improving the versatility and testing efficiency of the device.

[0015] 3. At the data processing level, this invention abandons the traditional step-by-step fitting method (fitting the center of the cross-section circle first and then fitting the axis), and innovatively adopts a nonlinear least squares global fitting algorithm based on the Gauss-Newton iteration method to directly perform a one-time spatial cylindrical surface fitting on all data points.

[0016] 4. This invention effectively avoids the problems of error propagation and accumulation in step-by-step fitting, fully utilizes all measurement information, and makes the solved ideal axis more consistent with the principle of minimum region, thereby significantly improving the accuracy and scientific nature of coaxiality assessment. This invention provides an indispensable precision testing method for high-quality manufacturing and assembly of CMG rotor shaft systems. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of a CMG rotor model.

[0018] Figure 2 This is a schematic diagram of the system composition of the present invention.

[0019] Figure 3 This is a schematic diagram of an air-supported (positive pressure) air flotation platform.

[0020] Figure 4 This is a schematic diagram of a negative pressure (static pressure) air flotation platform.

[0021] Figure 5 This is a design drawing of the negative pressure (static pressure) air flotation platform in this embodiment.

[0022] Figure 6 This is a schematic diagram of the weight reduction method for the negative pressure (static pressure) air flotation platform in this embodiment, involving drilling holes. Figure 7 This is a schematic diagram of the multi-degree-of-freedom adjustment module of the present invention.

[0023] Figure 8 This is a schematic diagram of the stator of the friction wheel drive shaft end unit of the device of the present invention.

[0024] Figure 9 This is a schematic diagram of the sensor fixing method in this invention.

[0025] Figure 10 A simplified diagram of the cross section of the shaft end unit and the axis of rotation is provided for this invention. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0027] This invention provides a device for measuring the coaxiality of CMG shaft end units. A support structure is used to support the rotating CMG body and establish a detection axis. Detection coordinates are established at both ends of the shaft system, and displacement changes of the shaft end units are detected simultaneously to obtain the coaxiality of the two shaft systems (single reference and common reference). This device is used for high-precision coaxiality detection of the end units on both sides of the CMG rotor shaft system. It employs a horizontal measurement method, using a high-precision air-bearing one-dimensional platform as a reference. Friction wheels drive the shaft end units to rotate, and two displacement sensors measure the radial runout of the rotor shaft system's end units. By collecting data from multiple cross-sectional positions, a spatial coordinate system is established, a cylinder representing the shaft end unit is fitted, and the coaxiality of the shaft end unit is calculated.

[0028] The coaxiality measuring device for CMG shaft end units in this embodiment is as follows: Figure 2 As shown, it includes a high-precision one-dimensional air flotation platform, a multi-degree-of-freedom adjustment stage, a data acquisition module, and a processing and analysis module.

[0029] A high-precision one-dimensional air-float platform serves as the benchmark for the entire measurement system, and its straightness accuracy directly determines the reliability of the final measurement results. Given that the required detection accuracy is better than 1μm, which is difficult to meet with ordinary linear guides, this device employs a negative pressure (static pressure) air-float platform. Figure 4 , Figure 5 This scheme is different from the pneumatic (positive pressure) type. Figure 3 The platform has higher rigidity and more stable air film pressure distribution, which can better resist load changes and overturning moment, ensuring that when bearing a load of more than 300kg, its motion straightness can still be controlled within 0.5μm and the range is not less than 250mm.

[0030] To reduce the overall weight of the equipment and meet on-site usage requirements (≤400kg / m²), a weight-reduction design was implemented for the marble stator of the platform, including thinning the wall thickness and creating through holes. Figure 6 To compensate for the potential decrease in rigidity resulting from weight reduction, multiple jacks are installed at the bottom of the platform to provide uniform and stable support, minimizing platform flexural deformation. Additionally, a locking knob is located on the side of the platform's mover, allowing it to be locked in non-measuring states to prevent accidental movement.

[0031] Multi-degree-of-freedom adjustment module, such as Figure 7 As shown, this module is used for precise clamping and alignment of the CMG rotor shaft system under test, ensuring its axis is parallel to the reference axis of the air-bearing platform, and accurately adjusting the measured section of the shaft end unit to the center of the displacement sensor's range. This module integrates three adjustment functions: Height adjustment: A combination of worm gear and linear guide is used. Worm gear transmission has the advantages of large speed ratio and good self-locking performance, which can safely and smoothly raise and lower heavy-duty rotor shafts.

[0032] Orientation adjustment: The combination of "servo motor + ball screw + rotary bearing" is used to achieve precise rotation of the rotor shaft around its center in the horizontal plane for axial alignment.

[0033] Pitch adjustment: A combination of "servo motor + threaded lifting pin" is adopted. By coordinating the lifting height of the pins at both ends, the pitch angle of the rotor shaft system can be finely adjusted.

[0034] Driver modules such as Figure 8 As shown, since the CMG rotor shaft system is a passive component in the detection state, it requires external drive to rotate. This device adopts a friction wheel drive scheme. A friction wheel driven by a motor is pressed against the stator outer circle of the shaft end unit through a spring hinge mechanism. The spring hinge can provide a constant and flexible clamping force, ensuring the stability of the friction transmission, while avoiding the application of additional radial interference force to the rotor shaft system due to rigid contact, thus ensuring the authenticity of the measurement data.

[0035] The data acquisition module is responsible for synchronously and accurately acquiring the radial runout data of the two shaft end units. Its core components include: Sensor arrangement: Two high-precision non-contact displacement sensors (such as laser displacement sensors) are fixed on the mover of the air-bearing platform by rigid brackets, and their probes are aligned with the radial measurement surfaces of the two shaft end units.

[0036] Equal-angle triggered sampling: To address potential speed fluctuations in friction wheel drives and avoid uneven data point distribution caused by equal-time sampling, this device employs equal-angle triggered sampling technology. A high-resolution encoder is installed on the drive shaft of the friction wheel. A programmable logic controller (PLC) reads the encoder signal in real time. Whenever the rotor rotates through a fixed small angle (e.g., 0.36°, i.e., 1000 points are collected per revolution), the PLC synchronously sends a trigger pulse to the controllers of the two displacement sensors. The controllers then collect and record the current displacement value. This method ensures that the data collected for each revolution is complete and evenly distributed at an angle.

[0037] The processing and analysis module, consisting of a computer and dedicated analysis software, is responsible for receiving and processing the massive amounts of displacement data transmitted from the data acquisition module, and calculating the final coaxiality error value through an established mathematical model. Its core algorithm flow will be described in detail in the method implementation examples.

[0038] Through the coordinated work of the above modules, this device constructs an ultra-high precision measurement system, which can directly, accurately, and efficiently measure the coaxiality of the shaft end units on both sides of the CMG rotor shaft system.

[0039] Specifically, in the high-precision air-float one-dimensional platform, due to the special structure of the rotor shaft system, a cylindricity gauge cannot detect the coaxiality of the shaft end units on both sides of the rotor shaft system. Therefore, a shaft system detection system is developed, with data acquisition devices installed on each of the shaft end units on both sides. As a high-precision, high-inertia motion actuator, the rotor shaft system places extremely high demands on coaxiality detection accuracy, requiring a detection accuracy better than 1μm. Ordinary linear guides cannot meet this requirement, hence the development of a high-precision air-float one-dimensional platform. The air-float platform has a straightness ≤0.5μm within its measurement range, a range ≥250mm, and a load ≥300kg.

[0040] There are two types of air flotation platforms: one is the air-sufficient (positive pressure) air flotation platform, and the other is the negative pressure (static pressure) air flotation platform. The air-sufficient (positive pressure) air flotation platform is as follows: Figure 3 As shown, the negative pressure (static pressure) air flotation platform is as follows: Figure 4 As shown. Air-footed air-float platforms create a high-pressure air film between the moving parts and the base, resulting in near-zero friction during movement. Due to the extremely low coefficient of friction, air-footed air-float platforms can achieve sub-micron level precision, making them ideal for high-precision machining and measurement. Utilizing air-float technology, air-footed air-float platforms create an air cushion between the platform and the ground, eliminating interference from ground movement and achieving highly stable motion. Because of its strict requirements for gas quality, interference from dust and impurities must be avoided during use. Maintaining a gas supply during operation may lead to some energy consumption. Negative-pressure (static-pressure) air-float platforms offer higher rigidity, suitable for ultra-high-precision applications requiring high stability and anti-interference capabilities. They provide a more uniform air film pressure distribution, reducing the likelihood of air hammer and making the system more stable, especially under overturning moments. The application of negative-pressure air-float platforms requires high flatness and smoothness of the test platform. Negative-pressure air-float platforms can only adapt to two-dimensional planar motion, limiting their application in multi-dimensional spaces. In summary, a negative pressure (static pressure) air flotation platform was selected as the technical solution for the air flotation platform. Figure 5 This is a design drawing of the negative pressure (static pressure) air flotation platform in this embodiment.

[0041] Air flotation platforms are generally made primarily of marble, making the equipment quite heavy. To meet customer requirements, the weight is limited to 400 kg / m². Therefore, weight reduction measures were implemented, including thinning the stator of the air flotation platform and creating through holes. Figure 6 As shown, the air-bearing platform is supported by multiple jacks to ensure sufficient rigidity to support the mover even after the stator is thinned, reducing flexural deformation and minimizing its impact on measurement accuracy. A locking knob is designed on the underside of the air-bearing platform to lock the mover in air-bearing mode.

[0042] (2) Multi-degree-of-freedom adjustment module, such as Figure 7As shown, it includes: 1) Height adjustment The height adjustment scheme uses a worm gear and guide rail configuration. The worm gear has a high load capacity and a self-locking function, and the linear guide rail provides guidance, meeting the lifting requirements of heavy-duty rotor shaft systems. The shaft system detection equipment needs to be compatible with five different rotor shaft specifications with significant dimensional differences. The selected high-precision displacement sensor has a relatively small range; therefore, the rotor shaft height needs to be adjusted to fall within the sensor's range.

[0043] 2) Orientation adjustment Orientation adjustment is achieved using a servo motor, ball screw, and rotary bearing.

[0044] 3) Pitch adjustment Pitch adjustment is achieved using a servo motor and a threaded lifting pin.

[0045] (3) Selection of driving method The rotor shaft system cannot be self-driven and requires external force to drive the stator of the shaft-end unit to rotate. Therefore, a friction wheel drive is used to rotate the shaft-end unit while the displacement sensor remains stationary, allowing for the collection of data for the entire revolution.

[0046] To maintain constant contact between the friction wheel and the stator of the shaft end unit, and to ensure a constant contact force, a spring hinge is used as the actuator to maintain this constant pressure. Maintaining a constant contact force prevents the friction wheel from applying additional radial force, which could interfere with the measurement results. The friction wheel drives the stator of the shaft end unit as follows: Figure 8 As shown. The sensor is fixed as follows. Figure 9 As shown.

[0047] (4) Data collection method The friction wheel drive uses line contact, and the friction wheel's rotational speed itself fluctuates. This fluctuation is amplified when it contacts the stator of the shaft end unit via line contact. Therefore, setting a fixed sampling rate to allow the sensor to collect cross-sectional runout data is not feasible, as it would be impossible to distinguish between complete rotations. Therefore, a trigger-based sampling method is used. A PLC monitors the encoder count of the drive wheel. Each time the wheel rotates a fixed angle, the PLC sends a pulse to the displacement sensor's controller for data sampling, achieving uniform angle sampling.

[0048] (5) Processing and Analysis Module Before collecting data, the rotor shaft system needs to be parallel to the direction of the air-bearing platform. Before each data collection, the shaft should be returned to the mechanical origin set by the encoder. Then, the shaft end unit cross-sectional data should be collected, and the position of the ideal axis of the bearing holes at both ends relative to the shaft axis can be determined.

[0049] Figure 10A simplified diagram of the shaft-end element cross-section and the axis of rotation is given. The cylinder represents the shaft-end element cross-section, OZ represents the axis of rotation, and XOY represents the cross-section where the data points are located during one revolution of the shaft. Along axis OZ, the number of planes perpendicular to axis OZ corresponds to the number of cross-sections measured by the laser sensor. O1Z1 represents the ideal axis of rotation of the shaft-end element. It is easy to see that when the sensor rotates around axis OZ, the laser beam at the shaft-end element cross-section XOY will be elliptical in shape. The goal is to find the equation of the straight line containing the ideal axis of rotation O1Z1 in the XYZ coordinate system. One method is to use the elliptic formula, fitting the center of the cross-section using the least squares method for the data points on cross-section XOY, and then fitting the ideal axis of rotation O1Z1 again using the least squares method through the center points of each cross-section to calculate the coaxiality. Another method is to directly fit the ideal axis of rotation using the least squares method for all points. This project adopts the latter approach because it only uses the first least squares method, and the formula used by the least squares method is the equation of a circular function, which can more accurately determine the ideal axis of the cylinder.

[0050] When the sum of the squares of the distances from each point in the shaft-end element to the axis is minimized, the axis of the cylinder is considered the ideal axis of the shaft-end element. Consider a complete rotation of the sensor; the laser points are all on the surface of the shaft-end element, and the resulting cross-section is the effective cross-section. Points on the effective cross-section are considered effective points. By performing least-squares fitting on all effective points, the linear equation of the ideal axis O1Z1 relative to the rotation axis coordinate system XYZ can be obtained. The relationship between the dependent and independent variables in this problem is a second-order function relationship, making it a nonlinear least-squares problem. For second-order nonlinear least-squares problems, the Gauss-Newton iteration method can be used for solution. The Gauss-Newton iteration method is a variation of Newton's method. Compared to Newton's method, the Gauss-Newton method can only be used for least-squares estimation, but its advantage lies in not needing to calculate the second derivative, greatly simplifying the calculation process, and having a fast iteration convergence speed. The Gauss-Newton method requires an initial value for iteration; we can set the axis OZ as the initial value and the ideal axis O1Z1 as the required final value.

[0051] Based on the above analysis, the following approach can be taken: In the coordinate system XYZ containing the axis OZ of the rotating shaft, the ideal axes O1Z1 of the bearing holes at both ends can be obtained. Axis O1Z1 needs to be obtained through multiple iterations from the initial value OZ. Each iteration is actually a superposition of three-dimensional rotation and translation transformations. After each iteration, the rotating shaft OZ is translated a small distance in the XOY plane, and then the coordinate system is rotated around the X and Y axes by a certain angle, centered on the origin O. After the iterations are complete, the rotating shaft OZ has moved by Y0 along the OY direction, moved by X0 along the OX direction, and rotated by α and α around the X and Y axes, respectively. The axis OZ is rotated until it coincides with the ideal axis O1Z1. For the data points, this transformation is the reverse process: a movement of Y0 along the OY direction, a movement of X0 along the OX direction, and a rotation of -α and -α around the X and Y axes, respectively. Rotate the ideal axis O1Z1 until it coincides with the axis OZ of the rotating shaft.

[0052] By transforming the data points, it is defined that in a right-handed coordinate system, the positive direction of the object's rotation is the right-hand helical direction, that is, counterclockwise when viewed from the origin along the positive half-axis of this axis. Assume the data points are rotated around O (X0=0, Y0=0, Z0=0) by α and α' respectively around OX and OY. Transform the data points spatially by translating them along the OX and OY directions by X0 and Y0, respectively. , , , , The coordinates of this data point are:

[0053] In the formula

[0054] The implicit function prototype of this problem is

[0055] Therefore, the residual formula can be obtained.

[0056] The goal is to find the optimal solution β that minimizes the sum of squared residuals. The sum of squared residuals is defined as follows:

[0057] The goal is to minimize the sum of squared residuals S, i.e., to ensure that the partial derivative of S with respect to β is zero.

[0058]

[0059] In nonlinear systems, It is a function of variables and parameters, and has no closed-form solution. Therefore, given an initial value, we can approximate the solution using an iterative method. The Gauss-Newton iterative formula is:

[0060] In the formula: Jr is the residual ri pair The Jacobian matrix. The Jr expression is...

[0061]

[0062] when The iteration ends when the error is less than the given allowable error e. That is, the final value of the iteration. For a point on the ideal axis, Let the direction vector of the ideal axis be denoted. This gives us the linear equation of the ideal axis of one bearing hole. Similarly, we can derive the linear equation of the ideal axis of the other bearing hole. When using a common axis as a reference, simply combine the valid data points of the left and right holes and calculate the ideal axis again. This ideal axis becomes the reference axis. Then, find the maximum value of twice the distance from the two endpoints of the two axes to the reference axis. This maximum value is the coaxiality value based on the common axis of the left and right bearing holes.

[0063] This invention also proposes a method for measuring the coaxiality of CMG shaft end units, implemented using the device of this invention. Its process is based on the device in Embodiment 1, and its core lies in extracting the coaxiality error from the original displacement data through a specific data acquisition strategy and mathematical modeling algorithm. Combined with... Figure 10 The method specifically includes the following steps: Step S1: System assembly and benchmark establishment The CMG rotor shaft system is hoisted onto and secured to the multi-degree-of-freedom adjustment module. The air-bearing platform is then activated, and the position and attitude of the rotor shaft system are finely adjusted using the module's height, orientation, and pitch functions until its theoretical axis is parallel to the air-bearing platform's motion reference axis (i.e., the OZ axis of the measurement coordinate system). Simultaneously, the position of the displacement sensors is adjusted so that the measured cross-sections of the shaft end units at both ends fall within the sensors' optimal measurement range.

[0064] Step S2: Isometric Data Acquisition The drive module is activated, and the friction wheel drives the rotor shaft system to rotate at a constant speed. The data acquisition module is activated, and the PLC, based on the encoder signal, synchronously triggers two displacement sensors at equal angular intervals (e.g., every 0.36°) to acquire data. The sensors acquire the radial displacement in their own coordinate system.

[0065] Subsequently, the air-floating platform is controlled to move stepwise along the Z-axis direction. The above rotation and data acquisition process is repeated at each preset axial measurement section to obtain a set of radial runout data points distributed at equal angles at multiple different axial positions of the two end shaft units.

[0066] Step S3: Data coordinate unification and preprocessing All data points collected in step S2, combined with the grating ruler readings (Z-axis coordinates) and encoder angle information of the air-float platform, are transformed into a unified spatial rectangular coordinate system O-XYZ based on the air-float platform. In this coordinate system, each data point can be represented as (Xi, Yi, Zi).

[0067] Step S4: Axis fitting based on nonlinear least squares The core of this method is to adopt a global fitting strategy, which directly processes all the effective data points of one-end shaft unit at once to fit its "ideal axis" O1Z1.

[0068] Objective function: Find a spatial cylindrical surface such that its axis (i.e., ideal axis) satisfies the condition that the sum of the squares of the distances from all valid data points of the end elements of the axis to the axis is minimized.

[0069] Mathematical Model: This is a nonlinear least squares problem. Let the parameters of the ideal axis be β = (X0, Y0, Z0, α, θ). Where (X0, Y0) is the offset of the axis in the XOY plane, Z0 is the axial reference point, and α and θ are the rotation angles of the axis around the X and Y axes, respectively. The data points are transformed to the new coordinate system using the spatial transformation matrices RY(θ) and RX(α).

[0070] Residuals and Solution: Define the residual ri = √(X1i² + Y1i²) - R (where R is the radius of the fitted cylinder). Use the Gauss-Newton iteration method to find the parameter β that minimizes the sum of squared residuals S = Σri². Use the measurement reference axis OZ as the initial value β for the iteration. (0) Through the iterative formula β (s+ ¹ ) = β (s) + (Jr Jr) - ¹ Jr ri(β (s) The process is iterated (where Jr is the Jacobian matrix) until convergence.

[0071] Obtaining the equation of the axis: After the iteration converges, the optimal solution β is obtained. Then the equation of the ideal axis O1Z1 can be determined by a point (-X0, -Y0, Z0) and the direction vector (tanθ, tanα, 1) on it.

[0072] Step S5: Coaxiality Calculation Single-benchmark evaluation: Using the method in step S4, calculate the ideal axes Lleft and Lright of the left and right end units respectively. Then calculate the distance from a specific point (usually the two endpoints) on one axis (such as Lright) to the other axis (Lleft). Twice the maximum value of this distance is the coaxiality error based on Lleft.

[0073] Common Benchmark Evaluation (Recommended): Merge all valid data points from the left and right axis units into a single dataset. Then, apply the nonlinear least squares fitting algorithm from step S4 again to calculate a common ideal reference axis Lcommon. Next, calculate the distances from feature points on the respective ideal axes Lleft and Lright at the left and right ends to the common axis Lcommon. Multiply the maximum value of all these distances by 2; this is defined as the coaxiality error value based on the common axis: Coaxiality = 2 × max(distance).

[0074] This method avoids the error accumulation caused by step-by-step fitting through overall fitting and precise mathematical iteration, making full use of all measurement information, thus reflecting the coaxiality level of the CMG rotor shaft system in the assembled state more realistically and accurately.

[0075] This invention includes, but is not limited to, the above embodiments. Any equivalent substitutions or partial improvements made under the spirit and principles of this invention shall be considered within the scope of protection of this invention.

Claims

1. A device for measuring the coaxiality of CMG shaft end units, characterized in that, include: A one-dimensional air-floating platform serves as a measurement reference, and its mover can move along a straight line. A multi-degree-of-freedom adjustment module is installed on the mover of the air flotation platform and is used to clamp and adjust the position and orientation of the CMG rotor shaft system. A drive module is used to drive the stator of the shaft end unit of the CMG rotor shaft system to rotate via a friction wheel; The data acquisition module includes at least two displacement sensors fixed to the mover of the air-bearing platform, used to measure the radial displacement of the two shaft end units respectively; the processing and analysis module is used to receive and process the data from the data acquisition module and calculate the coaxiality; wherein, the data acquisition module further includes an encoder and a programmable logic controller (PLC), the encoder is used to detect the rotation angle of the friction wheel, and the PLC is used to trigger the displacement sensors to perform synchronous data acquisition at equal angular intervals according to the signal from the encoder.

2. The apparatus according to claim 1, characterized in that, The one-dimensional air flotation platform is a negative pressure static pressure air flotation platform with a straightness ≤0.5μm, a range ≥250mm, and a load ≥300kg.

3. The apparatus according to claim 1 or 2, characterized in that, The multi-degree-of-freedom adjustment module includes: The combination of worm gear and linear guide rail is used to achieve height adjustment; A combination of servo motor, ball screw and rotary bearing used to achieve orientation adjustment; A servo motor combined with a threaded lifting pin is used to achieve pitch adjustment.

4. The apparatus according to claim 1, characterized in that, The friction wheel in the drive module is pressed against the stator of the shaft end unit by a spring hinge mechanism to provide constant contact pressure.

5. The apparatus according to any one of claims 1-4, characterized in that, The processing and analysis module is configured to perform the following operations: The collected displacement data are unified into a spatial rectangular coordinate system based on the air-floating platform; The nonlinear least squares method is used to fit all the effective data points of the shaft end element as a whole, and the ideal axis equation of the cylindrical surface of the shaft end element is solved by the Gauss-Newton iteration method. The coaxiality error value is calculated based on the ideal axis equation.

6. The apparatus according to claim 5, characterized in that, When the processing and analysis module calculates the coaxiality error, it merges all the valid data points of the two end shaft units and performs overall fitting to obtain a common ideal reference axis. The coaxiality error value is taken as twice the maximum distance from the feature points of the two end shafts to the common axis.

7. A method for measuring the coaxiality of CMG shaft end units, implemented using the apparatus described in any one of claims 1 to 6, characterized in that, Includes the following steps: System assembly and benchmark establishment: Adjust the CMG rotor shaft system to make its axis parallel to the motion axis of the air flotation platform; Equal-angle data acquisition: Drive the shaft end unit to rotate, and the PLC triggers the displacement sensor at equal angular intervals according to the encoder signal to synchronously acquire the radial displacement data of the two shaft end units on multiple axial sections; Unified data coordinates: Transform all data points to a unified spatial rectangular coordinate system; Axis fitting: The nonlinear least squares method is used to fit all data points of each axis end unit as a whole, and the Gauss-Newton iteration method is used to solve the ideal axis equation for each. Coaxiality calculation: Based on the ideal axis equation, calculate the coaxiality error with a single axis as the reference or a common axis as the reference.

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