Method for analyzing thermal performance of coordinate grinding machine under multi-process conversion driven by explicit-implicit mechanism

Abstract

The invention discloses an explicit-implicit mechanism driven thermal performance analysis method for a coordinate grinding machine under multi-process conversion, and relates to the technical field of equipment thermal performance analys.The method comprises the steps that firstly, based on thermodynamic laws of heat conduction, heat convection and process intermittent heat shock, elastic mechanics and contact mechanics theories are combined; establishing an explicit thermodynamic mechanism equation of the key component of the grinding machine under multiple processes; carrying out multi-process actual measurement and simulation data iterative optimization, and carrying out symbolization, symmetry and dimensionless processing to obtain a multi-process unified explicit thermal differential control equation; with the deviation between theoretical prediction and actual measurement data as a target, an implicit mathematical expression is obtained through analysis; and finally, taking the implicit expression as a compensation item to be fused with the explicit equation, and carrying out iterative correction through an alternating optimization mechanism until the prediction precision of the thermal field reaches the standard. The method gives consideration to physical consistency and prediction precision, can accurately predict the complete thermal field distribution of the machine tool based on sparse thermal sensing data, and provides reliable theoretical support for guaranteeing the machining precision of the machine tool.

Description

Technical Field

[0001] This application relates to the field of equipment thermal performance analysis technology, and in particular to a method for analyzing the thermal performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms. Background Technology

[0002] Precision machining of complex parts is a core capability of modern high-end manufacturing technology. Among high-end machine tools, composite coordinate grinding machines possess ultra-high coordinate positioning accuracy and multi-process composite machining capabilities, including turning, milling, drilling, and grinding. They are key equipment for achieving precision machining of core components in high-end equipment. However, the dynamic time-varying thermodynamic characteristics under multi-process conversion are the main bottleneck restricting the machining accuracy of composite coordinate grinding machines. Accurate calculation of the machine tool's thermodynamic performance is a necessary prerequisite for ensuring machining accuracy.

[0003] In recent years, mechanistic data fusion methods, represented by physical information neural networks, have demonstrated advantages in balancing efficiency and accuracy in the field of physical field computation. However, the thermodynamic mechanisms under multiple process transitions in composite coordinate grinding machines are complex, and traditional simplified mechanistic equations are insufficient to accurately describe dynamic thermodynamic characteristics. Directly embedding these equations as physical constraints into the computational model leads to insufficient accuracy in thermodynamic performance calculations, failing to meet the requirements for efficient and high-precision thermodynamic performance calculations under multiple operating conditions of composite coordinate grinding machines. Summary of the Invention

[0004] The purpose of this application is to provide a method for analyzing the thermal performance of coordinate grinding machines under multiple process conversions driven by explicit and implicit mechanisms. This method can achieve high-precision analysis of the thermal performance of composite coordinate grinding machines under multiple process conversions, providing reliable theoretical support for the analysis of machine tool thermal performance.

[0005] To achieve the above objectives, this application provides the following solution: A method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the explicit and implicit mechanism includes the following steps: Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during processes, and combined with the theories of elasticity and contact mechanics, explicit thermodynamic mechanism equations for key components of composite coordinate grinding machines under various processes are established.

[0006] Based on the measured data from thermodynamic experiments and the numerical simulation data from thermodynamics under various processes, the explicit thermodynamic mechanism equations are iteratively optimized. The optimized explicit thermodynamic mechanism equations are then symbolized, symmetricized, and dimensionless, resulting in a unified explicit thermodynamic differential control equation for various processes.

[0007] Using the deviation between the thermodynamic theoretical prediction data output by the explicit thermodynamic differential control equation and the thermodynamic experimental measured data under the corresponding operating conditions as the implicit mechanism analysis target, an implicit mechanism module is constructed to characterize the dynamic characteristics of the deviation, and the implicit mathematical expression corresponding to the deviation is obtained analytically.

[0008] Implicit mathematical expressions are used as compensation terms and fused with explicit thermodynamic differential control equations to obtain complete explicit and implicit thermodynamic mechanism equations. The explicit and implicit thermodynamic mechanism equations are iteratively corrected based on an alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update until the model prediction accuracy reaches a preset threshold. The explicit and implicit thermodynamic mechanism equations are used to predict the complete thermodynamic field distribution of the composite coordinate grinding machine based on sparse thermodynamic sensing data collected from the composite coordinate grinding machine. The model prediction accuracy is the prediction accuracy of the explicit and implicit thermodynamic mechanism equations for the thermodynamic field distribution.

[0009] Optionally, the explicit thermodynamic mechanism equations include the explicit heat transfer mechanism equation and the explicit stress distribution mechanism equation. Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during the process, and combined with the theories of elasticity and contact mechanics, explicit thermodynamic mechanism equations for key components of the composite coordinate grinding machine under various processes are established, specifically including the following steps: Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during the process, an explicit heat transfer mechanism equation for key components of a composite coordinate grinding machine is established.

[0010] Based on the theories of elasticity and contact mechanics, and combined with assembly preload, component gravity, and multi-axis motion coupling factors, an explicit stress distribution mechanism equation for key components of a composite coordinate grinding machine is established.

[0011] Based on the explicit heat transfer mechanism equation and the explicit stress distribution mechanism equation, the explicit thermodynamic mechanism equation is obtained by integration.

[0012] Optionally, key components of a composite coordinate grinding machine include the spindle box, column, guide rails, and worktable; the heat conduction process encompasses the heat diffusion process within the components, the heat convection process encompasses the heat exchange process between the cutting fluid, ambient air, and the component surface, and the intermittent thermal shock during the machining process is generated by the periodic feed, idle stroke, and tool change actions; the assembly preload is applied by the anchor bolts, guide rail inserts, and spindle bearing preload mechanism, and the component gravity is a constant load generated by the spindle box, column, workpiece, and fixture under the action of gravity field; the multi-axis motion coupling factor is the dynamic inertial force and torque generated on the structural components by the interaction of the acceleration and velocity of the multiple motion axes during the linkage machining of the composite coordinate grinding machine.

[0013] Optionally, based on measured thermodynamic experimental data and numerical simulation data under various processes, the explicit thermodynamic mechanism equation is iteratively optimized. The optimized explicit thermodynamic mechanism equation is then symbolized, symmetricized, and dimensionless, resulting in a unified explicit thermodynamic differential governing equation for various processes. This process includes the following steps: By substituting measured thermal experimental data and thermal numerical simulation data from various processes into the explicit thermal mechanism equation, and using a parameter identification algorithm to inversely calculate and correct the undetermined coefficients and functional relationships in the explicit thermal mechanism equation, the output value of the explicit thermal mechanism equation achieves the best fit with the measured thermal experimental data and thermal numerical simulation data within the global process range.

[0014] By symbolizing, symmetricizing, and dimensionless processing, the modified explicit thermodynamic mechanism equations corresponding to different processes are unified and standardized into explicit thermodynamic differential control equations with the same differential form; the differences between different processes are distinguished by the values ​​of the process coefficient matrix, input excitation vector, and boundary conditions in the explicit thermodynamic differential control equations.

[0015] Optionally, an implicit mechanism module is constructed to characterize the dynamic properties of the deviation, and the implicit mathematical expression corresponding to the deviation is obtained analytically. Specifically, the potential change patterns in the deviation are extracted by a data-driven nonlinear fitting model, the gradient of the deviation relative to each influencing variable is calculated using automatic differentiation technology, and the implicit mathematical expression of the deviation is obtained analytically based on gradient back-source tracing and sparse regression algorithms.

[0016] Optionally, the nonlinear fitting model is a deep neural network. The input layer of the deep neural network receives process parameters, motion state and time series monitoring data, and performs nonlinear transformation through at least one hidden layer. The output layer fits the current value of the thermal deviation. The influencing variables include process parameters and various process variables. The process parameters include depth of cut, feed rate and spindle speed. The process variables include spindle power, servo current of each axis and temperature of key parts.

[0017] Optionally, gradient back-source tracing specifically involves: based on the gradient relationship between the deviation value output by the nonlinear fitting model and the gradient of each influencing variable, ranking the influencing variables according to the significance of the gradient; and based on the ranked influencing variables, constructing a candidate function expression library using basic mathematical operators; the basic mathematical operators include addition, subtraction, multiplication, division, and exponentiation, and the candidate function expression library includes polynomial terms, trigonometric function terms, exponential function terms, and logarithmic function terms.

[0018] Optionally, the sparse regression algorithm employs LASSO regression, stepwise regression, or symbolic regression methods. By introducing regularization terms or setting significance thresholds, it selects sparse non-zero key terms from the candidate function expression library and combines these key terms to obtain the implicit mathematical expression of the bias.

[0019] Optionally, the alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update specifically includes the following steps: The measured sparse thermodynamic sensing data is input into the current explicit and implicit thermodynamic mechanism equation to predict the thermodynamic theoretical prediction data. Based on the measured thermodynamic experimental data and the thermodynamic theoretical prediction data under the corresponding operating conditions, the global prediction deviation of the current explicit and implicit thermodynamic mechanism equation is obtained.

[0020] Based on the global prediction bias, the model prediction accuracy is determined, and it is judged whether the model prediction accuracy has reached the preset threshold.

[0021] If the model's prediction accuracy does not reach the preset threshold, the backpropagation algorithm is used to analyze the gradient of the global prediction bias on each coefficient in the implicit mathematical expression to determine the direction of coefficient optimization.

[0022] An optimization algorithm based on the gradient direction is used to update the coefficients in the implicit mathematical expression to minimize the global prediction bias, thus obtaining the updated implicit mathematical expression.

[0023] The updated implicit mathematical expression is then re-integrated with the explicit thermodynamic differential control equation to obtain the updated explicit-implicit thermodynamic mechanism equation. This updated explicit-implicit thermodynamic mechanism equation is then used as the current explicit-implicit thermodynamic mechanism equation. The process then proceeds to the step "inputting the measured sparse thermodynamic sensing data into the current explicit-implicit thermodynamic mechanism equation to predict the thermodynamic theoretical prediction data. Based on the measured thermodynamic experimental data and the thermodynamic theoretical prediction data under the corresponding operating conditions, the global prediction deviation of the current explicit-implicit thermodynamic mechanism equation is obtained." This process continues until the model prediction accuracy reaches a preset threshold.

[0024] Optionally, the implicit mathematical expression can be used as a compensation term and fused with the explicit thermodynamic differential control equation to obtain a complete explicit-implicit thermodynamic mechanism equation. Specifically, the implicit mathematical expression can be used as a source term and superimposed on the explicit thermodynamic differential control equation to form a complete explicit-implicit thermodynamic mechanism equation.

[0025] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process transitions driven by explicit and implicit mechanisms. Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during the process, and combined with the theories of elasticity and contact mechanics, it establishes explicit thermodynamic mechanism equations for key components of a composite coordinate grinding machine under various processes. This method comprehensively covers the entire physical process of heat transfer and stress evolution during multi-process machining, laying a mechanistic foundation that conforms to deterministic physical laws for thermodynamic performance analysis. Based on measured data and numerical simulation data under multiple processes, the explicit thermodynamic mechanism equations are iteratively optimized. While improving the prediction accuracy of the explicit mechanism equations through multi-source data calibration, a unified and standardized characterization of the thermodynamic mechanism under multiple processes is achieved, solving the problems of fragmented multi-process modeling and calculation discontinuities in the thermodynamic behavior during process transitions in traditional methods. The deviation between the theoretical prediction data output by the differential control equation and the measured data under the corresponding working conditions is then used as the implicit mechanism analysis target. The implicit mathematical expression corresponding to the deviation is obtained analytically, and the nonlinear micro-thermal behaviors and dynamic disturbances not covered by the explicit mechanism during the multi-process conversion process are accurately extracted and quantified, making up for the deficiency of traditional simplified mechanism equations in characterizing complex dynamic working conditions. Finally, the implicit mathematical expression is fused with the explicit thermodynamic differential control equation as a compensation term to obtain the complete explicit and implicit thermodynamic mechanism equation. Based on the alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update, the explicit and implicit thermodynamic mechanism equation is iteratively corrected. Under the premise of not destroying the physical consistency of the explicit mechanism, the model prediction accuracy is continuously improved, which can provide reliable theoretical support for the analysis of machine tool thermodynamic performance and the assurance of machining accuracy under multi-process conversion. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms, provided as an embodiment of this application.

[0028] Figure 2 This is a detailed flowchart of step A1 in a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms, provided in an embodiment of this application.

[0029] Figure 3 This is a detailed flowchart of step A2 in a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms, provided in an embodiment of this application.

[0030] Figure 4 This is a detailed flowchart of step A4 in a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms, provided in an embodiment of this application. Detailed Implementation

[0031] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0032] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] This application provides a method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms. In one exemplary embodiment, such as... Figure 1 As shown, it includes the following steps: A1. Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during processes, and combined with the theories of elasticity and contact mechanics, explicit thermodynamic mechanism equations are established for key components of composite coordinate grinding machines under various processes. Specifically, the explicit thermodynamic mechanism equations include explicit heat transfer mechanism equations and explicit stress distribution mechanism equations; such as... Figure 2 As shown, step A1 specifically includes the following steps: A11. Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock in the process, establish explicit heat transfer mechanism equations for key components of the composite coordinate grinding machine.

[0034] A12. Based on the theories of elasticity and contact mechanics, and combined with assembly preload, component gravity and multi-axis motion coupling factors, an explicit stress distribution mechanism equation for key components of a composite coordinate grinding machine is established.

[0035] A13. Based on the explicit heat transfer mechanism equation and the explicit stress distribution mechanism equation, the explicit thermodynamic mechanism equation is obtained by integration. This enables the bidirectional coupled characterization of the temperature field and the stress field.

[0036] In an exemplary embodiment, the key components of the composite coordinate grinding machine include core structural components that directly participate in the machining process and have a direct impact on machining accuracy, such as the spindle box, column, guide rails, and worktable. The heat conduction process encompasses the internal heat diffusion process of the components; the heat convection process encompasses the heat exchange process between the cutting fluid, ambient air, and the component surface; intermittent thermal shocks during the machining process are generated by periodic feeds, idle strokes, and tool changes; the assembly preload is applied by the anchor bolts, guide rail inserts, and spindle bearing preload mechanism; the component gravity is a constant load generated by the spindle box, column, workpiece, and fixture under the action of gravity; and the multi-axis motion coupling factor is the dynamic inertial force and torque generated on the structural components by the interaction of the acceleration and velocity of the multiple motion axes during simultaneous machining.

[0037] In another exemplary embodiment, the explicit heat transfer mechanism equation is established based on Fourier's law of heat conduction and Newton's law of cooling, fully covering the heat diffusion process inside the component, the convective heat transfer process between the cutting fluid and ambient air and the component surface, and also incorporating the intermittent thermal shock loads caused by periodic feed, idle stroke, and tool change actions during machining, thus fully characterizing the heat transfer and temperature field evolution during machine tool operation. The explicit stress distribution mechanism equation is established based on the basic equations of linear elasticity and Hertzian contact theory of contact mechanics, comprehensively incorporating three types of load factors: first, the assembly preload force applied by the anchor bolts, guide rail inserts, and spindle bearing preload mechanism; second, the constant gravity load generated by the spindle box, column, workpiece, and fixture under the action of gravity field; and third, the dynamic inertial force and torque generated on the structural components by the interaction of acceleration and velocity of multiple motion axes during multi-axis linkage machining of the machine tool, thus fully characterizing the stress field and deformation field evolution of the machine tool structure under thermo-mechanical coupling.

[0038] A2. Based on measured thermodynamic experimental data and numerical simulation data under various processes, the explicit thermodynamic mechanism equation is iteratively optimized. The optimized explicit thermodynamic mechanism equation is then symbolized, symmetricized, and dimensionless, resulting in a unified explicit thermodynamic differential governing equation for various processes. In this embodiment, as... Figure 3 As shown, step A2 specifically includes the following steps: A21. Substitute the measured data from thermodynamic experiments and the numerical simulation data from thermodynamic experiments under various processes into the explicit thermodynamic mechanism equation. Use the parameter identification algorithm to inversely calculate and correct the undetermined coefficients and functional relationships in the explicit thermodynamic mechanism equation, so that the output value of the explicit thermodynamic mechanism equation achieves the best fit with the measured data from thermodynamic experiments and the numerical simulation data from thermodynamic experiments within the global process range.

[0039] As an optional implementation method, a test bench for key machine tool components is built to collect temperature, stress, and deformation data at key points of key components under different processes and working conditions, such as turning, milling, drilling, and grinding, forming thermodynamic test data. At the same time, a high-fidelity finite element model of the machine tool under the corresponding working conditions is established, and the temperature field, stress field, and deformation field under the corresponding working conditions are obtained through numerical simulation to form high-fidelity numerical simulation data. The thermodynamic test data and the thermodynamic numerical simulation dataset are integrated to form a multi-source data foundation.

[0040] A22. Through symbolization, symmetry, and dimensionless processing, the modified explicit thermodynamic mechanism equations corresponding to different processes are unified and standardized into explicit thermodynamic differential control equations with the same differential form; the differences between different processes are distinguished by the values ​​of the process coefficient matrix, input excitation vector, and boundary conditions in the explicit thermodynamic differential control equations.

[0041] In this step, the optimized explicit thermodynamic mechanism equations are standardized: symbolization unifies the physical quantities and parameters in the equations into a standardized symbol system; symmetry eliminates unnecessary differences caused by coordinate system selection and structural asymmetry; dimensionlessness eliminates the solution difficulties caused by differences in units and magnitudes of physical quantities. Finally, the specific forms of thermodynamic mechanism equations corresponding to different processes such as turning, milling, drilling, and grinding are unified and standardized into a single explicit thermodynamic differential control equation with the same differential form. The differences between different processing technologies are distinguished by the specific values ​​of the process coefficient matrix, input excitation vector, and boundary conditions in the explicit thermodynamic differential control equation, achieving a unified representation of the mechanism equations across different processes.

[0042] A3. Taking the deviation between the thermodynamic theoretical prediction data output by the explicit thermodynamic differential control equation and the thermodynamic experimental measured data under the corresponding working conditions as the implicit mechanism analysis target, an implicit mechanism module for characterizing the dynamic characteristics of the deviation is constructed, and the implicit mathematical expression corresponding to the deviation is obtained analytically.

[0043] Based on the corrected explicit thermodynamic mechanism equation, step A3 uses the thermodynamic theoretical prediction data and the actual thermodynamic experimental data predicted by the explicit thermodynamic mechanism equation to obtain the deviation between the two. This deviation covers the prediction errors caused by minor thermodynamic behaviors, nonlinear coupling effects, and dynamic disturbance factors that are not modeled by the explicit mechanism equation during multi-process conversion. The potential change patterns in the deviation are extracted using a data-driven nonlinear fitting model. The gradient of the deviation relative to its influencing variables is calculated using automatic differentiation technology. Based on gradient back-source tracing and sparse regression algorithms, the implicit mathematical expression of the deviation is analytically obtained.

[0044] In an exemplary embodiment, an implicit mechanism module for characterizing the dynamic properties of the deviation is constructed, and the implicit mathematical expression corresponding to the deviation is obtained by parsing. Specifically, the potential change patterns in the deviation are extracted by a data-driven nonlinear fitting model, the gradient of the deviation with respect to each influencing variable is calculated by automatic differentiation technology, and the implicit mathematical expression of the deviation is obtained by parsing based on gradient back-source tracing and sparse regression algorithms.

[0045] Specifically, in this embodiment, the nonlinear fitting model is a deep neural network. The input layer of the deep neural network receives process parameters, motion state, and time series monitoring data, and performs nonlinear transformation through at least one hidden layer. The output layer fits the current value of the thermal deviation. The influencing variables include directly controllable process parameters and various process variables that indirectly reflect the motion state. Process parameters include cutting depth, feed rate, and spindle speed, while process variables include spindle power, servo current of each axis, and temperature of key parts.

[0046] As an optional implementation method, gradient backpropagation specifically involves: based on the gradient relationship between the deviation value output by the nonlinear fitting model and the gradient of each influencing variable, the influencing variables are sorted according to the significance of the gradient; based on the sorted influencing variables, a candidate function expression library is constructed using basic mathematical operators; the basic mathematical operators include addition, subtraction, multiplication, division, and exponentiation; and the candidate function expression library includes polynomial terms, trigonometric function terms, exponential function terms, and logarithmic function terms.

[0047] The sparse regression algorithm can employ LASSO regression, stepwise regression, or symbolic regression methods. By introducing regularization terms or setting significance thresholds, sparse non-zero key terms are selected from the candidate function expression library, and the key terms are combined to obtain the implicit mathematical expression of the bias.

[0048] A4. The implicit mathematical expression is used as a compensation term and fused with the explicit thermodynamic differential control equation to obtain the complete explicit and implicit thermodynamic mechanism equation. The explicit and implicit thermodynamic mechanism equation is iteratively corrected based on the alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update until the model prediction accuracy reaches the preset threshold. The explicit and implicit thermodynamic mechanism equation is used to predict the complete thermodynamic field distribution of the composite coordinate grinding machine based on the sparse thermodynamic sensing data collected on the composite coordinate grinding machine. The model prediction accuracy is the prediction accuracy of the explicit and implicit thermodynamic mechanism equation for the thermodynamic field distribution.

[0049] In this implementation method, the implicit mathematical expression is used as a compensation term and fused with the explicit thermodynamic differential control equation to obtain a complete explicit-implicit thermodynamic mechanism equation. Specifically, the implicit mathematical expression is used as a source term and superimposed on the explicit thermodynamic differential control equation to form a complete explicit-implicit thermodynamic mechanism equation.

[0050] In one exemplary embodiment, such as Figure 4 As shown, step A4 specifically includes the following steps: A41. The implicit mathematical expression is used as the source term and superimposed onto the explicit thermodynamic differential control equation to form a complete explicit-implicit thermodynamic mechanism equation.

[0051] A42. Input the measured sparse thermodynamic sensing data into the current explicit-implicit thermodynamic mechanism equation to predict the thermodynamic theoretical prediction data.

[0052] A43. Based on the measured data of thermodynamic experiments and the predicted data of thermodynamic theory under the corresponding operating conditions, the global prediction deviation of the current explicit and implicit thermodynamic mechanism equations is obtained.

[0053] A44. Based on the global prediction bias, determine the model prediction accuracy and whether the model prediction accuracy has reached the preset threshold.

[0054] A45. If the model's prediction accuracy does not reach the preset threshold, the gradient of the global prediction bias on each coefficient in the implicit mathematical expression is analyzed through the backpropagation algorithm to determine the direction of coefficient optimization.

[0055] A46. Based on the gradient direction, an optimization algorithm is used to update the coefficients in the implicit mathematical expression to minimize the global prediction bias and obtain the updated implicit mathematical expression.

[0056] A47. Reintegrate the updated implicit mathematical expression with the explicit thermodynamic differential control equation to obtain the updated explicit-implicit thermodynamic mechanism equation. Use the updated explicit-implicit thermodynamic mechanism equation as the current explicit-implicit thermodynamic mechanism equation and jump to step A42. Continue until the model prediction accuracy reaches the preset threshold, then execute step A48.

[0057] A48. The current explicit-implicit thermodynamic mechanism equation is taken as the final optimized explicit-implicit thermodynamic mechanism equation.

[0058] In practical industrial applications, the optimized explicit-implicit thermodynamic mechanism equations are used to predict and generate a high-resolution thermodynamic field distribution inside the composite coordinate grinding machine based on sparse thermodynamic sensing data collected from a few key points of the composite coordinate grinding machine. This achieves a leap from discrete point sensing to continuous full-field perception, providing real-time and accurate thermal field monitoring and reconstruction capabilities for complex industrial processes.

[0059] The explicit-implicit mechanism-driven thermodynamic performance analysis method for coordinate grinding machines under multi-process conversion provided in the above embodiments of this application first establishes explicit thermodynamic mechanism equations based on deterministic physical laws and mechanical theories, ensuring the physical consistency and determinism of the mechanism model. Second, through iterative optimization and standardization of multi-source data, a unified representation of explicit mechanism equations under multi-process conditions is achieved, providing a standardized modeling framework for cross-process thermodynamic analysis. Third, by constructing an implicit mechanism module, the method accurately extracts and characterizes the minute thermodynamic behaviors and dynamic deviations that are not explicitly modeled during multi-process conversion, significantly improving the ability of the mechanism equations to characterize complex actual conditions. Finally, through the fusion and alternating optimization mechanism of explicit and implicit equations, the method achieves dynamic correction and continuous improvement of the accuracy of the mechanism model, enabling precise characterization of the dynamic thermodynamic characteristics of composite coordinate grinding machines under multi-process conversion, providing high-quality theoretical support for the calculation and accuracy assurance of machine tool thermodynamic performance.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for analyzing the thermodynamic properties of a coordinate grinding machine under multiple process conversions driven by explicit and implicit mechanisms, characterized in that, include: Based on the thermodynamic physical laws of heat conduction, heat convection, and intermittent thermal shock during processes, and combined with the theories of elasticity and contact mechanics, explicit thermodynamic mechanism equations for key components of composite coordinate grinding machines under various processes are established. Based on the measured data of thermodynamic experiments and the numerical simulation data of thermodynamics under various processes, the explicit thermodynamic mechanism equation is iteratively optimized, and the optimized explicit thermodynamic mechanism equation is symbolized, symmetricized and dimensionless, to obtain a unified explicit thermodynamic differential control equation under various processes. Using the deviation between the thermodynamic theoretical prediction data output by the explicit thermodynamic differential control equation and the thermodynamic experimental measured data under the corresponding working conditions as the implicit mechanism analysis target, an implicit mechanism module is constructed to characterize the dynamic characteristics of the deviation, and the implicit mathematical expression corresponding to the deviation is obtained analytically. The implicit mathematical expression is used as a compensation term and fused with the explicit thermodynamic differential control equation to obtain a complete explicit and implicit thermodynamic mechanism equation. The explicit and implicit thermodynamic mechanism equation is iteratively corrected based on the alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update until the model prediction accuracy reaches a preset threshold. The explicit and implicit thermodynamic mechanism equations are used to predict the complete thermodynamic field distribution of the composite coordinate grinding machine based on the sparse thermodynamic sensing data collected on the composite coordinate grinding machine; the prediction accuracy of the model is the prediction accuracy of the explicit and implicit thermodynamic mechanism equations for the thermodynamic field distribution.

2. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 1, characterized in that, The explicit thermodynamic mechanism equations include the explicit heat transfer mechanism equation and the explicit stress distribution mechanism equation. Based on the thermodynamic and physical laws of heat conduction, heat convection, and intermittent thermal shock during processes, and combined with the theories of elasticity and contact mechanics, explicit thermodynamic mechanism equations for key components of the composite coordinate grinding machine under various processes are established, specifically including: Based on the thermodynamic and physical laws of heat conduction, heat convection, and intermittent thermal shock in the process, an explicit heat transfer mechanism equation for key components of the composite coordinate grinding machine is established. Based on the theories of elasticity and contact mechanics, and combined with assembly preload, component gravity and multi-axis motion coupling factors, an explicit stress distribution mechanism equation for key components of a composite coordinate grinding machine is established. Based on the explicit heat transfer mechanism equation and the explicit stress distribution mechanism equation, the explicit thermodynamic mechanism equation is obtained by integration.

3. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 2, characterized in that, Key components of a composite coordinate grinding machine include the spindle box, column, guide rails, and worktable. The heat conduction process encompasses the internal heat diffusion process of the components, the heat convection process encompasses the heat exchange process between the cutting fluid, ambient air, and the component surface, and the intermittent thermal shock during the machining process is generated by the periodic feed, idle stroke, and tool change actions. The assembly preload is applied by the anchor bolts, guide rail inserts, and spindle bearing preload mechanism. The component gravity is a constant load generated by the spindle box, column, workpiece, and fixture under the action of gravity. The multi-axis motion coupling factor is the dynamic inertial force and torque generated on the structural components by the interaction of the acceleration and velocity of the multiple motion axes during the linkage machining of the composite coordinate grinding machine.

4. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 1, characterized in that, Based on experimental and numerical simulation data of thermodynamics under various processes, the explicit thermodynamic mechanism equation is iteratively optimized. The optimized explicit thermodynamic mechanism equation is then symbolized, symmetricized, and dimensionless, resulting in a unified explicit thermodynamic differential governing equation for various processes. Specifically, this includes: Substituting the measured thermal test data and thermal numerical simulation data under various processes into the explicit thermal mechanism equation, the undetermined coefficients and functional relationships in the explicit thermal mechanism equation are inversely calculated and corrected through parameter identification algorithm, so that the output value of the explicit thermal mechanism equation achieves the best fit with the measured thermal test data and thermal numerical simulation data within the global process range. By symbolizing, symmetricizing, and dimensionless processing, the modified explicit thermodynamic mechanism equations corresponding to different processes are unified and standardized into explicit thermodynamic differential control equations with the same differential form; the differences between different processes are distinguished by the values ​​of the process coefficient matrix, input excitation vector, and boundary conditions in the explicit thermodynamic differential control equations.

5. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 1, characterized in that, An implicit mechanism module is constructed to characterize the dynamic properties of the deviation, and the implicit mathematical expression corresponding to the deviation is obtained analytically. Specifically, the potential change patterns in the deviation are extracted by a data-driven nonlinear fitting model, the gradient of the deviation with respect to each influencing variable is calculated using automatic differentiation technology, and the implicit mathematical expression of the deviation is obtained analytically based on gradient back-source tracing and sparse regression algorithms.

6. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 5, characterized in that, The nonlinear fitting model is a deep neural network. The input layer of the deep neural network receives process parameters, motion state and time series monitoring data, and performs nonlinear transformation through at least one hidden layer. The output layer fits the current value of the thermal deviation. The influencing variables include process parameters and various process variables. The process parameters include depth of cut, feed rate and spindle speed. The process variables include spindle power, servo current of each axis and temperature of key components.

7. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 5, characterized in that, The gradient back-source tracing specifically involves: based on the gradient relationship between the deviation value output by the nonlinear fitting model and the gradient of each influencing variable, ranking the influencing variables according to the significance of the gradient; and constructing a candidate function expression library based on the ranked influencing variables using basic mathematical operators; the basic mathematical operators include addition, subtraction, multiplication, division, and exponentiation; and the candidate function expression library includes polynomial terms, trigonometric function terms, exponential function terms, and logarithmic function terms.

8. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 7, characterized in that, The sparse regression algorithm employs LASSO regression, stepwise regression, or symbolic regression methods. By introducing regularization terms or setting significance thresholds, it selects sparse non-zero key terms from the candidate function expression library and combines these key terms to obtain the implicit mathematical expression of the bias.

9. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 1, characterized in that, The alternating optimization mechanism of model prediction accuracy verification and implicit mathematical expression coefficient update specifically includes: The measured sparse thermodynamic sensing data is input into the current explicit and implicit thermodynamic mechanism equation to predict the thermodynamic theoretical prediction data. Based on the measured thermodynamic test data under the corresponding operating conditions and the thermodynamic theoretical prediction data, the global prediction deviation of the current explicit and implicit thermodynamic mechanism equation is obtained. Based on the global prediction bias, the model prediction accuracy is determined, and it is judged whether the model prediction accuracy has reached a preset threshold. If the model prediction accuracy does not reach the preset threshold, the gradient of the global prediction bias on each coefficient in the implicit mathematical expression is analyzed by the backpropagation algorithm to determine the direction of coefficient optimization. Based on the gradient direction, an optimization algorithm is used to update the coefficients in the implicit mathematical expression to minimize the global prediction bias, thereby obtaining the updated implicit mathematical expression. The updated implicit mathematical expression is then re-integrated with the explicit thermodynamic differential control equation to obtain the updated explicit-implicit thermodynamic mechanism equation. This updated explicit-implicit thermodynamic mechanism equation is then used as the current explicit-implicit thermodynamic mechanism equation. The process then proceeds to the step "inputting the measured sparse thermodynamic sensing data into the current explicit-implicit thermodynamic mechanism equation to predict the thermodynamic theoretical prediction data. Based on the measured thermodynamic experimental data under the corresponding operating conditions and the thermodynamic theoretical prediction data, the global prediction deviation of the current explicit-implicit thermodynamic mechanism equation is obtained," until the model prediction accuracy reaches a preset threshold.

10. The method for analyzing the thermodynamic performance of a coordinate grinding machine under multiple process conversions driven by the manifestation / concealment mechanism according to claim 1, characterized in that, The implicit mathematical expression is used as a compensation term and fused with the explicit thermodynamic differential control equation to obtain a complete explicit-implicit thermodynamic mechanism equation. Specifically, the implicit mathematical expression is used as a source term and superimposed on the explicit thermodynamic differential control equation to form a complete explicit-implicit thermodynamic mechanism equation.

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