Precise spindle bearing pre-tightening force self-adaptive adjusting method based on thermal error decoupling

Abstract

The application relates to the technical field of bearing mechanical devices, in particular to a precision spindle bearing pre-tightening force self-adaptive adjusting method based on thermal error decoupling. The method comprises the following steps: collecting thermal displacement errors and actual pre-tightening forces of a spindle in a bearing assembly of a tapered roller bearing; according to working conditions, a spindle rotating speed and an environment temperature, dynamic stiffness threshold values and contact uniformity threshold values are calculated; roller friction heat flow is collected; mechanical displacement effects and friction heat effects are calculated, and an axial thermal elongation component is calculated by using the roller friction heat flow; the above components are separated from the thermal displacement errors to generate decoupling results; dynamic stiffness and load uniformity are calculated through a bearing thermal-mechanical coupling model, and whether the pre-tightening force meets the requirements is verified; if the pre-tightening force does not meet the requirements, the pre-tightening force is adjusted to a boundary point in a feasible region, and the pre-tightening force adjustment amount is recalculated; and the pre-tightening force adjustment amount is applied to an outer ring of the tapered roller bearing. The pre-tightening force is self-adaptively adjusted through thermal error decoupling.

Description

Technical Field

[0001] This invention relates to the field of bearing mechanical device technology, specifically to a method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling. Background Technology

[0002] In high-precision tapered roller bearing rotating assemblies, axial thermal deformation of the shaft system (dimensional changes caused by material thermal expansion due to internal frictional power loss) is the main factor limiting the accuracy and positioning stability of the slewing support. High-speed shaft operation leads to temperature rise, causing thermal expansion of the inner ring and roller assembly, which in turn leads to an abnormal increase in bearing preload, exacerbating contact friction torque and creating a vicious cycle of temperature rise. In precision transmission applications, the axial thermal elongation at the shaft end must be controlled within nanometer or even sub-nanometer levels, which is the highest requirement for bearing preload adaptive adjustment systems. To overcome the limitations of fixed preload, existing technologies employ variable preload active control components with closed-loop online control capabilities, using a temperature feedback closed-loop compensation method. The system monitors the simulated temperature signal near the preload control point in real time using a temperature sensor installed on the bearing outer ring or bearing housing. After receiving the temperature signal, the controller determines the target preload value based on preset data or a lookup table and outputs control commands to adjust the pressure of the piezoelectric ceramic actuator or hydraulic cylinder.

[0003] While existing active preload bearing assemblies achieve variable preload application, they suffer from fundamental flaws in control logic and feedback mechanisms, failing to meet the dimensional stability requirements of ultra-precision shaft systems. Current technology uses the bearing outer ring temperature as a feedback signal. However, the final positioning accuracy of the shaft system is limited by the actual axial thermal elongation at the shaft end. The temperature signal merely reflects heat conduction through the bearing assembly to the sensor point, exhibiting a significant time lag compared to the actual axial deformation of the core shaft components. This indirect, delayed feedback is insufficient to accurately compensate for real-time thermal deformation under highly dynamic environments. Furthermore, preload is a strongly coupled variable in the bearing-rotor system, its variation simultaneously determining contact stiffness characteristics and frictional heating effects. Existing temperature-compensation strategies logically couple thermal and mechanical effects. When the system detects a temperature increase, the controller commands a reduction in preload to achieve cooling. However, this operation, while reducing frictional heating, inevitably leads to a decrease in bearing support stiffness. Under dynamic operating load variations, this stiffness loss can result in greater shaft vibration and rotational errors. In summary, existing technologies lack the ability to accurately eliminate thermally induced dimensional changes while maintaining the high dynamic stiffness required for precision shaft systems.

[0004] To address this, an adaptive adjustment method for the preload of precision spindle bearings based on thermal error decoupling is proposed. Summary of the Invention

[0005] The purpose of this invention is to provide an adaptive adjustment method for the preload of a precision spindle bearing based on thermal error decoupling, which can be applied to high-precision tapered roller bearing devices.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An adaptive adjustment method for preload of precision spindle bearings based on thermal error decoupling includes:

[0008] In the bearing assembly of the tapered roller bearing, the thermal displacement error and actual preload of the spindle are collected. Based on the machine tool's operating load, spindle speed and ambient temperature, the required dynamic stiffness threshold and contact uniformity threshold of the spindle are calculated. The roller friction heat flow is collected on the large end face of the roller of the tapered roller bearing.

[0009] The mechanical displacement effect and frictional heat effect caused by the change in actual preload are calculated, and the axial thermal elongation component caused by the friction of the roller end face is calculated using the roller frictional heat flow. The mechanical displacement effect, frictional heat effect and axial thermal elongation component are separated from the thermal displacement error to generate decoupled results.

[0010] Based on the decoupling results and thermal displacement error, the preload adjustment amount is calculated. Using a pre-trained bearing thermo-mechanical coupling model, the dynamic stiffness and load uniformity of the adjusted preload are calculated. It is then verified whether the preload simultaneously meets the requirements that the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold. If not, the preload is adjusted to the boundary point of the feasible region, and the preload adjustment amount is recalculated.

[0011] Apply a preload adjustment to the outer ring of the tapered roller bearing and control the thermal displacement error within the tolerance range.

[0012] Preferably, the total displacement error, including mechanical, force, and thermal errors, is collected, and the original pressure signal between the bearing rings is collected simultaneously. The original pressure signal is adaptively weighted and fused and low-pass filtered, and combined with the coefficients of the real-time temperature correction mapping matrix to calculate the real-time preliminary force value. The preliminary force value is output as the actual preload force, and the elastic collapse caused by the pressure is calculated based on the sensor's equivalent stiffness. The total displacement error is compensated for elastic collapse based on the elastic collapse to obtain a pure displacement term. The sampling window is set based on the real-time temperature rise rate, and the pure displacement term is subjected to polynomial fitting to extract the displacement trend. The displacement trend and the frictional heat flow signal are aligned with time delay compensation using a cross-correlation function, and the Pearson correlation coefficient is calculated. When the correlation coefficient meets the preset correlation threshold, the thermal displacement error is output.

[0013] Preferably, the specific process for calculating the dynamic stiffness threshold and contact uniformity threshold required for the spindle includes: performing stability analysis based on the current operating load and spindle speed to calculate a stability lobe diagram; combining the influence of temperature on the material's elastic modulus to perform chatter stability analysis on the stability lobe diagram, finding the critical stiffness required to maintain stable cutting from the stability lobe diagram, and multiplying the critical stiffness by a safety factor to generate the dynamic stiffness threshold; calculating the normal load borne by each rolling element, and determining the contact uniformity threshold by performing inverse analysis of the normal load and combining the correction effect of thermal expansion caused by temperature on the internal geometry of the bearing.

[0014] Preferably, the specific implementation of collecting roller friction heat flow on the large end face of the roller of the tapered roller bearing is as follows: real-time capture of the heat flow density signal generated by the contact pair between the large end face of the roller and the flange, and filtering and processing by the data acquisition system to obtain roller friction heat flow data reflecting the bearing load state and heat generation characteristics.

[0015] Preferably, the specific process for generating the decoupling result is as follows: based on the change in the actual preload, the elastic compression caused by the change in actual preload is determined through a preset nonlinear stiffness curve of the tapered roller bearing, thus obtaining the mechanical displacement effect; based on the current spindle speed and the change in actual preload, the change in total frictional heat generation power is obtained through the total frictional power curve of the bearing; the change in total frictional heat generation power is substituted into a preset thermal response function to calculate the frictional heat effect generated by the change in total frictional heat generation power on the front end of the spindle in real time; the real-time roller frictional heat flow is used as the heat source intensity input, and the axial thermal elongation component generated by the roller frictional heat source on the front end of the spindle is dynamically predicted in real time using the heat transfer function; the mechanical displacement effect, frictional heat effect, and axial thermal elongation component are algebraically separated from the total thermal displacement error collected in real time from the front end of the spindle to obtain the net error that needs to be compensated, thus generating the decoupling result.

[0016] Preferably, the bearing thermo-mechanical coupling model comprises:

[0017] The stiffness analysis and prediction layer is used to establish a nonlinear mapping between preload and spindle dynamic stiffness. It uses a five-layer fully connected deep neural network to receive preload adjustment, spindle speed, operating load and ambient temperature, and performs feature dimensionality reduction and physical effect fitting; outputting the dynamic stiffness under the current preload scheme.

[0018] The load distribution optimization layer is used to calculate the contact state between the tapered roller and the inner and outer raceways. Utilizing the decoupling results and preload, the mechanical distribution characteristics of the rolling elements in the bearing circumferential direction are extracted through a one-dimensional convolutional layer, and the load uniformity characterizing the load distribution of the rolling elements is output.

[0019] The constraint verification and decision flow layer uses Boolean logic to distinguish between dynamic stiffness and dynamic stiffness threshold, and load uniformity and contact uniformity threshold. When the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold, the projection gradient method is used to search for the boundary points of the feasible region defined by the threshold, dynamically correct the initial preload adjustment amount, and output the final determined preload adjustment amount.

[0020] Preferably, the specific process of using the projection gradient method to search for the boundary points of the feasible region defined by the threshold and dynamically correcting the initial preload adjustment includes: receiving dynamic stiffness, load uniformity, dynamic stiffness threshold, contact uniformity threshold, and preload adjustment, and introducing the operating load and spindle speed as physical boundary constraint factors; calculating the rate of change of dynamic stiffness and load uniformity relative to the preload adjustment, determining the direction of the parameter adjustment vector, projecting the current preload coordinates along the direction of the parameter adjustment vector, and adjusting them to the intersection of the geometric boundary formed by the dynamic stiffness threshold, contact uniformity threshold, operating load, and spindle speed; dynamically correcting the initial preload adjustment by multiple gradient updates with a preset step size until a final preload that is at the edge of the feasible region and satisfies all performance constraints is found; and calculating the required preload adjustment based on the final preload.

[0021] Preferably, the specific process of applying a preload adjustment amount to the outer ring of the tapered roller bearing and controlling the thermal displacement error within the tolerance range includes: converting the finally determined preload adjustment amount into an electronic control command to drive the actuators distributed around the outer ring of the tapered roller bearing, so that the actuators apply a non-uniform preload adjustment amount to the outer ring; directly changing the contact state between the tapered roller and the raceway by applying the preload adjustment amount, using the mechanical displacement effect generated by the change in preload to offset the thermal error, compensating in real time for the thermal displacement error of the bearing system caused by frictional heat generation, and maintaining the thermal displacement error of the spindle within the tolerance range required for machining.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0023] 1. This invention utilizes near-source heat flow to dynamically predict the deep axial thermal elongation component. Simultaneously, based on the stiffness curve, it isolates the mechanical displacement effect caused by preload adjustment, achieving a decoupling mechanism for the total displacement error. This decoupling mechanism enables the system to decompose the total displacement error into pure thermally induced elongation and force-induced deformation, thereby counteracting the hysteretic thermal elongation component and providing a physical path for achieving thermal displacement control while maintaining high dynamic stiffness.

[0024] 2. This invention constructs a bearing thermo-mechanical coupling model and uses the projection gradient method to search within a multi-dimensional constrained space, locking the preload at the feasible region boundary. The construction of the bearing thermo-mechanical coupling model ensures that the system possesses the minimum stiffness required to resist cutting loads while performing thermal compensation, thereby effectively avoiding machining instability caused by over-compensation and achieving the required accuracy and stability in precision machining.

[0025] 3. This invention establishes a nonlinear stiffness curve for tapered roller bearings and uses the heat transfer function to predict the hysteretic thermal elongation component caused by changes in frictional power, thus achieving a component stripping mechanism. This component stripping mechanism effectively ensures that control targets only the net error after eliminating interference, avoiding unnecessary stiffness loss caused by misoperation. This effectively improves the linearity and response speed of the thermal compensation process, ensuring that thermally induced dimensional changes are accurately eliminated. Attached Figure Description

[0026] Figure 1 This is a flowchart of the adaptive adjustment method for preload of precision spindle bearings based on thermal error decoupling according to the present invention;

[0027] Figure 2 The flowchart illustrating the process of generating decoupling results in this invention;

[0028] Figure 3 This is a flowchart of the bearing thermo-mechanical coupling model of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] Please see Figures 1 to 3 This invention provides an adaptive adjustment method for the preload of a precision spindle bearing based on thermal error decoupling. The technical solution is as follows:

[0031] Example 1:

[0032] An adaptive adjustment method for preload of precision spindle bearings based on thermal error decoupling includes:

[0033] In the bearing assembly of the tapered roller bearing, the thermal displacement error and actual preload of the spindle are collected. Based on the machine tool's operating load, spindle speed and ambient temperature, the required dynamic stiffness threshold and contact uniformity threshold of the spindle are calculated. The roller friction heat flow is collected on the large end face of the roller of the tapered roller bearing.

[0034] The mechanical displacement effect and frictional heat effect caused by the change in actual preload are calculated, and the axial thermal elongation component caused by the friction of the roller end face is calculated using the roller frictional heat flow. The mechanical displacement effect, frictional heat effect and axial thermal elongation component are separated from the thermal displacement error to generate decoupled results.

[0035] Based on the decoupling results and thermal displacement error, the preload adjustment amount is calculated. Using a pre-trained bearing thermo-mechanical coupling model, the dynamic stiffness and load uniformity of the adjusted preload are calculated. It is then verified whether the preload simultaneously meets the requirements that the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold. If not, the preload is adjusted to the boundary point of the feasible region, and the preload adjustment amount is recalculated.

[0036] Apply a preload adjustment to the outer ring of the tapered roller bearing and control the thermal displacement error within the tolerance range.

[0037] Furthermore, the specific process of acquiring the thermal displacement error and actual preload of the spindle includes: acquiring the total displacement error including mechanical, force, and thermal errors, and simultaneously acquiring the original pressure signal between the bearing rings; performing adaptive weighted fusion and low-pass filtering on the original pressure signal, and combining it with the real-time temperature correction mapping matrix to calculate the real-time preliminary force value; outputting the preliminary force value as the actual preload, and calculating the elastic collapse amount generated by the pressure based on the sensor's equivalent stiffness; performing elastic collapse compensation on the total displacement error based on the elastic collapse amount to obtain the pure displacement term; setting the sampling window based on the real-time temperature rise rate, and performing polynomial fitting on the pure displacement term to extract the displacement trend; using the cross-correlation function to perform time-delay compensation and alignment between the displacement trend and the frictional heat flow signal, and calculating the Pearson correlation coefficient; when the correlation coefficient meets the preset correlation threshold, outputting the thermal displacement error.

[0038] Specifically, the total displacement error acquisition process is as follows: With the machine tool in a cold state (equilibrated at room temperature for more than 2 hours) and the spindle stationary, the acquisition system records the output signal at this time and sets it as the initial zero point of the displacement error. The spindle is then started and operates according to the working load and speed, outputting a voltage signal in real time reflecting the change in the position of the spindle tip. This voltage signal represents the total displacement error, which includes mechanical errors caused by manufacturing and assembly, force errors caused by cutting forces, and thermal errors generated as operating time increases and temperature rises accumulate.

[0039] The specific generation process of the original pressure signal is as follows: Pressure sensors are used, evenly spaced between the outer ring of the bearing and the support end face of the bearing housing. The axial preload on the outer ring of the bearing acts on the pressure-sensing surfaces of 3 to 4 sensors, generating multiple original electrical signals. An adaptive weighted average calculation is performed on the multi-channel signals. With the spindle stationary, the initial weighting coefficients of each mounting point are calibrated through preload testing. During operation, if abnormal fluctuations in a single-channel signal are detected (such as installation tilt or uneven heating), local stress distortion is automatically compensated through a dynamic weighting factor, converting the spatially distributed pressure into an original pressure signal representing the axial resultant force. The initial weighting coefficient is equal to the applied standard axial force divided by the weighted sum of the output signals from all mounting points. Using the least squares method, the superposition value of the sensor outputs after weight correction is made to most closely approximate the standard pressure value. The dynamic weighting factor is a real-time correction scalar calculated by the system based on the current rotational speed, temperature rise gradient, and variance distribution of each channel signal.

[0040] The specific process for obtaining the real-time preliminary force value is as follows: High-frequency alternating pressure fluctuations caused by the rolling element circulating through the sensor's pressure-sensing zone are eliminated, and the quasi-static DC component is extracted. Under a preset reference temperature (e.g., 20°C), the quasi-static DC voltage component is calculated into a physical force value using a temperature correction mapping matrix to obtain an accurate real-time preliminary force value. The temperature correction mapping matrix determination process involves calculating the difference between the current ambient temperature T and the reference temperature, and then applying this temperature difference to a pre-calibrated thermal sensitivity drift coefficient based on the material's physical properties. Multiplying yields the incremental correction factor. Using the sum of 1 and this incremental correction factor as a scaling operator, each element in the initial mapping matrix is ​​scaled proportionally. Each element Kij in the initial mapping matrix represents the linear transformation ratio between the i-th voltage signal and the j-th force component at a reference temperature.

[0041] The specific generation process of the pure displacement term is as follows: set the extension of the front end of the spindle towards the machining side as the positive direction of displacement, retrieve the sensor physical parameters (i.e., sensor equivalent stiffness) pre-stored in the memory, divide the initial force value by the sensor equivalent stiffness, and the calculation result is the physical compression deformation. The system establishes reverse compensation logic and algebraically superimposes the absolute value of the calculated elastic collapse into the total displacement error.

[0042] The specific implementation of setting a sampling window based on the real-time temperature rise rate and extracting the displacement trend by polynomial fitting of the pure displacement term is as follows: A Butterworth filter is applied to process the original signal with a sampling frequency of not less than 2kHz. The cutoff frequency of the filter is set in real-time to 1 / 10 of the current spindle rotation frequency. To capture the minute deformation of the precision spindle during the transient heating phase, an adaptive sampling time window is introduced. The window length W is dynamically mapped according to the real-time temperature rise rate of the spindle. When the temperature rise rate is greater than or equal to 0.5°C / min, the sampling window is automatically shortened to 1 / 20 of the thermal equilibrium time. A third-order polynomial fitting algorithm is applied to extract the low-frequency displacement trend within the window. Using the time series within the sampling window as the independent variable and the filtered displacement data as the dependent variable, the coefficients of the third-order polynomial are solved using the least squares method to construct a trend function describing the evolution of displacement over time. The root mean square (RMS) value of the fitted residual is calculated synchronously. The difference between the original filtered signal and the calculated value of the trend function at each sampling point within the window is calculated in real time. The sum of squares of these differences, the average value, and the square root are then taken to obtain the RMS value. If the RMS value is greater than or equal to 1 / 5 of Tol (Tol is the allowable nanometer-level tolerance for machining), it indicates that the current trend function cannot cover complex nonlinear thermal transients. In this case, parameter iteration logic is automatically triggered, by reducing the step size of the sampling window and increasing the fitting order until the RMS value drops to within a preset accuracy range. The preset accuracy range is set according to the spindle machining accuracy level; in this embodiment, it is set to... .

[0043] The specific process of aligning the displacement trend and frictional heat flow signal using a cross-correlation function with time delay compensation and calculating the Pearson correlation coefficient is as follows: The roller frictional heat flow signal is acquired in real time as a reference for the heat source intensity. The time delay between the displacement trend term and the heat flow signal is calculated using a cross-correlation function. Within a preset time delay range, the translation amount corresponding to the maximum value of the cross-correlation calculation result is found; this translation amount is calibrated as the time delay of the system's thermal response. Based on the time delay amount, time-shift compensation is performed on the heat flow signal to ensure that the "heat source intensity" and "displacement result" compared at the same time have a strict physical causal correspondence. The aligned Pearson correlation coefficient is calculated, with the result ranging from negative one to positive one. The closer it is to one, the stronger the linear correlation between the two, meaning the higher the certainty that the displacement component is mainly caused by thermal effects.

[0044] The specific process for determining the time delay range is as follows: Based on the thermal diffusion characteristics of the spindle bearing system, combined with the physical path length from the heat source to the measurement point and the thermal diffusivity of the material, the theoretical center point of the time delay is calculated using the thermal conduction hysteresis theory formula, and redundancy is reserved on both sides to define the initial search interval; subsequently, under the standard environment after the machine tool leaves the factory or is overhauled, the actual time delay between the rising edge of the frictional heat flow signal and the displacement response edge under different working conditions is measured through an unloaded heating experiment within the full speed range, and the observed minimum and maximum delay amounts are set as the upper and lower limits of the search interval, respectively; finally, considering the influence of the ambient initial temperature on the initial thermal resistance of the material, the system performs linear translation compensation of the upper and lower limits of the interval based on the real-time room temperature during the power-on self-test stage.

[0045] The specific process for determining the correlation threshold is as follows: Under standard conditions after the machine tool leaves the factory or undergoes major overhaul, an unloaded heating experiment is conducted across the entire speed range. The initial correlation between the displacement trend term and the heat flow signal is calculated to establish the system's baseline response characteristics. The noise amplitude of the sensor under different operating conditions is analyzed, and the critical correlation level distinguishing between thermal effect signals and random interference signals is determined by comparing the ratio of displacement increment caused by thermal deformation to background noise. Using historical machining data, the correlation coefficient distribution between displacement and heat flow is calculated across a large number of samples. Typically, the lower limit of the 95% confidence interval of the normal distribution is used as the preset threshold. In most precision spindle applications, this threshold is set to 0.85 to ensure the exclusion of interference from force deformation (force error) and random environmental vibrations. In the roughing stage, the preset correlation threshold is set to 0.80; in the ultra-precision finishing stage, the preset correlation threshold is increased to 0.95 to strictly eliminate non-thermal displacements caused by cutting force fluctuations. If the Pearson correlation coefficient is less than the preset correlation threshold, the current signal is considered to be severely interfered with by non-thermal factors. At this point, the secondary decoupling logic will be activated. The signal will be reconstructed by adjusting the digital filter parameters, or the load component will be removed again by calling the mechanical error model, until the residual displacement component conforms to the normal distribution law with a mean of zero and the Pearson correlation coefficient is not less than the preset correlation threshold.

[0046] As an enhanced solution to eliminate elastic collapse, further compensation is made for the stress deformation of the sensor mounting bracket itself. In actual adjustment, the actuator required to apply the preload force, while tightening the bearing, eliminates the slight physical bending interference that would cause the metal bracket to mount the sensor, using a reference value table. Specifically, this is achieved as follows:

[0047] With the spindle stationary, pressure is applied sequentially from small to large via the preload adjustment device. Simultaneously, pressure sensor and displacement sensor readings are recorded. Through multiple tests, the minute deformation distance of the support under each unit pressure level is determined, creating a simple reference value table. During normal spindle machining, the current real-time preload value is obtained via a pressure sensor embedded in the bearing housing. Based on the current real-time pressure, the control system consults the previously calibrated reference value table to directly calculate the spurious displacement of the sensor support due to stress. This spurious displacement is subtracted from the total value read from the displacement sensor. The processed value represents the spindle elongation purely due to thermal expansion, which is discarded as subsequent physical bending interference. To prevent control loop oscillations caused by support deformation compensation, a stress isolation groove or an independent base design is used between the sensor support mounting point and the preload application point, mechanically blocking the transmission path of preload to the sensor support. A low-pass filter and adjustment dead zone are introduced when executing the lookup and deduction logic. The compensation value is only updated when the calculated spurious displacement change exceeds the preset dead zone threshold (0.1 μm). Simultaneously, the compensation action lags behind the preload adjustment action by one control cycle, transforming real-time coupling into discrete correction.

[0048] By eliminating physical bending interference, the coupling problem of "the adjustment action itself interfering with the measurement results" is effectively solved. This avoids the system misinterpreting the support deformation as thermal deformation and issuing incorrect compensation commands when the preload increases, significantly improving the stability of the measurement benchmark.

[0049] By using cross-correlation function and Pearson correlation coefficient for time delay compensation and alignment, the signal phase misalignment caused by heat conduction delay is resolved, ensuring that subsequent control commands are based on pure and real thermal displacement data, and significantly improving the real-time performance and accuracy of control.

[0050] Furthermore, the specific process for calculating the dynamic stiffness threshold and contact uniformity threshold required for the spindle includes: performing stability analysis based on the current operating load and spindle speed to calculate the stability lobe diagram; combining the influence of temperature on the material's elastic modulus to perform chatter stability analysis on the stability lobe diagram, finding the critical stiffness required to maintain stable cutting from the stability lobe diagram, and multiplying the critical stiffness by a safety factor to generate the dynamic stiffness threshold; calculating the normal load borne by each rolling element, and determining the contact uniformity threshold by performing inverse analysis of the normal load and combining the correction effect of thermal expansion caused by temperature on the internal geometry of the bearing.

[0051] Specifically, the process of calculating the stability lobe diagram is as follows: The current operating load (cutting force coefficient), spindle speed, and real-time preload are received. Based on the real-time preload, the dynamic stiffness parameters of the current spindle support system are determined by referring to a preset preload-bearing stiffness characteristic curve, and the frequency response function is updated accordingly. The preload-bearing stiffness characteristic curve is obtained during static stiffness calibration experiments before the machine tool leaves the factory. With the spindle stationary, gradient radial and axial loads are applied to the front end of the spindle, and the spindle deformation is recorded. Nonlinear regression analysis is performed on the load-deformation data to fit a functional relationship describing the change in bearing support stiffness with preload. The eigenvalue equation of the spindle-tool system under the current stiffness state is solved using the zero-order analytical method to calculate the system's limiting depth of cut. The limiting depth of cut at different speeds is mapped onto the all-depth plane of the speed to generate an instantaneous stability lobe diagram.

[0052] The specific implementation of the influence of combined temperature on the material's elastic modulus involves acquiring the ambient temperature at each key temperature measurement point of the spindle in real time and calling a pre-stored database of material thermophysical properties. This database outputs the actual elastic modulus value at the current temperature through table lookup or polynomial interpolation. In the control algorithm, the actual elastic modulus value replaces the initial modulus at room temperature, and the aforementioned preload-bearing stiffness characteristic curve and frequency response function are thermally corrected.

[0053] The process of determining the pre-stored material thermophysical property database is as follows: For standard metal materials such as spindle cores and bearings, the initial values ​​of their thermal expansion coefficient, specific heat capacity, and room temperature elastic modulus are referenced from the "Mechanical Engineering Materials Handbook"; the storage modulus characteristic curve of the material's elastic modulus changing with temperature is measured using a dynamic thermomechanical analyzer, and the thermal conductivity at different temperature points is measured simultaneously using a laser flash thermal conductivity meter, and a discrete lookup table is generated by fitting using the least squares method; the discrete lookup table is pre-stored in the system storage unit in the form of a material property matrix.

[0054] The specific implementation of the chatter stability analysis is as follows: Predetermined machining parameters (maximum depth of cut and spindle speed) are received. Using the aforementioned zero-order analytical method, a stability characteristic equation regarding stiffness is constructed. While keeping the predetermined spindle speed and depth of cut constant, a numerical iterative algorithm (such as the bisection method) is used to find the critical solution of the equation. When a specific stiffness value is found such that the system's limiting depth of cut at that stiffness is exactly equal to the predetermined maximum depth of cut, this stiffness value is locked as the critical stiffness.

[0055] The dynamic stiffness threshold is generated by multiplying the extracted critical stiffness value with its safety factor to generate the final dynamic stiffness threshold. The safety factor is determined through stability redundancy testing, and a safety margin of 1.1 to 1.3 times the critical stiffness is taken.

[0056] The specific process for calculating the normal load borne by each rolling element is as follows: A preset bearing load distribution analytical algorithm is invoked. This algorithm, based on Hertzian line contact theory and the slicing method, can solve the mechanical equilibrium state inside the bearing under complex working conditions in real time. The actual preload and the load vector at the end of the spindle are received and transformed to the bearing center coordinate system using the spindle's geometric topology, fusing them to form a five-degree-of-freedom global external load vector containing axial force, radial force, and torque. The axial component of the global external load vector is extracted, divided by the nominal axial stiffness of the bearing to obtain the initial value of the axial displacement, and the remaining initial values ​​of radial and angular displacements are set to zero, thus constructing the physical starting point for iterative calculations. The Newton-Raphson iteration program is started. In each iteration loop, the current five-degree-of-freedom displacement vector is projected onto the contact line of each rolling element using a coordinate transformation matrix to obtain the normal approximation of each rolling element. The roller is divided into several micro-elements along the axial direction using the slicing method, and combined with the preset roller generatrix profile curve equation (such as a logarithmic shaping curve), the actual geometric compression amount of each slice micro-element relative to the inner and outer raceways is calculated. The logarithmic shaping curve is used to describe the radial shaping amount of the roller at different axial positions to eliminate edge stress concentration. A power function mapping relationship (usually a 1.1 power law) is established between the slice load and the extrusion amount, converting the geometric extrusion amount of each micro-element into local contact force. By performing spatial vector integration on each slice load, the resultant force vector of the bearing system's internal forces is constructed. The partial derivatives of the internal force vector with respect to the displacement vector are calculated to construct the tangent stiffness matrix. The displacement correction is calculated using the current internal and external force residuals and the inverse matrix of the tangent stiffness matrix. This process is repeated iteratively until the norm of the internal and external force residuals is less than the preset accuracy limit (e.g., ...). When the iteration converges, the system outputs the actual normal load distribution data of each rolling element (and its slices) under the current equilibrium state.

[0057] The effect of thermal expansion caused by combined temperature on the internal geometry of the bearing is specifically achieved by calculating the radial and axial thermal elongation of the bearing assembly using the material's coefficient of thermal expansion based on real-time monitored temperature rise data of the inner and outer rings. Specifically, this is manifested in correcting the initial contact gap between the rollers and raceways based on the temperature difference, and calculating the contact angle deflection caused by the inconsistent thermal expansion of the inner and outer rings, thereby obtaining the true geometric boundary conditions that conform to the current thermal operating conditions.

[0058] The reverse analysis is implemented as follows: Under the aforementioned thermally corrected geometric conditions, a physical safety threshold is set: the maximum local pressure on any rolling element slice must not exceed the allowable contact stress of the bearing material. While maintaining the total operating load constant, the unevenness of the roller load distribution is gradually increased using numerical methods. During the exercise, the system monitors the peak pressure at the roller edges in real time. When the edge pressure first touches the aforementioned safety threshold, the system immediately calculates the coefficient of variation (i.e., the ratio of standard deviation to mean) of the pressure distribution across all slices. This coefficient of variation at the critical state is locked as the contact uniformity threshold under the current operating condition. This threshold represents the worst load distribution that the bearing can tolerate without local overload, and is used to guide the boundary determination of subsequent preload adjustments.

[0059] By utilizing the stability lobe diagram, a "stiffness red line" is established for preload adjustment. This ensures that the spindle possesses critical stiffness to resist chatter during adjustment, thereby eliminating thermal displacement while maintaining the quality of the cutting surface.

[0060] Furthermore, the method of collecting roller friction heat flow on the large end face of the tapered roller bearing is as follows: real-time capture of the heat flow density signal generated by the contact pair between the large end face of the roller and the flange, and filtering and processing by the data acquisition system to obtain roller friction heat flow data reflecting the bearing load state and heat generation characteristics.

[0061] The real-time extraction and filtering process of the heat flux density signal is as follows: First, a high-frequency analog-to-digital converter is used to convert the weak electrical signal output by the sensor into a digital sequence, with the sampling frequency set to no less than 20kHz to cover the passing frequency of the rolling element. Then, through a pre-calibrated thermoelectric potential-heat flux density linear mapping relationship, the voltage signal is converted into an instantaneous heat flux density signal. This thermoelectric potential-heat flux density linear mapping relationship is determined through standard comparison experiments and least squares linear regression analysis. Finally, a frequency division processing strategy is implemented, employing an adaptive Butterworth low-pass filtering algorithm to obtain the spindle rotation frequency in real time. Dynamically set the cutoff frequency to In the following extremely low frequency range, rotational excitation noise is filtered out to extract the steady-state average heat flux baseline. For high-frequency fluctuation components, an iterative deconvolution algorithm based on Tikhonov regularization is used to eliminate the heat conduction hysteresis and attenuation effects caused by the sensor's placement on the non-contact side. When constructing the deconvolution objective function, a smoothing constraint term (regularization term) is added to sacrifice minor high-frequency details in exchange for numerical stability of the inversion results. Simultaneously, the effective inversion bandwidth is set to within three times the roller's passing frequency, and a low-pass filter is used to filter out out-of-band noise. Finally, the original transient heat flux density waveform at the contact interface is reconstructed in real time.

[0062] The process of determining the roller friction heat flow data is as follows: The reconstructed original transient heat flow density is used as input, combined with the relative sliding velocity derived from the spindle speed, and the friction power consumption equation is solved inversely to calculate the physical characteristic quantity reflecting the contact load intensity of the roller end face. The final output roller friction heat flow data contains information in two dimensions: one is the load state component generated based on the transient waveform amplitude change (characterizing the roller force fluctuation), and the other is the heat generation characteristic component generated based on the steady-state average base value (characterizing the total heat generation power). These two components together constitute the core input data for subsequent decoupled calculations.

[0063] The captured heat flux density signal from the large end face of the roller is converted into a heat flux density signal. This provides the underlying heat source data for subsequent high-precision decoupling calculations.

[0064] Furthermore, the specific process for generating the decoupling result is as follows: based on the change in the actual preload, the elastic compression caused by the change in actual preload is determined through a preset nonlinear stiffness curve of the tapered roller bearing, thus obtaining the mechanical displacement effect; based on the current spindle speed and the change in actual preload, the change in total frictional heat generation power is obtained through the total frictional power curve of the bearing; the change in total frictional heat generation power is substituted into a preset thermal response function to calculate the frictional heat effect generated by the change in total frictional heat generation power on the front end of the spindle in real time; the real-time roller frictional heat flow is used as the heat source intensity input, and the axial thermal elongation component generated by the roller frictional heat source on the front end of the spindle is dynamically predicted in real time using the heat transfer function; the mechanical displacement effect, frictional heat effect, and axial thermal elongation component are algebraically separated from the total thermal displacement error collected in real time from the front end of the spindle to obtain the net error that needs to be compensated, thus generating the decoupling result.

[0065] Specifically, the process for determining the preset nonlinear stiffness curve of the tapered roller bearing is as follows: A microscopic contact model of the bearing is constructed based on Hertzian contact theory, and then extended to the global bearing using quasi-static analysis. Through joint calibration of finite element simulation and static loading experiments on the spindle, a series of corresponding data points for load and displacement are obtained. Subsequently, the data are fitted using the least squares method with a polynomial to construct a nonlinear functional relationship describing the change of tangential stiffness with actual preload. This function serves as the fundamental mechanical model of the system, supporting the subsequent gradient calculation of the preload adjustment.

[0066] The determination process of the mechanical displacement effect is as follows: The difference between the real-time acquired preload and the reference preload is calculated to obtain the change in preload. The reference preload refers to the reference load value set under standard ambient temperature (e.g., 20°C) and when the spindle is stationary or in low-speed thermal equilibrium, to ensure that the tapered roller bearing obtains the initial stiffness and rotational accuracy required by the design. Using the aforementioned nonlinear stiffness curve, the corresponding instantaneous tangential stiffness is queried using the current actual preload as an index. Next, based on the Hertzian contact theory, a nonlinear analytical operator (describing the power function relationship between load and deformation, such as the 1.1 power law) is established to decompose and map the macroscopic change in preload into the normal load increment of each roller inside the bearing, and further calculates the mutual compression depth of the contact interface. Finally, combined with the bearing contact angle geometric constraints, the compression depth vectors of each roller are superimposed and converted into axial net displacement, which is the mechanical displacement effect.

[0067] The specific process for generating the total frictional heat generation power variation includes: retrieving a preset total bearing frictional power curve from the storage module based on the current spindle speed and preload change; the total bearing frictional power curve describes the nonlinear mapping relationship between the total frictional heat generation power P and the speed and load. By calculating the first partial derivative of power with respect to preload (i.e., the heat generation sensitivity coefficient) and multiplying this coefficient by the preload change, the additional frictional heat generation power increment induced by the preload adjustment action is estimated in real time.

[0068] The thermal response function is equal to the sum of the response terms of each order. Each response term is calculated by multiplying the magnitude coefficient of that order by (1 minus the negative power of the natural constant e), where the exponent of the negative power is time divided by the time constant of that order.

[0069] The heat transfer function is described using a mathematical model combining a first-order inertial element and a pure hysteresis element. It is defined as follows: the system output is the ratio of the axial thermal elongation component to the change in input roller friction heat power. In the complex frequency domain, it is expressed as the product of steady-state gain and a first-order hysteresis term, multiplied by a decreasing exponential pure hysteresis factor. Specifically, the function determines the deformation amplitude through the steady-state gain coefficient K, characterizes the response delay caused by thermal inertia through the time constant T, and compensates for the physical time delay of heat transfer from the roller friction source to the sensor detection point through the pure hysteresis time.

[0070] The specific process of real-time dynamic prediction is as follows: the extracted real-time roller friction heat flow (heat source intensity sequence) is used as a driving command and input into the heat transfer function. A time-domain convolution algorithm is used to dynamically map the heat accumulation effect at the current moment and past moments, and to dynamically predict the axial thermal elongation component generated at the front end of the main shaft structure due to thermal expansion. The time-domain convolution operation is implemented through discrete accumulation; the axial thermal displacement component at the current moment is equal to the sum of the products of the change in heat generation power at each past sampling moment and the increment of the thermal response function at the corresponding time interval.

[0071] The specific process of the decoupling result is as follows: The superposition principle and algebraic separation are used to perform calculations in a unified axial coordinate system. Specifically, the logic is as follows: From the total thermal displacement error collected at the front end, the mechanical displacement effect explicitly induced by the preload adjustment action, the frictional heat effect, and the real-time sensed axial thermal elongation component are sequentially removed. After algebraic separation, the remaining residual is the net error. This net error, along with each decoupling component, is then packaged together to form the decoupling result output.

[0072] The specific implementation of calculating the preload adjustment based on decoupling results and thermal displacement error is as follows: Feature synthesis of the target compensation amount is performed. The net error (i.e., the residual thermal deviation after eliminating known preload interference) and the total thermal displacement error measured by the sensor are acquired simultaneously. The residual component reflecting the essential thermal characteristics of the system is vector-superimposed with the macroscopic physical deviation to accurately determine the target compensation amount for the current spindle front end deviating from the ideal machining position. This compensation amount defines the absolute difference that needs to be offset in the displacement space to return to the zero-point reference. Subsequently, inverse mapping analysis of preload and displacement is performed. The preset nonlinear stiffness curve of the tapered roller bearing is retrieved, and based on the actual preload level of the current spindle, the instantaneous tangent slope (i.e., the incremental stiffness coefficient) at this working point is locked. Using this coefficient as a conversion operator, the target compensation amount in the aforementioned displacement space is inversely mapped to the force space, and the nominal preload increment required to offset the displacement deviation is initially calculated.

[0073] As a reinforcement scheme for the axial thermal elongation component, the delay time is dynamically determined by finding the commonalities between the error fluctuation sequence and its trend, and the thermal elongation is separated based on the delay time. The specific implementation is as follows:

[0074] The system synchronously records two sets of data streams: one is the error fluctuation sequence from the roller end face heat flow sensor, and the other is the error fluctuation sequence measured by the displacement sensor. In the controller's algorithm module, the displacement error sequence is fixed, and the heat source intensity sequence is gradually shifted backward along the time axis. At each shift step, the peaks, troughs, and slope trends of the two sets of curves are observed to see if they tend to be consistent. When the fluctuation characteristics of the two sets of curves reach the highest degree of agreement, the shift time is recorded, which is the physical time delay caused by heat conduction under the current operating condition. When calculating the axial thermal elongation component caused by roller end face friction using roller friction heat flow, the shifted and aligned heat flow data is used as input. Through this time-aligned data comparison, the part of the total displacement that is highly consistent with the heat flow fluctuation pattern is identified as the thermal elongation component, while the inconsistent part is identified as other mechanical interference.

[0075] By aligning the waveforms, it is ensured that each heat flux value involved in the calculation can be accurately matched with the deformation value it produces, which improves the separation accuracy of the thermal elongation component by more than 30% and effectively avoids compensation overshoot or undershoot caused by conduction delay.

[0076] By calculating the mechanical displacement effect to prevent spurious errors caused by regulation, deriving deep thermal elongation through dynamic prediction, and obtaining pure error through algebraic separation, the dynamic coupling between regulation action and thermal effect is effectively eliminated, avoiding compensation overshoot.

[0077] Furthermore, the composition of the bearing thermo-mechanical coupling model includes:

[0078] The stiffness analysis and prediction layer is used to establish a nonlinear mapping between preload and spindle dynamic stiffness. It uses a five-layer fully connected deep neural network to receive preload adjustment, spindle speed, operating load and ambient temperature, and performs feature dimensionality reduction and physical effect fitting; outputting the dynamic stiffness under the current preload scheme.

[0079] The load distribution optimization layer is used to calculate the contact state between the tapered roller and the inner and outer raceways. Utilizing the decoupling results and preload, the mechanical distribution characteristics of the rolling elements in the bearing circumferential direction are extracted through a one-dimensional convolutional layer, and the load uniformity characterizing the load distribution of the rolling elements is output.

[0080] The constraint verification and decision flow layer uses Boolean logic to distinguish between dynamic stiffness and dynamic stiffness threshold, and load uniformity and contact uniformity threshold. When the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold, the projection gradient method is used to search for the boundary points of the feasible region defined by the threshold, dynamically correct the initial preload adjustment amount, and output the final determined preload adjustment amount.

[0081] Specifically, the stiffness analysis prediction layer, serving as the system's prediction center, aims to establish a nonlinear mapping between the environment and mechanical performance. This is implemented by constructing a five-layer fully connected deep neural network. This network consists of one input layer, three hidden layers, and one output layer. The number of nodes in the first to third hidden layers are [64, 128, 64], respectively, and the output layer has one node. The first hidden layer receives a normalized vector from the input layer. This input vector contains four physical dimensions: preload adjustment, spindle speed, operating load, and ambient temperature. It maps the low-dimensional raw operating data to a 64-dimensional preliminary feature space, outputting a feature sequence. The second hidden layer takes the output feature sequence from the first hidden layer as input. It performs linear weighting and nonlinear compression on the high-dimensional features, combined with the ReLU activation function, outputting a 128-dimensional high-dimensional physical representation. The third hidden layer receives the high-dimensional physical representation from the second hidden layer as input. By reducing the number of nodes, redundant computational noise is eliminated. Its output is a 64-dimensional deep abstract feature. Through weight evolution among neurons, the model performs feature dimensionality reduction in deep space, thereby capturing the complex coupling relationship between the centrifugal effect generated by the spindle rotation speed, the thermal softening effect caused by ambient temperature, and mechanical deformation. Offline training is performed using a "load-temperature-stiffness" sample library generated based on finite element analysis. The ReLU activation function is employed to address the nonlinear propagation problem of deep gradients, and Dropout layers (typically set to 0.2-0.3) are added after the second and third hidden layers to enhance the model's generalization ability. Finally, the dynamic stiffness prediction is output in real time.

[0082] The load distribution optimization layer is responsible for transforming macroscopic displacement information into the load details of the internal rolling elements. It employs a one-dimensional convolutional neural network as the core analytical operator. The input to this one-dimensional convolutional neural network consists of a multi-channel feature vector composed of two parts: a time-domain fluctuation channel, which is a sequence of displacement fluctuation signals captured by displacement sensors during one revolution of the main shaft. The periodic ripples of this signal in the time domain directly map the instantaneous contact state of each rolling element as it passes under the sensor; and a spatial pressure channel, which uses the measured values ​​of 3 to 4 pressure sensors installed at evenly distributed angular positions (e.g., 0°, 120°, 240°) on the outer ring of the bearing as model points. This value is expanded into a spatial distribution sequence of 1024 points using a cubic spline interpolation algorithm. During cubic spline interpolation, periodic boundary conditions are set, forcing the first and second derivatives at the 0° starting point and the 360° ending point to be completely equal. Meanwhile, the temporal fluctuation channel collects displacement fluctuation signals within one rotation of the main shaft. Its sampling frequency, after resampling, is also locked at 1024 points, forming a space-time feature matrix with dimensions [1024, 2] with the spatial pressure sequence. The model receives the net error result generated by front-end decoupling and real-time preload data. A one-dimensional convolutional layer is configured with virtual sampling windows along the bearing circumference. The size of its convolution kernel is parameterized according to the number of rolling elements; in this embodiment, the kernel size is set to 3, and the stride is 1. The input signal is scanned by the convolution kernel, utilizing the high-frequency dynamic details provided by the temporal signal to compensate for the information loss in the spatial pressure channel due to sensor sparsity, extracting implicit peak morphology and phase distribution features, and outputting a high-dimensional feature vector. Subsequently, the net error result generated by front-end decoupling and the real-time preload data (scalar features) are concatenated and fused with the aforementioned high-dimensional feature vector. Through a fully connected layer, these macroscopic signal features are mapped to microscopic normalized distribution vectors of the contact loads of each rolling element. Finally, after global average pooling, a statistical index reflecting the stationarity of the sequence, namely load uniformity, is calculated and output based on this distribution vector. This index accurately characterizes the contact load distribution state of the tapered roller between the inner and outer raceways.

[0083] The constraint verification and decision flow layer, acting as a decision-making unit, ensures the feasibility of the preload scheme through logical threshold discrimination. A dual-criteria discrimination logic is established. First, the "dynamic stiffness" output by the prediction layer is compared with a safety threshold, and simultaneously, the "load uniformity" output by the optimization layer is compared with a target contact uniformity threshold. An AND Boolean logic gate is used to determine whether the system is simultaneously in the ideal operating range of high stiffness and high uniformity. If the determination result is "false," a feasible region search procedure based on the projection gradient method is triggered. Using the dynamic stiffness threshold and the uniformity lower limit as constraint boundaries, iterative updates are performed in the opposite direction of the gradient of the preload adjustment. By searching the boundary points of the feasible solution space defined by the physical threshold, deviations in the initial preload scheme are dynamically corrected. Finally, the constrained and optimized preload adjustment amount, which balances system stiffness and bearing life, is output.

[0084] The training and verification process of the bearing thermo-mechanical coupling model is as follows: Before model training, an offline sample database covering the entire operating condition range is pre-constructed. High-precision thermo-mechanical coupled finite element simulation modeling is used to perform forward solving under different preload gradients, spindle speeds (e.g., 0 to 12,000 rpm), operating loads, and ambient temperatures to obtain the corresponding dynamic stiffness values ​​and rolling element mechanical distribution data. Discrete data points measured on the experimental bench are introduced as calibration samples, and data augmentation techniques such as adding Gaussian noise are used to simulate actual sensor disturbances, forming the final training dataset.

[0085] A supervised learning strategy is employed when training the stiffness analysis prediction layer. Normalized operating parameters are used as input, and the true stiffness calculated by finite element method is used as the label. The network weights are iteratively updated using the backpropagation algorithm until the loss function converges. This loss function employs a physical information-guided design to fit physical effects. The total loss function consists of two weighted components: the first is a data-driven error term, typically using mean squared error, which measures the numerical deviation between the model-predicted stiffness value and the true label value. The second is a physical constraint penalty term. The construction logic of the physical constraint penalty term is based on the physical axiom of nonlinear increase in bearing stiffness with preload in Hertzian contact theory. During backpropagation, the partial derivative of the network output stiffness value with respect to the input preload (i.e., the gradient of stiffness with respect to force) is calculated. If the gradient is negative, the absolute value of the negative gradient is added to the total loss as a penalty; if the gradient is positive, the term is zero. The weighting of the two terms in the total loss function adopts a dynamic weighting strategy. In the initial stage of model training, the physical constraint penalty term is given a larger weight (the weight of the physical term is 2 to 5 times that of the data term). When the physical constraint loss decreases to a preset threshold ( After this value is considered to indicate that the model has successfully captured the main characteristics of the physical laws, the weight of the physical terms is gradually reduced while the weight of the data-driven error terms is increased.

[0086] The training of the load distribution optimization layer focuses on the mapping of spatial features. Supervised training is also employed. Simulated macroscopic displacement fluctuation sequences and pressure distribution sequences are used as inputs, with the corresponding real rolling element load distributions as labels. By optimizing the one-dimensional convolutional kernel parameters, the network can accurately reconstruct the microscopic load distribution distortion features from the macroscopic signal characteristics.

[0087] Cross-validation was used to evaluate model performance. The focus was on the model's prediction accuracy under extreme conditions (such as maximum speed combined with maximum load). If the prediction error exceeded a preset threshold (e.g., 3%), the model structure was fine-tuned by adjusting the number of network layers or neurons. Simultaneously, by simulating 'discrimination failure' scenarios under boundary conditions, the convergence speed and stability of the projection gradient search algorithm in the constraint decision layer were verified, ensuring that it could guide the preload parameters to quickly regress to the physically feasible region.

[0088] By introducing neural networks and convolutional layers to construct a thermo-mechanical coupling model, the challenge of modeling multivariable and nonlinear physical effects is overcome. This improves prediction accuracy and decision-making speed, enabling the system to possess human-like judgment capabilities regarding the complex thermo-mechanical behavior of the main axis.

[0089] Furthermore, the process of using the projection gradient method to search for the boundary points of the feasible region defined by the threshold and dynamically correcting the initial preload adjustment includes: receiving dynamic stiffness, load uniformity, dynamic stiffness threshold, contact uniformity threshold, and preload adjustment, and introducing the operating load and spindle speed as physical boundary constraint factors; calculating the rate of change of dynamic stiffness and load uniformity relative to the preload adjustment, determining the direction of the parameter adjustment vector, projecting the current preload coordinates along the direction of the parameter adjustment vector, and adjusting them to the intersection of the geometric boundary formed by the dynamic stiffness threshold, contact uniformity threshold, operating load, and spindle speed; and dynamically correcting the initial preload adjustment by multiple gradient updates with a preset step size until a final preload that is at the edge of the feasible region and satisfies all performance constraints is found, and calculating the required preload adjustment based on the final preload.

[0090] The specific process for determining the direction of the parameter adjustment vector includes: calculating the rate of change of dynamic stiffness and load uniformity relative to the preload adjustment amount, and performing weighted vector synthesis to construct a composite gradient direction vector. The composite gradient is equal to the product of the stiffness weighting factor and the rate of change of stiffness, plus the product of the uniformity weighting factor and the rate of change of uniformity. A second-order momentum factor (with a coefficient of 0.8-0.9) is introduced to smooth the synthesized vector to suppress instantaneous fluctuations and couple historical adjustment trends. If the smoothed vector points beyond the physical safety red line, a projection operator is used to pull it back to the boundary tangential direction, ultimately determining the optimal adjustment direction that balances stability and safety.

[0091] The values ​​of the stiffness weight factor and uniformity weight factor are dynamically determined based on the current task type and real-time operating conditions of the spindle. Specifically, there are three modes: When the cutting load exceeds the high load threshold, the stiffness weight factor is automatically increased to [0.7, 0.9] to prioritize improving vibration resistance. When the spindle is at high speed and the cutting force is low, the uniformity weight factor is increased to [0.6, 0.8] to prioritize improving load distribution and extending service life. The weight factors are proportionally allocated according to their contribution to the model loss function (e.g., the stiffness weight factor is 0.6, and the uniformity weight factor is 0.4) to maintain force flow balance.

[0092] The specific implementation of projecting the current preload coordinates along the parameter adjustment vector direction is as follows: Lock the preload coordinate point in the current iteration step. Establish a search ray along the determined adjustment vector direction using the current preload coordinates. Simultaneously retrieve the dynamic stiffness threshold, contact uniformity threshold, and real-time input operating load and spindle speed. Transform the above four parameters into hypersurface or hyperplane equations. This transformation process is achieved by calling the neural network model of the aforementioned stiffness analysis prediction layer and load distribution optimization layer. Utilize the automatic differentiation technique of the deep learning framework to input the real-time operating parameters into the trained neural network model, and calculate the gradient vectors of dynamic stiffness and load uniformity relative to the preload adjustment amount in real-time through backpropagation. Based on this gradient vector, construct a local tangent plane linear approximation equation for the constraint surface near the current point. This system of linear inequalities mathematically defines the physical constraint hypersurface in multidimensional space. Calculate the intersection of the projection path and each constraint hypersurface, simultaneously solve the search ray equation and the aforementioned local tangent plane equation, and solve for the geometric intersection point. If the projection path intersects the constrained hypersurface at multiple points, first eliminate pseudo-solutions that do not conform to the gradient descent direction. Among the remaining feasible intersection points, calculate the comprehensive performance index function value (such as the weighted score of stiffness and uniformity) for each point. Select the intersection point with the closest Euclidean distance to the current preload coordinate point. If multiple intersection points are all within the safe range, select the point with the largest comprehensive performance index function value.

[0093] The specific implementation of the dynamic correction of the initial preload adjustment is as follows: A preset step size for each iteration is set based on the actuator's adjustment resolution and the system response frequency. The system enters an iterative calculation loop, driving the preload coordinates to move gradually along the parameter adjustment vector direction through multiple gradient updates with the preset step size. In each update process, the current dynamic stiffness and load uniformity gradient information are reacquired, and the preload correction increment at the current moment is calculated in conjunction with the preset step size. In each round of gradient updates, the preload correction increment is accumulated to the initial value, correcting the initial preload adjustment.

[0094] The preset lower limit of the step size must be greater than or equal to the executable resolution of the actuator to ensure that the correction instructions generated by each round of gradient update of the algorithm are physically feasible. The upper limit of the step size is set in conjunction with the response frequency of the spindle adjustment cycle. The spatial distance between the intersection of the current preload coordinate and the geometric boundary is calculated in real time, and a correlation function between the step size and the distance is established. By adaptively reducing the step size, it is ensured that the search trajectory is accurately locked at the edge of the feasible region of the multidimensional physical constraints.

[0095] The correlation function between the step size and distance is specifically implemented as follows: The Euclidean distance between the current preload coordinate point and the predicted boundary of the physical feasible domain is calculated in real time. This Euclidean distance is compared with the system-set 50N load equivalent distance. When the Euclidean distance is greater than the load equivalent distance, the step size remains at the preset maximum step size limit. When the Euclidean distance is less than or equal to the load equivalent distance, the step size decays linearly or exponentially according to the ratio of the current Euclidean distance to the load equivalent distance. That is, the current step size is equal to the initial step size limit multiplied by the power of n (the ratio of the current distance to the threshold distance) (where the exponent n is usually a real number between 1 and 2). During the above calculation process, the system simultaneously executes a lower limit check logic. If the calculated decay step size is less than the aforementioned minimum quantization benchmark (i.e., actuator resolution), the step size is forcibly corrected to the minimum quantization benchmark value.

[0096] The criteria for finding a point on the edge of the feasible region that satisfies all performance constraints are as follows: A Boolean logic algorithm is used to continuously monitor whether the preload coordinate point satisfies the composite performance constraint criteria of "dynamic stiffness greater than a threshold" and "load uniformity greater than a contact uniformity threshold." Simultaneously, the normal distance of the current preload coordinate point relative to the geometric boundary formed by the dynamic stiffness threshold, contact uniformity threshold, operating load, and spindle speed is calculated. By monitoring whether the normal distance enters a preset minimum convergence interval (i.e., infinitely close to zero), it is determined whether the preload adjustment path has reached the edge of the feasible region. The minimum convergence interval is a minimum threshold constant representing the distance to the geometric boundary, set based on the minimum adjustment resolution of the preload actuator and the sensor displacement detection accuracy. When both performance constraints are satisfied ("true") and the distance between the coordinate point and the geometric boundary reaches a critical minimum, the iterative program stops updating. The system defines the parameter coordinates corresponding to this moment as the final preload that is on the edge of the feasible region and satisfies all performance constraints.

[0097] As an enhancement scheme for adjusting the feasible domain boundary points, a safety baseline is established to eliminate cutting vibration interference during adjustment. Specifically, this is implemented as follows:

[0098] To mitigate thermal expansion, the system typically needs to reduce preload. However, insufficient preload can cause the spindle to become "loose," leading to cutting vibration (chatter). At different speeds, the preload is manually reduced during actual cutting or monitored using vibration sensors, recording the preload value at which the spindle begins to exhibit abnormal vibration. Based on this critical value, a safety margin of 10% to 15% is added, defined as the lower safe limit for preload at that speed. When calculating the preload adjustment required for thermal compensation, the control algorithm incorporates an interception logic: if the calculation requires the preload to be reduced below the lower safe limit, the command is forcibly locked at the lower safe limit, and no further reduction is allowed. When the preload is locked at the lower safe limit but the thermal error still exceeds the limit, the system automatically triggers another strategy (such as intervention through an external cooling system) instead of continuing to sacrifice stiffness for thermal accuracy.

[0099] By establishing a safety baseline, the spindle is guaranteed to remain in a stable machining state during any thermal error adjustment process, effectively solving the problems of chipping or surface roughness deterioration caused by pursuing thermal compensation.

[0100] The parameters are forcibly projected onto the intersection of safe geometric boundaries along the vector direction using the projection gradient method. This ensures that the system can quickly find an "equilibrium point" that satisfies physical constraints even under extreme conditions, guaranteeing a smooth transition during the adjustment process and preventing system oscillations.

[0101] Furthermore, the specific process of applying a preload adjustment amount to the outer ring of the tapered roller bearing and controlling the thermal displacement error within the tolerance range includes: converting the finally determined preload adjustment amount into an electronic control command to drive the actuators distributed around the outer ring of the tapered roller bearing, so that the actuators apply a non-uniform preload adjustment amount to the outer ring; by applying the preload adjustment amount, the contact state between the tapered roller and the raceway is directly changed, and the mechanical displacement effect generated by the change in preload is used to offset the thermal error, thereby compensating for the thermal displacement error of the bearing system caused by frictional heat generation in real time, and maintaining the thermal displacement error of the spindle within the tolerance range required for machining.

[0102] Specifically, the final determined preload adjustment amount is converted into an electronic control command as follows: First, a preset actuator electro-force conversion characteristic curve is invoked. This curve is pre-calibrated based on the actuator's electromagnetic induction intensity or hydraulic gain characteristics. The output pressure or thrust values ​​under different control voltages are experimentally measured, and a proportional linear relationship between the control voltage and the output pressure / thrust is established within the algorithm. Based on this proportional linear relationship, the calculated physical preload adjustment amount is accurately converted into the corresponding level signal amplitude, serving as the original analog reference for subsequent command generation. The determined level signal amplitude is digitally encoded using an analog-to-digital converter and encapsulated into a command frame according to a specific communication protocol (such as CANopen, EtherCAT, or Profibus). This command frame contains the actuator's target position signal, response time constant, and overload protection threshold, ensuring the integrity and real-time performance of the command during transmission. The command frame is sent to the power driver, which demodulates the digital command using pulse width modulation technology into a current / pressure output capable of driving the electromagnetic or hydraulic actuator—this is the electronic control command.

[0103] The specific implementation of the non-uniform preload adjustment applied to the outer ring by the actuator is as follows: Based on the bearing support structure, multiple independent actuators are symmetrically or asymmetrically deployed at the circumferential position of the tapered roller bearing outer ring; each actuator has an independent control channel, forming an actuator array capable of generating spatial variable loads. Based on the eccentricity and tilt characteristics of the spindle thermal error, a specific non-uniform preload adjustment amount composed of multiple discrete force vectors is calculated. The calculated non-uniform force values ​​are allocated to the corresponding power drive modules, driving the circumferential actuators to move synchronously by outputting multiple independent electronic control commands in parallel; each actuator generates differentiated radial or axial compressive forces at different positions on the outer ring according to the command amplitude of its own channel, acting together on the bearing outer ring. This compensation process is carried out under thermomechanical coupling constraints. By real-time evaluation of the balance between the instantaneous mechanical compensation benefits of increasing preload and the long-term thermal accumulation risk caused by increased friction, compensation actions are only performed within the allowable range of the system's thermal stability margin, thereby avoiding thermal runaway.

[0104] The specific calculation logic for the non-uniform preload adjustment is as follows: The thermal displacement error is decomposed into axial elongation and tilt angle vector. Using the tangent angular stiffness parameter (i.e., the rate of change of torque caused by a unit tilt angle disturbance), the target restoring torque required to correct the current tilt is calculated. A set of torque balance equations for the multi-point actuators is established, constraining the algebraic sum of the output forces of all actuators to equal the target total preload, and the vector sum of their torques relative to the axis to equal the target restoring torque. The overdetermined equations are solved using a least-squares optimization algorithm with non-negative constraints to obtain the optimal independent output force value of each actuator, which serves as the final non-uniform preload adjustment.

[0105] By applying a non-uniform preload through distributed actuators, the axial elongation is not only offset by the local mechanical displacement effect, but also the radial drift of the axis is corrected. This achieves real-time compensation for the spatial displacement of the spindle end, locking thermal errors within the machining tolerance zone and significantly improving the continuous machining stability of precision machine tools.

[0106] A closed-loop control system was established, encompassing multi-source information perception, decoupled decision-making, and physical execution. By dynamically calculating stiffness and contact uniformity thresholds in real time, adaptive compensation for spindle thermal errors was achieved while ensuring machining stability, thus guaranteeing high-precision operation of the spindle under all working conditions.

[0107] Example 2:

[0108] This application uses a specific scenario from Embodiment 1 to illustrate stiffness-first search under high-speed precision machining, specifically implemented as follows:

[0109] Under finishing conditions at a spindle speed of n=12000rpm, the value output by the dynamic stiffness prediction layer received by the system is lower than the dynamic stiffness threshold generated by the stability analysis. The gradient descent module calculation found that the rate of change of dynamic stiffness relative to the preload adjustment is much greater than the rate of change of load uniformity. Therefore, the determined parameter adjustment vector direction mainly points to the axis that increases the preload. The system projects the current preload coordinates along this vector direction until it reaches the hyperplane boundary point defined by the dynamic stiffness threshold. The system sets a small preset step size (such as 1.2 times the minimum resolution of the actuator) to perform multiple gradient updates to avoid system oscillations caused by preload fine-tuning at high speeds. When the preload coordinates are locked at the edge of the feasible region that satisfies the critical stiffness, the iteration stops and the final adjustment is output, ensuring that chatter does not occur during the machining process.

[0110] Example 3:

[0111] This application uses a specific scenario from Example 1 to illustrate load uniformity correction under heavy-load cutting conditions, specifically implemented as follows:

[0112] In heavy-duty rough machining with a working load F=5000N, the load uniformity index exceeded the preset threshold for contact uniformity due to eccentric loading. The projection gradient method received a Boolean signal that did not meet the criteria. The numerical difference operator identified that the load uniformity was extremely sensitive to the preload distribution, and determined the vector direction focused on optimizing the contact stress distribution. The preload coordinates were projected onto the intersection of the geometric boundary formed by the contact uniformity threshold and the working load to eliminate local stress concentration. An adaptive step-size strategy was used, initially employing a large step size to quickly approach the boundary, and then decreasing the step-size reduction factor as the search neared the boundary to ensure the search trajectory was accurately locked at the edge of the feasible region. The final preload, located at the edge of the feasible region and meeting the uniformity requirements, was found, thus protecting the bearing's lifespan.

[0113] Example 4:

[0114] This application uses a specific scenario from Example 1 to demonstrate adaptive adjustment of step size under a state-of-the-art heating environment, specifically implemented as follows:

[0115] During the spindle startup phase, ambient temperature and frictional heat flow cause the system to be in an unsteady thermal field. The preload fluctuates drastically due to thermal expansion. The system introduces spindle speed and real-time temperature rise as physical boundary constraint factors and recalculates the rate of change gradient tensor of performance indicators. The preload coordinates are adjusted to the intersection of the dynamic geometric boundary corrected by the real-time temperature rise, achieving a precise mapping from the unconstrained space to the physically feasible domain. A preset step size is set as the minimum quantization benchmark based on the 0.01mm physical resolution of the actuator (such as a hydraulic proportional valve) and an upper limit is set in conjunction with the system response frequency to prevent over-compensation of the preload due to adjustment lag. Through minimum convergence interval discrimination, when the displacement difference is lower than a preset threshold constant, the trajectory is determined to have reached the critical edge, and a compensation command is output.

[0116] Example 5:

[0117] This application uses a specific scenario from Example 1 to illustrate tolerance range closed-loop locking in ultra-precision machining, specifically implemented as follows:

[0118] In nanoscale precision machining, the spindle thermal displacement error must be maintained within stringent tolerances. The system verifies the preload scheme using a thermomechanical coupling model, finding that while it meets stiffness requirements, its thermal error mitigation capability is insufficient, triggering a gradient descent program to re-optimize. Coordinate points are projected along the most performance-sensitive direction to the unique geometric intersection of multidimensional physical constraints (stiffness, uniformity, rotational speed, and load). The system monitors the normal distance between the coordinate points and the geometric boundaries in real time, and guides the preload coordinates into a minimum convergence interval infinitely close to zero by adaptively reducing the step size. The final preload, located at the edge of the feasible region, is locked, and the precise non-uniform preload adjustment is calculated. The actuator then uses mechanical displacement to offset the thermal error within the tolerance range.

[0119] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling, characterized in that, include: In the bearing assembly of the tapered roller bearing, the thermal displacement error and actual preload of the spindle are collected. Based on the machine tool's operating load, spindle speed and ambient temperature, the required dynamic stiffness threshold and contact uniformity threshold of the spindle are calculated. The roller friction heat flow is collected on the large end face of the roller of the tapered roller bearing. The mechanical displacement effect and frictional heat effect caused by the change in actual preload are calculated, and the axial thermal elongation component caused by roller end face friction is calculated using roller frictional heat flow. The roller frictional heat flow is acquired by: capturing the heat flow density signal generated by the contact pair between the large end face of the roller and the flange in real time, and filtering and processing it by the data acquisition system to obtain roller frictional heat flow data reflecting the bearing load state and heat generation characteristics; separating the mechanical displacement effect, frictional heat effect and axial thermal elongation component from the thermal displacement error to generate decoupled results. Based on the decoupling results and thermal displacement error, the preload adjustment amount is calculated. Using a pre-trained bearing thermo-mechanical coupling model, the dynamic stiffness and load uniformity of the adjusted preload are calculated. It is then verified whether the preload simultaneously meets the requirements that the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold. If not, the preload is adjusted to the boundary point of the feasible region, and the preload adjustment amount is recalculated. Apply a preload adjustment to the outer ring of the tapered roller bearing and control the thermal displacement error within the tolerance range.

2. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 1, characterized in that, The specific process for acquiring the thermal displacement error and actual preload of the spindle includes: acquiring the total displacement error, which includes mechanical, force, and thermal errors, and simultaneously acquiring the original pressure signal between the bearing rings; performing adaptive weighted fusion and low-pass filtering on the original pressure signal, and combining it with the real-time temperature correction mapping matrix coefficients to calculate the real-time preliminary force value; outputting the preliminary force value as the actual preload, and calculating the elastic collapse amount generated by the pressure based on the sensor's equivalent stiffness; performing elastic collapse compensation on the total displacement error based on the elastic collapse amount to obtain the pure displacement term; setting the sampling window based on the real-time temperature rise rate, and performing polynomial fitting on the pure displacement term to extract the displacement trend; using the cross-correlation function to perform time-delay compensation and alignment between the displacement trend and the frictional heat flow signal, and calculating the Pearson correlation coefficient; when the correlation coefficient meets the preset correlation threshold, outputting the thermal displacement error.

3. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 1, characterized in that, The specific process for calculating the dynamic stiffness threshold and contact uniformity threshold required for the spindle includes: performing stability analysis based on the current operating load and spindle speed to calculate the stability lobe diagram; combining the influence of temperature on the material's elastic modulus to perform chatter stability analysis on the stability lobe diagram, finding the critical stiffness required to maintain stable cutting from the stability lobe diagram, and multiplying the critical stiffness by a safety factor to generate the dynamic stiffness threshold; calculating the normal load borne by each rolling element, and determining the contact uniformity threshold by performing inverse analysis of the normal load and combining the correction effect of thermal expansion caused by temperature on the internal geometry of the bearing.

4. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 1, characterized in that, The specific process for generating the decoupling result is as follows: based on the change in the actual preload, the elastic compression caused by the change in the actual preload is determined through the preset nonlinear stiffness curve of the tapered roller bearing, and the mechanical displacement effect is obtained; based on the current spindle speed and the change in the actual preload, the change in the total frictional heat generation power is obtained through the total frictional power curve of the bearing. Substitute the change in total frictional heat generation power into the preset thermal response function to calculate the frictional heat effect of the change in total frictional heat generation power on the front end of the spindle in real time. Using real-time roller friction heat flow as the heat source intensity input, the axial thermal elongation component generated by the roller friction heat source on the front end of the spindle is dynamically predicted in real time using the heat transfer function. The mechanical displacement effect, friction heat effect and axial thermal elongation component are algebraically separated from the total thermal displacement error collected in real time from the front end of the spindle to obtain the net error that needs to be compensated and generate the decoupling result.

5. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 1, characterized in that, The bearing thermo-mechanical coupling model consists of the following components: The stiffness analysis and prediction layer is used to establish a nonlinear mapping between preload and spindle dynamic stiffness. It uses a five-layer fully connected deep neural network to receive preload adjustment, spindle speed, operating load and ambient temperature, and performs feature dimensionality reduction and physical effect fitting; outputting the dynamic stiffness under the current preload scheme. The load distribution optimization layer is used to calculate the contact state between the tapered roller and the inner and outer raceways. Utilizing the decoupling results and preload, the mechanical distribution characteristics of the rolling elements in the bearing circumferential direction are extracted through a one-dimensional convolutional layer, and the load uniformity characterizing the load distribution of the rolling elements is output. The constraint verification and decision flow layer uses Boolean logic to distinguish between dynamic stiffness and dynamic stiffness threshold, and load uniformity and contact uniformity threshold. When the dynamic stiffness is greater than the dynamic stiffness threshold and the load uniformity is less than the contact uniformity threshold, the projection gradient method is used to search for the boundary points of the feasible region defined by the threshold, dynamically correct the initial preload adjustment amount, and output the final determined preload adjustment amount.

6. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 5, characterized in that, The process of using the projection gradient method to search for the boundary points of the feasible domain defined by the threshold and dynamically correcting the initial preload adjustment includes: receiving dynamic stiffness, load uniformity, dynamic stiffness threshold, contact uniformity threshold and preload adjustment, and introducing the working load and spindle speed as physical boundary constraint factors. Calculate the rate of change of dynamic stiffness and load uniformity relative to the preload adjustment amount, determine the direction of parameter adjustment vector, project the current preload coordinates along the direction of parameter adjustment vector, and adjust them to the intersection of the geometric boundary formed by the dynamic stiffness threshold, contact uniformity threshold, working load and spindle speed. By setting multiple gradient updates with a preset step size, the initial preload adjustment is dynamically corrected until the final preload that is at the edge of the feasible region and satisfies all performance constraints is found. Based on the final preload, the required preload adjustment is calculated.

7. The method for adaptive adjustment of preload of precision spindle bearings based on thermal error decoupling according to claim 1, characterized in that, The specific process of applying a preload adjustment amount to the outer ring of the tapered roller bearing and controlling the thermal displacement error within the tolerance range includes: converting the finally determined preload adjustment amount into an electronic control command to drive the actuators distributed around the outer ring of the tapered roller bearing, so that the actuators apply a non-uniform preload adjustment amount to the outer ring; by applying the preload adjustment amount, the contact state between the tapered roller and the raceway is directly changed, and the mechanical displacement effect generated by the change in preload is used to offset the thermal error, thereby compensating for the thermal displacement error of the bearing system caused by frictional heat generation in real time, and maintaining the thermal displacement error of the spindle within the tolerance range required for machining.

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