A worm grinding machine spindle thermal error mechanism-data modeling method considering electro-mechanical-thermal coupling effect

Abstract

This invention discloses a data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect. The steps include: 1) establishing the correlation between the thermal expansion deformation of the spindle system and temperature variables; 2) establishing the thermal balance equation of the spindle system and deriving the correlation between the spindle thermal error and the heat absorption of the spindle structure; 3) constructing a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables; 4) constructing a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables; 5) establishing a theoretical model for the thermal error of the spindle system with respect to the electromechanical-thermal variables; 6) converting the solution of the spindle system thermal error model into an optimization problem, and solving it using the HPSO-GA optimization algorithm to obtain the thermal error of the spindle system. This invention can accurately predict the spindle thermal error while revealing the influence of the electromechanical-thermal coupling effect of the spindle system on the thermal error.

Description

Technical Field

[0001] This invention relates to the field of machine tool control technology, specifically a data modeling method for the thermal error mechanism of a worm gear grinding machine spindle that considers the electromechanical-thermal coupling effect. Background Technology

[0002] Factors affecting machine tool machining accuracy mainly include geometric errors, thermal errors, motion errors, and machining errors, with thermal errors accounting for 40% to 70% of the total error. For gear machining tools, such as worm gear grinding machines, the spindle is the most critical functional component, directly affecting gear machining accuracy and efficiency. However, due to the integrated design of the spindle system, and the combined effect of internal and external heat sources, the internal thermal environment of the spindle becomes unstable, resulting in uneven temperature distribution and ultimately thermal deformation of the spindle structure. Therefore, revealing the thermal deformation mechanism of the worm gear grinding machine spindle and establishing an accurate thermal error model are crucial for improving machining accuracy and ensuring accuracy consistency.

[0003] However, due to the unclear electromechanical-thermal coupling mechanism of the worm gear grinding machine spindle system and the unclear laws governing the spindle's thermal characteristics, establishing an accurate spindle thermal error model remains challenging. Traditional thermal error modeling methods mainly fall into two categories: mechanism-based models (black box models) and data-driven models (white box models). The former, based on fundamental theories of thermodynamics and thermoelasticity, can reveal the formation mechanism of spindle thermal errors, but the modeling process is complex, requiring numerous assumptions and simplifications, and exhibits poor robustness. The latter aims to establish a mapping relationship between thermal errors and temperature variables through intelligent algorithms, but obtaining model coefficients is difficult, and the model cannot provide intuitive interpretations or physical meanings. Summary of the Invention

[0004] The purpose of this invention is to provide a data modeling method for the thermal error mechanism of a worm gear grinding machine spindle that considers the electromechanical-thermal coupling effect, including the following steps:

[0005] 1) Analyze the multi-energy coupling characteristics of the spindle system's electromechanical-thermal system, and construct the correlation between the thermal expansion deformation of the spindle system and temperature variables based on thermoelasticity.

[0006] 2) Combining thermodynamic analysis and the law of conservation of energy, establish the thermal balance equation of the main shaft system, and derive the correlation between the thermal error of the main shaft and the heat absorption of the main shaft structure;

[0007] 3) Analyze the heat generation characteristics of the spindle system and construct a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables;

[0008] 4) Analyze the heat dissipation characteristics of the spindle system and construct a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables;

[0009] 5) The thermal balance equation of the spindle system is derived, and a theoretical model of the thermal error of the spindle system with respect to the electromechanical-thermal variables is established;

[0010] 6) Conduct cutting experiments to obtain real-time data on electromechanical-thermal elements, and train the theoretical model of the thermal error of the spindle system with respect to electromechanical-thermal variables to obtain the thermal error model of the spindle system;

[0011] 7) The thermal error model of the spindle system is transformed into an optimization problem, and the HPSO-GA optimization algorithm is used to solve it to obtain the thermal error of the spindle system.

[0012] Furthermore, in step 1), the steps for establishing the correlation between the thermal expansion deformation of the spindle system and temperature variables include:

[0013] 1.1) Simplify the spindle system as a thin-walled cylinder and construct an expression for the thermal expansion deformation at r = b on the spindle shell, namely:

[0014] (1)

[0016] In the formula, u r＝b The coefficient of thermal expansion is represented by r, the radius is represented by a and b, the inner and outer radii of the spindle are represented by a and b respectively, α is the linear expansion coefficient of the spindle material, c1 is a constant, T is the spindle temperature; T a T b These represent the temperatures of the inner and outer diameters of the spindle, respectively.

[0017] 1.2) Set all variables except temperature as constants, simplify the expression for thermal expansion deformation at r=b on the spindle housing, and establish the correlation between the thermal expansion deformation of the spindle system and the temperature variable, i.e.:

[0018] δ spindle =u r＝b =k1(T b -T a )+c1 (2)

[0019] In the formula, k1 represents the coefficient; δ spindle This is the spindle thermal error.

[0020] Furthermore, in step 2), the thermal balance equation of the spindle system is as follows:

[0021]

[0022] In the formula, Q represents the heat absorbed by the spindle structure. accum Heat accumulation in the spindle system; Q gen and Q dis These represent the heat generated and heat dissipated by the spindle system, respectively. and These represent the heat generated by the spindle system bearings and the heat generated by the motor, respectively. and These represent the heat dissipation of the spindle system through heat conduction, heat convection, and heat radiation, respectively.

[0023] Among them, the spindle system absorbs heat. As shown below:

[0024]

[0025] In the formula, m, c, ρ and l0 represent the main shaft structure mass, specific heat capacity, average density and length, respectively; k2 and k3 represent coefficients; c2 represents a constant; ΔT is the temperature difference; d represents the bearing diameter; and T0 represents the initial temperature of the external environment.

[0026] Furthermore, in step 2), the correlation between spindle thermal error and spindle structural heat absorption is as follows:

[0027]

[0028] In the formula, k2 and k3 represent coefficients.

[0029] Furthermore, in step 3), the steps for constructing a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables include:

[0030] 3.1) Calculate the heat generated by the spindle bearing, i.e.:

[0031]

[0032]

[0033] In the formula, M and n represent the total bearing friction torque and rotational speed, respectively; M0 and M1 represent the friction torque caused by the bearing lubricant viscosity and the friction torque caused by the bearing load, respectively; f0 and f1 are constants; γ is the kinematic viscosity of the lubricant; and d m This represents the average bearing diameter, and F1 is the equivalent load. This indicates that the spindle system bearings generate heat.

[0034] 3.2) Combining formulas (6) and (7), we get:

[0035]

[0036] In the formula, X0 and Y0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A These represent the radial load and axial load of the bearing, respectively.

[0037] 3.3) Simplifying formula (8), we get:

[0038]

[0039] In the formula, k4 and k5 represent coefficients; c3 represents a constant.

[0040] 3.4) Calculate the heat generated by the spindle motor, i.e.:

[0041]

[0042]

[0043] In the formula, and These represent the heat generated by rotor, stator, and air resistance losses, respectively. This represents the amount of heat per unit time, i.e., the first differential of heat, hereinafter the same, P. motor and η motor D represents the motor power and efficiency, respectively. rotor L rotor and f rotor These represent the rotor diameter, length, and frequency, respectively, μ air The value represents the dynamic viscosity of air, and h represents the distance between the rotor and the stator. express and The first differential;

[0044] 3.5) Simplifying formula (10), we obtain the mathematical expression for the heat generation of the main shaft system with respect to the electromechanical-thermal variables, namely:

[0045]

[0046] In the formula, k6 and k7 are coefficients.

[0047] Furthermore, in step 4), the steps for constructing a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables include:

[0048] 4.1) Calculate the cooling water heat dissipation for motor cooling. Right now:

[0049]

[0050] In the formula, c W and T represents the specific heat capacity and mass flow rate of the cooling water, respectively. W,out and T W,in These represent the inlet and outlet temperatures of the cooling water, respectively.

[0051] 4.2) Simplifying formula (11), we get:

[0052]

[0053] In the formula, k8 is a coefficient.

[0054] 4.3) Calculate the heat dissipation of compressed air in the motor. Right now:

[0055]

[0056]

[0057] In the formula, T rotor T stator and T ca,in These represent the rotor, stator, and compressed air temperatures, respectively. These represent the convective heat transfer coefficients of the rotor and stator, respectively; A rotor A stator D represents the convective heat transfer area of ​​the rotor and stator, respectively. cg L cg and h W These represent the diameter, length, and convective heat transfer coefficient of the cooling tank, respectively; k9, k 10 k 11 k 12 κ represents the coefficient.

[0058] 4.4) Simplifying formula (14), we get:

[0059]

[0060] In the formula, k 13 k 14 k 15 Represents the coefficient.

[0061] 4.5) Calculate the heat dissipation from natural convection in the motor. Right now:

[0062]

[0063] In the formula, k am and D represents the thermal conductivity and average Nusselt coefficient of natural convection, respectively. sh and A sh T represents the outer diameter and surface area of ​​the spindle motor housing, respectively. sh and T am These represent the spindle housing temperature and the external ambient temperature, respectively; k 16 Represents the coefficient.

[0064] 4.6) Calculate the heat dissipation between the bearing and compressed air, and the heat dissipation between the bearing and ambient air via natural convection, i.e.:

[0065]

[0066] In the formula, These represent the convective heat dissipation between compressed air and the front bearing, the convective heat dissipation between compressed air and the rear bearing, the convective heat dissipation between air and the front bearing, and the convective heat dissipation between air and the rear bearing, respectively. T represents the convective heat transfer coefficient of compressed air in the front and rear bearings, respectively; front T rear These represent the temperatures of the front and rear bearings, respectively; D front D rear These represent the diameters of the front and rear bearings, respectively; A front A rear These represent the convective heat transfer areas of the front and rear bearings, respectively. These represent the average Nusselt number of compressed air flowing in the front and rear bearings, respectively.

[0067] 4.7) Simplifying formula (17), we get:

[0068]

[0069] In the formula, k 17 k 18 k 19 k 20 Indicates coefficient;

[0070] 4.8) Calculate the heat dissipation through spindle heat conduction. Right now:

[0071]

[0072] In the formula, λ and A SC These represent thermal conductivity and equivalent surface area of ​​the spindle system, respectively. l0 represents the spindle length.

[0073] 4.9) Simplifying formula (19), we get:

[0074]

[0075] In the formula, k 21 Indicates coefficient;

[0076] 4.10) Calculate the heat dissipation from the spindle:

[0077]

[0078] In the formula, ξ represents the thermal emissivity of the material, and k B ξ represents a constant, T represents temperature; sh A represents the emissivity of the spindle motor housing material. sh ξ represents the outer surface area of ​​the spindle motor housing. rearξ represents the emissivity of the front bearing material. front Indicates the emissivity of the rear bearing material. T front、 T rear These represent the front and rear bearing temperatures, respectively; T sh Indicates the temperature of the spindle motor housing;

[0079] 4.11) Simplifying formula (21), we obtain the mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables, namely:

[0080]

[0081] In the formula, k 22 k 23 k 24 Represents the coefficient.

[0082] Furthermore, in step 5), the steps for establishing a theoretical model of the spindle system's thermal error with respect to electromechanical-thermal variables include:

[0083] 5.1) Establish the thermal balance equation of the principal shaft system based on the law of conservation of energy, namely:

[0084]

[0085] 5.2) After rearranging the thermal balance equations of the spindle system, we obtain:

[0086]

[0087] In the formula, K1, K2, K3, K4, K5, K6, K7, K8, K9, K 10 K 11 K 12 K 13 K 14 K 15 K 16 denoted by , where represents the electromechanical-thermal variable coefficient, and C represents a constant.

[0088] ΔT ca-fb ΔT ca-rb ΔT am-fb ΔT am-rb ΔT am-sh ΔT b-0 These represent the temperature difference between compressed air and the front bearing, the temperature difference between compressed air and the rear bearing, the temperature difference between the external environment and the front bearing, the temperature difference between the external environment and the rear bearing, and the initial temperature difference between the spindle housing and the external environment, respectively.

[0089] 5.3) Considering the time characteristics of the spindle system's thermal error, a matrix-form thermal error model is constructed:

[0090]

[0091] In the formula, K = [K1…K7 K8…K] 16 ] represents the coefficient matrix, and C represents the constant matrix. This represents an electromechanical-thermal element matrix, where the elements are experimentally measured real-time electromechanical-thermal data. t1, t i t n Indicates a time step.

[0092] Furthermore, in step 6), the real-time data of the electromechanical-thermal elements includes the temperature data of the worm gear grinding machine, current and voltage signals, and displacement signals of the thermal deformation characteristic points of the spindle system.

[0093] Furthermore, the temperature data of the worm gear grinding machine is acquired through temperature sensors and temperature acquisition cards;

[0094] Current and voltage signals are obtained through current transformers, voltage transformers, and power meters;

[0095] The displacement signals of the thermal deformation characteristic points of the spindle system are acquired through a laser displacement sensor and a displacement acquisition card.

[0096] Furthermore, step 7) transforms the solution of the spindle system thermal error model into an optimization problem, and the steps for solving it using the HPSO-GA optimization algorithm include:

[0097] 7.1) Establish the equation for solving the coefficients of the spindle thermal error model, i.e.:

[0098]

[0099] In the formula, This represents the spindle thermal error value obtained from experimental measurements. This represents the spindle thermal error value obtained from the established model. F(K1,K2,…,K) 15 ,K 16 C) represents the coefficient function to be solved;

[0100] 7.2) The genetic algorithm is embedded into the particle swarm optimization algorithm to obtain the hybrid optimization algorithm HPSO-GA;

[0101] 7.3) Solve formula (26) using the hybrid optimization algorithm HPSO-GA to obtain the thermal error.

[0102] The technical effectiveness of this invention is undeniable. Firstly, based on mechanistic analysis, a theoretical model of the spindle thermal error in relation to electromechanical-thermal variables is established using fundamental theories of thermoelasticity and thermodynamics. Then, the solution of the model coefficients is transformed into an optimization problem, and the HPSO-GA algorithm is proposed to solve the model coefficients. Finally, cutting experiments are conducted to obtain the real-time electromechanical-thermal data required for the model, which is then used to train the model, resulting in an accurate spindle system thermal error model. This invention combines the advantages of mechanistic models and data-driven models, proposing a thermal error mechanism-data modeling method. This method offers strong interpretability, generalization ability, and high accuracy, accurately predicting spindle thermal errors while revealing the influence of the electromechanical-thermal coupling effect of the spindle system on the thermal error. Therefore, this invention will be widely applicable to various worm gear grinding machines. Attached Figure Description

[0103] Figure 1 The flowchart of the data modeling of the thermal error mechanism of the worm gear grinding machine proposed in this invention is as follows;

[0104] Figure 2 This is a schematic diagram of the electromechanical-thermal coupling of the spindle system of a worm gear grinding machine.

[0105] Figure 3 A schematic diagram of the thermal characteristics of the spindle system of a worm gear grinding machine;

[0106] Figure 4 Here is a flowchart of the HPSO-GA algorithm;

[0107] Figure 5 Fit the curve to the model. Detailed Implementation

[0108] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0109] Example 1:

[0110] See Figures 1 to 5 A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect includes the following steps:

[0111] 1) Analyze the multi-energy coupling characteristics of the spindle system's electromechanical-thermal system, and construct the correlation between the thermal expansion deformation of the spindle system and temperature variables based on thermoelasticity.

[0112] 2) Combining thermodynamic analysis and the law of conservation of energy, establish the thermal balance equation of the main shaft system, and derive the correlation between the thermal error of the main shaft and the heat absorption of the main shaft structure;

[0113] 3) Analyze the heat generation characteristics of the spindle system and construct a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables;

[0114] 4) Analyze the heat dissipation characteristics of the spindle system and construct a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables;

[0115] 5) The thermal balance equation of the spindle system is derived, and a theoretical model of the thermal error of the spindle system with respect to the electromechanical-thermal variables is established;

[0116] 6) Conduct cutting experiments to obtain real-time data on electromechanical-thermal elements, and train the theoretical model of the thermal error of the spindle system with respect to electromechanical-thermal variables to obtain the thermal error model of the spindle system;

[0117] 7) The thermal error model of the spindle system is transformed into an optimization problem, and the HPSO-GA optimization algorithm is used to solve it to obtain the thermal error of the spindle system.

[0118] Step 1), the steps for establishing the correlation between the thermal expansion deformation of the spindle system and temperature variables include:

[0119] 1.1) Simplify the spindle system as a thin-walled cylinder and construct an expression for the thermal expansion deformation at r = b on the spindle shell, namely:

[0120]

[0121]

[0122] In the formula, u r＝b The coefficient of thermal expansion is represented by r, the radius is represented by a and b, the inner and outer radii of the spindle are represented by a and b respectively, α is the linear expansion coefficient of the spindle material, c1 is a constant, T is the spindle temperature; T a T b These represent the temperatures of the inner and outer diameters of the spindle, respectively.

[0123] 1.2) Set all variables except temperature as constants, simplify the expression for thermal expansion deformation at r=b on the spindle housing, and establish the correlation between the thermal expansion deformation of the spindle system and the temperature variable, i.e.:

[0124] δ spindle =u r＝b =k1(T b -T a )+c1 (2)

[0125] In the formula, k1 represents the coefficient; δ spindle This is the spindle thermal error.

[0126] In step 2), the thermal balance equation of the spindle system is as follows:

[0127]

[0128] In the formula, Q represents the heat absorbed by the spindle structure. accum Heat accumulation in the spindle system; Q gen and Q dis These represent the heat generated and heat dissipated by the spindle system, respectively. and These represent the heat generated by the spindle system bearings and the heat generated by the motor, respectively. and These represent the heat dissipation of the spindle system through heat conduction, heat convection, and heat radiation, respectively.

[0129] Among them, the spindle system absorbs heat. As shown below:

[0130]

[0131] In the formula, m, c, ρ and l0 represent the main shaft structure mass, specific heat capacity, average density and length, respectively; k2 and k3 represent coefficients; c2 represents a constant; ΔT is the temperature difference; d represents the bearing diameter; and T0 represents the initial temperature of the external environment.

[0132] In step 2), the relationship between spindle thermal error and spindle structural heat absorption is as follows:

[0133]

[0134] In the formula, k2 and k3 represent coefficients.

[0135] Step 3) involves constructing a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables.

[0136] 3.1) Calculate the heat generated by the spindle bearing, i.e.:

[0137]

[0138]

[0139] In the formula, M and n represent the total bearing friction torque and rotational speed, respectively; M0 and M1 represent the friction torque caused by the bearing lubricant viscosity and the friction torque caused by the bearing load, respectively; f0 and f1 are constants; γ is the kinematic viscosity of the lubricant; and d m This represents the average bearing diameter, and F1 is the equivalent load. This indicates that the spindle system bearings generate heat.

[0140] 3.2) Combining formulas (6) and (7), we get:

[0141]

[0142] In the formula, X0 and Y0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A These represent the radial load and axial load of the bearing, respectively.

[0143] 3.3) Simplifying formula (8), we get:

[0144]

[0145] In the formula, k4 and k5 represent coefficients; c3 represents a constant.

[0146] 3.4) Calculate the heat generated by the spindle motor, i.e.:

[0147]

[0148]

[0149] In the formula, and These represent the heat generated by rotor, stator, and air resistance losses, respectively. This represents the amount of heat per unit time, i.e., the first differential of heat, hereinafter the same, P. motor and η motor D represents the motor power and efficiency, respectively. rotor L rotor and f rotor These represent the rotor diameter, length, and frequency, respectively, μ air The value represents the dynamic viscosity of air, and h represents the distance between the rotor and the stator. express and The first differential;

[0150] 3.5) Simplifying formula (10), we obtain the mathematical expression for the heat generation of the main shaft system with respect to the electromechanical-thermal variables, namely:

[0151]

[0152] In the formula, k6 and k7 are coefficients.

[0153] Step 4) involves constructing a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables.

[0154] 4.1) Calculate the cooling water heat dissipation for motor cooling. Right now:

[0155]

[0156] In the formula, c W and T represents the specific heat capacity and mass flow rate of the cooling water, respectively. W,out and T W,in These represent the inlet and outlet temperatures of the cooling water, respectively.

[0157] 4.2) Simplifying formula (11), we get:

[0158]

[0159] In the formula, k8 is a coefficient.

[0160] 4.3) Calculate the heat dissipation of compressed air in the motor. Right now:

[0161]

[0162]

[0163] In the formula, T rotor T stator and T ca,in These represent the rotor, stator, and compressed air temperatures, respectively. These represent the convective heat transfer coefficients of the rotor and stator, respectively; A rotor A stator D represents the convective heat transfer area of ​​the rotor and stator, respectively. cg L cg and h W These represent the diameter, length, and convective heat transfer coefficient of the cooling tank, respectively; k9, k 10 k 11 k 12 κ represents the coefficient.

[0164] 4.4) Simplifying formula (14), we get:

[0165]

[0166] In the formula, k 13 k 14 k 15 Represents the coefficient.

[0167] 4.5) Calculate the heat dissipation from natural convection in the motor. Right now:

[0168]

[0169] In the formula, These represent the convective heat dissipation between compressed air and the front bearing, the convective heat dissipation between compressed air and the rear bearing, the convective heat dissipation between air and the front bearing, and the convective heat dissipation between air and the rear bearing, respectively. T represents the convective heat transfer coefficient of compressed air in the front and rear bearings, respectively; front T rear These represent the temperatures of the front and rear bearings, respectively; D front D rear These represent the diameters of the front and rear bearings, respectively; A front A rear These represent the convective heat transfer areas of the front and rear bearings, respectively. The number represents the average Nusselt number of compressed air flowing in the front and rear bearings.

[0170] 4.6) Calculate the heat dissipation between the bearing and compressed air, and the heat dissipation between the bearing and ambient air via natural convection, i.e.:

[0171]

[0172] In the formula, These represent the convective heat dissipation between compressed air and the front bearing, the convective heat dissipation between compressed air and the rear bearing, the convective heat dissipation between air and the front bearing, and the convective heat dissipation between air and the rear bearing, respectively. T represents the convective heat transfer coefficient of compressed air in the front and rear bearings, respectively; front T rear These represent the temperatures of the front and rear bearings, respectively; D front D rear These represent the diameters of the front and rear bearings, respectively; A front A rear These represent the convective heat transfer areas of the front and rear bearings, respectively. These represent the average Nusselt number of compressed air flowing in the front and rear bearings, respectively.

[0173] 4.7) Simplifying formula (17), we get:

[0174]

[0175] In the formula, k 17 k 18 k 19 k 20 Indicates coefficient;

[0176] 4.8) Calculate the heat dissipation through spindle heat conduction. Right now:

[0177]

[0178] In the formula, λ and A SC These represent thermal conductivity and equivalent surface area of ​​the spindle system, respectively. l0 represents the spindle length.

[0179] 4.9) Simplifying formula (19), we get:

[0180]

[0181] In the formula, k 21 Indicates coefficient;

[0182] 4.10) Calculate the heat dissipation from the spindle:

[0183]

[0184] In the formula, ξ represents the thermal emissivity of the material, and k B ξ represents a constant, T represents temperature; sh A represents the emissivity of the spindle motor housing material. sh ξ represents the outer surface area of ​​the spindle motor housing. rear ξ represents the emissivity of the front bearing material. front Indicates the emissivity of the rear bearing material. T front T rear These represent the front and rear bearing temperatures, respectively; T sh Indicates the temperature of the spindle motor housing;

[0185] 4.11) Simplifying formula (21), we obtain the mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables, namely:

[0186]

[0187] In the formula, k 22 k 23 k 24 Represents the coefficient.

[0188] Step 5) involves establishing a theoretical model of the spindle system's thermal error with respect to electromechanical-thermal variables, including:

[0189] 5.1) Establish the thermal balance equation of the principal shaft system based on the law of conservation of energy, namely:

[0190]

[0191] 5.2) After rearranging the thermal balance equations of the spindle system, we obtain:

[0192]

[0193] In the formula, K1, K2, K3, K4, K5, K6, K7, K8, K9, K 10 K 11 K 12 K 13 K 14 K 15 K 16 The electromechanical-thermal variable coefficient is represented by C, which represents a constant; ΔT ca-fb ΔTca-rb ΔT am-fb ΔT am-rb ΔT am-sh ΔT b-0 These represent the temperature difference between compressed air and the front bearing, the temperature difference between compressed air and the rear bearing, the temperature difference between the external environment and the front bearing, the temperature difference between the external environment and the rear bearing, and the initial temperature difference between the spindle housing and the external environment, respectively.

[0194] 5.3) Considering the time characteristics of the spindle system's thermal error, a matrix-form thermal error model is constructed:

[0195]

[0196] In the formula, K = [K1…K7 K8…K] 16 ] represents the coefficient matrix, and C represents the constant matrix. This represents an electromechanical-thermal element matrix, where the elements are experimentally measured real-time electromechanical-thermal data. t1, t i t n Indicates a time step.

[0197] In step 6), the real-time data of the electromechanical-thermal elements includes the temperature data of the worm gear grinding machine, current and voltage signals, and displacement signals of the thermal deformation characteristic points of the spindle system.

[0198] Temperature data for worm gear grinding machines is acquired via temperature sensors and temperature acquisition cards.

[0199] Current and voltage signals are obtained through current transformers, voltage transformers, and power meters;

[0200] The displacement signals of the thermal deformation characteristic points of the spindle system are acquired through a laser displacement sensor and a displacement acquisition card.

[0201] Step 7) transforms the thermal error model of the spindle system into an optimization problem, and the steps for solving it using the HPSO-GA optimization algorithm include:

[0202] 7.1) Establish the equation for solving the coefficients of the spindle thermal error model, i.e.:

[0203]

[0204] In the formula, This represents the spindle thermal error value obtained from experimental measurements. This represents the spindle thermal error value obtained from the established model.

[0205] 7.2) The genetic algorithm is embedded into the particle swarm optimization algorithm to obtain the hybrid optimization algorithm HPSO-GA;

[0206] 7.3) Solve formula (26) using the hybrid optimization algorithm HPSO-GA to obtain the thermal error.

[0207] Example 2:

[0208] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect includes the following steps:

[0209] 1) Analyze the multi-energy coupling characteristics of the spindle system's electromechanical-thermal system, and construct the correlation between the thermal expansion deformation of the spindle system and temperature variables based on thermoelasticity.

[0210] 2) Combining thermodynamic analysis and the law of conservation of energy, establish the thermal balance equation of the main shaft system, and derive the correlation between the thermal error of the main shaft and the heat absorption of the main shaft structure;

[0211] 3) Analyze the heat generation characteristics of the spindle system and construct a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables;

[0212] 4) Analyze the heat dissipation characteristics of the spindle system and construct a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables;

[0213] 5) The thermal balance equation of the spindle system is derived, and a theoretical model of the thermal error of the spindle system with respect to the electromechanical-thermal variables is established;

[0214] 6) Conduct cutting experiments to obtain real-time data on electromechanical-thermal elements, and train the theoretical model of the thermal error of the spindle system with respect to electromechanical-thermal variables to obtain the thermal error model of the spindle system;

[0215] 7) The thermal error model of the spindle system is transformed into an optimization problem, and the HPSO-GA optimization algorithm is used to solve it to obtain the thermal error of the spindle system.

[0216] Example 3:

[0217] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with the same technical content as Embodiment 2, further comprising the following steps in step 1) for constructing the correlation between the thermal expansion deformation of the spindle system and temperature variables:

[0218] 1.1) Simplify the spindle system as a thin-walled cylinder and construct an expression for the thermal expansion deformation at r = b on the spindle shell, namely:

[0219]

[0220] In the formula, u represents the coefficient of thermal expansion, r represents the radius, a and b represent the inner and outer radii of the spindle, respectively, α represents the linear expansion coefficient of the spindle material, c1 represents a constant, T represents the spindle temperature, and T0 represents the temperature of the spindle.a T b These represent the temperatures of the inner and outer diameters of the spindle, respectively.

[0221] 1.2) Set all variables except temperature as constants, simplify the expression for thermal expansion deformation at r=b on the spindle housing, and establish the correlation between the thermal expansion deformation of the spindle system and the temperature variable, i.e.:

[0222] δ spindle =u r＝b =k1(T b -T a )+c1 (2)

[0223] In the formula, k1 represents the coefficient; δ spindle This is the spindle thermal error.

[0224] Example 4:

[0225] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with the same technical content as any one of embodiments 2-3, further, in step 2), the thermal balance equation of the spindle system is as follows:

[0226]

[0227] In the formula, Q represents the heat absorbed by the spindle structure. accum Heat accumulation in the spindle system; Q gen and Q dis These represent the heat generated and heat dissipated by the spindle system, respectively. and These represent the heat generated by the spindle system bearings and the heat generated by the motor, respectively. and These represent the heat dissipation of the spindle system through heat conduction, heat convection, and heat radiation, respectively.

[0228] Among them, the spindle system absorbs heat. As shown below:

[0229]

[0230] In the formula, m, c, ρ and l0 represent the main shaft structure mass, specific heat capacity, average density and length, respectively; k2 and k3 represent coefficients; c2 represents a constant; ΔT is the temperature difference; d represents the bearing diameter; and T0 represents the initial temperature of the external environment.

[0231] Example 5:

[0232] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with the technical content being the same as any one of embodiments 2-4. Further, in step 2), the correlation between the spindle thermal error and the heat absorption of the spindle structure is as follows:

[0233]

[0234] In the formula, k2 and k3 represent coefficients.

[0235] Example 6:

[0236] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with technical content the same as any one of embodiments 2-5, further comprising, in step 3), the step of constructing a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables, including:

[0237] 3.1) Calculate the heat generated by the spindle bearing, i.e.:

[0238]

[0239]

[0240] In the formula, M and n represent the total bearing friction torque and rotational speed, respectively; M0 and M1 represent the friction torque caused by the bearing lubricant viscosity and the friction torque caused by the bearing load, respectively; f0 and f1 are constants; γ is the kinematic viscosity of the lubricant; and d m This represents the average bearing diameter, and F1 is the equivalent load. This indicates that the spindle system bearings generate heat.

[0241] 3.2) Combining formulas (6) and (7), we get:

[0242]

[0243] In the formula, X0 and Y0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A These represent the radial load and axial load of the bearing, respectively.

[0244] 3.3) Simplifying formula (8), we get:

[0245]

[0246] In the formula, k4 and k5 represent coefficients; c3 represents a constant.

[0247] 3.4) Calculate the heat generated by the spindle motor, i.e.:

[0248]

[0249]

[0250] In the formula, and These represent the heat generated by rotor, stator, and air resistance losses, respectively. This represents the amount of heat per unit time, i.e., the first differential of heat, hereinafter the same, P. motor and η motor D represents the motor power and efficiency, respectively. rotor L rotor and f rotor These represent the rotor diameter, length, and frequency, respectively, μ air The value represents the dynamic viscosity of air, and h represents the distance between the rotor and the stator.

[0251] 3.5) Simplifying formula (10), we obtain the mathematical expression for the heat generation of the main shaft system with respect to the electromechanical-thermal variables, namely:

[0252]

[0253] In the formula, k6 and k7 are coefficients.

[0254] Example 7:

[0255] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with technical content the same as any one of embodiments 2-6, further comprising, in step 4), the step of constructing a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables, including:

[0256] 4.1) Calculate the cooling water heat dissipation for motor cooling. Right now:

[0257]

[0258] In the formula, c W and T represents the specific heat capacity and mass flow rate of the cooling water, respectively. W,out and T W,in These represent the inlet and outlet temperatures of the cooling water, respectively.

[0259] 4.2) Simplifying formula (11), we get:

[0260]

[0261] In the formula, k8 is a coefficient;

[0262] 4.3) Calculate the heat dissipation of compressed air in the motor. Right now:

[0263]

[0264]

[0265] In the formula, T rotor T stator and T ca,in These represent the rotor, stator, and compressed air temperatures, respectively. These represent the convective heat transfer coefficients of the rotor and stator, respectively; A rotor A stator D represents the convective heat transfer area of ​​the rotor and stator, respectively. cg L cg and h W These represent the diameter, length, and convective heat transfer coefficient of the cooling tank, respectively; k9, k 10 k 11 k 12 Represents the coefficient.

[0266] 4.4) Simplifying formula (14), we get:

[0267]

[0268] In the formula, k 13 k 14 k 15 Represents the coefficient.

[0269] 4.5) Calculate the heat dissipation from natural convection in the motor. Right now:

[0270]

[0271] In the formula, k am and D represents the thermal conductivity and average Nusselt coefficient of natural convection, respectively. sh and A sh T represents the outer diameter and surface area of ​​the spindle motor housing, respectively. sh and T am These represent the spindle housing temperature and the external ambient temperature, respectively; k 16 Represents the coefficient.

[0272] 4.6) Calculate the heat dissipation between the bearing and compressed air, and the heat dissipation between the bearing and ambient air via natural convection, i.e.:

[0273]

[0274] In the formula, These represent the convective heat dissipation between compressed air and the front bearing, the convective heat dissipation between compressed air and the rear bearing, the convective heat dissipation between air and the front bearing, and the convective heat dissipation between air and the rear bearing, respectively. T represents the convective heat transfer coefficient of compressed air in the front and rear bearings, respectively;front T rear These represent the temperatures of the front and rear bearings, respectively; D front D rear These represent the diameters of the front and rear bearings, respectively; A front A rear These represent the convective heat transfer areas of the front and rear bearings, respectively. These represent the average Nusselt number of compressed air flowing in the front and rear bearings, respectively.

[0275] 4.7) Simplifying formula (17), we get:

[0276]

[0277] In the formula, k 17 k 18 k 19 k 20 Indicates coefficient;

[0278] 4.8) Calculate the heat dissipation through spindle heat conduction. Right now:

[0279]

[0280] In the formula, λ and A SC These represent thermal conductivity and equivalent surface area of ​​the spindle system, respectively.

[0281] 4.9) Simplifying formula (19), we get:

[0282]

[0283] 4.10) Calculate the heat dissipation from the spindle:

[0284]

[0285] In the formula, ξ represents the thermal emissivity of the material, and k B ξ represents a constant, T represents temperature; sh A represents the emissivity of the spindle motor housing material. sh ξ represents the outer surface area of ​​the spindle motor housing. rear ξ represents the emissivity of the front bearing material. front This indicates the emissivity of the bearing material.

[0286] 4.11) Simplifying formula (21), we obtain the mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables, namely:

[0287]

[0288] Example 7:

[0289] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with technical content the same as any one of embodiments 2-6, further comprising the following steps in step 5):

[0290] 5.1) Establish the thermal balance equation of the principal shaft system based on the law of conservation of energy, namely:

[0291]

[0292] 5.2) After rearranging the thermal balance equations of the spindle system, we obtain:

[0293]

[0294] In the formula, K represents the electromechanical-thermal variable coefficient, and C represents a constant; ΔT ca-fb ΔT ca-rb ΔT am-fb ΔT am-rb ΔT am-sh ΔT b-0 These represent the temperature difference between compressed air and the front bearing, the temperature difference between compressed air and the rear bearing, the temperature difference between the external environment and the front bearing, the temperature difference between the external environment and the rear bearing, and the initial temperature difference between the spindle housing and the external environment, respectively.

[0295] 5.3) Considering the time characteristics of the spindle system's thermal error, a matrix-form thermal error model is constructed:

[0296]

[0297] In the formula, K = [K1…K7 K8…K] 16 ] represents the coefficient matrix, and C represents the constant matrix. This represents the electromechanical-thermal element matrix, where the elements are experimentally measured real-time electromechanical-thermal data.

[0298] Example 9:

[0299] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with the same technical content as any one of embodiments 2-8. Further, in step 6), the real-time data of the electromechanical-thermal elements includes the temperature data of the worm gear grinding machine, current and voltage signals, and displacement signals of thermal deformation characteristic points of the spindle system.

[0300] Example 10:

[0301] A data modeling method for the thermal error mechanism of the spindle of a worm gear grinding machine considering the electromechanical-thermal coupling effect, the technical content of which is the same as any one of embodiments 2-9, further wherein the temperature data of the worm gear grinding machine is acquired through a temperature sensor and a temperature acquisition card;

[0302] Current and voltage signals are obtained through current transformers, voltage transformers, and power meters;

[0303] The displacement signals of the thermal deformation characteristic points of the spindle system are acquired through a laser displacement sensor and a displacement acquisition card.

[0304] Example 11:

[0305] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, with the same technical content as any one of embodiments 2-10, further comprising the following steps in step 7), where the solution of the spindle system thermal error model is transformed into an optimization problem, and the solution is obtained using the HPSO-GA optimization algorithm:

[0306] 7.1) Establish the equation for solving the coefficients of the spindle thermal error model, i.e.:

[0307]

[0308] In the formula, This represents the spindle thermal error value obtained from experimental measurements. This represents the spindle thermal error value obtained from the established model. F(K1,K2,…,K) 15 ,K 16 C) represents the coefficient function to be solved;

[0309] 7.2) The genetic algorithm is embedded into the particle swarm optimization algorithm to obtain the hybrid optimization algorithm HPSO-GA;

[0310] 7.3) Solve formula (26) using the hybrid optimization algorithm HPSO-GA to obtain the thermal error.

[0311] Example 12:

[0312] A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, comprising the following steps:

[0313] (1) Analyze the multi-energy coupling characteristics of the spindle system's electromechanical-thermal system to reveal the influence of electromechanical-thermal variables on the spindle's thermal error;

[0314] (2) Based on thermoelasticity, construct the relationship between the thermal expansion deformation of the main shaft system and temperature variables;

[0315] (3) Combining thermodynamic analysis and the law of conservation of energy, establish the thermal balance equation of the main shaft system, and derive the correlation between the thermal error of the main shaft and the heat absorption of the main shaft structure;

[0316] (4) Analyze the heat generation characteristics of the spindle system and derive the mathematical expression of the heat generation of the spindle system with respect to the electromechanical-thermal variables;

[0317] (5) Analyze the heat dissipation characteristics of the spindle system and derive the mathematical expression of the heat dissipation of the spindle system with respect to the electromechanical-thermal variables;

[0318] (6) The thermal balance equation of the spindle system is derived and organized, and a theoretical model of the thermal error of the spindle system with respect to the electromechanical-thermal variables is established;

[0319] (7) The solution of the coefficients of the thermal error theoretical model is transformed into an optimization problem and solved using the HPSO-GA optimization algorithm;

[0320] (8) Conduct cutting experiments to obtain real-time data of the electrical-mechanical-thermal elements required for the model and use them to train the thermal error model to obtain an accurate thermal error model of the spindle system.

[0321] Specifically, for a certain type of worm gear grinding machine, the specific process of spindle system thermal error mechanism-data modeling based on the present invention is as follows: Figure 1 As shown; after determining the specific model and structure of the machine tool, the electromechanical-thermal coupling mechanism of the machine tool spindle system is analyzed, revealing the correlation between spindle thermal error and the electromechanical-thermal coupling effect. The electromechanical-thermal coupling of the spindle system is as follows: Figure 2 As shown; combining thermoelasticity and thermodynamics analysis, the thermal characteristics of the spindle system are revealed, with a focus on the heat generation and dissipation of the spindle motor and bearings. The thermal characteristic analysis of the spindle system is as follows: Figure 3 As shown, based on the law of conservation of energy, a mechanistic model of the spindle thermal error with respect to the electromechanical-thermal variables is established. Solving for the model coefficients is transformed into an optimization problem, and the HPSO-GA algorithm is proposed to solve for the model coefficients. The flowchart of the HPSO-GA algorithm is shown below. Figure 4 As shown; grinding gear machining experiments were conducted, real-time data of electrical-mechanical-thermal elements and spindle thermal error data were measured, and the above data were substituted into the proposed model to obtain an accurate mechanism-data driven spindle system thermal error model. The thermal error prediction effect is as follows: Figure 5 As shown.

[0322] In the above process, based on thermoelasticity, the relationship between the thermal expansion deformation of the main shaft system and temperature variables is constructed as follows:

[0323] Simplifying the spindle system as a thin-walled cylinder, the thermal expansion deformation of the spindle housing at r=b is:

[0324]

[0325] In the formula, u represents the coefficient of thermal expansion, r represents the radius, a and b represent the inner and outer radii of the spindle, respectively, α represents the linear expansion coefficient of the spindle material, c1 represents a constant, T represents the spindle temperature, and T0 represents the temperature of the spindle. a T b These represent the temperatures of the inner and outer diameters of the spindle, respectively.

[0326] Spindle radial thermal expansion error δ spindle (Hereinafter referred to as thermal error) can be represented by the thermal expansion deformation at r=b on the spindle housing. Treating quantities other than temperature as constants, the spindle thermal error is simplified to:

[0327] δ spindle =u r＝b =k1(T b -T a )+c1 (2)

[0328] In the formula, k1 represents the coefficient, and the same applies below.

[0329] Based on thermodynamic analysis and the law of conservation of energy, the thermal balance equation of the spindle system is established, and the correlation between the thermal error of the spindle and the heat absorption of the spindle structure is derived, as follows:

[0330] The thermal balance equation of the spindle system is:

[0331]

[0332] In the formula, This represents the heat absorbed by the spindle structure, and its value is related to the heat accumulation Q of the spindle system. accum Equal, Q gen and Q dis These represent the heat generated and heat dissipated by the spindle system, respectively. and These represent the heat generated by the spindle system bearings and the heat generated by the motor, respectively. and These represent the heat dissipation of the spindle system through heat conduction, heat convection, and heat radiation, respectively.

[0333] The heat absorbed by the spindle system is:

[0334]

[0335] In the formula, m, c, ρ and l0 represent the main shaft structure mass, specific heat capacity, average density and length, respectively; k2 and k3 represent coefficients; c2 represents a constant; ΔT is the temperature difference; d represents the bearing diameter; and T0 represents the initial temperature of the external environment.

[0336] Based on formula (2), the heat absorbed by the spindle system is:

[0337]

[0338] The above content reveals the thermal energy balance mechanism of the spindle system and establishes the correlation between the thermal error of the spindle system and the accumulation of thermal energy and temperature variables, providing a theoretical basis for the subsequent establishment of a mechanism model of spindle thermal error with respect to electromechanical and thermal variables.

[0339] Thermal characteristic analysis and thermal error mechanism modeling of spindle system

[0340] Step 4 involves analyzing the heat generation characteristics of the spindle system and deriving the mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables, as detailed below:

[0341] Step 4.1: Calculate the heat generated by the spindle bearing:

[0342]

[0343] In the formula, M and n represent the total bearing friction torque and rotational speed, respectively; M0 and M1 represent the friction torque caused by the bearing lubricant viscosity and the friction torque caused by the bearing load, respectively; f0 and f1 are constants; γ is the kinematic viscosity of the lubricant; and d m This represents the average diameter of the bearing, and F1 is the equivalent load.

[0344] Further derivation:

[0345]

[0346] In the formula, X0 and Y0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A These represent the radial load and axial load of the bearing, respectively.

[0347] Simplifying, we get:

[0348]

[0349] Step 4.2: Calculate the heat generated by the spindle motor:

[0350]

[0351] In the formula, and These represent the heat generated by rotor, stator, and air resistance losses, respectively. This represents the amount of heat per unit time, i.e., the first differential of heat, hereinafter the same, P. motor and η motor D represents the motor power and efficiency, respectively. rotor L rotor and f rotor These represent the rotor diameter, length, and frequency, respectively, μ airThe value represents the dynamic viscosity of air, and h represents the distance between the rotor and the stator.

[0352] Simplifying, we get:

[0353]

[0354] Step 5 involves analyzing the heat dissipation characteristics of the spindle system and deriving the mathematical expression for the heat dissipation of the spindle system in relation to the electromechanical-thermal variables, as detailed below:

[0355] Step 5.1: Calculate the spindle heat dissipation via convection, where the cooling water dissipation for motor cooling is:

[0356]

[0357] In the formula, c W and T represents the specific heat capacity and mass flow rate of the cooling water, respectively. W,out and T W,in These represent the inlet and outlet temperatures of the cooling water, respectively.

[0358] The quantification of cooling water heat dissipation is simplified as follows:

[0359]

[0360] The heat dissipation of compressed air in the motor is:

[0361]

[0362] In the formula, T rotor T stator and T ca,in These represent the rotor, stator, and compressed air temperatures, respectively; h and A represent the convective heat transfer coefficient and convective heat transfer area, respectively; and D represents the convective heat transfer area. cg L cg and h W These represent the diameter, length, and convective heat transfer coefficient of the cooling tank, respectively.

[0363] The quantification of compressed air heat dissipation is simplified as follows:

[0364]

[0365] The amount of heat dissipated by natural convection in the motor is:

[0366]

[0367] In the formula, k am and D represents the thermal conductivity and average Nusselt coefficient of natural convection, respectively. sh and A sh T represents the outer diameter and surface area of ​​the spindle motor housing, respectively. sh and Tam These represent the spindle housing temperature and the external ambient temperature, respectively.

[0368] The heat dissipation from the bearing to compressed air and the heat dissipation from the bearing to ambient air via natural convection are as follows:

[0369]

[0370] The symbols in the formula have the same meanings as those above, and will not be repeated here.

[0371] Simplifying, we get:

[0372]

[0373] Step 5.2: Calculate the heat dissipation through spindle heat conduction:

[0374]

[0375] In the formula, λ and A SC These represent thermal conductivity and equivalent surface area of ​​the spindle system, respectively.

[0376] Simplifying, we get:

[0377]

[0378] Step 5.3: Calculate the heat dissipation from the spindle:

[0379]

[0380] In the formula, ξ represents the thermal emissivity of the material, and k B ξ represents a constant, T represents temperature; sh A represents the emissivity of the spindle motor housing material. sh ξ represents the outer surface area of ​​the spindle motor housing. rear ξ represents the emissivity of the front bearing material. front This indicates the emissivity of the bearing material.

[0381] Simplifying, we get:

[0382]

[0383] The derivation and simplification of the spindle system thermal balance equations in step 6, and the establishment of a theoretical model of the spindle system thermal error with respect to electromechanical-thermal variables, are detailed below:

[0384] Step 6.1: Establish the thermal balance equation of the principal shaft system based on the law of conservation of energy:

[0385]

[0386] Step 6.2: Rearrange the thermal balance equations of the spindle system:

[0387]

[0388] ΔT ca-fb ΔT ca-rb ΔT am-fb ΔT am-rb ΔT am-sh ΔT b-0 These represent the temperature difference between compressed air and the front bearing, the temperature difference between compressed air and the rear bearing, the temperature difference between the external environment and the front bearing, the temperature difference between the external environment and the rear bearing, and the initial temperature difference between the spindle housing and the external environment, respectively.

[0389] Step 6.3: Considering the time characteristics of the spindle system's thermal error, construct a matrix-form thermal error model:

[0390]

[0391] In the formula, K = [K1…K7 K8…K] 16 ] represents the coefficient matrix, and C represents the constant matrix. This represents the electromechanical-thermal element matrix, where the elements are experimentally measured real-time electromechanical-thermal data.

[0392] The above analysis examines the thermal characteristics of the spindle system, focusing on the heat generated by the spindle motor and bearings, and the corresponding heat dissipation through heat conduction, convection, and radiation. Based on the law of conservation of energy, the thermal energy balance equation of the spindle system is derived, resulting in a coefficient-based thermal error mechanism model for the spindle system.

[0393] Solving the coefficients of the thermal error mechanism model of the spindle system and combining mechanism and data-driven thermal error model

[0394] Step 7 involves transforming the solution of the thermal error theoretical model coefficients into an optimization problem, which is then solved using the HPSO-GA optimization algorithm, as detailed below:

[0395] Step 7.1: Establish the coefficients of the spindle thermal error model and solve the equations:

[0396]

[0397] In the formula, This represents the spindle thermal error value obtained from experimental measurements. This represents the spindle thermal error value obtained from the established model.

[0398] Step 8 involves conducting cutting experiments to obtain real-time data on the electrical, mechanical, and thermal elements required for the model, which is then used to train the thermal error model, resulting in an accurate thermal error model for the spindle system. The details are as follows:

[0399] Based on the location of the temperature-sensitive points of the worm gear grinding machine, temperature sensors are installed and connected to a temperature acquisition card to collect the corresponding temperature. Current transformers and voltage transformers are installed and connected to a power meter to collect the machine tool's current and voltage signals. Based on the location of the thermal deformation characteristic points of the worm gear grinding machine's spindle system, laser displacement sensors are installed and connected to a displacement acquisition card to collect the displacement of the laser displacement sensors.

[0400] The final accurate thermal error model of the spindle system is as follows:

[0401]

[0402] Comparing the experimentally obtained spindle thermal error measurement value with the thermal error prediction value obtained by formula (26), for example... Figure 5 As shown.

Claims

1. A data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect, characterized in that, Includes the following steps: 1) Analyze the multi-energy coupling characteristics of the spindle system's electromechanical-thermal system, and construct the correlation between the thermal expansion deformation of the spindle system and temperature variables based on thermoelasticity. 2) Combining thermodynamic analysis and the law of conservation of energy, establish the thermal balance equation of the main shaft system, and derive the correlation between the thermal error of the main shaft and the heat absorption of the main shaft structure; 3) Analyze the heat generation characteristics of the spindle system and construct a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables; 4) Analyze the heat dissipation characteristics of the spindle system and construct a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables; 5) The thermal balance equation of the spindle system is derived, and a theoretical model of the thermal error of the spindle system with respect to the electromechanical-thermal variables is established; 6) Conduct cutting experiments to obtain real-time data on electromechanical-thermal elements, and train the theoretical model of the thermal error of the spindle system with respect to electromechanical-thermal variables to obtain the thermal error model of the spindle system; 7) The thermal error model of the spindle system is transformed into an optimization problem, and the HPSO-GA optimization algorithm is used to solve it to obtain the thermal error of the spindle system; Step 1), the steps for establishing the correlation between the thermal expansion deformation of the spindle system and temperature variables include: 1.1) Simplify the spindle system as a thin-walled cylinder and construct an expression for the thermal expansion deformation at r = b on the spindle shell, namely: In the formula, u r＝b The coefficient of thermal expansion is represented by r, the radius is represented by a and b, the inner and outer radii of the spindle are represented by a and b respectively, α is the linear expansion coefficient of the spindle material, c1 is a constant, T is the spindle temperature; T a T b These represent the temperatures of the spindle's inner and outer diameters, respectively. 1.2) Set all variables except temperature as constants, simplify the expression for thermal expansion deformation at r=b on the spindle housing, and establish the correlation between the thermal expansion deformation of the spindle system and the temperature variable, i.e.: δ spindle =u r＝b =k1(T b -T a )+c1 (2) In the formula, k1 represents the coefficient; δ spindle Main spindle thermal error; In step 2), the thermal balance equation of the spindle system is as follows: In the formula, Q represents the heat absorbed by the spindle structure. accum Heat accumulation in the spindle system; Q gen and Q dis These represent the heat generated and heat dissipated by the spindle system, respectively. and These represent the heat generated by the spindle system bearings and the heat generated by the motor, respectively. and These represent the heat dissipation of the spindle system through heat conduction, heat convection, and heat radiation, respectively. Among them, the spindle system absorbs heat. As shown below: In the formula, m, c, ρ and l0 represent the main shaft structure mass, specific heat capacity, average density and length, respectively; k2 and k3 represent coefficients; c2 represents a constant; ΔT is the temperature difference; d represents the bearing diameter; T0 represents the initial temperature of the external environment; In step 2), the relationship between spindle thermal error and spindle structural heat absorption is as follows: In the formula, k2 and k3 represent coefficients; δ spindle This is the spindle thermal error.

2. The data modeling method for thermal error mechanism of worm gear grinding machine spindle considering electromechanical-thermal coupling effect as described in claim 1, characterized in that: Step 3) involves constructing a mathematical expression for the heat generation of the spindle system with respect to the electromechanical-thermal variables. 3.1) Calculate the heat generated by the spindle bearing, i.e.: In the formula, M and n represent the total bearing friction torque and rotational speed, respectively; M0 and M1 represent the friction torque caused by the bearing lubricant viscosity and the friction torque caused by the bearing load, respectively; f0 and f1 are constants; γ is the kinematic viscosity of the lubricant; and d m This represents the average bearing diameter, and F1 is the equivalent load. This indicates that the spindle system bearings generate heat; 3.2) Combining formulas (6) and (7), we get: In the formula, X0 and Y0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A These represent the radial load and axial load of the bearing, respectively. 3.3) Simplifying formula (8), we get: In the formula, k4 and k5 represent coefficients; c3 represents a constant. 3.4) Calculate the heat generated by the spindle motor, i.e.: In the formula, and These represent the heat generated by rotor, stator, and air resistance losses, respectively. express and First-order differential; P motor and η motor D represents the motor power and efficiency, respectively. rotor L rotor and f rotor These represent the rotor diameter, length, and frequency, respectively, μ air The value represents the dynamic viscosity of air, and h represents the distance between the rotor and the stator. 3.5) Simplifying formula (10), we obtain the mathematical expression for the heat generation of the main shaft system with respect to the electromechanical-thermal variables, namely: In the formula, k6 and k7 are coefficients.

3. The method for data modeling the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect as described in claim 1, characterized in that: Step 4) involves constructing a mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables. 4.1) Calculate the cooling water heat dissipation for motor cooling. Right now: In the formula, c W and T represents the specific heat capacity and mass flow rate of the cooling water, respectively. W,out and T W,in These represent the inlet and outlet temperatures of the cooling water, respectively. 4.2) Simplifying formula (12), we get: In the formula, k8 is a coefficient; 4.3) Calculate the heat dissipation of compressed air in the motor. Right now: In the formula, T rotor T stator and T ca,in These represent the rotor, stator, and compressed air temperatures, respectively. These represent the convective heat transfer coefficients of the rotor and stator, respectively; A rotor A stator D represents the convective heat transfer area of ​​the rotor and stator, respectively. cg L cg and h W These represent the diameter, length, and convective heat transfer coefficient of the cooling tank, respectively; k9, k 10 k 11 k 12 κ represents the coefficient; κ represents the intermediate coefficient. 4.4) Simplifying formula (14), we get: In the formula, k 13 k 14 k 15 Indicates coefficient; 4.5) Calculate the heat dissipation from natural convection in the motor. Right now: In the formula, k am and D represents the thermal conductivity and average Nusselt coefficient of natural convection, respectively. sh and A sh T represents the outer diameter and surface area of ​​the spindle motor housing, respectively. sh and T am These represent the spindle housing temperature and the external ambient temperature, respectively; k 16 Indicates coefficient; 4.6) Calculate the heat dissipation between the bearing and compressed air, and the heat dissipation between the bearing and ambient air via natural convection, i.e.: In the formula, These represent the convective heat dissipation between compressed air and the front bearing, the convective heat dissipation between compressed air and the rear bearing, the convective heat dissipation between air and the front bearing, and the convective heat dissipation between air and the rear bearing, respectively. T represents the convective heat transfer coefficient of compressed air in the front and rear bearings, respectively; front T rear These represent the temperatures of the front and rear bearings, respectively; D front D rear These represent the diameters of the front and rear bearings, respectively; A front A rear These represent the convective heat transfer areas of the front and rear bearings, respectively. These represent the average Nusselt number of compressed air flowing in the front and rear bearings, respectively. 4.7) Simplifying formula (17), we get: In the formula, k 17 k 18 k 19 k 20 Indicates coefficient; 4.8) Calculate the heat dissipation through spindle heat conduction. Right now: In the formula, λ and A SC represents thermal conductivity and equivalent surface area of ​​the spindle system, respectively; l0 represents the spindle length. 4.9) Simplifying formula (19), we get: In the formula, k 21 Indicates coefficient; 4.10) Calculate the heat dissipation from the spindle: In the formula, ξ represents the thermal emissivity of the material, and k B Let ξ represent a constant. sh A represents the emissivity of the spindle motor housing material. sh ξ represents the outer surface area of ​​the spindle motor housing. rear ξ represents the emissivity of the front bearing material. front Indicates the emissivity of the rear bearing material; T front T rear These represent the front and rear bearing temperatures, respectively; T sh Indicates the temperature of the spindle motor housing; 4.11) Simplifying formula (21), we obtain the mathematical expression for the heat dissipation of the spindle system with respect to the electromechanical-thermal variables, namely: In the formula, k 22 k 23 k 24 Represents the coefficient.

4. The data modeling method for the thermal error mechanism of a worm gear grinding machine spindle considering the electromechanical-thermal coupling effect as described in claim 1, characterized in that: Step 5) involves establishing a theoretical model of the spindle system's thermal error with respect to electromechanical-thermal variables, including: 5.1) Establish the thermal balance equation of the principal shaft system based on the law of conservation of energy, namely: In the formula, k1, k2, k3, k4, k5, k6, k7, k8, k 13 k 14 k 15 k 16 k 17 k 18 k 19 k 20 k 21 k 22 k 23 k 24 Indicates coefficient; 5.2) After rearranging the thermal balance equations of the spindle system, we obtain: In the formula, K1, K2, K3, K4, K5, K6, K7, K8, K9, K 10 K 11 K 12 K 13 K 14 K 15 K 16 The electromechanical-thermal coefficient represents the coefficient of variation, and C represents a constant; ΔT ca-fb ΔT ca-rb ΔT am-fb ΔT am-rb ΔT am-sh ΔT b-0 These represent the temperature difference between compressed air and the front bearing, the temperature difference between compressed air and the rear bearing, the temperature difference between the external environment and the front bearing, the temperature difference between the external environment and the rear bearing, and the initial temperature difference between the spindle housing and the external environment, respectively. 5.3) Considering the time characteristics of the spindle system's thermal error, a matrix-form thermal error model is constructed: In the formula, K = [K1 … K7 K8 … K 16 ] represents the coefficient matrix, and C represents the constant matrix. This represents an electromechanical-thermal element matrix, where the elements are experimentally measured real-time electromechanical-thermal data; t1, t i t n Indicates a time step.

5. The data modeling method for thermal error mechanism of worm gear grinding machine spindle considering electromechanical-thermal coupling effect according to claim 1, characterized in that: In step 6), the real-time data of the electromechanical-thermal elements includes the temperature data of the worm gear grinding machine, current and voltage signals, and displacement signals of the thermal deformation characteristic points of the spindle system.

6. The data modeling method for thermal error mechanism of worm gear grinding machine spindle considering electromechanical-thermal coupling effect according to claim 5, characterized in that: Temperature data for worm gear grinding machines is acquired via temperature sensors and temperature acquisition cards. Current and voltage signals are obtained through current transformers, voltage transformers, and power meters; The displacement signals of the thermal deformation characteristic points of the spindle system are acquired through a laser displacement sensor and a displacement acquisition card.

7. The method for data modeling the thermal error mechanism of a worm gear grinding machine spindle considering electromechanical-thermal coupling effect according to claim 1, characterized in that: Step 7) transforms the thermal error model of the spindle system into an optimization problem, and the steps for solving it using the HPSO-GA optimization algorithm include: 7.1) Establish the equation for solving the coefficients of the spindle thermal error model, i.e.: In the formula, This represents the spindle thermal error value obtained from experimental measurements. This represents the spindle thermal error value obtained from the established model; F(K1,K2,…,K) 15 ,K 16 C) represents the coefficient function to be solved; 7.2) The genetic algorithm is embedded into the particle swarm optimization algorithm to obtain the hybrid optimization algorithm HPSO-GA; 7.3) Solve formula (26) using the hybrid optimization algorithm HPSO-GA to obtain the thermal error.

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