A method for establishing a thermal error prediction model for machine tool feed system

Abstract

The present invention discloses a method for establishing a thermal error prediction model of a machine tool feed system, constructing a feed system thermal error prediction model; obtaining key parameters such as thermal conductivity and convective heat transfer coefficient through parameter identification; applying the same working conditions to the feed system model and the feed system thermal error prediction model, and collecting output data of the two under different working conditions; optimizing the key parameters of the feed system thermal error prediction model using the thermal error data of the feed system model based on a genetic algorithm; and correcting the high-precision prediction model using the final parameter values ​​obtained by multiple rounds of genetic optimization to obtain the final thermal error prediction value. The method realizes accurate prediction of the feed system thermal error prediction model by comprehensively analyzing the thermal error mechanism of the CNC machine tool feed system, the feed system thermal error prediction model, and combining it with a data-driven genetic optimization algorithm, thereby providing effective support for high-precision machining of CNC machine tools.

Description

Technical Field

[0001] The invention relates to the technical field of numerically controlled machine tools, and in particular to a method for establishing a thermal error prediction model of a machine tool feeding system. Background Art

[0002] The feed system is the intermediate link between the CNC device and the bed. It is a complex multi-input and multi-output nonlinear system. Its performance directly affects the machining accuracy and production efficiency of the machine tool. In the high-precision machining process, thermal error is one of the main factors affecting the accuracy of the feed system. Since the feed system generates heat when working, this heat will cause thermal deformation of the machine tool structure, which will lead to the generation of machining errors. With the continuous improvement of machine tool speed and precision requirements, if the thermal error of the feed system can be effectively predicted, the machining accuracy of the machine tool can be improved through some compensation methods. At present, there are two main methods for predicting the thermal error of the feed system: 1. Prediction based on simulation based on physical models; 2. Prediction based on data-driven models.

[0003] The simulation method based on physical models usually refers to modeling the mechanical structure of the CNC machine tool feed system through a variety of simulation tools such as Ansys, and simulating thermal errors through different initial conditions. In recent years, with the development of multi-domain modeling languages, some researchers have also used modeling languages ​​such as Modelica and Simscape to model and simulate the entire system, solving the problem of incompatibility of multiple modeling software interfaces. However, the simulation modeling method is insufficient in its ability to express some nonlinear elements (friction, clearance, lubrication, etc.) of the machine tool feed system, and it is difficult to adapt to the accurate description of the actual situation under multiple working conditions.

[0004] Traditional thermal error prediction methods are usually based on a large amount of experimental data and are based on pure data-driven models. They are end-to-end modeling methods that use data-driven models such as multivariate linear regression or neural networks to predict thermal errors. However, these methods often have problems such as insufficient model accuracy and poor generalization ability when dealing with complex feed system thermal error problems. In addition, these methods lack an in-depth understanding of the physical mechanism of the feed system and cannot accurately capture the time-varying characteristics of thermal errors. Summary of the invention

[0005] In view of the problems that physical models are difficult to adapt to and accurately describe the actual conditions under multiple working conditions, and that thermal error prediction methods have insufficient model accuracy and poor generalization ability, the present invention provides a method for establishing a thermal error prediction model for a machine tool feed system with strong adaptability, good versatility and high prediction accuracy.

[0006] The present invention provides the following technical solution: a method for establishing a thermal error prediction model of a machine tool feed system, specifically comprising the following steps: S1, establishing a feed system model, the feed system model including a servo drive system, a permanent magnet synchronous motor and a ball screw transmission system, the feed system thermal error prediction model including a heat generation module and a heat transfer module, the heat generation module including heat generation of a screw nut pair and heat generation of a bearing, the heat transfer module including heat conduction, heat convection and heat radiation, the heat generation module and the heat transfer module are coupled and connected;

[0007] S2, performing parameter identification on the heat generation module and the heat transfer module;

[0008] S3, applying the same working conditions to the feed system model and the feed system thermal error prediction model, setting a plurality of temperature sensors on the ball screw of the ball screw transmission system, and collecting thermal error data and temperature data of the feed system model and the feed system thermal error prediction model respectively;

[0009] S4, using the simulation speed, simulation acceleration, simulation table position, command speed, command acceleration, command position, simulation temperature, simulation thermal error and simulation coefficients of the feed system model as input data, and using the sum of squares of thermal errors of each target point actually measured by the feed system model, the temperature of each target point and the end elongation of the ball screw as optimization targets to construct a multi-round evolutionary genetic algorithm, and obtain the optimized optimal identification parameters a, b, c, d, k and m;

[0010] S5, inputting the various coefficients optimized in step S4 into the feed system thermal error prediction model in step S1, comparing the data output by the feed system thermal error prediction model with the actual measured data of the feed system model, and if the data difference between the two does not meet the requirements, correcting the data output by the feed system thermal error prediction model, repeating step S5 until the data between the two meet the requirements, and obtaining the final feed system thermal error prediction model;

[0011] S6. Based on the feed system thermal error prediction model obtained in step S5, the overall thermal error of the CNC machine tool feed system is predicted.

[0012] In some embodiments, in step S1: the ball screw transmission system includes a ball screw, and the temperature field of the ball screw is equivalent to the linear superposition of the temperature fields under the action of each single point heat source, and the formula is:

[0013] , where the temperature field expression of the ball screw under the friction between the ball screw and its nut pair is: The temperature field expressions of the ball screw under the action of a single point heat source on the bearing support seats at the left and right ends of the ball screw are: , .

[0014] In some embodiments, friction characteristics based on the LuGre theoretical model are added during the modeling process of the thermal error prediction model of the feed system; data of the ball screw operation process of the feed system model is collected, and the heat generation rate, convection heat transfer coefficient, and thermal conductivity parameters of the nut pair are identified; temperature sensors, displacement sensors, and position sensors are installed on the ball screw, and relevant data is collected to identify the parameters in the LuGre theoretical model; after the parameter identification is completed, the relevant parameters of the thermal error prediction model of the feed system are optimized and adjusted.

[0015] In some embodiments, the discretized form of the LuGre theoretical model is expressed as:

[0016] z(k+1)=[v(k)- σ 0 g(k) z(k)|v(k)|]⋅ Δ T+z(k) g(k)= F c +( F s - F c ) e -(v(k) / ν(s) ) 2 F f (k)= σ 0 z(k)+ σ 1 z(k+1)-z(k) Δ T + σ 2 ν(k) ,

[0017] In the formula is the average elastic deformation, is the relative velocity between contact surfaces; is StriBeck speed; is the Coulomb friction force; is the maximum static friction; is the stiffness coefficient; is the damping coefficient; is the viscosity coefficient; For friction.

[0018] In some embodiments, the conversion ratio of frictional heat generated by the ball screw to internal energy is , and perform parameter identification. The friction heat generation rate of the nut pair is: ,in In the formula is the parameter to be identified; the convective heat transfer coefficient is proportional to the flow rate, and the expression is , where is the proportionality coefficient, For speed, is a constant.

[0019] In some embodiments, in step S5, the data output by the feed system thermal error prediction model is compared with the actual data measured by the feed system model, and the evaluation indicators are SSE, : SSE (Sum of Squared Errors): represents the sum of squares of the differences between the model prediction value and the actual value. The smaller the SSE, the better the model fit. (Coefficient of determination): This indicator measures the degree to which the model explains the variation in the data, and its value is between 0 and 1. =1 indicates a perfect fit, =0 means the model cannot explain any variation; , where TSS is the total sum of squares, which represents the sum of squares of the differences between the experimental data and the mean until The value of is greater than 0.98, which means that the data differences are consistent and a prediction model is obtained.

[0020] In some embodiments, the temperature data sequence and thermal error data sequence of the feed system model are arranged in chronological order, and the time intervals between the sequences are equal; the temperature data sequence and thermal error data sequence of the feed system thermal error prediction model are arranged in chronological order, and the time intervals between the sequences are equal.

[0021] In some embodiments, in step S4: a multi-round evolutionary genetic algorithm framework under multiple working conditions is established; using simulation speed, simulation acceleration, simulation workbench position, command speed, command acceleration and command position as input data, and using the actual measurement of the target point errors and temperatures of the feed system model as optimization targets to construct a multi-round evolutionary genetic algorithm to obtain the optimized coefficients.

[0022] In some embodiments, the feed system model includes a control box, a servo motor, a coupling, a bearing, a bearing support seat, a nut pair, a panel, a ball screw and a limit bracket. The control box controls the rotation of the servo motor. The servo motor is connected to one end of the ball screw through a coupling. The end of the ball screw close to the coupling is inserted into the bearing. The bearing is arranged on the bearing support seat. The other end of the ball screw is arranged on the limit bracket. A nut pair is fixed to the lower end surface of the panel, and the nut pair cooperates with the ball screw.

[0023] In some embodiments, guide rails parallel to the ball screw are provided on both sides of the ball screw, a guide rail slider cooperating with the guide rail is provided on the panel, and a displacement sensor is installed on the outer side of the limit bracket.

[0024] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention combines the physical mechanism and the data-driven model to fuse the thermodynamic model of the machine tool feed system with the actual measurement data to improve the accuracy and robustness of the thermal error prediction model of the feed system. The thermal error prediction model of the feed system can simulate the temperature field distribution and thermal deformation of the feed system under different working conditions by means of finite element analysis, thermodynamic simulation and the like; the data fusion part uses the measurement data to calibrate and optimize the model, so that the model can better reflect the thermal error distribution in actual work; compared with the traditional purely data-driven method, the prediction accuracy of the thermal error prediction model of the feed system of the present invention can meet the needs of small batch, personalized, and variable working condition production. At the same time, the physical mechanism of the feed system is flexibly used to accurately capture the time-varying characteristics of the thermal error, and accurate prediction of the thermal error and temperature of the feed system can be achieved, providing a solid foundation for subsequent error compensation and other work. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0026] Figure 1 It is a method framework diagram of the thermal error prediction model of the feed system of the present invention;

[0027] Figure 2 It is the overall method framework diagram of the present invention;

[0028] Figure 3 It is a schematic diagram of the overall structure of the feeding system model of the present invention;

[0029] Figure 4 It is a partial structural schematic diagram of the feeding system model of the present invention;

[0030] Figure 5 It is a simplified structural schematic diagram of the feeding system model of the present invention;

[0031] Figure 6 It is a temperature field modeling module diagram of the thermal error prediction model of the feed system of the present invention;

[0032] Figure 7 This is a model diagram of the main heat-generating part of the feeding system model of the present invention;

[0033] Figure 8 This is a model diagram of the temperature measurement point installation position of the present invention;

[0034] Fig. 9 This is a framework diagram of the multi-round evolutionary genetic algorithm of the present invention.

[0035] In the figure: 1. Control box; 2. Servo motor; 3. Coupling; 4. Bearing; 5. Bearing support seat; 6. Guide rail slider; 7. Nut pair; 8. Panel; 9. Guide rail; 10. Ball screw; 11. Limit bracket; 12. Displacement sensor; 13. Grating ruler; 14. Temperature sensor. DETAILED DESCRIPTION

[0036] The present application is described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0038] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present application, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number and aspect described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0039] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show the components related to the present application rather than being drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0040] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the examples can be practiced without these specific details.

[0041] The technical solutions provided by various embodiments of the present application are described below in conjunction with the accompanying drawings.

[0042] See also Figure 1-6In this embodiment: a method for establishing a thermal error prediction model of a machine tool feed system, specifically comprising the following steps: S1, establishing a feed system model, the feed system model comprising a servo drive system, a permanent magnet synchronous motor and a ball screw transmission system, the feed system thermal error prediction model comprising a heat generation module and a heat transfer module, the heat generation module comprising heat generation of a screw nut pair and heat generation of a bearing, the heat transfer module comprising heat conduction, heat convection and heat radiation, the heat generation module and the heat transfer module being coupled;

[0043] S2, performing parameter identification on the heat generation module and the heat transfer module;

[0044] S3, applying the same working conditions to the feed system model and the feed system thermal error prediction model, setting a plurality of temperature sensors 14 on the ball screw 10 of the ball screw transmission system, and collecting thermal error data and temperature data of the feed system model and the feed system thermal error prediction model respectively;

[0045] S4, using the simulation speed, simulation acceleration, simulation table position, command speed, command acceleration, command position, simulation temperature, simulation thermal error and simulation coefficients of the feed system model as input data, and using the sum of squares of thermal errors of each target point actually measured by the feed system model, the temperature of each target point and the end elongation of the ball screw 10 as optimization targets to construct a multi-round evolutionary genetic algorithm, and obtain the optimized optimal identification parameters a, b, c, d, k and m;

[0046] S5, inputting the various coefficients optimized in step S4 into the feed system thermal error prediction model in step S1, comparing the data output by the feed system thermal error prediction model with the actual measured data of the feed system model, and if the data gap between the two does not meet the requirements, correcting the data output by the feed system thermal error prediction model, repeating step S5 until the data gap between the two meets the requirements, and obtaining the final feed system thermal error prediction model;

[0047] S6. Based on the feed system thermal error prediction model obtained in step S5, the overall thermal error of the CNC machine tool feed system is predicted.

[0048] In some embodiments, in step S1: the ball screw transmission system includes a ball screw 10, and the temperature field of the ball screw 10 is equivalent to the linear superposition of the temperature fields under the action of each single point heat source, and the formula is:

[0049] , where the temperature field expression of the ball screw 10 under the friction between the ball screw 10 and its nut pair 7 is: The temperature field expressions of the ball screw 10 under the action of a single point heat source on the bearing support seat 5 of the bearings 4 at the left and right ends of the ball screw 10 are respectively , .

[0050] It should be pointed out that : The temperature of the ball screw 10 at a certain point x at time t.

[0051] It should be pointed out that: considering the frictional heat generated by the reciprocating motion of the ball screw 10 and the nut pair 7 and the rotational heat generated by the bearings 4 at both ends, the contact surface of the ball and the raceway in the nut pair 7 will be deformed due to the axial force, thereby generating a friction torque, and the friction torque caused by the load on the bearing 4 Viscous friction torque The total friction torque of bearing 4 is determined by the sum of the two, and it is more comprehensive to consider both comprehensively.

[0052] It should be pointed out that in the heat transfer module, the heat conduction between the connection pairs, the heat radiation and heat convection between the components and between the components and the outside air are comprehensively considered.

[0053] In some embodiments, friction characteristics based on the LuGre theoretical model are added during the modeling process of the thermal error prediction model of the feed system; data of the ball screw 10 of the feed system model during operation are collected, and the heat generation rate, convection heat transfer coefficient, and thermal conductivity parameters of the nut pair 7 are identified; the temperature sensor 14, displacement sensor 12, and position sensor are installed on the ball screw 10, and relevant data is collected to identify the parameters in the LuGre theoretical model; after the parameter identification is completed, the relevant parameters of the thermal error prediction model of the feed system are optimized and adjusted.

[0054] It should be pointed out that: in the modeling process of the thermal error prediction model of the feed system, the friction torque based on the LuGre friction theory combining the effects of static friction, dynamic friction and viscous friction is added; and a parameterized model of the convective heat transfer coefficient related to heat transfer is added.

[0055] It should be pointed out that the position sensor is a grating ruler 13 , which is used to detect positioning errors and is arranged on one side of the panel 8 .

[0056] In some embodiments, the discretized form of the LuGre theoretical model is expressed as:

[0057] z(k+1)=[v(k)- σ 0 g(k) z(k)|v(k)|]⋅ Δ T+z(k) g(k)= F c +( F s - F c ) e -(v(k) / ν(s) ) 2 F f (k)= σ 0 z(k)+ σ 1 z(k+1)-z(k) Δ T + σ 2 ν(k) ,

[0058] In the formula is the average elastic deformation, is the relative velocity between contact surfaces; is StriBeck speed; is the Coulomb friction force; is the maximum static friction; is the stiffness coefficient; is the damping coefficient; is the viscosity coefficient; For friction.

[0059] In some embodiments, the conversion ratio of the friction heat generated by the ball screw 10 to the internal energy is , and perform parameter identification, the friction heat generation rate of the nut pair 7 is: ,in In the formula is the parameter to be identified; the convective heat transfer coefficient is proportional to the flow rate, and the expression is , where is the proportionality coefficient, For speed, is a constant.

[0060] In some embodiments, the temperature data sequence and thermal error data sequence of the feed system model are arranged in chronological order, and the time intervals between the sequences are equal; the temperature data sequence and thermal error data sequence of the feed system thermal error prediction model are arranged in chronological order, and the time intervals between the sequences are equal.

[0061] In some embodiments, in step S5: the data output by the feed system thermal error prediction model is compared with the actual data measured by the feed system model, and the evaluation indicators are SSE, : SSE (Sum of Squared Errors): represents the sum of squares of the differences between the model prediction value and the actual value. The smaller the SSE, the better the model fit. (Coefficient of Determination): This indicator measures the degree to which the model explains the variation in the data. Its value is between 0 and 1. The closer it is to 1, the better the model can explain the variation in the data, indicating that the model has a better fitting effect. =1 indicates a perfect fit, =0 means the model cannot explain any variation; , where TSS is the total sum of squares, which represents the sum of squares of the differences between the experimental data and the mean until The value of is greater than 0.98, which means that the data differences are consistent and a prediction model is obtained.

[0062] In some embodiments, Figure 3-Figure 5As shown, the feed system model includes a control box 1, a servo motor 2, a coupling 3, a bearing 4, a bearing support seat 5, a nut pair 7, a panel 8, a ball screw 10 and a limit bracket 11. The control box 1 controls the rotation of the servo motor 2. The servo motor 2 is connected to one end of the ball screw 10 through the coupling 3. The end of the ball screw 10 close to the coupling 3 is inserted into the bearing 4. The bearing 4 is arranged on the bearing support seat 5. The other end of the ball screw 10 is arranged on the limit bracket 11. The nut pair 7 is fixed to the lower end surface of the panel 8, and the nut pair 7 cooperates with the ball screw 10.

[0063] In some embodiments, guide rails 9 parallel to the ball screw 10 are provided on both sides of the ball screw 10 , and guide rail sliders 6 cooperating with the guide rails 9 are provided on the panel 8 .

[0064] In some embodiments, a displacement sensor 12 is installed on the outer side of the limiting bracket 11 .

[0065] It should be pointed out that the displacement sensor 12 measures the overall thermal deformation elongation of the ball screw 10 along the feeding direction.

[0066] In some embodiments, Figure 6 As shown, the temperature field modeling module diagram of the feed system thermal error prediction model includes: Heat conduction: There is a temperature gradient inside the ball screw 10, and its main heat transfer method is heat conduction. The heat flow per unit area is proportional to the normal temperature gradient: , after adding the proportional constant, it is expressed as ; In the formula, is the heat flux density of heat conduction, in units of ; is the temperature gradient in the direction of heat flow; is the thermal conductivity of the material, in units of ; Indicates the component temperature, unit ; The negative sign in the formula indicates that heat conduction obeys the second law of thermodynamics, that is, heat must be transmitted in the direction of decreasing temperature.

[0067] Convection heat transfer: The surface of the ball screw 10 is constantly in contact with the air, and the air removes the heat by convection: ,in, is the heat flux density of the convective heat transfer process, in units of ; Indicates the air convection heat transfer coefficient, unit ; Indicates the surface temperature of the component, unit ; Indicates the air temperature, unit .

[0068] Radiation heat transfer: For comprehensive heat transfer problems involving both radiation heat transfer and convection heat transfer, the radiation heat transfer coefficient is often introduced, and the radiation heat transfer process is expressed in the form of Newton's cooling formula for engineering heat transfer calculations; at this time, the heat flux density of the radiation heat transfer process is: ;in, is the heat flux density of the radiation heat transfer process, in units of ; It represents the radiation heat transfer coefficient, unit ; The heat flux density of the comprehensive heat transfer process of radiation heat transfer and convection heat transfer can be expressed as: ;in, is the heat flux density of the radiation heat transfer process, in units of ; It represents the radiation heat transfer coefficient, unit .

[0069] In some embodiments, Figure 7 As shown in the figure, the main heat generating part model of the feed system model includes: the temperature field under the friction between the nut pair 7 and the ball screw 10: the heat increment of the heat conduction process is , when only the friction between the nut pair 7 and the ball screw 10 is considered, the temperature of the ball screw 10 is , the total length of the ball screw 10 will be divided into x segments. Moment, ball screw 10 micro segment (The heat balance formula of the ball screw 10 micro-segment dx is a unit segment) is: , for Micro segment at location With nut pair 7 Frictional heat generation during time period: , where It is the nut pair 7 friction ball screw 10 micro segment The amount of heat generated at one time; is the average number of frictions between the nut pair 7 and the micro-segment dx of the ball screw 10 per unit time; , for Heat conduction of ball screw 10 micro-segment dx during the time period: , ; for The heat transfer of the comprehensive heat transfer process of radiation and convection during the time period: Q cr (x,t)= ∫ t -Δ t t k p ⋅ h cr ⋅ [ T s (x,t) - T r (t)] ⋅ 2 π R ⋅ dx ⋅ dt . for Energy gain during the time period: ; Substituting into the equilibrium formula, the temperature field function is: .

[0070] Temperature field of ball screw 10 under the action of single point heat source at both ends of the bearing seat: Micro segment of ball screw 10 under the action of single point heat source of bearing support seat 5 and limit bracket 11 The heat energy equation for heat conduction is: According to the temperature field distribution of ball screw 10 under the action of single point heat source, the micro-segment of ball screw 10 The temperature gradient on both sides has the following relationship: , assuming Can be used and in The derivative at is expressed as: , substituting into the heat energy equation: Therefore, the temperature field of the ball screw 10 under the action of the single point heat source of the bearing support seat 5 and the limit bracket 11 is: , , obtain the ambient temperature around the semi-closed loop linear feed axis ball screw 10 , the real-time temperature of the bearing support 5 and the limit bracket 11 , , the temperature field of the ball screw 10 under the friction between the nut pair 7 and the ball screw 10 can be calculated Temperature field of ball screw 10 under the action of single point heat source of bearing support seat 5 and limit bracket 11 , .

[0071] In some embodiments, Figure 7 As shown, the thermal expansion error calculation: According to the temperature field superposition principle, under the simultaneous action of multiple heat sources, the temperature field of the ball screw 10 is equivalent to the linear superposition of the temperature fields under the action of each single point heat source; the temperature field of the ball screw 10 is affected by the friction heat between the nut pair 7 and the ball screw 10 and the single point heat source of the bearing seats at both ends, and its temperature field is: , the thermal expansion error of the ball screw 10 at any time t: ; In the formula, is the thermal expansion coefficient of the ball screw 10; and The unit is , assuming that the calculation range of the thermal expansion error of the ball screw 10 is l, when the temperature of the bearing seats at both ends of the ball screw 10 is considered when calculating the thermal expansion error, , when the bearing seat temperature at both ends of the ball screw 10 is not considered, , is the total length of the ball screw 10, The length of the ball screw 10 from both ends to the bearing support seat 5 and the limit bracket 11 is removed.

[0072] like Figure 8 As shown, the measuring point positions of the temperature sensor 14 are T1, T5, T7, and T13, respectively, and the distance from the origin Ti = [0.020, 0.244, 0.351, 0.809] m, i = 1, 5, 7, 13. The specific selection method is: using the FCM clustering algorithm to establish a corresponding clustering prototype vector set for the classified objects, , and each data vector There are n characteristic indicators, namely ; Using fuzzy feature function Representation sample Subset The membership degree of ,but Each classification result corresponds to a Boolean fuzzy function matrix of order c×N ; Specify the cluster center vector of class c V=[ v 1 , v 2 , ⋯ , v c ] , the objective function of the FCM fuzzy clustering algorithm defined in this space can be defined as: ,in Indicates Samples in the class For Typical samples in the class The distortion degree is measured by the Euclidean distance between the two vectors; the weighted index m is also called the smoothing index, and its value has not yet been effectively proved or supported by theory. Generally, the best value interval is determined to be [1.5, 3] based on practical experience; based on this, a new objective function can be constructed: ,in, is the Lagrange multiplication factor; the criterion of fuzzy clustering is that the algorithm iteration ends when the new objective function reaches the minimum value, and the temperature point corresponding to the maximum membership value in the membership matrix U is determined as the final selected temperature sensitive point; the FCM fuzzy clustering algorithm is used to optimize the measurement point position of this device, and the weighted index m=2 and the number of clusters c=4 are set to obtain the clustering result of the temperature measurement point; the preliminary selected temperature measurement point with the largest membership value in each category is used as the temperature sensitive point of this category, and the final selection is and Three locations are helpful to eliminate the multicollinearity problem that may be caused by too many temperature measurement points.

[0073] It should be pointed out that: when the total length of the ball screw 10 is 1m, 13 temperature sensors 14 are provided on the ball screw 10, and the temperature sensor 14 divides the ball screw 10 into 14 equal sections. The 13 temperature sensors 14 are set to be T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11, T12 and T13 from the short distance to the long distance to the origin of the ball screw 10 respectively.

[0074] In some embodiments, Fig. 9 As shown in the figure, the framework diagram of the multi-round evolutionary genetic algorithm includes initialization, selection, crossover and mutation, fitness evaluation, iteration and phase switching. In the initialization phase, the initial population is randomly generated. , each individual represents a potential solution, the fitness function Used to evaluate the fitness value of each individual; in the selection stage, according to the fitness value Select the parent individual, and the selection probability can be expressed as , the parent individual is selected by this probability ; Then, new offspring individuals are generated through crossover and mutation operations. Crossover can use single-point crossover to generate offspring individuals. , while mutation increases population diversity and has an impact on individuals Apply mutation: ,in is the amplitude of variation, and When applying mutation operation, is the mutation probability; after generating a new population, calculate the fitness value of each individual again, and Recalculate fitness value , and according to the set termination conditions (such as reaching the maximum number of generations or fitness threshold ) Check whether the algorithm has ended, make a judgment on the termination of the algorithm, adjust the algorithm parameters at different stages as needed, and finally implement multiple rounds of optimization to obtain the optimal identification parameters.

[0075] The same and similar parts between the various embodiments in this specification can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0076] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for establishing a thermal error prediction model for a machine tool feed system, characterized in that: The specific steps include: S1. Establish a feeding system model, wherein the feeding system model includes a servo drive system, a permanent magnet synchronous motor and a ball screw transmission system, wherein the feeding system thermal error prediction model includes a heat generation module and a heat transfer module, wherein the heat generation module includes heat generation of a screw nut pair and heat generation of a bearing, wherein the heat transfer module includes heat conduction, heat convection and heat radiation, and the heat generation module and the heat transfer module are coupled and connected; S2, performing parameter identification on the heat generating module and the heat transfer module; S3, applying the same working conditions to the feed system model and the feed system thermal error prediction model, arranging a plurality of temperature sensors (14) on the ball screw (10) of the ball screw transmission system, and collecting thermal error data and temperature data of the feed system model and the feed system thermal error prediction model respectively; S4, using the simulated speed, simulated acceleration, simulated workbench position, command speed, command acceleration, command position, simulated temperature, simulated thermal error and various simulation coefficients of the feed system model as input data, and using the sum of squares of thermal errors of each target point actually measured by the feed system model, the temperature of each target point and the end elongation of the ball screw (10) as optimization targets to construct a multi-round evolutionary genetic algorithm to obtain the optimized optimal identification parameters a, b, c, d, k and m; S5, inputting the various coefficients optimized in step S4 into the feed system thermal error prediction model in step S1, comparing the data output by the feed system thermal error prediction model with the actual measured data of the feed system model, and if the data difference between the two does not meet the requirements, correcting the data output by the feed system thermal error prediction model, repeating step S5 until the data between the two meet the requirements, and finally obtaining the feed system thermal error prediction model; S6, based on the feed system thermal error prediction model obtained in step S5, complete the prediction of the overall thermal error of the CNC machine tool feed system; In step S1: the ball screw transmission system includes a ball screw (10), and the temperature field of the ball screw (10) is equivalent to the linear superposition of temperature fields under the action of each single point heat source, and the formula is: , wherein the temperature field expression of the ball screw (10) under the friction between the ball screw (10) and its nut pair (7) is: The temperature field expressions of the ball screw (10) under the action of a single point heat source on the bearing support seat (5) of the bearings (4) at the left and right ends of the ball screw (10) are respectively: , .

2. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 1, characterized in that: In the process of modeling the feed system thermal error prediction model, friction characteristics based on the LuGre theoretical model are added; data during the operation of the ball screw (10) of the feed system model are collected, and the heat generation rate, convection heat transfer coefficient, and thermal conductivity parameters of the nut pair (7) are identified; and the temperature sensor (14), displacement sensor (12), and position sensor installed on the ball screw (10) are collected, and relevant data are collected to identify the parameters in the LuGre theoretical model; After the parameter identification is completed, the relevant parameters of the thermal error prediction model of the feed system are optimized and adjusted.

3. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 2, characterized in that: The discrete form of the LuGre theoretical model is expressed as: ， In the formula is the average elastic deformation, is the relative velocity between contact surfaces; is StriBeck speed; is the Coulomb friction force; is the maximum static friction; is the stiffness coefficient; is the damping coefficient; is the viscosity coefficient; For friction.

4. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 3, characterized in that: Assume that the conversion ratio of the frictional heat generated by the ball screw (10) into internal energy is , and parameter identification is performed, the friction heat generation rate of the nut pair (7) is: ,in In the formula is the parameter to be identified; the convective heat transfer coefficient is proportional to the flow rate, and the expression is , where is the proportionality coefficient, For speed, is a constant.

5. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 1, characterized in that: In the step S5, the data output by the feed system thermal error prediction model is compared with the actual measured data of the feed system model, and the evaluation indicators are SSE, : SSE is the sum of squared errors: it represents the sum of squares of the differences between the model prediction value and the actual value. The smaller the SSE, the better the model fit. The coefficient of determination is a measure of the degree to which the model explains the variation in the data, and its value is between 0 and 1. =1 indicates a perfect fit, =0 means the model cannot explain any variation; ， TSS is the total sum of squares, which is the sum of squares of the differences between the experimental data and the mean until The value of is greater than 0.98, which means that the data differences are consistent and a prediction model is obtained.

6. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 1, characterized in that: The temperature data sequence and thermal error data sequence of the feed system model are arranged in chronological order, and the time intervals between the sequences are equal; the temperature data sequence and thermal error data sequence of the feed system thermal error prediction model are arranged in chronological order, and the time intervals between the sequences are equal.

7. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 1, characterized in that: The feeding system model comprises a control box (1), a servo motor (2), a coupling (3), a bearing (4), a bearing support seat (5), a nut pair (7), a panel (8), a ball screw (10) and a limit bracket (11); the control box (1) controls the rotation of the servo motor (2); the servo motor (2) is connected to one end of the ball screw (10) through the coupling (3); one end of the ball screw (10) close to the coupling (3) is inserted into the bearing (4); the bearing (4) is arranged on the bearing support seat (5); the other end of the ball screw (10) is arranged on the limit bracket (11); the nut pair (7) is fixed to the lower end surface of the panel (8); the nut pair (7) cooperates with the ball screw (10).

8. The method for establishing a thermal error prediction model for a machine tool feed system according to claim 7, characterized in that: Guide rails (9) parallel to the ball screw (10) are provided on both sides of the ball screw (10), guide rail sliders (6) cooperating with the guide rails (9) are provided on the panel (8), and a displacement sensor (12) is installed on the outer side of the limit bracket (11).

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