CN-119620683-B - Worm grinding wheel gear grinding machine spindle thermal error mechanism-data modeling method considering electric-mechanical-thermal coupling effect

CN119620683BCN 119620683 BCN119620683 BCN 119620683BCN-119620683-B

Abstract

The invention discloses a worm grinding wheel gear grinding machine spindle thermal error mechanism-data modeling method considering an electric-mechanical-thermal coupling effect, which comprises the steps of 1) constructing an association relation between thermal expansion deformation of a spindle system and a temperature variable, 2) constructing a spindle system thermal balance equation and deducing the association relation between the spindle thermal error and the heat absorption of a spindle structure, 3) constructing a mathematical expression of heat generation quantity of the spindle system relative to the electric-mechanical-thermal variable, 4) constructing a mathematical expression of heat dissipation quantity of the spindle system relative to the electric-mechanical-thermal variable, 5) constructing a theoretical model of the spindle system thermal error relative to the electric-mechanical-thermal variable, 6) solving and converting the spindle system thermal error model into an optimization problem, and solving by utilizing a HPSO-GA optimization algorithm to obtain the spindle system thermal error. The invention can accurately predict the thermal error of the main shaft and simultaneously reveal the influence of the electric-mechanical-thermal coupling effect of the main shaft system on the thermal error.

Inventors

CAO HUAJUN
Lai Kexu
TAO GUIBAO
HOU SHENGWEN
YAN PENGHUI
YAO JINGCHAO
TAN YANFANG

Assignees

重庆大学
陕西法士特齿轮有限责任公司

Dates

Publication Date: 20260505
Application Date: 20241104

Claims (7)

1. The method for modeling the thermal error mechanism-data of the main shaft of the worm grinding wheel gear grinding machine by considering the electric-mechanical-thermal coupling effect is characterized by comprising the following steps of: 1) Analyzing the electric-mechanical-thermal multi-energy coupling characteristic of the main shaft system, and constructing the association relation between the thermal expansion deformation of the main shaft system and the temperature variable according to the thermoelastic mechanics; 2) By combining thermodynamic analysis and energy conservation law, a main shaft system heat balance equation is established, and the association relation between a main shaft heat error and main shaft structure heat absorption is deduced; 3) Analyzing the heat generation characteristic of the main shaft system, and constructing a mathematical expression of the heat generation quantity of the main shaft system about the electric-mechanical-thermal variables; 4) Analyzing the heat dissipation characteristic of the main shaft system, and constructing a mathematical expression of the heat dissipation capacity of the main shaft system on the electric-mechanical-thermal variables; 5) Deducing a heat balance equation of the main shaft system, and establishing a theoretical model of the heat error of the main shaft system related to an electric-mechanical-thermal variable; 6) Carrying out a cutting experiment, acquiring real-time data of an electric machine-thermal element, and training a theoretical model of a main shaft system thermal error related to an electric machine-thermal variable to obtain a main shaft system thermal error model; 7) Solving and converting the thermal error model of the main shaft system into an optimization problem, and solving by utilizing HPSO-GA optimization algorithm to obtain the thermal error of the main shaft system; in the step 1), the step of constructing the association relation between the thermal expansion deformation of the spindle system and the temperature variable comprises the following steps: 1.1 Simplified spindle system into a thin-walled cylinder, a thermal expansion deformation expression at the spindle housing r=b is constructed, namely: Wherein u r＝b represents a thermal expansion coefficient, r represents a radius, a and b represent an inner radius and an outer radius of the spindle respectively, α represents a linear expansion coefficient of the spindle material, c 1 represents a constant, T represents a spindle temperature, and T a 、T b represents an inner diameter and an outer diameter temperature of the spindle respectively; 1.2 Setting variables except the temperature variable as constants, simplifying the thermal expansion deformation expression at the position of the spindle housing r=b, and constructing the association relation between the thermal expansion deformation of the spindle system and the temperature variable, namely: δ spindle ＝u r＝b ＝k 1 (T b -T a )+c 1 (2) Wherein k 1 represents a coefficient, delta spindle is a principal axis thermal error; In step 2), the spindle system thermal equilibrium equation is as follows: In the formula, Represents the heat absorption capacity of the spindle structure, Q accum is the heat accumulation capacity of the spindle system, Q gen and Q dis respectively represent the heat generation capacity and the heat dissipation capacity of the spindle system, And Respectively represent the main shaft system the bearing generates heat and the motor generates heat, And Respectively representing heat conduction, heat convection and heat radiation heat dissipation of the spindle system; Wherein, the main shaft system absorbs heat The following is shown: Wherein m, c, ρ and l 0 respectively represent the main shaft structural mass, specific heat capacity, average density, length, k 2 、k 3 represents a coefficient, c 2 represents a constant, deltaT is a temperature difference, d represents a bearing diameter, and T 0 represents an external environment initial temperature; In step 2), the association relationship between the spindle thermal error and the spindle structure heat absorption is as follows: Where k 2 、k 3 denotes the coefficient and delta spindle is the principal axis thermal error.
2. The method for modeling thermal error mechanism-data of a spindle of a worm grinding wheel gear grinding machine taking into account the effect of electro-mechanical-thermal coupling as defined in claim 1, wherein in step 3), the step of constructing a mathematical expression of the heat generation amount of the spindle system with respect to the electro-mechanical-thermal variables comprises: 3.1 Calculating the heat generation quantity of the main shaft bearing, namely: wherein M and n respectively represent the total friction torque and the rotating speed of the bearing, M 0 and M 1 respectively represent the friction torque caused by the viscosity of the lubricating oil of the bearing and the friction torque caused by the load of the bearing, F 0 and F 1 are constants, gamma is the kinematic viscosity of the lubricating oil, d m represents the average diameter of the bearing, and F 1 is the equivalent load; Representing heat generated by a main shaft system bearing; 3.2 Combining formulas (6) - (7), yields: Wherein X 0 and Y 0 represent the radial and axial static load coefficients of the bearing, respectively, and F R and F A represent the radial and axial loads of the bearing, respectively; 3.3 Simplifying the formula (8) to obtain: Wherein k 4 、k 5 represents a coefficient, c 3 represents a constant; 3.4 Calculating the heat generation amount of the spindle motor, namely: In the formula, And Respectively represents the heat generation amount caused by the loss of the rotor, the stator and the windage, Representation of And P motor and η motor represent motor power and efficiency, respectively, D rotor 、L rotor and f rotor represent rotor diameter, length and frequency, respectively, μ air represents air dynamic viscosity, h represents the distance between rotor and stator; 3.5 Simplifying the formula (10) to obtain a mathematical expression of the heat generation quantity of the main shaft system about the electric-mechanical-thermal variable, namely: Where k 6 、k 7 is a coefficient.
3. The method for modeling thermal error mechanism-data of a worm grinding wheel gear grinding machine spindle taking into account the effect of electric-mechanical-thermal coupling according to claim 1, wherein in step 4), the step of constructing a mathematical expression of the heat dissipation capacity of the spindle system with respect to the electric-mechanical-thermal variables comprises: 4.1 Calculating cooling water heat dissipation capacity for motor heat dissipation Namely: Wherein, c W and Respectively representing the specific heat capacity and the mass flow of cooling water, and T W,out and T W,in respectively representing the inlet and outlet temperatures of the cooling water; 4.2 Simplifying the formula (12) to obtain: wherein k 8 is a coefficient; 4.3 Calculating heat dissipation capacity of compressed air in motor Namely: Wherein, T rotor 、T stator and T ca,in respectively represent rotor, stator and compressed air temperature; A rotor 、A stator represents the heat convection area of the rotor and the stator, D cg 、L cg and h W represent the diameter, the length and the heat convection coefficient of the cooling tank, k 9 、k 10 、k 11 、k 12 represents the coefficient, and k represents the intermediate coefficient; 4.4 Simplifying formula (14) to obtain: Wherein k 13 、k 14 、k 15 represents a coefficient; 4.5 Calculating natural convection heat dissipation in a motor Namely: Wherein k am and The thermal conductivity and the average knoop-Seal coefficient of natural convection are respectively represented, D sh and A sh are respectively represented by the outer diameter and the surface area of a motor shell of a main shaft, T sh and T am are respectively represented by the temperature of the shell of the main shaft and the temperature of the external environment, and k 16 is a coefficient; 4.6 The heat dissipation capacity of the bearing and the compressed air and the natural convection heat dissipation capacity of the bearing and the ambient air are calculated, namely: In the formula, The heat dissipation of the compressed air and the front bearing, the heat dissipation of the compressed air and the rear bearing, the heat dissipation of the air and the front bearing and the heat dissipation of the air and the rear bearing are respectively shown; Respectively representing convection heat exchange coefficients of compressed air in front and rear bearings, T front 、T rear respectively representing temperatures of the front and rear bearings, D front 、D rear respectively representing diameters of the front and rear bearings, and A front 、A rear respectively representing convection heat exchange areas of the front and rear bearings; representing the average number of knoop-seels of compressed air flowing in the front and rear bearings, respectively; 4.7 Simplifying the formula (17) to obtain: wherein k 17 、k 18 、k 19 、k 20 represents a coefficient; 4.8 Calculating the heat conduction and dissipation capacity of the spindle Namely: Wherein λ and A SC respectively represent the thermal conductivity and the equivalent surface area of the spindle system, and l 0 represents the length of the spindle; 4.9 Simplifying formula (19) to obtain: wherein k 21 represents a coefficient; 4.10 Calculating the heat radiation heat dissipation capacity of the main shaft: Wherein, xi represents the material heat emissivity, k B represents a constant, xi sh represents the material emissivity of the spindle motor housing, A sh represents the outer surface area of the spindle motor housing, xi rear represents the front bearing material emissivity, xi front represents the rear bearing material emissivity, T front 、T rear represents the front and rear bearing temperatures respectively, T sh represents the spindle motor housing temperature; 4.11 Simplifying the formula (21) to obtain a mathematical expression of the heat dissipation capacity of the main shaft system about the electro-mechanical-thermal variable, namely: where k 22 、k 23 、k 24 denotes a coefficient.
4. The method for modeling mechanism-data of thermal error of spindle of worm grinding wheel gear grinding machine taking into account electric-mechanical-thermal coupling effect as defined in claim 1, wherein in step 5), the step of establishing a theoretical model of the thermal error of the spindle system with respect to electric-mechanical-thermal variables comprises: 5.1 Establishing a main shaft system heat balance equation according to the law of conservation of energy, namely: Wherein ,k 1 、k 2 、k 3 、k 4 、k 5 、k 6 、k 7 、k 8 、k 13 、k 14 、k 15 、k 16 、k 17 、k 18 、k 19 、k 20 、k 21 、k 22 、k 23 、k 24 denotes a coefficient; 5.2 Finishing a main shaft system heat balance equation to obtain: Wherein ,K 1 、K 2 、K 3 、K 4 、K 5 、K 6 、K 7 、K 8 、K 9 、K 10 、K 11 、K 12 、K 13 、K 14 、K 15 、K 16 represents an electro-mechanical-thermal coefficient, C represents a constant, and DeltaT ca-fb 、ΔT ca-rb 、ΔT am-fb 、ΔT am-rb 、ΔT am-sh 、ΔT b-0 represents a temperature difference between compressed air and a front bearing, a temperature difference between compressed air and a rear bearing, a temperature difference between an external environment and the front bearing, a temperature difference between the external environment and the rear bearing, and a temperature difference between a main shaft housing and an initial temperature of an external environment, respectively; 5.3 Taking the thermal error time characteristic of the main shaft system into consideration, constructing a matrix thermal error model: Where k= [ K 1 … K 7 K 8 … K 16 ] represents a coefficient matrix, C represents a constant matrix, Represents an electro-mechanical-thermal element matrix, the elements in the matrix are experimentally measured electro-mechanical-thermal real-time data, and t 1 、t i 、t n represents a time step.
5. The method for modeling thermal error mechanism-data of a worm grinding wheel gear grinding machine spindle taking into account the effect of electric-mechanical-thermal coupling according to claim 1, wherein in step 6), the real-time data of electric-mechanical-thermal elements comprise temperature data, current and voltage signals of the worm grinding wheel gear grinding machine and thermal deformation characteristic displacement signals of a spindle system.
6. The method for modeling the thermal error mechanism-data of the main shaft of the worm grinding wheel gear grinding machine by taking the electric-mechanical-thermal coupling effect into consideration as claimed in claim 5 is characterized in that the temperature data of the worm grinding wheel gear grinding machine are obtained through a temperature sensor and a temperature acquisition card; The current and voltage signals are obtained through a current transformer, a voltage transformer and a power meter; The thermal deformation characteristic point displacement signal of the spindle system is obtained through a laser displacement sensor and a displacement acquisition card.
7. The method for modeling the thermal error mechanism-data of the main shaft of the worm grinding wheel gear grinding machine by considering the electric-mechanical-thermal coupling effect according to claim 1, wherein the step 7) of solving and converting the thermal error model of the main shaft system into an optimization problem and utilizing HPSO-GA optimization algorithm comprises the following steps: 7.1 Establishing a principal axis thermal error model coefficient solving equation, namely: In the formula, Representing the experimentally measured spindle thermal error value, F (K 1 ,K 2 ,…,K 15 ,K 16 , C) is a coefficient function to be solved; 7.2 Embedding the genetic algorithm into a particle swarm algorithm to obtain a hybrid optimization algorithm HPSO-GA; 7.3 And (3) solving a formula (26) by utilizing a hybrid optimization algorithm HPSO-GA to obtain a thermal error.

Description

Worm grinding wheel gear grinding machine spindle thermal error mechanism-data modeling method considering electric-mechanical-thermal coupling effect Technical Field The invention relates to the technical field of machine tool control, in particular to a worm grinding wheel gear grinding machine spindle thermal error mechanism-data modeling method considering an electric-mechanical-thermal coupling effect. Background The factors influencing the machining precision of the machine tool mainly comprise geometric errors, thermal errors, motion errors, machining errors and the like, wherein the thermal errors account for 40% -70% of the total errors. For gear processing machine tools, such as worm grinding wheel gear grinding machine tools, a main shaft is the most critical functional component, and the gear processing precision and efficiency are directly affected. However, due to the integrated design of the spindle system, the combined action of the internal heat source and the external heat source causes unstable internal heat environment of the spindle and uneven temperature distribution, and finally causes thermal deformation of the spindle structure. Therefore, the thermal deformation mechanism of the main shaft of the worm grinding wheel gear grinding machine is revealed, and the establishment of an accurate thermal error model is crucial for the improvement of machining precision and the guarantee of precision consistency. However, because the electric-mechanical-thermal coupling mechanism of the main shaft system of the worm grinding wheel gear grinding machine and the main shaft thermal characteristic rule are not clear, the establishment of an accurate main shaft thermal error model still has challenges. The traditional thermal error modeling method mainly comprises two types of models (black box model) based on mechanisms and models (white box model) driven by data. The method is characterized in that the method comprises the steps of establishing a thermal error and a temperature variable mapping relation through an intelligent algorithm, obtaining a model coefficient is difficult, and the model cannot provide visual explanation and physical significance. Disclosure of Invention The invention aims to provide a worm grinding wheel gear grinding machine main shaft thermal error mechanism-data modeling method considering an electric-mechanical-thermal coupling effect, which comprises the following steps of: 1) Analyzing the electric-mechanical-thermal multi-energy coupling characteristic of the main shaft system, and constructing the association relation between the thermal expansion deformation of the main shaft system and the temperature variable according to the thermoelastic mechanics; 2) By combining thermodynamic analysis and energy conservation law, a main shaft system heat balance equation is established, and the association relation between a main shaft heat error and main shaft structure heat absorption is deduced; 3) Analyzing the heat generation characteristic of the main shaft system, and constructing a mathematical expression of the heat generation quantity of the main shaft system about the electric-mechanical-thermal variables; 4) Analyzing the heat dissipation characteristic of the main shaft system, and constructing a mathematical expression of the heat dissipation capacity of the main shaft system on the electric-mechanical-thermal variables; 5) Deducing a heat balance equation of the main shaft system, and establishing a theoretical model of the heat error of the main shaft system related to an electric-mechanical-thermal variable; 6) Carrying out a cutting experiment, acquiring real-time data of an electric machine-thermal element, and training a theoretical model of a main shaft system thermal error related to an electric machine-thermal variable to obtain a main shaft system thermal error model; 7) And solving and converting the thermal error model of the main shaft system into an optimization problem, and solving by utilizing HPSO-GA optimization algorithm to obtain the thermal error of the main shaft system. Further, in step 1), the step of constructing the association relationship between the thermal expansion deformation of the spindle system and the temperature variable includes: 1.1 Simplified spindle system into a thin-walled cylinder, a thermal expansion deformation expression at the spindle housing r=b is constructed, namely: (1) Wherein u r＝b denotes a thermal expansion coefficient, r denotes a radius, a and b denote an inner radius and an outer radius of the spindle, respectively, α denotes a linear expansion coefficient of the spindle material, c 1 denotes a constant, T denotes a spindle temperature, and T a、Tb denotes an inner diameter and an outer diameter temperature of the spindle, respectively. 1.2 Setting variables except the temperature variable as constants, simplifying the thermal expansion deformation expression at the position of the spindle housing r=b,