Lead screw thermal error compensation method and device, electronic equipment and computer storage medium

Abstract

This invention relates to a method, device, electronic device, and computer storage medium for compensating for thermal errors in lead screws, belonging to the field of machine tool processing technology. The thermal error compensation method for lead screws is applicable to lead screw feed systems with fixed ends. It includes: acquiring real-time temperatures at key temperature points in the lead screw feed system and the positioning error at those real-time temperatures based on a preset experimental platform; constructing a three-dimensional model of the lead screw feed system based on the thermal deformation effects and complexity of each structure; performing transient temperature-structure coupled field analysis on the lead screw feed system based on the three-dimensional model to determine the correlation between the lead screw pre-tension and the thermal deformation under thermal steady-state conditions; constructing a quantitative mapping model between lead screw temperature and thermal deformation based on this correlation; and performing thermal error compensation on the lead screw based on the quantitative mapping model. This invention can accurately achieve thermal error compensation for lead screws.

Description

Technical Field

[0001] This invention relates to the field of machine tool processing technology, and in particular to a method, device, electronic device, and computer storage medium for compensating for thermal errors in lead screws. Background Technology

[0002] High-precision CNC machine tools, as core equipment in modern intelligent manufacturing, directly determine the machining quality and efficiency of complex curved surfaces, precision molds, optical components, and key aerospace structural parts through their positioning accuracy and repeatability. The lead screw feed system, as the key actuator for achieving precise linear motion in CNC machine tools, is crucial to the dynamic response, positioning accuracy, and long-term stability of the entire machine.

[0003] Thermal deformation of the ball screw feed system is a key factor limiting the ultimate accuracy of machine tools. Current research on the thermal characteristics of ball screw feed systems in machine tools mostly focuses on the installation method of one end fixed and the other end supported, which is common in applications with medium accuracy requirements. However, research on the thermo-mechanical coupling behavior and thermal deformation characteristics of the pre-tensioned ball screw feed system with fixed installation at both ends, which is widely used in high-precision CNC machine tools, is relatively lacking, thus limiting its application in lead screw thermal error compensation.

[0004] Therefore, it is evident that existing technologies cannot accurately compensate for thermal errors in lead screw feed systems. Summary of the Invention

[0005] In view of this, it is necessary to provide a method, device, electronic device and computer storage medium for compensating for thermal errors in lead screws, so as to solve the problem that the existing technology cannot accurately perform thermal error compensation for lead screw feed systems.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides a lead screw thermal error compensation method, applicable to a lead screw feed system with both ends fixed, comprising: Based on a pre-set experimental platform, the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature are collected. Based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure, a three-dimensional model of the lead screw feed system is constructed. Based on a three-dimensional model, transient temperature and structural coupled field analysis was performed on the lead screw feed system to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state. A quantitative mapping model between the lead screw temperature and the lead screw thermal deformation is constructed based on the correlation, and thermal error compensation of the lead screw is performed based on the quantitative mapping model.

[0007] In one possible implementation, a three-dimensional model of the screw feed system is constructed based on the thermal deformation effects and complexity of each structure within the system, including: Based on the degree of thermal deformation of each structure in the lead screw feed system, the degree of influence on the thermal deformation of the lead screw, and the complexity of each structure, a simplified model of each structure is determined. Based on the installation scheme and connection relationship of each structure in the lead screw feed system, the simplified models of each structure are assembled to construct a three-dimensional model of the lead screw feed system.

[0008] In one possible implementation, a transient temperature-structure coupled field analysis is performed on the lead screw feed system based on a three-dimensional model to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state, including: The thermal boundary conditions of the lead screw feed system are defined based on the real-time temperature, and the mechanical boundary conditions of the lead screw feed system are defined based on the three-dimensional model. Based on thermal and mechanical boundary conditions, the pre-tensioning, processing, and cooling simulations of the lead screw feed system were performed. The relationship between the transient temperature distribution field and the transient thermal deformation distribution field along the lead screw axis during the simulation was extracted, and the correlation between the lead screw pre-tensioning amount and the thermal deformation amount under the lead screw thermal steady state was obtained.

[0009] In one possible implementation, the thermal boundary conditions of the screw feed system are defined based on a three-dimensional model, including: The temperature of the key characteristic point of the lead screw feed system is determined based on the real-time temperature. Calculate the convective heat transfer on the external surface of the screw feed system based on the thermal convection coefficient between the screw feed system and the air. Calculate the heat conduction between components of the lead screw feed system based on the heat conduction principle of the internal structure of the lead screw feed system; The thermodynamic boundary of the screw feed system is constructed based on the temperature of key feature points, the convective heat transfer on the external surface, and the heat conduction between components.

[0010] In one possible implementation, the mechanical boundary conditions include the constant feed rate of the nut on the screw, the effective travel range of the nut on the screw, and the duration of the screw motion.

[0011] In one possible implementation, a quantitative mapping model between the screw temperature and the screw thermal deformation is constructed based on the correlation, including: Collect the temperature at multiple temperature points along the lead screw axis and the corresponding thermal deformation of multiple lead screws; The temperatures at multiple temperature points and their corresponding thermal deformations are used as training data. A pre-defined multiple linear regression model is then used to train the model, resulting in a quantitative mapping model between the screw temperature and the screw thermal deformation.

[0012] In one possible implementation, thermal error compensation for the lead screw is based on a quantitative mapping model, including: The system acquires the real-time temperature of each temperature point along the lead screw axis and the real-time position of the nut along the lead screw axis in the lead screw feed system. The thermal error compensation displacement of the lead screw feed system is determined based on a quantitative mapping model, real-time temperature, and real-time position. Displacement compensation for the lead screw feed system is performed based on thermal error compensation displacement.

[0013] Secondly, the present invention also provides a lead screw thermal error compensation device, comprising: The model building module is used to collect the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature based on a preset experimental platform, and to build a three-dimensional model of the lead screw feed system based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure. The correlation determination module is used to perform transient temperature and structural coupling field analysis on the lead screw feed system based on a three-dimensional model, and to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state. The displacement error compensation module is used to construct a quantitative mapping model between the lead screw temperature and the lead screw thermal deformation based on the correlation, and to perform thermal error compensation on the lead screw based on the quantitative mapping model.

[0014] Thirdly, the present invention also provides an electronic device, including a memory and a processor, wherein, Memory, used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the lead screw thermal error compensation method of any of the above embodiments.

[0015] Fourthly, the present invention also provides a computer-readable storage medium for storing a computer-readable program or instruction, which, when executed by a processor, can implement the steps in the lead screw thermal error compensation method of any of the above embodiments.

[0016] The beneficial effects of this invention are as follows: The lead screw thermal error compensation method provided by this invention is applicable to lead screw feeding systems with fixed ends. Based on a preset experimental platform, the real-time temperature of key temperature points in the lead screw feeding system and the positioning error of the system at those real-time temperatures are collected. A three-dimensional model of the lead screw feeding system is constructed based on the thermal deformation effects and complexity of each structure within the system. The real-time temperature and positioning error during the operation of the lead screw feeding system are measured using the experimental platform. By analyzing the structure of the lead screw feeding system and combining the thermal deformation effects and complexity of each structure, a three-dimensional model of the system is constructed, ensuring the correlation between the model and the lead screw thermal deformation effect, improving the accuracy of the model simulation, and providing a more likely source of simulation data for subsequent thermal error compensation of the lead screw feeding system. By performing transient temperature and structural coupling field analysis on the lead screw feed system based on a 3D model, the correlation between the lead screw pretension and the thermal deformation under thermal steady state was determined. Based on this correlation, a quantitative mapping model of lead screw temperature and thermal deformation was constructed. Thermal error compensation was then performed on the lead screw based on this quantitative mapping model. The finite element method (FEM) simulation technology was innovatively applied to accurately solve the transient thermo-mechanical coupling field distribution of the lead screw pretension feed system during operation. The thermal deformation of the fixed lead screw shafts at both ends under pretension under time was quantitatively analyzed, providing crucial data support for understanding its complex thermal deformation behavior. By using the quantitative mapping model of lead screw temperature and thermal deformation to compensate for thermal errors during the operation of the lead screw feed system, the system can accurately predict and effectively compensate for the temperature distribution and thermal error distribution during the approach to and after reaching thermal steady state, thereby improving the accuracy of the lead screw feed system. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 A schematic flowchart of a lead screw thermal error compensation method provided in an embodiment of the present invention; Figure 2 A flowchart illustrating a three-dimensional model construction method provided in an embodiment of the present invention; Figure 3 A flowchart illustrating a method for determining association relationships provided in an embodiment of the present invention; Figure 4 A flowchart illustrating a method for determining thermal boundary conditions provided in an embodiment of the present invention; Figure 5A flowchart illustrating a method for determining a quantitative mapping model provided in an embodiment of the present invention; Figure 6 A steady-state temperature distribution diagram with a pre-stretch amount of 0 mm provided for an embodiment of the present invention; Figure 7 A steady-state temperature distribution with a pre-stretch amount of 0.01 mm is provided for an embodiment of the present invention; Figure 8 A steady-state temperature distribution with a pre-stretch amount of 0.02 mm is provided for an embodiment of the present invention; Figure 9 A steady-state temperature distribution with a pre-stretch amount of 0.03 mm is provided for an embodiment of the present invention; Figure 10 A steady-state temperature distribution with a pre-stretch amount of 0.04 mm is provided for an embodiment of the present invention; Figure 11 A temperature curve and a heat deformation curve with a pre-stretch amount of 0 mm are provided for embodiments of the present invention. Figure 12 A temperature curve and a heat distortion curve with a pre-stretch amount of 0.01 mm are provided for embodiments of the present invention. Figure 13 A temperature curve and a heat distortion curve with a pre-stretch amount of 0.02 mm are provided for embodiments of the present invention. Figure 14 A temperature curve and a heat distortion curve with a pre-stretch amount of 0.03 mm are provided for embodiments of the present invention. Figure 15 A temperature curve and a heat distortion curve with a pre-stretch amount of 0.04 mm are provided for embodiments of the present invention. Figure 16 This is a schematic diagram illustrating a specific process for lead screw thermal compensation according to an embodiment of the present invention; Figure 17 This is a schematic diagram of the structure of a lead screw thermal error compensation device provided in an embodiment of the present invention; Figure 18 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which constitute a part of the present invention and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0020] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0021] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0022] A specific embodiment of the present invention, such as Figure 1 As shown, a method for compensating for thermal errors in a lead screw is disclosed, applicable to a lead screw feed system with both ends fixed, comprising: S101, based on a preset experimental platform, collect the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature, and construct a three-dimensional model of the lead screw feed system based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure.

[0023] In this embodiment of the invention, the lead screw feed system with fixed ends refers to a system that moves along the lead screw axis through a lead screw control structure, and the two ends of the lead screw are fixedly installed on a machine tool, such as a tool feed system in a machine tool. Because the lead screw generates heat due to friction between components during operation, it causes slight deformation of the lead screw, which in turn affects the accuracy of the lead screw stroke. This embodiment of the invention determines the relationship between the lead screw temperature and thermal deformation by performing three-dimensional simulation of the lead screw feed system, and then constructs a quantitative mapping model to compensate for the thermal error of the lead screw.

[0024] First, an experimental measurement platform was built, and PT100 temperature sensors were placed at key temperature monitoring points (front bearing, rear bearing, and nut) to monitor the temperature changes of the three components during the simulated machining process. Second, a laser interferometer was set up next to the lead screw feed system to measure the positioning errors of multiple positioning points along the lead screw axis at the initial temperature at the start of the simulated machining process, and the positioning errors of the same positioning points at the thermal steady-state temperature at the end of the machining process. To achieve temperature testing of the lead screw feed system under given working conditions and thermal deformation testing of the feed system before and after simulated machining, the test bench included feed system functional components, a temperature testing device, and a thermal deformation (displacement) testing device. The system functional components included a complete lead screw feed system with fixed installation at both ends, commonly used in high-precision machine tools, mainly covering the motor, coupling, lead screw, nut, front bearing, and rear bearing. The motor transmits torque through the coupling, driving the lead screw to rotate, which in turn drives the nut to move linearly. The bearings at both ends are fixedly connected to the bearing seats, thus limiting the axial displacement of the lead screw. The temperature rise of the key heat-generating components of the feed system was measured using a temperature acquisition system. These were selected as the nut, front bearing, and rear bearing. A displacement acquisition system is used to acquire the thermal deformation of various positioning points along the axial direction of the ball screw before and after the simulated machining process, thereby enabling the testing of the thermal characteristics of the feed system and verifying the accuracy of the temperature-structure coupling simulation model of the feed system. A laser interferometer is selected to measure the positioning error of the ball screw pair. The laser interferometer, in conjunction with optical lenses such as refracting mirrors and reflecting mirrors, can be used to measure various performance parameters of precision equipment, such as linear position, speed, angle, flatness, straightness, parallelism, and perpendicularity. It can also be used for calibration of precision machine tools or measuring instruments. In this measurement system, the main function used is the measurement of the positioning error of the ball screw shaft. The built-in software allows for setting the measurement points, measurement intervals, and data acquisition time, as well as completing the data saving and analysis. Further analysis of the acquired data allows for the acquisition of the thermal deformation of multiple positioning points along the axial direction of the ball screw required for the experiment. Because the thermal deformation effects of various structures in the lead screw feed system differ, some structures are not highly sensitive to temperature and may not deform with temperature changes, while others are highly sensitive to temperature and deform significantly with temperature changes. Furthermore, the complexity of each structure varies. Therefore, the structure of the lead screw feed system can be appropriately simplified to construct a simpler 3D model, facilitating model construction without affecting subsequent simulation accuracy. For example, structures with low temperature sensitivity are simplified as much as possible, while structures with high temperature sensitivity need to retain their original form as much as possible. The simplification of each structure in the 3D model and the specific construction process of the 3D model will be described in detail later in this invention.

[0025] Furthermore, performance testing was conducted on the ball screw assembly. The brand-new ball screw assembly was tested in a laboratory using specialized testing equipment for temperature rise, stroke error, and other related tests. The test data was compared with the data provided by the manufacturer to ensure the test sample was in good condition. The operation of the laser interferometer was checked, and the temperature sensor was calibrated to ensure the data accuracy met the test requirements. The ball screw assembly was installed and pre-stretched to determine its operating speed and mode. A break-in test was performed on the feed system of the screw under test. The layout of the test system was determined based on the specific working conditions and break-in status to improve the speed of relevant performance measurements of the ball screw assembly during the test. This embodiment of the invention uses a nut rapid traverse speed of 120 mm / s and a working stroke of 400 mm. The test system layout was determined based on this condition. During the break-in process of the ball screw assembly, the laser interferometer needs to determine the location of the acquisition positioning points to facilitate subsequent formal data acquisition. To obtain the overall thermal deformation of the effective stroke segment of the ball screw assembly, positioning points were taken throughout the entire stroke. When selecting positioning points, the ball screw was divided into 10mm segments, resulting in 41 positioning points. During the running-in process, temperature sensors were used to monitor the temperature rise at various points in the screw feed system. The main temperature rise areas were the nut and the front and rear bearings, consistent with the sensor placement areas selected based on previous literature. After the running-in was completed, the motor output power was stopped, the nut was returned to its initial position, and the sensors were arranged after the system cooled down. Temperature measurement required two probe-type temperature sensors, installed by drilling mating holes in the bearing seats at both ends, and one patch-type temperature sensor, attached to the nut. The laser interferometer was placed next to the machine tool. The formal test began, with the nut movement time set to 8550 seconds, and the temperature data of the three components measured every 150 seconds. The positioning error of the 41 axial positioning points of the entire screw was measured using the laser interferometer before and after the nut movement began. If no abnormal data was generated during the test, the ball screw system was detached from the worktable after reaching thermal equilibrium; if abnormal data was generated during the test, fault analysis was performed, the problem was resolved, and the test was restarted. The obtained temperature data was matched with time, and the temperature change curves of the three components were obtained, which were used as the data source for the thermal boundary conditions of the subsequent simulation. The positioning errors of the lead screw axial multi-positioning points before and after the nut movement were collected and exported. Two positioning error curves were established with the theoretical position of the lead screw in the axial direction as the abscissa and the corresponding positioning error as the ordinate, which were used to verify the effectiveness of the thermal deformation output results of the subsequent simulation model.

[0026] S102, based on the three-dimensional model, the transient temperature and structural coupled field analysis of the lead screw feed system is performed to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state.

[0027] In this embodiment of the invention, after constructing a three-dimensional model of the lead screw feed system, the operation process of the lead screw feed system is simulated based on the three-dimensional model. Transient temperature and structural coupling field analysis of the lead screw are performed to determine the correlation between the lead screw pre-tension and the thermal deformation of the lead screw under thermal steady state. The transient temperature of the lead screw refers to the instantaneous temperature at various temperature measurement points during the operation of the lead screw, and the structural coupling field refers to the coupled deformation between various structures of the lead screw feed system under the influence of temperature. The specific simulation process will be described in detail later in this invention.

[0028] S103, a quantitative mapping model between the lead screw temperature and the lead screw thermal deformation is constructed based on the correlation, and thermal error compensation of the lead screw is performed based on the quantitative mapping model.

[0029] In this embodiment of the invention, based on the simulation data obtained in the foregoing embodiments, a quantitative mapping model between the lead screw temperature and the lead screw thermal deformation is constructed. This model can reflect the deformation of various parts of the lead screw at different temperatures. Based on this quantitative mapping model, thermal error compensation can be performed on the lead screw according to the lead screw temperature during actual operation.

[0030] The lead screw thermal error compensation method provided by this invention constructs a three-dimensional model of the lead screw feed system based on the thermal deformation effect and complexity of each structure. By analyzing the structure of the lead screw feed system and combining the thermal deformation effect and complexity of each structure, the three-dimensional model of the lead screw feed system is constructed, ensuring the correlation between the model and the thermal deformation effect of the lead screw, improving the accuracy of the model simulation, and providing a more likely source of simulation data for subsequent thermal error compensation of the lead screw feed system. By performing transient temperature and structural coupling field analysis on the lead screw feed system based on a 3D model, the correlation between the lead screw pretension and the thermal deformation under thermal steady state was determined. Based on this correlation, a quantitative mapping model between the lead screw temperature and thermal deformation was constructed. Thermal error compensation was then performed on the lead screw based on this quantitative mapping model. The finite element simulation technology was innovatively applied to accurately solve the transient thermo-mechanical coupling field distribution of the lead screw pretension feed system during operation, providing crucial data support for understanding its complex thermal deformation behavior. The quantitative mapping model between the lead screw temperature and thermal deformation was used to perform thermal error compensation during the operation of the lead screw feed system, enabling accurate prediction and effective compensation of the temperature and thermal error distribution during the approach to and after reaching thermal steady state, thus improving the accuracy of the lead screw feed system.

[0031] In some possible embodiments of the present invention, such as Figure 2 As shown, a three-dimensional model of the screw feed system is constructed based on the thermal deformation effect and complexity of each structure, including: S201, Based on the degree of thermal deformation of each structure in the lead screw feed system, the degree of influence on the thermal deformation of the lead screw, and the complexity of each structure, a simplified model of each structure is determined; S202. Based on the installation scheme and connection relationship of each structure in the lead screw feed system, the simplified models of each structure are assembled to construct a three-dimensional model of the lead screw feed system.

[0032] In this embodiment of the invention, the main components of the lead screw feed system include a motor, bearing housing, front bearing, rear bearing, lead screw shaft, and lead screw nut. The lead screw shaft is fixed at both ends. When the system is working, the motor drives the lead screw shaft to rotate, and the rotational motion is converted into the linear motion of the nut through the ball bearing assembly, thereby pushing the slide to complete the axial feed. The influence of the motor heat transferred to the lead screw through the coupling is negligible. To reduce the complexity of the model and the difficulty of solution convergence, the motor, coupling, and other components are omitted in the modeling process.

[0033] Furthermore, the small features such as the screw shaft threads and chamfers, as well as the complex assembly relationships in actual components, increase the difficulty of mesh generation and computational burden, while having a limited impact on the overall thermal deformation simulation results. To improve computational efficiency and facilitate simulation operation, the screw structure is simplified while ensuring the reliability of the results. Bearings in the ball screw system generate relatively low heat, are fixed in position, and are not the primary heat source; therefore, the front and rear bearings are simplified as fixed heat sources located at both ends of the screw shaft. To facilitate the application of loads and constraints, their geometry is simplified to hollow cylinders, rigidly connected to the corresponding positions on the screw shaft. The main temperature rise of the screw shaft originates from the frictional heat generated between the balls and the screw raceway. Given that the balls are located within the helical grooves of the screw shaft and nut, in the simulation, the frictional heat generated by the balls and nut is equivalent to a moving heat source moving along the screw shaft. The length of this heat source is the same as the length of the nut, and its position dynamically changes as the nut moves. Therefore, the ball bearing entity is omitted during modeling, and the nut is simplified to this moving heat source; the threaded grooves, chamfers, and other subtle features on the lead screw shaft are ignored, and it is simplified to a smooth cylinder for analysis; the final finite element model consists of three parts: the lead screw shaft, the moving heat source representing the nut, and the hollow cylindrical support representing the front / rear bearings. Furthermore, the material of the core components of the lead screw feed system must possess high wear resistance, excellent machinability, and low thermal deformation characteristics. Material properties can be defined according to actual conditions. After assigning material properties, the finite element model of the lead screw feed system is meshed, with the specific parameters as follows: (1) Lead screw shaft: The global mesh size is 3mm, and C3D4T (four-node linear thermally coupled tetrahedron) element is used, with a total of 165043 elements.

[0034] (2) Simplified support components for front / rear bearings: The global mesh size is 2mm, using C3D8T (eight-node linear thermally coupled hexahedron) elements, with a total of approximately 34,200 elements.

[0035] (3) The moving heat source representing the nut: The global mesh size is 3mm, using C3D8T (eight-node linear thermally coupled hexahedron) elements, with a total of 11880 elements.

[0036] The embodiments of the present invention simplify and model the structure of the lead screw feed system, thereby reducing the computational load of the model while ensuring the simulation accuracy of the model.

[0037] In some possible embodiments of the present invention, such as Figure 3 As shown, a transient temperature-structure coupled field analysis is performed on the lead screw feed system based on a three-dimensional model to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state, including: S301, define the thermal boundary conditions of the lead screw feed system based on the real-time temperature, and define the mechanical boundary conditions of the lead screw feed system based on the three-dimensional model; S302, based on thermal and mechanical boundary conditions, simulates the pre-tensioning, processing, and cooling of the lead screw feed system, and extracts the relationship between the transient temperature distribution field and the transient thermal deformation distribution field along the lead screw axis with time during the simulation, thus obtaining the correlation between the lead screw pre-tensioning amount and the thermal deformation amount under the lead screw thermal steady state.

[0038] In this embodiment of the invention, the thermal boundary conditions of the lead screw feed system mainly include three parts: the temperature field of key feature points, convective heat transfer on the external surface, and contact heat conduction between components. The selected key feature points of the lead screw feed system include the front bearing, rear bearing, nut, and the surface of the meshing lead screw shaft region that contacts the moving nut. The criterion is that these regions are the heat-generating areas of the lead screw feed system. The application of the temperature field is divided into two types: fixed temperature field at region nodes and variable temperature field at region nodes, and the application methods differ. For the front bearing, rear bearing, and nut, since the region nodes for applying the temperature field are fixed, it can be completed entirely within the ABAQUS CAE interface; only the corresponding model surface region needs to be selected and input. However, the application of the temperature field to the meshing region of the lead screw's outer surface that the moving nut contacts requires the use of a user-defined FORTRAN subroutine via the ABAQUS external interface, because the lead screw-ball-nut meshing area changes continuously in space over time, belonging to a variable temperature field at region nodes. For the boundary load definition of the fixed temperature field at three nodes, the temperature of three temperature characteristic points (front bearing, rear bearing, and nut) can be measured using a PT100 temperature sensor as described in S3. The data can be summarized to obtain three temperature curves. These three temperature curves are discretized, and the data is input into the corresponding temperature numerical conditions of the simulation model at regular time intervals. For the temperature field applied to the meshing area of ​​the lead screw outer surface in contact with the moving nut, considering the temperature continuity mechanism, the nut temperature is assumed to be consistent with the corresponding lead screw meshing area temperature. The experimentally measured nut temperature curve is fitted using a polynomial function (the highest degree of the polynomial is 6), and the coefficients of each term (a total of 7 coefficients) are extracted. A FORTRAN subroutine is written and linked to the ABAQUS external interface. During the ABAQUS solution calculation, this lead screw shaft temperature subroutine is automatically called in each analysis substep to define the temperature field for the corresponding area. When performing transient temperature and structural coupled field analysis on a lead screw feed system based on a model, the temperature field results obtained from the thermal analysis are transmitted as thermal loads to the mechanical analysis in real time. Simultaneously, the physical field results obtained from the mechanical analysis update the geometric configuration in real time, thus influencing the thermal boundary conditions and thermal field distribution. Both processes iteratively solve for each other within each increment step. Throughout the analysis time history, the system couples the solutions of the heat conduction equation and the structural mechanical equilibrium equations in real time, with the analysis step size dynamically adjusted based on solution convergence, accuracy requirements, and the time scale of the physical process.

[0039] Furthermore, thermal analysis aims to determine the transient temperature field distribution and heat flux density distribution of a structure under given thermal boundary conditions. There are three basic modes of heat transfer in engineering: conduction, convection, and radiation. The governing equations for the thermal field are:

[0040] Where ρ represents the material density, c represents the material specific heat capacity, k represents the material thermal conductivity, Q is the internal heat source, T is the temperature, and t is the time.

[0041] Mechanical analysis specifically refers to transient dynamic analysis, used to solve the dynamic response of a structure under the combined action of time-varying mechanical and thermal loads. Its governing equations are:

[0042] Where [K] represents a constant and continuous stiffness matrix, [M] is a continuous mass matrix, and [C] is a continuous damping matrix. （t）} represents the displacement vector, {F （t）} represents a time-varying load.

[0043] Furthermore, the entire transient temperature-structure coupling analysis process is divided into three key analysis steps, each corresponding to a working stage with clear physical meaning: (1) Step 1: Pre-stretching application stage Objective: To simulate the initial application process of the lead screw pretension.

[0044] Mechanical boundary conditions: Bind the front and rear bearings to the ball screw shoulder, fix the three degrees of freedom of the front bearing, and apply displacement constraints to the rear bearing so that the ball screw reaches the required pre-tension.

[0045] Thermal boundary conditions: No motion-related heat sources (nut friction heat, bearing heat) are activated in this stage, and basic heat dissipation such as environmental convection is not considered.

[0046] Time setting: This analysis step is independent of subsequent machining movements and is in the State1 state of the feed movement in terms of time. It is used to establish the initial prestress state.

[0047] (2) Step 2: Processing Operation Stage Objective: To simulate the process of a lead screw feed system performing machining tasks under fixed constraints at both ends.

[0048] Mechanical boundary conditions: Activate fixed constraints at both ends: Apply three-degree-of-freedom fixed constraints to the circumferential surface of the rear bearing to form a complete fixed boundary at both ends. Drive nut motion: Apply axial displacement boundary conditions to the moving heat source model representing the nut, causing it to perform reciprocating periodic feed motion according to the State2 motion state parameters defined in S3.2.

[0049] Thermal boundary conditions: Activate all heat sources, apply the calculated nut-screw frictional heat power to the moving heat source model, apply the calculated fixed bearing heat source power to the front and rear bearings, and apply the defined convection heat transfer and contact heat conduction boundary conditions.

[0050] Time setting: This analysis step covers the total time history corresponding to the State2 motion state in the feed motion simulation, simulating the thermo-mechanical coupling dynamic behavior during the processing.

[0051] (3) Step 3: Cooling stage Objective: To simulate the natural cooling process of the lead screw system after the machining task is completed and the system is in a stopped state.

[0052] Mechanical boundary conditions: Maintain fixed constraints at both ends. Fixed nut position: Constrain the moving heat source model representing the nut at the initial position of the lead screw shaft and remove its axial displacement drive.

[0053] Thermal boundary conditions: Disable all internal frictional heat sources. Maintain convective heat transfer and contact heat conduction boundary conditions, allowing the system to dissipate heat to the environment.

[0054] Time setting: This analysis step covers the total time history corresponding to the State3 motion state in the feed motion simulation, and is used to study the cooling characteristics of the system after it approaches thermal steady state.

[0055] By extracting and analyzing the simulation data, the correlation between the pre-tension of the lead screw and the thermal deformation of the lead screw under thermal steady state can be obtained.

[0056] In some possible embodiments of the present invention, such as Figure 4 As shown, the thermal boundary conditions of the lead screw feed system are defined based on a three-dimensional model, including: S401, Determine the temperature of key characteristic points of the lead screw feed system based on the real-time temperature; S402, Calculate the convective heat transfer on the external surface of the screw feed system based on the thermal convection coefficient between the screw feed system and the air; S403, Calculate the heat conduction between components of the lead screw feed system based on the heat conduction principle of the internal structure of the lead screw feed system; S404 constructs the thermodynamic boundary of the screw feed system based on heat generated by internal friction, heat transfer from external surface convection, and heat conduction between components.

[0057] In this embodiment of the invention, the heat transfer methods of the feeding system are divided into three categories: heat conduction, heat convection, and heat radiation. Heat radiation has a negligible impact on the thermal characteristics of the ball screw pair and is therefore not considered. Considering that the ambient heat source temperature is lower than the ball screw pair mechanism temperature under non-extreme operating conditions, the heat loss process during the heat transfer of the ball screw pair is concentrated in the heat convection stage. The heat convection flow rate at the contact surface between the ball screw pair and the environment can be expressed by the following formula:

[0058] in, This is for the convective heat on the surface of the ball screw assembly; The heat transfer coefficient of the ball screw assembly material; For the convective contact surface area of ​​the nut or lead screw; Temperature variation of nut or lead screw.

[0059] Where the convective thermal conductivity It can be expressed by the following formula:

[0060] in, For the thermal conductivity of air, The diameter of the ball screw pair The Nurse coefficient can be obtained from the following formula:

[0061] in, For Reynolds coefficient, is Planck's coefficient.

[0062] Reynolds coefficient It can be expressed by the following formula:

[0063] in, For the velocity of the ambient fluid, The kinematic viscosity of the environmental fluid.

[0064] Prandt coefficient It can be expressed by the following formula:

[0065] in, For the specific heat capacity of the ambient fluid, This is the dynamic viscosity coefficient.

[0066] Combining the above equations, we get:

[0067] In actual operation, ball screw pairs in thermal equilibrium experience uneven heating due to the influence of the moving heat source of the nut, internal heat conduction, and external heat convection, resulting in temperature differences between different parts. A heat transfer analysis of ball screw pairs in thermal equilibrium was conducted. Since the running-in stroke of the ball screw pair is not consistent with the total length of the screw, positions outside the running-in stroke are not directly affected by the moving heat source of the nut.

[0068] Furthermore, regarding convective heat transfer between the stator and rotor, the fluid in the air gap between the stator and rotor is generally considered to be in a turbulent state. The formula for calculating the fluid velocity in the air gap between the stator and rotor is as follows:

[0069] Where V is the airflow rate. d 0 and d r These are the inner surface diameters of the stator and rotor, respectively; ω r ω is the rotor angular velocity.

[0070] The convective heat transfer coefficient at the bearing was calculated in this paper based on the method proposed by Bossmanns. The calculation formula is as follows:

[0071] In the formula: c 0、 c 1 and c 2 is a constant, which is taken as 9.7, 5.33, and 0.8 respectively.

[0072] The average velocity of the gas inside the bearing is calculated using the following formula:

[0073] in, Δh This refers to the clearance between the inner and outer rings of the bearing and the cage.

[0074] Because the heat sources along the axial direction of the lead screw are distributed in multiple areas such as bearings and nuts, temperature differences will occur in various places inside the lead screw during the movement of the feed system, and heat conduction will also occur between components. The overall heat transfer coefficient of the moving pair surfaces determines the relationship between the transferred heat and the surface temperature difference:

[0075] The heat transfer coefficient between two closely fitting contact surfaces h c The calculation is as follows:

[0076] In the formula, A This represents the total area of ​​the contact region; A c This refers to the actual contact area of ​​the contact region; A v The contact area where gaps exist in the contact region; k 1 represents the thermal conductivity of the material on the main surface; k 2 represents the thermal conductivity of the material on the surface; k f It is the equivalent thermal conductivity of the region with voids; L g This represents the gap distance.

[0077] Finally, based on the actual working environment of the lead screw feed system, the preloaded temperature field value is set to 19℃, and the ambient temperature of the aforementioned air convection heat transfer coefficient is 19℃. Substituting the known parameters, the calculated thermal boundary conditions of the lead screw feed system are summarized in the following table: Table 3: Thermal Boundary Conditions of the Lead Screw Feed System

[0078] In this embodiment of the invention, the thermal boundary of the lead screw feed system is set to ensure the accuracy of subsequent simulation results.

[0079] In some possible embodiments of the present invention, the mechanical boundary conditions include the constant feed rate of the nut on the lead screw, the effective travel range of the nut on the lead screw, and the duration of the lead screw movement.

[0080] In this embodiment of the invention, within the transient temperature-displacement direct coupling analysis framework, mechanical boundary conditions and loads can be defined simultaneously with the application of thermal boundary conditions. The mechanical boundary conditions involved in this analysis mainly include two parts: feed motion simulation and the application of lead screw preload.

[0081] To accurately simulate the actual working motion of the nut on the leadscrew shaft (corresponding to the feed of the slide), this analysis defines three independent motion states (State1-State3) for the nut. These three motion states have clear technological meanings, representing the leadscrew pre-tensioning stage, the workpiece machining stage, and the machine tool cooling stage, respectively. The motion characteristics of the nut are defined by the following kinematic parameters: Movement speed: The constant feed rate (mm / min) of the nut during this stage.

[0082] Range of motion: The effective travel range (mm) of the nut on the lead screw shaft during this stage.

[0083] Movement time: The duration (s) of this movement phase.

[0084] In theory, the preload of a ball screw assembly can be selected within a certain range. However, in practical engineering applications, the upper limit of the preload is subject to key constraints: Bearing load capacity limitation: Excessive preload can significantly increase the additional axial load on the bearing (especially the front bearing), potentially exceeding its rated static load or causing premature fatigue failure.

[0085] Assembly feasibility limitations: With fixed installation at both ends, excessive pre-tension will lead to excessively high initial assembly stress of the lead screw shaft, increasing assembly difficulty and the risk of deformation of structural components (such as bearing housings).

[0086] In this embodiment of the invention, the mechanical boundaries of the lead screw feed system are set to ensure the accuracy of subsequent simulation results.

[0087] In some possible embodiments of the present invention, such as Figure 5 As shown, a quantitative mapping model between screw temperature and screw thermal deformation is constructed based on the correlation, including: S501 collects the temperature of multiple temperature points along the screw axis and the corresponding thermal deformation of multiple screws. S502 uses the temperatures at multiple temperature points and the corresponding thermal deformation amounts as training data to train a preset multiple linear regression model, thereby obtaining a quantitative mapping model between the screw temperature and the screw thermal deformation amount.

[0088] In this embodiment of the invention, based on the three-dimensional model designed in the foregoing embodiments, the screw feed system is simulated. To study the influence of pre-tension on thermal deformation, the following parametric simulation sequence is executed: (1) Case 1: Set the pre-stretching amount to 0 mm, perform a complete transient temperature-displacement coupling analysis (including Step 1-Step 3), and obtain the simulation result dataset Result1.

[0089] (2) Case 2: Set the pre-stretch amount to 0.01 mm, keep all other boundary conditions and analysis settings consistent with Case 1, execute the analysis, and obtain the result dataset Result2.

[0090] (3) Case 3: Set the pre-stretch amount to 0.02 mm, perform the analysis, and obtain the result dataset Result3.

[0091] (4) Case 4: Set the pre-stretch amount to 0.03 mm, perform the analysis, and obtain the result dataset Result4.

[0092] (5) Case 5: Set the pre-stretch amount to 0.04 mm, perform the analysis, and obtain the result dataset Result5.

[0093] Through this parametric analysis, such as Figures 6 to 10 As shown, complete thermo-mechanical response data of the lead screw feed system during the machining operation and cooling stages were obtained under five different pre-stretching amounts (δpre=0, 0.01, 0.02, 0.03, 0.04 mm).

[0094] Furthermore, such as Figures 11 to 15 As shown, the temperature and axial thermal deformation at several key monitoring points along the axial stroke of the lead screw during the extraction and cooling stages change with time.

[0095] Analysis of the temperature-time and axial thermal deformation-time curves revealed that, in the later stages of processing, both the temperature and axial thermal deformation at each monitoring point tended to stabilize, with the rate of change approaching zero. This observation indicates that the system reached thermal steady state at the end of the processing stage.

[0096] Temperature is the dominant factor driving the thermal deformation of the leadscrew. To quantitatively analyze the influence of different pretension amounts on the steady-state operating temperature of the leadscrew, the steady-state temperature value at the midpoint of the leadscrew's axial stroke at the end of the machining stage (i.e., the thermal steady-state moment) was extracted. The steady-state temperature data at this point under different pretension conditions are summarized in the table below: Table 4: Midpoint Temperature of Lead Screw Stroke After Machining Stage

[0097] Based on a comprehensive analysis of the steady-state temperature at the midpoint of the screw stroke under different pretension amounts and the extracted steady-state temperature field cloud maps corresponding to five different pretension amounts, the following important observations were made: Under different pretension values ​​(δpre=0, 0.01, 0.02, 0.03, 0.04 mm), the overall temperature field distribution of the lead screw feed system when it reaches thermal steady state is highly similar. The steady-state temperature values ​​at key locations (such as the midpoint of the lead screw stroke) differ only slightly, all within 1℃.

[0098] The above results indicate that, within the considered range of pretension variation (Δδpre = 0.04 mm), the different amounts of pretension have no significant impact on the steady-state temperature rise and overall temperature field distribution of the lead screw shaft. The steady-state temperature reached by the system mainly depends on thermal factors such as frictional heat power and heat dissipation conditions, and is essentially independent of the magnitude of the pretension.

[0099] The effect of pretension on the thermally induced axial deformation of the leadscrew shaft is considered. To quantitatively characterize this effect, the steady-state axial thermal deformation at five key points along the leadscrew axis at the end of the machining stage (thermal steady-state moment) is extracted. The points are defined as follows: P1: Travel coordinate 0mm; P2: Travel coordinate 80mm; P3: Travel coordinate 160mm (travel midpoint); P4: Travel coordinate 240mm; P5: Travel coordinate 320mm.

[0100] The table below summarizes the steady-state axial thermal deformation data (unit: mm) at the five locations (P1-P5) under five different pre-tension conditions:

[0101] By comparing the thermal deformation curves of the lead screw shaft at five monitoring points (P1-P5) under five different pretension conditions with the data in the table above, it can be observed that the steady-state axial thermal deformation is relatively small for different pretension values, and the deformation deviation at each location is basically controlled within the range of 0.001–0.003 mm.

[0102] The above analysis shows that when pretension is applied to a ball screw assembly fixed at both ends, the change in the value of the pretension directly affects the stress state of the bearing and connecting components (such as the additional load on the bearing and contact pressure). However, due to the strong constraint characteristics of the system (high-rigidity bearing) and the buffering effect of the assembly clearance, the difference in pretension has no significant effect on the macroscopic thermal deformation of the screw shaft under thermal equilibrium (the observation deviation is only 0.001–0.003 mm).

[0103] Furthermore, such as Figure 16 As shown, thermal error compensation for the lead screw is performed based on a quantitative mapping model, including: S1601, acquire the real-time temperature of each temperature point along the screw axis and the real-time position of the nut along the screw axis in the screw feed system; S1602, the thermal error compensation displacement of the screw feed system is determined based on the quantitative mapping model, real-time temperature and real-time position; S1603, displacement compensation for the lead screw feed system based on thermal error compensation displacement.

[0104] In this embodiment of the invention, a real-time thermal error compensation method suitable for a lead screw feed system is constructed based on temperature field and thermal deformation field data obtained from simulation. A multiple linear regression (MLR) algorithm is used to establish a quantitative mapping relationship between multiple independent variables (temperature monitoring points) and the dependent variable (thermal deformation) through statistical analysis of sample data. Compared to a univariate model, MLR significantly improves the model's ability to represent complex thermal deformation behavior by incorporating multiple temperature variables, ensuring that the compensation model possesses both high accuracy and strong robustness. For the commonly used pre-stretch (0.03mm) working condition, a quantitative relationship model is constructed between five preset temperature monitoring points (positions corresponding to lead screw travel coordinates of 0mm, 80mm, 160mm, 240mm, and 320mm) and the axial thermal deformation of the lead screw. The mathematical expression of the model is:

[0105] Where Y is the thermal error; X is the temperature; It is a coefficient; It's the residuals; we use multiple linear regression modeling to find suitable coefficients. And ensure that the residual is minimized at each data point relative to the objective function value.

[0106] Transient temperature-structure coupling simulation results based on a pre-tension of 0.03 mm: (1) Temperature data acquisition: Three values ​​of different temperature fields during the machining process were extracted from three key characteristic locations of the lead screw system (front bearing, rear bearing, and nut), and denoted as T. b1 T b2 T n .

[0107] (2) Simultaneous extraction of slope k and intercept b of deformation data: Obtain the slope and intercept coefficients corresponding to the thermally induced axial deformation fields at different temperatures in (1), denoted as k and b.

[0108] Using the above multiple sets of temperature-deformation data as training samples, a matrix-form multiple linear regression model is constructed:

[0109] After model performance validation, the regression model's coefficient of determination was... =0.99, indicating a good fit.

[0110] The obtained relationship between error and temperature can be input into the CNC system of the machine tool, and the temperature error generated by the lead screw shaft can be compensated by combining interpolation and the actual stroke coordinates of the lead screw and nut during operation.

[0111] The obtained thermal error coefficient and its relationship with temperature can be input into the machine tool CNC system, and combined with the feedback of the theoretical stroke coordinate y during the working of the lead screw and nut, the thermal deformation error ΔY generated by the lead screw shaft can be compensated.

[0112] The formula is as follows, where y is the theoretical stroke position of the lead screw nut, and ΔY is the real-time axial thermal error compensation displacement value required by the CNC system.

[0113]

[0114] CNC machine tools can compensate values ΔY Theoretical feed rate superimposed on the tool's feed axis direction a Above, the final actual feed rate a p It should be:

[0115] By compensating for the feed rate, the machining accuracy of machine tools can be improved.

[0116] The thermal error simulation calculation provided by this invention fully considers the unique two-end fixed installation method and pre-tensioning process of the high-precision lead screw pre-tensioning feed system, and effectively incorporates the dynamic influence of nut movement on the thermal deformation of the lead screw. The simulation test process is relatively simple to design, and the required data source is easy to measure or calculate. Unlike existing technologies that are mostly based on the "one-end fixed, one-end supported" installation method and generally do not consider the interaction between the pre-tension amount and the two-end fixed installation method, this invention significantly improves the accuracy of the simulation model in representing the complexity of actual machining scenarios. In addition, existing methods usually ignore the differences in thermal deformation at different stroke positions on the lead screw shaft, resulting in an inability to fully describe the overall thermal deformation state of the feed system, while this invention effectively overcomes this limitation. Based on the temperature-displacement data obtained from transient thermo-mechanical coupling field simulation, the constructed multivariate linear regression model has high accuracy and strong robustness. In actual machining applications, this model uses temperature data obtained from a multi-temperature sensor array to accurately map the axial thermal error at different stroke positions of the lead screw, thereby providing a reliable real-time compensation data source for the CNC system. By combining interpolation algorithms and real-time travel coordinates of the nut's movement, the overall compensation process is streamlined. This linear model boasts high computational efficiency, and subsequent parameter adjustments can be manually performed directly within the CNC system, facilitating coordination with equipment commissioning personnel.

[0117] To better implement the lead screw thermal error compensation method in the embodiments of the present invention, based on the lead screw thermal error compensation method, correspondingly, as follows: Figure 17 As shown, this embodiment of the invention also provides a lead screw thermal error compensation device, the lead screw thermal error compensation device 1700 comprising: The model building module 1701 is used to collect the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature based on a preset experimental platform, and to build a three-dimensional model of the lead screw feed system based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure. The correlation determination module 1702 is used to perform transient temperature and structural coupling field analysis on the screw feed system based on a three-dimensional model, and to determine the correlation between the screw pretension and the screw thermal deformation under thermal steady state. The displacement error compensation module 1703 is used to construct a quantitative mapping model between the screw temperature and the screw thermal deformation based on the correlation relationship, and to perform thermal error compensation on the screw based on the quantitative mapping model.

[0118] The lead screw thermal error compensation device 1700 provided in the above embodiments can realize the technical solution described in the above lead screw thermal error compensation method embodiments. The specific implementation principle of each module or unit can be found in the corresponding content in the above lead screw thermal error compensation method embodiments, and will not be repeated here.

[0119] like Figure 18 As shown, the present invention also provides an electronic device 1800. The electronic device 1800 includes a processor 1801, a memory 1802, and a display 1803. Figure 18 Only some components of the electronic device 1800 are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0120] In some embodiments, processor 1801 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in memory 1802 or process data, such as the lead screw thermal error compensation method of the present invention.

[0121] In some embodiments, processor 1801 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 1801 may be local or remote. In some embodiments, processor 1801 may be implemented on a cloud platform. In some embodiments, the cloud platform may include a private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, internal cloud, multi-cloud, or any combination thereof.

[0122] In some embodiments, memory 1802 may be an internal storage unit of electronic device 1800, such as a hard disk or memory of electronic device 1800. In other embodiments, memory 1802 may also be an external storage device of electronic device 1800, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on electronic device 1800.

[0123] Furthermore, the memory 1802 may include both internal storage units of the electronic device 1800 and external storage devices. The memory 1802 is used to store application software and various types of data installed on the electronic device 1800.

[0124] In some embodiments, display 1803 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 1803 is used to display information from electronic device 1800 and to display a visual user interface. Components 1801-1803 of electronic device 1800 communicate with each other via a system bus.

[0125] In some embodiments, when the processor 1801 executes the leadscrew thermal error compensation program in the memory 1802, the following steps may be implemented: Based on a pre-set experimental platform, the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature are collected. Based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure, a three-dimensional model of the lead screw feed system is constructed. Based on a three-dimensional model, transient temperature and structural coupled field analysis was performed on the lead screw feed system to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state. A quantitative mapping model between the lead screw temperature and the lead screw thermal deformation is constructed based on the correlation, and thermal error compensation of the lead screw is performed based on the quantitative mapping model.

[0126] It should be understood that when the processor 1801 executes the lead screw thermal error compensation program in the memory 1802, in addition to the functions mentioned above, it can also perform other functions, as can be found in the description of the corresponding method embodiments above.

[0127] Furthermore, this embodiment of the invention does not specifically limit the type of electronic device 1800 mentioned. Electronic device 1800 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the invention, electronic device 1800 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).

[0128] Accordingly, embodiments of the present invention also provide a computer-readable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions of the lead screw thermal error compensation methods provided in the above-described method embodiments.

[0129] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0130] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for compensating for thermal errors in a lead screw, applicable to a lead screw feed system with both ends fixed, characterized in that, include: Based on a pre-set experimental platform, the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature are collected. Based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure, a three-dimensional model of the lead screw feed system is constructed. Based on the real-time temperature and the positioning error, combined with the three-dimensional model, a transient temperature and structural coupled field analysis is performed on the screw feed system to determine the correlation between the screw pretension and the screw thermal deformation under thermal steady state. Based on the aforementioned correlation, a quantitative mapping model is constructed between the lead screw temperature and the lead screw thermal deformation. Thermal error compensation is then performed on the lead screw based on the quantitative mapping model.

2. The lead screw thermal error compensation method according to claim 1, characterized in that, The construction of a three-dimensional model of the lead screw feed system based on the thermal deformation effect and complexity of each structure includes: Based on the degree of thermal deformation of each structure in the lead screw feed system, the degree of influence on the thermal deformation of the lead screw, and the complexity of each structure, a simplified model of each structure is determined. Based on the installation scheme and connection relationship of each structure in the lead screw feed system, the simplified models of each structure are assembled to construct a three-dimensional model of the lead screw feed system.

3. The lead screw thermal error compensation method according to claim 1, characterized in that, The transient temperature and structural coupled field analysis of the lead screw feed system based on the three-dimensional model is used to determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state, including: The thermal boundary conditions of the lead screw feed system are defined based on the real-time temperature, and the mechanical boundary conditions of the lead screw feed system are defined based on the three-dimensional model. Based on the aforementioned thermal and mechanical boundary conditions, the pre-tensioning, processing, and cooling simulations of the lead screw feed system were performed. The relationship between the transient temperature distribution field and the transient thermal deformation distribution field along the lead screw axial direction during the simulation was extracted over time, thus obtaining the correlation between the lead screw pre-tensioning amount and the thermal deformation amount under the lead screw thermal steady state.

4. The lead screw thermal error compensation method according to claim 3, characterized in that, The thermal boundary conditions of the lead screw feed system defined based on the real-time temperature include: The temperature of the key characteristic point of the lead screw feed system is determined based on the real-time temperature. The heat transfer rate of the external surface of the screw feed system is calculated based on the thermal convection coefficient between the screw feed system and the air. The heat conduction between the components of the lead screw feed system is calculated based on the heat conduction principle of the internal structure of the lead screw feed system. The thermodynamic boundary of the screw feed system is constructed based on the temperature of the key feature points, the convective heat transfer on the external surface, and the heat conduction between the components.

5. The lead screw thermal error compensation method according to claim 3, characterized in that, The mechanical boundary conditions include the constant feed rate of the nut on the lead screw, the effective stroke range of the nut on the lead screw, and the duration of the lead screw movement.

6. The lead screw thermal error compensation method according to claim 3, characterized in that, The quantitative mapping model for the relationship between the lead screw temperature and the lead screw thermal deformation is constructed based on the aforementioned correlation, including: Collect the temperature at multiple temperature points along the lead screw axis and the corresponding thermal deformation of multiple lead screws; The temperatures at the multiple temperature points and the corresponding thermal deformations are used as training data to train a preset multiple linear regression model, thereby obtaining a quantitative mapping model between the screw temperature and the screw thermal deformation.

7. The lead screw thermal error compensation method according to claim 6, characterized in that, The thermal error compensation of the lead screw based on the quantitative mapping model includes: The system acquires the real-time temperature of each temperature point along the lead screw axis and the real-time position of the nut along the lead screw axis in the lead screw feed system. The thermal error compensation displacement of the lead screw feed system is determined based on the quantitative mapping model, the real-time temperature, and the real-time position. The lead screw feed system is subjected to displacement compensation based on the thermal error compensation displacement.

8. A lead screw thermal error compensation device, characterized in that, include: The model building module is used to collect the real-time temperature of key temperature points in the lead screw feed system and the positioning error of the lead screw feed system at the real-time temperature based on a preset experimental platform, and to build a three-dimensional model of the lead screw feed system based on the thermal deformation effect of each structure in the lead screw feed system and the complexity of each structure. The correlation determination module is used to perform transient temperature and structural coupling field analysis on the lead screw feed system based on the three-dimensional model, and determine the correlation between the lead screw pretension and the thermal deformation of the lead screw under thermal steady state. The displacement error compensation module is used to construct a quantitative mapping model between the lead screw temperature and the lead screw thermal deformation based on the correlation, and to perform thermal error compensation on the lead screw based on the quantitative mapping model.

9. An electronic device, characterized in that, Including memory and processor, among which, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the lead screw thermal error compensation method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the lead screw thermal error compensation method according to any one of claims 1 to 7.

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