Methods and apparatus for calculating temperature field in ultrasonic vibration grinding of gears

Abstract

This application discloses a method and apparatus for calculating the temperature field in ultrasonic vibration grinding of gears. The method first constructs a nonlinear macroscopic heat source model; then, it corrects the nonlinear macroscopic heat source model using modified microscopic perturbation terms and shape correction parameters to obtain a corrected nonlinear macroscopic heat source model; the constructed three-dimensional heat conduction partial differential equation, first boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are used to construct a functional, and the initial temperature field is calculated; based on the initial temperature field, the shape correction parameters are iteratively optimized; the corrected nonlinear macroscopic heat source model is further corrected using target shape parameters, and target boundary conditions are constructed; the constructed three-dimensional heat conduction partial differential equation, target boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are used to construct a target functional, and the target temperature field is calculated based on the target functional. This application can improve the accuracy of temperature field calculation.

Description

Technical Field

[0001] This application relates to the field of temperature field calculation technology, and in particular to a method and apparatus for calculating the temperature field in ultrasonic vibration grinding of gears. Background Technology

[0002] Ultrasonic vibration grinding of gears is a precision machining technology that superimposes high-frequency micro-amplitude vibration on traditional gear forming grinding. It is widely used to improve the geometric accuracy and surface quality of gear teeth and enhance transmission performance. During gear grinding, a large amount of mechanical energy is released as heat, especially under dry grinding or heavy-load grinding conditions. The heat generated in the grinding zone is mainly transferred to the workpiece, causing a sharp increase in the local temperature of the tooth surface. Excessive temperature can cause a series of thermal damage problems, such as thermal cracks on the tooth surface, residual tensile stress, grinding burns (white layer), microstructure annealing, and thermal deformation of the tooth profile. In severe cases, it can even affect the fatigue life and transmission reliability of the gear. Therefore, accurately predicting the temperature field distribution in the grinding zone and effectively controlling thermal damage during ultrasonic vibration grinding of gears is one of the key technical challenges in the gear manufacturing field.

[0003] Existing grinding heat source models are mostly based on single shape assumptions or empirical corrections under specific working conditions, making it difficult to simultaneously take into account the combined effects of multiple disturbance factors. The accuracy and generalization ability of the models are insufficient under different working conditions. At the same time, they are highly dependent on experimental calibration, which is not conducive to achieving efficient temperature field prediction and rapid process optimization. Summary of the Invention

[0004] This application aims to propose a method and apparatus for calculating the temperature field in ultrasonic vibration grinding of gears, which can improve the accuracy of temperature field calculation, enhance generalization ability, and achieve efficient temperature field prediction and rapid process optimization.

[0005] In a first aspect, embodiments of this application provide a method for calculating the temperature field in ultrasonic vibration grinding of gears, the method comprising:

[0006] Based on the involute parametric equation, the grinding wheel linear velocity and equivalent contact arc length are calculated, and the total heat flux intensity in the discrete grinding region is calculated according to the grinding wheel linear velocity and the equivalent contact arc length.

[0007] Based on the total heat flux intensity, the heat flux intensity flowing into the gear tooth surface is determined, and the heat flux intensity flowing into the gear tooth surface is constructed as a nonlinear macroscopic heat source model;

[0008] The shape parameters in the nonlinear macroscopic heat source model are corrected by ultrasonic amplitude and frequency to construct shape correction parameters; micro-perturbation terms are added to the nonlinear macroscopic heat source model, and the micro-perturbation terms are corrected by the calculated perturbation correlation length and perturbation variance to obtain the corrected micro-perturbation terms.

[0009] The nonlinear macroscopic heat source model is corrected by the modified microscopic perturbation term and the shape correction parameter to obtain the modified nonlinear macroscopic heat source model.

[0010] Based on the modified nonlinear macroscopic heat source model, a first boundary condition is constructed, and a second boundary condition, a third boundary condition, and an initial value condition are also constructed.

[0011] The constructed three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition are used to construct a functional, and the initial temperature field is calculated based on the functional. Based on the initial temperature field, the shape correction parameters are iteratively optimized to obtain the target shape parameters.

[0012] The modified nonlinear macroscopic heat source model is corrected by the target shape parameters to obtain the target nonlinear macroscopic heat source model. Based on the target nonlinear macroscopic heat source model, the target boundary conditions are constructed.

[0013] The constructed three-dimensional heat conduction partial differential equation, the target boundary condition, the second boundary condition, the third boundary condition, and the initial condition are used to construct a target functional, and the target temperature field is calculated based on the target functional.

[0014] Compared with the prior art, the first aspect of this application has the following beneficial effects:

[0015] This method constructs a nonlinear macroscopic heat source model by integrating the heat flow intensity flowing into the gear tooth surface into a physically meaningful model. This enables more accurate prediction of the peak temperature and its spatial location on the tooth surface, reducing errors in peak temperature estimation and temperature gradient calculation. This provides a reliable basis for identifying and avoiding thermal damage such as grinding burns and thermal cracks. Shape parameters in the nonlinear macroscopic heat source model are corrected using ultrasonic amplitude and frequency to construct shape correction parameters. Microscopic perturbation terms are added to the nonlinear macroscopic heat source model, and these terms are corrected using the calculated perturbation correlation length and variance. The heat source distribution is then corrected using the macroscopic parameter mapping relationship and the microscopic random perturbation terms. High prediction accuracy can be maintained by adjusting only the input parameters, significantly enhancing the generalization and adaptability of the heat source model. The corrected nonlinear macroscopic heat source model and the shape correction parameters are iteratively optimized to construct a target functional. Based on this target functional, the target temperature field is calculated, improving the accuracy of temperature field calculation and enabling efficient temperature field prediction and rapid process optimization.

[0016] Secondly, embodiments of this application also provide a temperature field calculation device for gear ultrasonic vibration grinding, the device comprising:

[0017] The first calculation unit is used to calculate the grinding wheel linear velocity and equivalent contact arc length based on the involute parametric equation, and to calculate the total heat flux intensity in the discrete grinding region based on the grinding wheel linear velocity and the equivalent contact arc length.

[0018] The first construction unit is used to determine the heat flow intensity flowing into the gear tooth surface based on the total heat flow intensity, and to construct the heat flow intensity flowing into the gear tooth surface as a nonlinear macroscopic heat source model;

[0019] The first correction unit is used to correct the shape parameters in the nonlinear macro heat source model by ultrasonic amplitude and frequency, and construct shape correction parameters; add micro-perturbation terms to the nonlinear macro heat source model, and correct the micro-perturbation terms by calculating the perturbation correlation length and perturbation variance, to obtain the corrected micro-perturbation terms.

[0020] The second correction unit is used to correct the nonlinear macroscopic heat source model using the corrected microscopic perturbation term and the shape correction parameter to obtain the corrected nonlinear macroscopic heat source model.

[0021] The second construction unit is used to construct the first boundary condition, the second boundary condition, the third boundary condition, and the initial value condition based on the modified nonlinear macroscopic heat source model.

[0022] The parameter optimization unit is used to construct a functional from the constructed three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition, and to calculate the initial temperature field based on the functional; and to iteratively optimize the shape correction parameters based on the initial temperature field to obtain the target shape parameters.

[0023] The third construction unit is used to modify the modified nonlinear macroscopic heat source model through the target shape parameters to obtain the target nonlinear macroscopic heat source model, and to construct the target boundary conditions based on the target nonlinear macroscopic heat source model.

[0024] The temperature field calculation unit is used to construct a target functional from the constructed three-dimensional heat conduction partial differential equation, the target boundary condition, the second boundary condition, the third boundary condition, and the initial condition, and to calculate the target temperature field based on the target functional.

[0025] Thirdly, embodiments of this application also provide an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform a temperature field calculation method in gear ultrasonic vibration grinding as described above.

[0026] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a temperature field calculation method for gear ultrasonic vibration grinding as described above.

[0027] It is understood that the beneficial effects of the second to fourth aspects compared with the related technologies are the same as the beneficial effects of the first aspect compared with the related technologies. Please refer to the relevant description in the first aspect above, which will not be repeated here. Attached Figure Description

[0028] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0029] Figure 1 This is a schematic flowchart of an embodiment of the temperature field calculation method in ultrasonic vibration grinding of gears provided in this application;

[0030] Figure 2 This is a schematic diagram illustrating the motion relationship between the gear ultrasonic vibration grinding wheel and the gear tooth surface in the preferred embodiment of the temperature field calculation method for gear ultrasonic vibration grinding provided in this application.

[0031] Figure 3 This is a schematic diagram of the grinding heat source discreteness and distribution pattern in the optimal embodiment of the temperature field calculation method in ultrasonic vibration grinding of gears provided in this application;

[0032] Figure 4 This is a schematic diagram of the gear surface boundary and mesh division in the preferred embodiment of the temperature field calculation method in ultrasonic vibration grinding of gears provided in this application;

[0033] Figure 5 This is a schematic diagram of the boundary load optimization in ultrasonic vibration grinding of gears, in the best embodiment of the temperature field calculation method in ultrasonic vibration grinding of gears provided in this application.

[0034] Figure 6 This is a schematic diagram of the overall process for calculating the temperature field in ultrasonic vibration grinding of gears in the preferred embodiment of the temperature field calculation method in ultrasonic vibration grinding of gears provided in this application.

[0035] Figure 7 This is a schematic diagram of an embodiment of the temperature field calculation device for gear ultrasonic vibration grinding provided in this application. Detailed Implementation

[0036] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0037] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0038] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0039] Existing grinding heat source models are mostly based on single shape assumptions or empirical corrections under specific working conditions, making it difficult to simultaneously take into account the combined effects of multiple disturbance factors. The accuracy and generalization ability of the models are insufficient under different working conditions. At the same time, they are highly dependent on experimental calibration, which is not conducive to achieving efficient temperature field prediction and rapid process optimization.

[0040] To address the problems existing in the prior art, this application proposes a method and apparatus for calculating the temperature field in ultrasonic vibration grinding of gears.

[0041] Reference Figure 1 This application provides a schematic flowchart of a method for calculating the temperature field in ultrasonic vibration grinding of gears. This method is applied to electronic devices, such as servers or mobile terminals. Figure 1 As shown, the method for calculating the temperature field in ultrasonic vibration grinding of gears may include the following steps:

[0042] Step S101: Based on the involute parametric equation, calculate the grinding wheel linear velocity and equivalent contact arc length, and calculate the total heat flux intensity in the discrete grinding region according to the grinding wheel linear velocity and equivalent contact arc length.

[0043] Step S102: Based on the total heat flux intensity, determine the heat flux intensity flowing into the gear tooth surface, and construct the heat flux intensity flowing into the gear tooth surface as a nonlinear macroscopic heat source model;

[0044] Step S103: Correct the shape parameters in the nonlinear macro heat source model by ultrasonic amplitude and frequency to construct shape correction parameters; add micro-perturbation terms to the nonlinear macro heat source model, and correct the micro-perturbation terms by calculating the perturbation correlation length and perturbation variance to obtain the corrected micro-perturbation terms.

[0045] Step S104: The nonlinear macroscopic heat source model is corrected by the modified microscopic perturbation term and shape correction parameter to obtain the corrected nonlinear macroscopic heat source model.

[0046] Step S105: Based on the modified nonlinear macroscopic heat source model, construct the first boundary condition, and construct the second boundary condition, the third boundary condition, and the initial value condition.

[0047] Step S106: Construct the three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition into a functional, and calculate the initial temperature field based on the functional; based on the initial temperature field, iteratively optimize the shape correction parameters to obtain the target shape parameters.

[0048] Step S107: Correct the modified nonlinear macroscopic heat source model by using the target shape parameters to obtain the target nonlinear macroscopic heat source model. Based on the target nonlinear macroscopic heat source model, construct the target boundary conditions.

[0049] Step S108: Construct the constructed three-dimensional heat conduction partial differential equation, target boundary conditions, second boundary conditions, third boundary conditions, and initial conditions into a target functional, and calculate the target temperature field based on the target functional.

[0050] In this embodiment, the grinding wheel linear velocity and equivalent contact arc length are calculated based on the involute parametric equation. The total heat flux intensity within the discrete grinding region is then calculated based on the grinding wheel linear velocity and equivalent contact arc length. Based on the total heat flux intensity, the heat flux intensity flowing into the gear tooth surface is determined, and this heat flux intensity is constructed into a nonlinear macroscopic heat source model. By constructing a physically meaningful nonlinear macroscopic heat source model, the peak temperature of the tooth surface and its spatial location can be predicted more accurately, reducing the temperature peak estimation error and temperature gradient calculation error. This provides a reliable basis for identifying and avoiding thermal damage such as grinding burns and thermal cracks.

[0051] The shape parameters in the nonlinear macroscopic heat source model are corrected by ultrasonic amplitude and frequency to construct shape correction parameters. Microscopic perturbation terms are added to the nonlinear macroscopic heat source model, and the microscopic perturbation terms are corrected by calculating the perturbation correlation length and perturbation variance to obtain the corrected microscopic perturbation terms. The nonlinear macroscopic heat source model is then corrected by the corrected microscopic perturbation terms and the shape correction parameters to obtain the corrected nonlinear macroscopic heat source model. The heat source distribution is corrected by the macroscopic parameter mapping relationship and the microscopic random perturbation terms. High prediction accuracy can be maintained by adjusting only the input parameters, which significantly enhances the generalization and adaptive ability of the heat source model.

[0052] Based on the modified nonlinear macroscopic heat source model, first boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are constructed. The constructed three-dimensional heat conduction partial differential equations, first boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are then used to construct a functional, and the initial temperature field is calculated based on this functional. Based on the initial temperature field, the shape correction parameters are iteratively optimized to obtain the target shape parameters. The modified nonlinear macroscopic heat source model is then modified using the target shape parameters to obtain the target nonlinear macroscopic heat source model. Based on the target nonlinear macroscopic heat source model, target boundary conditions are constructed. The constructed three-dimensional heat conduction partial differential equations, target boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are then used to construct a target functional, and the target temperature field is calculated based on this target functional. Through the modified nonlinear macroscopic heat source model and iterative optimization of the shape correction parameters, the accuracy of temperature field calculation can be improved, enabling efficient temperature field prediction and rapid process optimization.

[0053] The above involute parametric equations can be constructed by transforming the involute parametric equations in the machining coordinate system based on the actual machining position of the tooth surface.

[0054] The above calculation of the grinding wheel linear velocity and equivalent contact arc length is based on the involute parametric equation. Since the equivalent linear velocity of the grinding wheel is in the machining coordinate system... The axial direction is variable. The linear velocity of the grinding wheel during grinding can be calculated based on the maximum actual radius of the grinding wheel and the tooth surface parameters. Then, the equivalent contact arc length can be calculated based on the change in the grinding wheel radius and the radial grinding depth.

[0055] The total heat flux intensity mentioned above is usually divided into the heat flux intensity flowing into the surface of the gear workpiece, the heat flux intensity carried away by the grinding debris generated during the machining process, the heat flux intensity flowing into the grinding wheel, and the heat flux intensity carried away by the grinding fluid.

[0056] The above-mentioned heat flux intensity is determined based on the total heat flux intensity. Since this embodiment studies dry grinding, there is no heat flux intensity carried away by the grinding fluid, and the non-machined surface of the gear is under natural convection heat transfer conditions. The heat flux intensity carried away by the grinding debris can be calculated according to methods known to those skilled in the art. At this point, only the heat flux intensity flowing into the grinding wheel and the heat flux intensity flowing into the gear tooth surface remain. By subtracting the other heat flux intensities from the total heat flux intensity, the heat flux intensity flowing into the gear tooth surface can be obtained.

[0057] The aforementioned functional can be a function that acts on a function in mathematics, referring to a mapping from a function space to a number field; its essence is a function of a function.

[0058] The aforementioned iterative optimization of the shape correction parameters can be achieved by using a non-dominated sorting genetic algorithm II to iteratively optimize the shape correction parameters.

[0059] In some implementations, the heat flow intensity flowing into the gear tooth surface is constructed as a nonlinear macroscopic heat source model, including:

[0060] Calculate the heat flux density at any roll angle position on the contact surface between the grinding wheel and the gear;

[0061] Multiple heat source distribution expressions are constructed along the contact arc length direction, including piecewise triangular distribution expression, trapezoidal distribution expression and parabolic distribution expression;

[0062] Based on heat flux density and the distribution expression for each heat source, a classic heat source distribution model is constructed;

[0063] Using the normalized coordinates of the contact arc length as independent variables, the classical heat source distribution model is constructed into a nonlinear macroscopic heat source model.

[0064] In this embodiment, by constructing the classical heat source distribution model into a nonlinear macroscopic heat source model, the peak temperature of the tooth surface and its spatial location can be predicted more accurately, reducing the temperature peak estimation error and the temperature gradient calculation error, and providing a reliable basis for identifying and avoiding thermal damage such as grinding burns and thermal cracks.

[0065] The above-mentioned piecewise triangular distribution expression, trapezoidal distribution expression, and parabolic distribution expression are all conventional grinding (CG) designs. The single idealized heat source model is a distribution known to those skilled in the art, and this embodiment will not describe it in detail.

[0066] In some implementations, the shape parameters in the nonlinear macroscopic heat source model are corrected by ultrasonic amplitude and frequency to construct shape correction parameters, including:

[0067] The ultrasonic amplitude and frequency are mapped to the shape parameters in the nonlinear macroscopic heat source model through empirical regression, which include the initial thermal intensity, attenuation coefficient, and linear tail weight.

[0068] In this embodiment, a quantitative relationship between "ultrasonic vibration parameters and heat source shape parameters" is established on a macroscopic scale. This allows the heat source distribution to be reconstructed under different ultrasonic amplitudes and frequencies. The corresponding nonlinear heat source curve can be obtained simply by adjusting the shape parameters, which significantly enhances the generalization and adaptability of the heat source model.

[0069] In some implementations, the micro-perturbation term is corrected by calculating the perturbation correlation length and perturbation variance to obtain the corrected micro-perturbation term, including:

[0070] Obtain the disturbance variance, abrasive particle size, concentration, dressing depth, empirical coefficient, and projected area of ​​the grinding wheel surface under the reference working conditions;

[0071] The effective number of abrasive grains with cutting capability is calculated based on abrasive grain size, concentration, empirical coefficient, and the projected area of ​​the grinding wheel surface.

[0072] Calculate the average abrasive grain spacing based on the effective number of abrasive grains and the projected area of ​​the grinding wheel surface;

[0073] The average abrasive grain spacing is normalized to the contact arc length direction to obtain the disturbance correlation length;

[0074] Calculate the smoothing coefficient that affects the magnitude of the perturbation variance based on the ultrasonic amplitude and frequency;

[0075] The perturbation variance is calculated based on the smoothing coefficient, dressing depth, perturbation variance under the reference working condition, and abrasive particle size.

[0076] Based on the disturbance correlation length and disturbance variance, determine the magnitude of the amplitude and the total number of harmonics in the micro disturbance term;

[0077] Based on the magnitude of the amplitude and the total number of harmonics in the micro-perturbation term, the micro-perturbation term is corrected to obtain the corrected micro-perturbation term.

[0078] In this embodiment, the micro-perturbation term is corrected according to the magnitude of the amplitude and the total number of harmonics in the micro-perturbation term. Only the input parameters need to be adjusted to maintain high prediction accuracy, which significantly enhances the generalization and adaptive ability of the heat source model.

[0079] In some implementations, based on the modified nonlinear macroscopic heat source model, a first boundary condition is constructed, and second boundary conditions, third boundary conditions, and initial conditions are also constructed, including:

[0080] The gear surface is delineated by boundary and mesh to determine the adiabatic boundary surface, the convective heat transfer boundary surface, and the grinding heat source input boundary surface.

[0081] For the grinding heat source input boundary surface, the first boundary condition is constructed based on the modified nonlinear macroscopic heat source model;

[0082] For the adiabatic boundary surface, construct a second boundary condition;

[0083] For the convective heat transfer boundary surface, a third boundary condition is constructed;

[0084] The initial temperature of the workpiece at the beginning of grinding is used as the initial condition.

[0085] In this embodiment, based on the modified nonlinear macroscopic heat source model, a first boundary condition is constructed, which can couple the optimization process of the heat source model parameters with the temperature field simulation to achieve intelligent adjustment. The constructed first boundary condition, second boundary condition, third boundary condition and initial condition lay a good data foundation for the accurate calculation of the temperature field in the later stage.

[0086] The initial temperature of the workpiece being ground can be set according to the actual situation. This embodiment does not impose a specific limitation. For example, the initial temperature of the workpiece being ground can be set to 298.15K, then the initial condition is 298.15K.

[0087] The aforementioned adiabatic boundary surface, convective heat transfer boundary surface, and grinding heat source input boundary surface can be determined based on the defined boundaries and grids to identify which positions on the gear surface correspond to the adiabatic boundary surface, convective heat transfer boundary surface, and grinding heat source input boundary surface.

[0088] In some implementations, the shape correction parameters are iteratively optimized based on the initial temperature field to obtain the target shape parameters, including:

[0089] Based on the initial temperature field and the nonlinear macroscopic heat source model, the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function are constructed.

[0090] Based on the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function, the shape correction parameters are iteratively optimized using a non-dominated sorting genetic method.

[0091] When the number of iterations does not reach the preset upper limit or the Pareto front does not converge, the shape correction parameters updated in the current iteration are obtained;

[0092] The nonlinear macroscopic heat source model is repeatedly corrected by the shape correction parameters updated in the current iteration, resulting in the repeatedly corrected nonlinear macroscopic heat source model.

[0093] Based on the repeatedly modified nonlinear macroscopic heat source model, the first boundary condition after repeated modification is constructed.

[0094] The constructed three-dimensional heat conduction partial differential equation, the repeatedly corrected first boundary conditions, second boundary conditions, third boundary conditions, and initial conditions are used to construct a first functional, and the first temperature field is calculated based on the first functional.

[0095] Based on the first temperature field, the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function, the non-dominated sorting genetic method is used to iteratively optimize the shape correction parameters after the current iteration until the number of iterations reaches the preset upper limit or the Pareto front converges, thus obtaining the target shape parameters.

[0096] In this embodiment, a first objective function, a second objective function, a third objective function, a fourth objective function, and a fifth objective function are constructed based on the initial temperature field and the nonlinear macroscopic heat source model. Then, based on the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function, the shape correction parameters are iteratively optimized using a non-dominated sorting genetic method. This can improve the accuracy of temperature field calculation and achieve efficient temperature field prediction and rapid process optimization.

[0097] The above-mentioned iterative optimization of shape correction parameters using non-dominated sorting genetic method can be achieved by using non-dominated sorting genetic method II (i.e., NSGA-II) to iteratively optimize shape correction parameters.

[0098] In some implementations, the target temperature field is calculated based on the target functional, including:

[0099] The solution space domain in the objective functional is divided into multiple elements, and the functional of each element is constructed. Each element is an eight-node hexahedral element.

[0100] Based on the extremum conditions of the functional, the Euler equations of the functionals for each unit are obtained;

[0101] Based on the Euler equations of the functional of each element, the element stiffness matrix equation of each element is determined.

[0102] The time domain corresponding to the element stiffness matrix equation is independently discretized by the finite difference method to obtain the fully discretized element stiffness matrix equation.

[0103] The fully discretized element stiffness matrix equations corresponding to each element are combined to form the global stiffness matrix equation with nodal temperature as the unknown parameter.

[0104] By solving the global stiffness matrix equation, the temperature of each node in each element is obtained, and the temperatures of all nodes in all elements are used to construct the target temperature field.

[0105] In this embodiment, by simulating the actual physical process as a mathematical model, based on the principle of functional minimum and the finite difference method, numerical calculations are performed on the gear ultrasonic vibration grinding process by simultaneously solving the partial differential equations of heat conduction using a heat source model. This enables accurate prediction of the three-dimensional dynamic temperature field of gear ultrasonic vibration grinding.

[0106] To facilitate understanding by those skilled in the art, a set of preferred embodiments is provided below:

[0107] To address the problems of insufficient accuracy in temperature field prediction, poor model versatility, and high dependence on experimental calibration during gear ultrasonic vibration grinding, this embodiment proposes a method for calculating the temperature field in gear ultrasonic vibration grinding. Based on traditional kinematics and mechanothermal analysis, this method introduces a nonlinear adjustable heat source model, a multi-source disturbance correction mechanism, and the NSGA-II multi-objective optimization algorithm. This achieves deep coupling between heat source modeling and three-dimensional transient temperature field simulation, improving the accuracy of temperature field calculation and enabling efficient temperature field prediction and rapid process optimization. The specific technical solution of this embodiment includes the following:

[0108] Step 1: Kinematic analysis and force and heat load calculation of gear ultrasonic vibration grinding.

[0109] Ultrasonic vibration grinding of gears involves superimposing high-frequency micro-amplitude ultrasonic vibrations onto traditional gear forming grinding. This allows for the removal of excess material from the tooth surface using a disc grinding wheel dressed to the target involute shape, achieving the required tooth surface accuracy. In ultrasonic vibration-assisted grinding, the application of vibration can be categorized into two types: applying vibration to the workpiece or applying it to the grinding wheel. Applying ultrasonic vibration to the workpiece is relatively simple but lacks versatility. In actual production, applying ultrasonic vibration to the grinding wheel is usually considered. This embodiment adds ultrasonic vibration of a certain frequency and amplitude to the grinding wheel to investigate the reduction of grinding temperature through ultrasonic vibration. During grinding, the diameter of the grinding wheel along the tooth profile direction and the grinding depth along the normal direction change, leading to a complex contact relationship between the grinding wheel and the workpiece. Therefore, establishing a coordinate system for ultrasonic-assisted forming grinding of gears with the grinding wheel axis as the reference is an important foundation for further modeling. Meanwhile, in the modeling of gear tooth surface grinding temperature calculation, according to Fourier's law, heat flux is the normal input load of the tooth surface. Therefore, it is necessary to transform the radial grinding parameters into normal grinding parameters in the machining coordinate system.

[0110] Taking the contact surface between the grinding wheel and the gear as the research object, such as Figure 2 As shown, the radial feed depth of the grinding wheel relative to the gear axis is... The grinding wheel maintains a certain rotational direction. At the same time, at the feed rate During processing, there is an amplitude of [value missing] perpendicular to the feed speed of the grinding wheel, i.e., along the axis of the grinding wheel. The vibration frequency is The ultrasonic reciprocating vibration completes the machining of the entire tooth surface. Adding ultrasonic-assisted vibration along the grinding wheel axis has little impact on the grinding wheel's trajectory, but it can reduce the grinding force during the grinding process, thereby lowering the grinding temperature and improving the surface quality of the machined gear. (See figure) This indicates the radial grinding depth of the grinding wheel. This indicates the local normal grinding depth on the involute of a gear. The base circle radius and the roll angle are given. , For the exhibition angle, For pressure angle, It is half of the central angle corresponding to the base tooth pitch. The angle between the rotating plane of the grinding wheel and the normal cutting plane of the abrasive grain. .

[0111] Coordinate system for ultrasonic vibration grinding of gears - ,in The shaft is parallel to the grinding wheel axis. shaft and Axis perpendicular, coordinate system - Its origin is Based on the actual machining position of the tooth surface (in this embodiment, the tooth surface refers to the gear tooth surface), the parametric equation of the involute is transformed using coordinate transformation. In the machining coordinate system, the parametric equation of the involute becomes:

[0112] (1);

[0113] in, Indicates matrix transpose. express Coordinate values ​​on the axis express The coordinate values ​​on the axis.

[0114] In actual machining, the grinding wheel has a fixed offset depth relative to the gear axis. However, the actual normal offset depth varies considerably at different positions on the involute of the gear tooth surface, affecting the grinding depth. With radial grinding depth The relationship between them is as follows:

[0115] (2);

[0116] The radius of the grinding wheel along the involute line throughout the entire grinding zone. to The involute height changes constantly, causing the grinding wheel's linear velocity along the tooth profile to change continuously. The distance from the grinding wheel's axis to different involute height positions is not equal. Therefore, the actual grinding wheel radius at different positions on the tooth surface is also different relative to the grinding wheel's axis. This process converts the actual grinding wheel radius at the tooth surface position into the equivalent normal grinding wheel radius. Represented as:

[0117] (3);

[0118] in, express Coordinate values ​​on the axis This represents the maximum radius of the grinding wheel.

[0119] The equivalent linear velocity of the grinding wheel in the machining coordinate system The axial direction is variable. Based on the maximum actual radius of the grinding wheel and the tooth surface parameters, the relationship between the linear velocity and rotational speed of the grinding wheel during grinding can be obtained as follows:

[0120] (4);

[0121] in, This indicates the grinding wheel linear velocity at the grinding position on the involute curve. This indicates the rotational speed of the grinding wheel.

[0122] The equivalent contact arc length can be calculated based on the variation of the grinding wheel radius and the radial grinding depth. for:

[0123] (5);

[0124] The essence of the grinding process is a combination of sliding, plowing, and cutting actions by a large number of randomly distributed abrasive grains on the surface of the grinding wheel. From the perspective of grinding thermal effects, each abrasive grain undergoing cutting can be considered as a continuously generating point heat source. When the abrasive grains cut the workpiece, the combined effect of a large number of discretely distributed point heat sources leads to an increase in temperature near the contact surface between the grinding wheel and the workpiece. In the actual grinding process, the grinding energy consumed by the surface energy of the newly formed surface, the strain energy remaining on the grinding surface, and the kinetic energy of the flying grinding chips is minimal. Therefore, most of the grinding energy is converted into heat energy and transferred to the grinding wheel, workpiece, grinding wheel, and grinding fluid through heat convection and heat conduction. However, the proportion of heat transferred to each part varies with the grinding process parameters and the thermal characteristics of the workpiece and grinding wheel. The friction between the abrasive grains and the workpiece, as well as the energy that causes plastic deformation of the metal, are all converted into heat energy. Without coolant, the total heat flux intensity in the gear ultrasonic vibration grinding area is... It is usually classified as the heat flux intensity flowing into the surface of the gear workpiece. The heat flux carried away by the grinding debris generated during the processing The intensity of the heat flow into the grinding wheel and the heat flux intensity carried away by the grinding fluid The heat flowing into the surface of the gear workpiece is the main research object in this embodiment. The established gear ultrasonic vibration grinding distribution model is the heat source in the grinding area, that is, the contact area between the grinding wheel and the gear workpiece tooth surface, during the processing.

[0125] According to classical grinding theory, the heat flux generated during grinding is distributed differently at different locations along the involute and the contact arc length. By incorporating involute parameters and substituting the normal grinding parameters along the involute, the total heat flux intensity within the discrete grinding region can be determined. for:

[0126] (6);

[0127] in, This refers to the tangential grinding force within the gear tooth surface grinding region. For grinding width, This represents a time shift function.

[0128] This embodiment is dry grinding, therefore there is no heat flux carried away by the grinding fluid. The unmachined surfaces of the gear are subjected to natural convection heat transfer. The heat flux carried away by the wear debris can be calculated using techniques known to those skilled in the art. At this point, only the heat flow intensity flowing into the grinding wheel remains. Intensity of heat flow into the tooth surface Based on the well-known grinding heat distribution theory, the heat flow intensity flowing into the tooth surface within the discrete grinding region can be calculated as follows:

[0129] (7);

[0130] in, The melting point temperature of the workpiece material. The thermal conductivity of the abrasive particles, The thermal conductivity of the workpiece. The average effective grinding radius of the abrasive grains. Indicates density, This indicates specific heat capacity.

[0131] Based on the material removal process during grinding, grinding force can be divided into friction force, plowing force, and cutting force, among which friction force is relatively small and usually negligible. After the grinding region of the tooth surface is discretized, each small region can be approximated as a plane. Based on the established planar grinding force calculation model considering thermal softening effect, shear strain, and shear strain rate, and previous work, the formula for the tangential grinding force in each element considering involute parameters can be obtained:

[0132] (8);

[0133] in, The constants are determined experimentally and can be obtained by solving linear equations based on experimental data.

[0134] In conventional grinding, according to the binomial theorem of friction, the coefficient of friction is... for:

[0135] (9);

[0136] in, , and It is a coefficient related to the physical properties of the processed materials. This represents a certain friction-related angular parameter.

[0137] In ultrasonic vibration grinding, the friction coefficient between the abrasive grains and the workpiece surface can be effectively reduced due to the action of ultrasonic vibration. By studying the effect of ultrasonic vibration on the reduction of grinding force, the ratio of the cutting friction coefficient under vibrating motion state to that under non-vibrating motion state is proposed.

[0138] (10);

[0139] in, It represents the ratio of the object's motion velocity to the maximum value of its vibration velocity. The angle between the direction of vibration and the velocity of the object during axial ultrasonic vibration. The value is taken as , It is a dimensionless time variable.

[0140] The method for calculating grinding force under ultrasonic-assisted vibration grinding is as follows:

[0141] (11);

[0142] in, This represents the tangential force after considering changes in friction.

[0143] Step 2: Construction of intelligent optimization heat source model for multi-source disturbance in gear ultrasonic vibration grinding.

[0144] Based on the kinematic analysis and force-thermal load calculation of gear ultrasonic vibration grinding given in step 1, this embodiment further constructs an intelligent heat source model that can explicitly consider multi-source disturbance factors. This model employs a physically meaningful adjustable nonlinear heat source distribution at the macroscopic scale and introduces abrasive particle disturbances under mechanical and stochastic statistical meanings at the microscopic scale, thereby obtaining a dedicated ultrasonic vibration grinding heat source model with sufficient flexibility.

[0145] This step first presents a macroscopically adjustable nonlinear distributed heat source model in step 2.1; then, in step 2.2, multi-source disturbances such as ultrasonic vibration parameters, abrasive characteristics, and dressing state are introduced into the heat source model to perform multi-scale corrections on the adjustable nonlinear distributed heat source model, thus forming the multi-source disturbance intelligent optimization heat source model of this embodiment.

[0146] Step 2.1, Adjustable nonlinear distributed heat source model.

[0147] In gear forming grinding, the grinding wheel and gear tooth surface are in line contact, and the grinding process exhibits significant transient and nonlinear characteristics. The heat source distribution pattern is typically described based on energy input and material removal mechanisms. In the contact arc region between the grinding wheel and the workpiece, the contact arc length is much smaller than the tooth height and tooth width, and along the tooth profile and tooth width directions, it can be approximated as a transient heat conduction problem in an infinitely large heat conductor. Therefore, any point on the involute can be considered as a point heat source moving along the forming profile curve. Integrating the point heat source from the starting point to the ending point yields the temperature field of the curved heat source, such as... Figure 3 As shown.

[0148] According to existing research, the heat source in gear forming grinding is often assumed to be triangularly distributed along the involute curve, and the heat flux density at any rolling angle position on the contact surface between the grinding wheel and the gear is considered. The calculation formula is:

[0149] (12);

[0150] in, For any position, the roll angle is... The rolling angle at the tooth tip position. The heat transfer ratio to the workpiece at different roll angle positions on the involute of the gear. The average heat flux density is denoted as .

[0151] To describe the overall heat source distribution in the three-dimensional contact area between the grinding wheel and the gear, this embodiment considers the contact area as consisting of countless differentially wide lines. It is composed of narrow involute stripes, among which The coordinates are local coordinates along the grinding contact arc length direction, with a coordinate range of... , Let be the equivalent contact arc length between the grinding wheel and the tooth surface under the working conditions of this embodiment. The heat source distribution along the contact arc length direction can be uniformly described using typical forms such as segmented triangular distribution, trapezoidal distribution, and parabolic distribution, as shown in the expressions in equations (13) to (15). The average heat flux density over the grinding contact arc length, To determine the coefficients of the piecewise triangular heat source distribution pattern and ; , , , , as well as To determine the shape factor of the start and end positions of each line segment and the peak height of the trapezoidal distribution; , and The shape coefficient of the parabolic distribution is used to control the opening direction and peak position of the curve.

[0152] (13);

[0153] (14);

[0154] (15);

[0155] Regardless of the distribution pattern chosen, the total heat flux flowing into the surface of the gear workpiece on a macroscopic scale is... The double integral of equation (16) gives the value at the involute roll angle. and contact arc length coordinates The local heat flux density is integrated within the range. Based on the grinding heat calculated from the grinding force and grinding wheel linear velocity in step 1, this embodiment can determine the energy input per unit time in the grinding zone, thereby determining the constraint between the average heat flux density and the total heat through the energy conservation relationship, so that various classical heat source distribution models can maintain consistency in overall energy.

[0156] (16);

[0157] However, standard heat source distribution models such as piecewise triangular, trapezoidal, and parabolic distributions were originally proposed for conventional grinding (CG), assuming stable contact conditions and that the shape of the heat source does not change over time. Under ultrasonic gear grinding (UVG) conditions, high-frequency vibration causes periodic changes in the contact and separation between the grinding wheel and the gear surface, resulting in a significant asymmetry in the actual heat source distribution, leading-edge offset, and local peak distortion. Traditional piecewise triangular, parabolic, and trapezoidal distribution models are insufficient to reflect this.

[0158] (1) High-frequency modulation of contact conditions in the grinding zone;

[0159] (2) Nonlinear coupling between grinding wheel linear velocity, normal grinding depth and roll angle;

[0160] (3) The law of change of energy ratio of abrasive friction / plowing and cutting stages with vibration conditions.

[0161] During grinding, a large amount of heat is generated when individual abrasive grains remove material from the workpiece surface through friction. From the perspective of the temperature field, each abrasive grain can be regarded as a moving point heat source, and the increase in workpiece surface temperature is the result of the combined effect of these randomly distributed point heat sources. Although some progress has been made in grinding heat source models, specific heat source distributions for ultrasonic vibration grinding (UVG) are still lacking. Widely used distribution methods include piecewise triangular, parabolic, and trapezoidal distributions, which are mainly designed for conventional grinding (CG). A single idealized distribution heat source model cannot accurately describe the temperature field of the entire grinding region, and they do not take into account the high-frequency contact modulation characteristics of ultrasonic vibration, which leads to a decrease in the accuracy of temperature prediction. Specifically, the high-frequency vibration caused by ultrasonic vibration leads to continuous changes in contact conditions within the grinding region, thereby affecting the material removal mechanism and heat conduction characteristics, and thus affecting the heat source distribution pattern. Standard piecewise triangular, parabolic, and trapezoidal distribution curves are designed for stable contact, but cannot represent the asymmetric and offset deposition conditions observed under vibration. The piecewise triangular distribution defines a segmented, time-invariant heat distribution along the arc, which conflicts with the rapidly changing contact conditions of ultrasonic vibration. Parabolic and trapezoidal distributions, with their simple symmetrical shapes, cannot represent the asymmetric and offset deposition observed under vibration. These structural limitations led to the design of a dedicated ultrasonic vibration grinding heat source model with sufficient flexibility in this embodiment.

[0162] Therefore, this embodiment proposes a nonlinear macroscopic heat source model with adjustable parameters based on the aforementioned classical heat source distribution model. This model uses coordinates normalized to the contact arc length. Using the independent variable, the macroscopic heat source model is written as:

[0163] (17);

[0164] in, The initial heat flux density at the arc-length inlet, i.e. , representing "initial thermal intensity" (the heat flux density per unit area when the grinding wheel just enters the contact arc). This is a dimensionless "decay coefficient" that controls the decay rate of the exponential term. The larger the size, the more concentrated the heat is in the front section. The linear tail weighting coefficients are... The time corresponds to a pure exponential decay (with almost no linear tail). It degenerates into a linear triangular distribution; This indicates the combination of "exponential peak and linear tail" to distinguish the energy ratio between the main cutting zone and the sliding / tillage zone.

[0165] To facilitate compatibility with the finite element / finite difference discretization scheme, this embodiment further modifies the three-parameter heat source model shown in equation (17) in... The interval is fitted using the least squares method as follows The order polynomial form is shown in equation (18):

[0166] (18);

[0167] Among them, polynomial system , ,..., for The function is defined, and the total heat is conserved through integral constraints:

[0168] (19);

[0169] in, For grinding width, This represents the heat source value obtained from the macroscopic heat source model.

[0170] By increasing the order of the polynomial It can approximate various complex nonlinear distribution shapes, including peak shifts and curve asymmetry; when The time-varying model degenerates into a traditional linear triangular heat source. (Polynomial coefficients) The model can be calibrated using a small amount of temperature and time data measured by embedded thermocouples or infrared thermography, and then used as a general parameter for similar operating conditions. For operating conditions with significant differences in materials or grinding parameters, the parameters can be recalibrated to maintain the prediction accuracy of the macroscopic heat source model. Based on this nonlinear adjustable heat source model, step 2.2 will further superimpose multi-source disturbance effects such as ultrasonic vibration and abrasive particle distribution on the macroscopic distribution.

[0171] Step 2.1, Multi-source perturbation correction.

[0172] The adjustable nonlinear distributed heat source model obtained in step 2.1 (i.e., the nonlinear macroscopic heat source model with adjustable parameters) mainly reflects the macroscopic average heat flux distribution under a given operating condition. In actual gear ultrasonic vibration grinding, multiple factors such as ultrasonic amplitude and frequency, abrasive grain size and concentration of the grinding wheel, and the dressing state of the grinding wheel will jointly affect the shape of the heat source distribution: on the one hand, it changes the distribution of macroscopic heat flux along the contact arc length, and on the other hand, it causes random fluctuations in heat flux density at the microscopic scale. To more realistically characterize these effects, this embodiment constructs a multi-source disturbance correction module based on the macroscopic heat source model, including:

[0173] (1) The effect of ultrasonic vibration parameters on the shape parameters of macroscopic heat source The impact;

[0174] (2) The effect of random distribution and dressing state of abrasive particles on micro-perturbation term Influence.

[0175] Step 2.2.1: Multi-source disturbance affects macroscopic heat source shape parameters The impact.

[0176] This embodiment will measure the amplitude of ultrasonic vibration. and frequency By empirical regression and the shape parameters of the heat source model and Establish linear or power function mappings, for example , ;and initial heat flux density Then, through the friction coefficient reduction factor Contact duty cycle correction factor This is linked to a vibration-free baseline, thus explicitly representing the multi-source disturbance effect of ultrasonic vibration at the macroscopic heat source model level. As shown below:

[0177] This embodiment will use ultrasonic amplitude. and frequency An empirical mapping relationship is established with the shape parameters in the macroscopic heat source model to construct shape correction parameters (including initial heat intensity, attenuation coefficient, and linear tail weight). Among these, the initial heat flux density... Through the friction coefficient reduction factor Contact duty cycle correction factor Reference value for ordinary grinding The association is shown in equation (20):

[0178] (20);

[0179] in, The baseline initial heat flux density under normal grinding (A=0, f=0) can be calculated by Rowe distribution theory and equation (7). This reflects the effect of ultrasonic vibration in reducing the coefficient of friction between abrasive particles and workpieces; The reduction in effective contact time due to contact and separation cycles is characterized. Both are dimensionless empirical coefficients and can be approximated using linear or power function forms:

[0180] (twenty one);

[0181] (twenty two);

[0182] in, , and These are the empirical coefficients calibrated in the experiment. and These are the selected reference amplitude and frequency, used to normalize different vibration conditions.

[0183] Attenuation coefficient and linear tail weights The degree of inclination of the heat flow along the contact arc length and the proportion of energy at the tail are described respectively. Ultrasonic vibration often concentrates the cutting stage in the front section and weakens the sliding / plowing effect in the rear section. Therefore, this embodiment adopts the linear empirical model shown in equations (23) and (24):

[0184] (twenty three);

[0185] (twenty four);

[0186] in, and This is the reference value under normal grinding. , , and The sensitivity coefficients for amplitude and frequency are determined by experimental regression. As A and f increase, Generally, the increase is slight, indicating that the heat source distribution has shifted forward; The decrease indicates a reduction in the proportion of linear tail energy.

[0187] Through the above mapping relationship, this embodiment establishes a quantitative connection between "ultrasonic vibration parameters and heat source shape parameters" on a macroscopic scale. This allows for adjustments to the shape parameters without reconstructing the heat source distribution under different amplitude and frequency conditions. The corresponding nonlinear heat source curve can then be obtained.

[0188] Step 2.2.2: Correction of microscopic disturbances in abrasive particles.

[0189] Beyond the macroscopic heat source distribution, the random geometry of the abrasive grains on the grinding wheel surface and the non-uniform load distribution cause significant fluctuations in heat flux density at the local scale. To characterize this effect, this embodiment uses a macroscopic continuous heat source model. A statistically significant micro-perturbation term is superimposed on top. The total heat source intensity is expressed as equation (25):

[0190] (25);

[0191] in, This is a zero-mean random function used to reflect local heat flow fluctuations during abrasive cutting. It can be represented by a finite-term random Fourier series, as shown in equation (26):

[0192] (26);

[0193] in, and Let be the random amplitude and phase of the m-th harmonic, respectively. This represents the total number of harmonics. Controlled by... The statistical characteristics of each harmonic can reproduce the random roughness of the grinding wheel surface under different grain sizes and concentrations. In engineering implementation, to ensure physical rationality, this embodiment... The amplitude is set to an upper limit to ensure that the total heat flux density after superposition will not have a negative value or an unrealistically high peak value.

[0194] Spatial correlation scales are given by equations (27) to (29). (Approximately how many) The unit exhibits a distinct peak); the disturbance variance is given by equations (30) to (31). (Strength of fluctuation); and then, based on these statistics, determine the Fourier expansion. and The size and spectral distribution of the [something] can be determined based on techniques known to those skilled in the art or historical experience. For example, when the spatial correlation scale and perturbation variance reach a certain level, a corresponding [something] can be set. and Size and spectral distribution.

[0195] Let the projected area of ​​the grinding wheel surface be... The number of effective abrasive grains with cutting capability is The average abrasive grain spacing :

[0196] (27);

[0197] For a given abrasive grain size Concentration and trimming depth It can be estimated through empirical relationships. and And introduce empirical coefficients Consider the influence of grinding wheel structure and abrasive grain arrangement.

[0198] (28);

[0199] Normalizing the average abrasive grain spacing to the contact arc length direction yields the normalized length:

[0200] (29);

[0201] in, It means "every approximately" A significant heat flux disturbance peak occurs, the magnitude of which can be used as the disturbance correlation length. Approximate to .

[0202] Furthermore, this embodiment explicitly parameterizes the effects of abrasive grain size, dressing interval, and ultrasonic vibration parameters on the disturbance intensity. Disturbance variance Expressed in the form of equation (30):

[0203] (30);

[0204] in, The disturbance variance under the baseline operating condition. and These are the sensitivity coefficients for particle size and trimming interval, respectively. This refers to the cumulative grinding time (or length) between two dressing cycles. This serves as the baseline dressing cycle. Generally speaking, the coarser the grit and the longer the dressing interval, the more uneven the load on the grinding wheel surface. The larger the value. Considering that ultrasonic vibration has a "dispersing" effect on locally overloaded abrasive particles, this embodiment... The introduction of smoothing coefficients that decrease with increasing amplitude and frequency means that the larger A and f are, the smaller the variance, and the heat flux fluctuations are "dispersed and averaged out" by vibration; when A and f are equal to 0, Return to the value for the vibration-free operating condition. It is not directly added to the macro level. Instead of going up, it is through changing The amplitude statistical characteristics are used to correct the heat source. As shown in equation (31):

[0205] (31);

[0206] in, The corresponding sensitivity coefficient is given. The disturbance variance is calculated using equations (30) to (31). Used to uniformly scale the amplitude values ​​of each harmonic in a random Fourier series. , making The variance satisfies This allows for the statistical correction of the heat source model by the random distribution and dressing state of abrasive particles.

[0207] In summary, on a macro scale through , as well as Characterizing the effect of ultrasonic vibration on the average heat source shape at the microscale through , The description of the influence of abrasive particle geometry, dressing state, and ultrasonic vibration on local fluctuations, together constitute the multi-source perturbation intelligent optimization heat source model in this embodiment. Subsequent calculations are based on the NSGA-II distribution shape parameters (including...). , as well as ) provides a unified description of thermal loads for optimization and numerical solution of the three-dimensional temperature field. , Used to correct heat source models without requiring parameter optimization by NSGA-II.

[0208] Step 3: Numerical calculation of the three-dimensional dynamic temperature field.

[0209] In the grinding process, heat transfer is a combination of transient and steady-state responses. Heat is generated through intermittent contact between particles and the workpiece, and this heat accumulates during transfer. Therefore, a numerical method can be used to simulate the heat flow process and temperature changes on the workpiece surface. This method simulates the actual physical process as a mathematical model, based on the functional minimum principle, the Ritz method, and finite element numerical calculation methods. For the ultrasonic vibration grinding process of gears, numerical calculations are performed using a heat source model and simultaneous partial differential equations of heat conduction, enabling the solution and prediction of the three-dimensional dynamic temperature field in ultrasonic vibration grinding of gears. This method has significant advantages in computational efficiency and model adaptability, providing more accurate approximate solutions compared to analytical methods, and offering an effective means for parameterizing and solving the heat source model. By using the heat source as a moving thermal load boundary condition on the gear tooth surface to simulate the ultrasonic vibration grinding of gears, this research problem can be considered a three-dimensional unsteady-state heat transfer problem, whose three-dimensional partial differential equations of heat conduction are as follows:

[0210] (32);

[0211] in, It is a temperature distribution function that varies with time t and location x, y, z. Indicates the temperature distribution of the workpiece. This represents the thermal conductivity of the workpiece, expressed in W / (m·K). Indicates density, Indicates specific heat capacity. Indicates a region.

[0212] For unstable heat conduction problems, in order to specifically determine the solution to the heat transfer problem, in addition to satisfying equation (32), the corresponding basic conditions, namely the initial conditions and boundary conditions, must also be satisfied. Assuming that the initial temperature of the workpiece being ground is 298.15 K (25℃), then in the process of modeling the three-dimensional dynamic temperature field of gear ultrasonic vibration grinding, the gear surface boundary and mesh division are as follows: Figure 4 As shown, its initial conditions (i.e., initial conditions) and boundary conditions are:

[0213] (33);

[0214] The boundary conditions (i.e., the second boundary conditions) for the adiabatic boundary surfaces A, B, and C in the figure are as follows:

[0215] (34);

[0216] The boundary conditions (i.e., the third boundary condition) of the air convection heat transfer boundary surfaces D, E, F, G, and H in the figure are as follows:

[0217] (35);

[0218] in, The convective heat transfer coefficient is used for dry grinding in this embodiment. =15 W / (m2·k)); The external ambient temperature is specified as 293.15 K (25°C) in this embodiment.

[0219] The boundary conditions (i.e., the first boundary conditions) of the grinding heat source input boundary surface I in the figure are as follows:

[0220] (36);

[0221] in, The heat source distribution function for discrete points in the grinding region is the heat source model obtained in step 2 (which can be the heat source model after NSGA-II parameter optimization and multi-source perturbation correction).

[0222] Having determined the above conditions, according to the variational principle, solving the three-dimensional heat conduction partial differential equation within the domain can be transformed into finding the extrema of a functional. The functional form of the heat transfer differential equation and boundary conditions is as follows:

[0223] (37);

[0224] Let functional exist The maximum value is achieved on the upper bound. According to Euler's equation, we know that... It must satisfy equations (32) to (33) within region G, and at the boundary The above satisfies equations (34) to (36). Therefore, in The value of T at the minimum point is an approximate solution to the heat transfer differential equation under the given boundary conditions.

[0225] The solution space domain G is divided into multiple elements, and the temperature field within each element can be approximated using a local interpolation function. A single gear, i.e., the solution space domain G, is divided into several 8-node hexahedral elements, which offer higher computational accuracy than 4-node tetrahedral elements. Due to the extremely high temperature gradient in the grinding zone, a denser mesh is used at this tooth surface, while a sparser mesh is used in regions with lower temperature gradients.

[0226] The temperature field of each element can be obtained by linearly combining the basis functions in the Ritz method. Approximate as a new function :

[0227] (38);

[0228] in, Representative node The temperature at that location Represents a node The basis functions at that location.

[0229] In this embodiment, the basis functions of the 8-node hexahedral element are constructed using three-dimensional Lagrange basis functions. Assume that the vertices of a hexahedral element are... This transforms a point (x, y, z) in the global coordinate system into a point (ξ, η, δ) in the local coordinate system. It is the hexahedral unit number The global coordinates of each node in the local coordinate system are used to determine the shape and size of the hexahedral element. These coordinate values ​​are fixed and independent of the specific size and position of the hexahedral element. Hereafter, ξ, η, and δ refer to the coordinates of the parent element and are unrelated to ξ in the heat source model described earlier.

[0230] If the origin O of the local coordinate system is placed on the centroid of the element, then the first... The three-dimensional Lagrange basis function corresponding to each node can be expressed as:

[0231] (39);

[0232] To accommodate gear forming and grinding, the hexahedral elements used in this model are not uniform in size, thus requiring isoparametric coordinate transformation. By using interpolation functions for spatial coordinate transformation, sub-elements with curved or surface boundaries in the Cartesian coordinate system (x,y,z) can be transformed into regular hexahedral parent elements in the local coordinate system (ξ,η,δ), geometrically adaptable to actual structures with sub-elements of various complex shapes. The interpolation function used for coordinate transformation has formal consistency with the element shape function. This process gives the element a dual characteristic: firstly, the geometric features and loads of the sub-elements are derived from the actual structure, fully reflecting the actual situation; secondly, a large amount of computation is performed within a simple and regular parent element, making it efficient and convenient.

[0233] After dividing the spatial domain G into a finite number of 8-node hexahedral elements, the functional form of the element is:

[0234] (40);

[0235] Where ΔR is the subdomain contained in element e; ΔC is the boundary... The area on it is only near the boundary. The ΔC term will only appear in the cells that meet the requirements.

[0236] According to the extremum condition of the functional We obtain the Euler equation for the functional:

[0237] (41);

[0238] Thus, all the partial derivative forms appearing in the formula can be completely replaced by the partial derivatives of the shape functions, thereby transferring the difficult-to-calculate temperature field partial derivatives to the more easily derived shape functions. Therefore, the equations within the discrete element can be obtained as follows:

[0239] (42);

[0240] in, This represents the basis function at node j.

[0241] Based on this, the time domain is divided into a series of time periods, and the temperature at each node is... It is transformed into a function with time t as the variable, and then the time domain is further discretized independently using the finite difference method, that is:

[0242] (43);

[0243] in, In time The temperature at time node j In time The temperature at time node j .

[0244] Common difference methods include forward difference, backward difference, and midpoint difference. Here, we use the backward difference method, which has strong convergence. The fully discretized equation of equation (42) can be obtained:

[0245] (44);

[0246] Equation (42) yields the element stiffness matrix equation for each 8-node hexahedral element, which is the heat conduction solution equation with the element node temperature as the unknown parameter and varying with time t. Then, the time domain is independently discretized using the finite difference method to obtain the fully discretized element stiffness matrix equation (44). The element stiffness matrix equations of each element are then used to form a set of equations with the node temperature as the unknown parameter, i.e., the overall stiffness matrix equation. By solving this set of equations simultaneously with the initial and boundary conditions, the temperature of each node of the gear at different time periods can be obtained iteratively, and thus the entire temperature field of the gear can be calculated.

[0247] The grinding heat source is applied as a boundary condition on the tooth surface to simulate ultrasonic vibration grinding of gears. Therefore, the grinding area needs to be spatially discretized to facilitate the definition of nodal loads on the tooth surface. Based on this, the heat source is discretized into a finite number of heat source points that move at a certain speed to simulate the movement of the grinding wheel on the tooth surface at different time intervals, such as... Figure 5 As shown. To ensure the accuracy of the heat source intensity value corresponding to the node in the tooth surface grinding area, a second-order Lagrange interpolation formula is used, based on the node... Based on the coordinates, locate the 9 nearest heat sources. to ), calculate the equivalent nodal thermal loads. replace The heat source intensity is incorporated into the overall stiffness matrix equation to obtain the overall effect of heat source loading at each time step. In this embodiment, the heat source intensity is distributed among the tooth surface nodes using quadratic interpolation, balancing computational efficiency and accuracy. However, for regions with steep temperature rises and falls, quadratic interpolation may slightly smooth the peak values. To further improve peak value capture accuracy, higher-order interpolation methods (such as cubic spline interpolation) can be used to reconstruct the heat source distribution. Higher-order interpolation can more accurately reproduce changes in heat flux gradient, but the computational cost increases slightly; therefore, it should be selected judiciously based on the simulation accuracy requirements.

[0248] Constructing the heat flux distribution function :

[0249] (45);

[0250] in, Indicates the corresponding node The amount of heat flowing in, Represents coordinates, This represents the nth point in the x-direction. This represents the i-th point in the x-direction. This represents the m-th point in the z-direction. This represents the j-th point in the z-direction. This represents the magnitude of the heat source corresponding to the i-th point in the x-direction and the j-th point in the z-direction.

[0251] In actual grinding, the grinding zone extends along the tooth surface in the direction of the grinding wheel feed. The grinding contact area, representing the instantaneous contact point between the grinding wheel and the gear tooth surface, is determined by the axis movement. The area the wheel traverses indicates the completion of the machining process; therefore, the grinding area is also a function of time. As a complex curved surface, the gear tooth surface faces complex and difficult-to-handle boundary conditions of time-varying moving heat sources and convective heat transfer at each time step. This necessitates establishing a local coordinate system ξ-η on the tooth surface through coordinate transformation, such as... Figure 5 As shown. Suppose the boundary surface with δ=1 in the unit structure is subjected to a thermal load. The parametric equation of this surface in global coordinates can be obtained through coordinate transformation. In the local coordinate system, let the equation of the surface be δ=1, then... It can be obtained from the cross product of two vectors, combined with the heat flux distribution function. The equivalent nodal thermal load of the heat source load can then be obtained. ,Right now:

[0252] (46);

[0253] in, This represents the partial derivative of the y-coordinate based on the ξ-axis in a local coordinate system. This represents the partial derivative of the z-coordinate based on the ξ-axis in a local coordinate system. This represents the partial derivative of the x-coordinate based on the ξ-axis in a local coordinate system. This represents the partial derivative of the y-coordinate based on the η-axis in the local coordinate system. This represents the partial derivative of the z-coordinate based on the η-axis in the local coordinate system. This indicates the partial derivative of the x-coordinate based on the η-axis in the local coordinate system.

[0254] Step 4: Optimize the shape parameters of the heat source model distribution based on the non-dominated sorting genetic algorithm II (NSGA-II).

[0255] The heat source model can more realistically reflect the energy input characteristics in gear ultrasonic vibration grinding and is a key foundation for temperature field numerical simulation. Different heat source distribution shape parameters directly affect multiple performance indicators such as peak temperature, temperature distribution uniformity, and the spatial range of the high-temperature influence zone. Therefore, this embodiment constructs the solution of the heat source model distribution shape parameters as a multi-objective optimization problem, no longer using a single objective or simple weighted sum optimization, but introducing a Non-dominated Sorting Genetic Algorithm II (NSGA-II) based on Pareto optimality to intelligently optimize the heat source shape coefficients. This embodiment introduces NSGA-II into the heat source model parameter solution process, innovatively combining multi-objective intelligent optimization with numerical simulation to optimize the distribution shape parameters of the heat source model in gear ultrasonic vibration grinding. This method can simultaneously consider multiple evaluation indicators, accurately assess the impact of heat source distribution on the temperature field, more reliably predict workpiece temperature changes during grinding, and provide a basis for process optimization.

[0256] Step 4.1: Mathematical modeling of the multi-objective optimization problem.

[0257] Based on the nonlinear adjustable heat source model in step 2.1, the macroscopic heat flux density along the normalized coordinates ξ∈[0,1] of the grinding contact arc length can be expressed as:

[0258] (47);

[0259] in, Let be the vector of shape parameters for the heat source distribution to be optimized. For ease of optimization, all parameters to be optimized are collectively denoted as a design variable vector:

[0260] (48);

[0261] Each component Corresponding to a shape parameter in the heat source model, D is the total number of parameters. Each parameter is constrained within a given physically reasonable range:

[0262] (49);

[0263] For a given design variable (i.e., a set of heat source shape parameters), by substituting them into the heat source model and coupling them with a three-dimensional transient heat conduction numerical model, the temperature field distribution of the workpiece during the grinding process can be obtained. Based on this temperature field result, this embodiment constructs the following multi-objective function:

[0264] (1) Objective function of temperature field prediction error (i.e., the first objective function).

[0265] The deviation between the simulated temperature and the measured temperature should be as small as possible, which can be characterized by the root mean square value of the temperature error at several temperature measurement points in the grinding contact arc area. For example, define... It is the temperature at the i-th calculation point. This represents the temperature value at the measurement point corresponding to the i-th calculation point, where N is the total number of temperature points. It can be set as follows:

[0266] (50);

[0267] (2) Total heat flux matching objective function (i.e., the second objective function).

[0268] The total heat generated by the macroscopic heat source model should be calculated by back-calculating the total heat from the theoretical heat input or experiments during the grinding process. Matching. Assuming a contact arc length... Grinding width The total heat flowing into the workpiece within the range is ,but:

[0269] (51);

[0270] (3) Objective function for smoothness of heat source distribution (i.e., the third objective function).

[0271] To avoid excessively drastic changes in the heat source along the contact arc, the square integral of the derivative of the heat flux density with respect to the normalized coordinate ξ is introduced as a smoothness index:

[0272] (52);

[0273] (4) Objective function of the high temperature influence area (i.e., the fourth objective function).

[0274] To control the temperature from exceeding the safe temperature threshold The volume V is defined as:

[0275] (53);

[0276] in, The function is a step function, taking the value 1 when the value inside the parentheses is greater than 0, and 0 otherwise; the integration range is the gear volume and the entire grinding time domain.

[0277] (5) Objective function for peak temperature deviation (i.e., the fifth objective function).

[0278] To ensure that the maximum value of the workpiece temperature does not exceed the desired distribution. Defined as:

[0279] (54);

[0280] in, This is a weighting coefficient used to unify dimensions or highlight the importance of temperature peak constraints.

[0281] Traditional methods often use a weighted summation approach to combine multiple objectives into a single scalar objective:

[0282] (55);

[0283] in, The weights for each sub-objective. However, they differ. Choices can lead to drastically different optimization results, and it is difficult to provide an objective and uniform weight setting. This embodiment uses the Pareto optimality concept and the NSGA-II algorithm to directly search for a set of non-dominated solutions in the multi-objective space, avoiding the bias caused by subjective weights.

[0284] Step 4.2, Mathematical definition of Pareto optimality and non-dominated relationship.

[0285] set up and There are two feasible solutions, and their corresponding objective value vectors are:

[0286] (56);

[0287] If the following conditions are met:

[0288] For all targets i, we have:

[0289] (57);

[0290] And there exists at least one objective j that satisfies:

[0291] (58);

[0292] Then it is called a solution Dominant Solution , recorded as .

[0293] In the set of all feasible solutions, if a certain solution If it is not dominated by any other solution, then it is called This represents a Pareto optimal solution. The set of all Pareto optimal solutions is called the Pareto front. The goal of this embodiment is to solve for a set of Pareto optimal heat source shape parameters. Instead of a single weighted sum of optimal solutions.

[0294] Step 4.3, NSGA-II algorithm iterative mechanism and key formulas.

[0295] NSGA-II is a multi-objective optimization algorithm based on population evolution. Unlike particle swarm optimization, which updates particles through an iterative formula of "velocity and position," NSGA-II updates the next generation of the population through "selection, crossover, and mutation." Its core components include:

[0296] Fast non-dominated sorting (assigning a "rank" to each individual); crowding distance calculation to characterize the "sparseness" of individuals in the target space; binary tournament selection based on "rank priority, crowding distance sub-optimal"; simulated binary crossover (SBX) and polynomial mutation to generate offspring; selection of the next generation from parents and offspring based on an elite strategy.

[0297] (1) Population and generational renewal patterns.

[0298] Let the g-th generation population be... for:

[0299] (59);

[0300] Where N is the population size. Represents the g-th generation population The Nth particle. From... through selection, crossover, and mutation operations, from... Produce offspring populations of the same size. :

[0301] (60);

[0302] in, Represents the g-th generation offspring population The Nth particle.

[0303] By merging the parent and child generations, we obtain:

[0304] (61);

[0305] In merging populations Perform non-dominated sorting and crowding distance (i.e.) ) Calculate and use an elite retention strategy to select N individuals to form the next generation population:

[0306] (62);

[0307] Repeat the above process until the number of iterations or the convergence condition is met.

[0308] (2) Non-dominated sorting and rank assignment.

[0309] For merged populations All individuals are ranked according to the aforementioned dominance relationship using a fast non-dominated ordering, dividing them into multiple Pareto levels:

[0310] (63);

[0311] in, This is the first Pareto front (completely non-dominated solution set). This is the second frontier, and so on. For those belonging to the... All individuals in the layer Assign it a rank:

[0312] (64);

[0313] (3) Formula for calculating crowding distance.

[0314] In the same Pareto level Within this framework, to maintain the uniform distribution of solutions in the target space, for each individual... Calculate crowd distance The specific approach is as follows: for each objective function... According to the target value Sort the individuals in the middle, and denote the index of the sorted individuals as . Then the crowding distance of the boundary individuals is set to infinity:

[0315] (65);

[0316] For internal individuals The congestion distance is calculated by summing the normalized differences:

[0317] (66);

[0318] in, and These are the maximum and minimum values ​​of the Pareto layer for the m-th objective, respectively. After accumulating all objectives, the total crowding distance for each individual is obtained.

[0319] (67);

[0320] The greater the crowding distance, the sparser the solutions around the individual, and the more likely it is to be retained during the selection process.

[0321] (4) Binary tournament selection based on rank and crowd distance.

[0322] When selecting a crossover paternity from the parent population, NSGA-II employs a binary tournament rule prioritizing rank over crowding distance. For two candidate individuals... , :

[0323] like Then choose ;

[0324] like Then choose ;

[0325] If the two are of the same level, then compare the crowding distance, giving priority to individuals with larger crowding distances. For example: if ,and Then choose .

[0326] (5) The formula for updating the “sub-solution” by simulating binary cross (SBX).

[0327] In NSGA-II, the main pathways to "updating solutions" are crossover and mutation. For two parent individuals... and (Obtained through selection), its j-th variable , Two child variables are generated using SBX. , Specifically, first generate a uniformly random number that follows the interval (0,1). According to the cross-distribution index Calculate the cross coefficient :

[0328] (68);

[0329] Then, generate two offspring according to the following formula:

[0330] (69);

[0331] Repeating the above process for all variables j=1,…,D will yield two sub-solutions. and If the parameter value boundaries are considered, adjustments can be made after the crossover. Truncation:

[0332] (70);

[0333] in, Indicates the lower bound of a variable. Indicates the upper bound of the variable.

[0334] It can be seen that the "update formula" of SBX is essentially to interpolate / extrapolate between the parent parameters according to a certain probability, thereby iteratively generating a new generation of candidate heat source parameters. Functionally, it plays a role similar to the speed and position update of PSO (Particle Swarm Optimization Algorithm) in "searching for new solutions".

[0335] (6) Polynomial mutation update formula.

[0336] To enhance population diversity and prevent getting trapped in local optima, NSGA-II also performs polynomial mutation on the offspring generated by crossover. For a given offspring, the j-th variable of solution c... If we consider the mutation probability If a mutation is decided to occur, then random numbers must be generated first. According to the variation index Calculate the variance :

[0337] (71);

[0338] Then Updated to :

[0339] (72);

[0340] And perform boundary truncation as well:

[0341] (73);

[0342] Variable after mutation Replace the original This will yield new child solutions. By continuously generating new solutions through SBX and polynomial mutation in successive iterations, and combining non-dominated sorting and crowding distance selection, NSGA-II can gradually approximate the Pareto optimal set of the heat source model distribution shape parameters.

[0343] Step 4.4, Coupling with the three-dimensional temperature field numerical model and process description.

[0344] The overall process for optimizing the shape parameters of the heat source model using NSGA-II in this embodiment is as follows:

[0345] Initialization: Randomly generate the initial population within the parameter constraint range. Each individual corresponds to a set of heat source distribution shape parameters .

[0346] Temperature field simulation and objective function calculation: For each individual in the population, its heat source model The temperature field was obtained by applying boundary conditions to the three-dimensional heat conduction finite element model of the gear and solving for the temperature field. And calculate accordingly to .

[0347] Non-dominated sorting and crowding distance calculation: Perform fast non-dominated sorting on the current merged population to obtain each Pareto level. And calculate the crowding distance for each individual. .

[0348] Selection, crossover, and mutation: Parent individuals are selected using a binary tournament based on "rank priority, crowding distance second best," and offspring are generated by executing the SBX crossover formula and the polynomial mutation formula. .

[0349] Elite retention and iterative updates: [This refers to the parent generation / generation] With offspring Merging Then, perform non-dominated sorting and crowding distance calculations again, and select N optimal individuals to form the next generation. .

[0350] Termination and Pareto Optimal Solution Output: When the number of iterations reaches the preset upper limit or the Pareto front converges, the algorithm terminates and outputs the non-dominated solution set in the current population, which is the Pareto optimal solution set of the heat source model distribution shape parameter (i.e., the target shape parameter).

[0351] like Figure 6 As shown, the calculation process for the temperature field in ultrasonic vibration grinding of gears includes the following steps:

[0352] (1) Input stage: Input gear geometric parameters, grinding wheel geometric and structural parameters, workpiece and grinding wheel material thermophysical parameters, grinding process parameters, and ultrasonic vibration amplitude and frequency, etc. At the same time, input various initial conditions related to multi-source disturbances such as grinding wheel grit size, concentration and dressing interval.

[0353] (2) Heat source model construction: Based on the nonlinear adjustable heat source model given in step 2.1, a macroscopic continuous heat flux density distribution is generated, and the multi-source disturbance correction module in step 2.2 is introduced on this basis to obtain the heat source model expression containing ultrasonic vibration and abrasive random characteristics.

[0354] (3) Boundary condition transformation: The heat source model is transformed from the parameterized form in the contact arc length direction to the moving surface thermal load boundary condition on the gear tooth surface, thus completing the mapping of the loading area and loading path of the heat source in the three-dimensional finite element model.

[0355] (4) Three-dimensional temperature field simulation and objective function calculation: Under the current candidate heat source parameters, three-dimensional transient heat conduction numerical calculation is performed on the gear workpiece to obtain the temperature field distribution during the grinding process, and based on this, the temperature field prediction error, total heat matching degree, heat source distribution smoothness, high temperature influence zone volume and temperature peak constraint and other multi-objective function values ​​are calculated.

[0356] (5) NSGA-II multi-objective optimization: The above objective function value is used as the fitness index. The NSGA-II algorithm is used to perform non-dominated sorting, crowding distance calculation, tournament selection, and simulated binary crossover and polynomial mutation operations on the heat source model distribution shape parameters to generate a new generation of candidate parameter set.

[0357] (6) Elite retention and iterative update: merge the parent generation and the offspring generation to retain the elite, form the next generation population, and repeat steps (2) to (5) until the number of iterations reaches the preset upper limit or the Pareto front converges, to obtain the Pareto optimal solution set (i.e. the target shape parameter) of the heat source model distribution shape parameter.

[0358] (7) Output and process decision: Output the optimized heat source model shape parameters (i.e., target shape parameters) and, based on the target shape parameters, calculate the transient three-dimensional dynamic temperature field distribution of the tooth surface corresponding to the target shape parameters (i.e., target temperature field) again through steps (2) to (4). Based on the emphasis on temperature peak, safety margin or temperature uniformity under different working conditions, select the final implementation scheme by combining the multi-objective decision method, and use it to guide the design of process parameters and thermal damage prevention and control of gear ultrasonic vibration grinding.

[0359] For the obtained Pareto optimal solution set, a multi-objective decision-making method can be used to select the final implementation scheme according to specific process requirements (e.g., prioritizing the control of temperature peak safety or prioritizing the improvement of temperature field uniformity). The multi-objective decision-making method can be a weighted scoring method based on engineering experience, a ranking method for approximating the ideal solution, or other multi-index decision-making methods known to those skilled in the art; this embodiment does not limit this approach. The selected heat source model parameters can be used as input for subsequent temperature field simulation and process design, enabling customized heat source modeling for different operating conditions.

[0360] Compared with the prior art, the technical solution of this embodiment has the following beneficial effects:

[0361] 1. Significantly improves the accuracy of temperature field prediction. This embodiment constructs a physically meaningful nonlinear adjustable heat source model (i.e., a nonlinear macroscopic heat source model), using a polynomial / exponential-linear combination to characterize the heat flux density distribution in the grinding contact arc region, replacing the traditional simple rectangular or triangular distribution assumptions. Simultaneously, it combines a three-dimensional transient thermal conductivity numerical model to perform multi-objective matching between the heat source distribution and temperature measurement data. Compared to existing single-distribution models, this embodiment can more accurately predict the peak temperature of the tooth surface and its spatial location, reducing the error in temperature peak estimation and temperature gradient calculation, providing a reliable basis for identifying and avoiding thermal damage such as grinding burns and thermal cracks.

[0362] 2. Enhancing the generalization and adaptability of the heat source model. This embodiment explicitly introduces multiple perturbation factors into the heat source model structure, such as ultrasonic amplitude and frequency, grinding wheel abrasive grain size and concentration, and dressing status. The heat source distribution is corrected through macroscopic parameter mapping relationships and microscopic random perturbation terms. The model parameters are no longer rigidly bound to a single working condition but can automatically adjust the heat flux distribution pattern according to changes in process parameters. For different linear velocities, feed rates, grinding depths, cooling conditions, and different workpiece / grinding wheel material combinations, the method in this embodiment only needs to adjust the input parameters to maintain high prediction accuracy, significantly enhancing the model's versatility and adaptability.

[0363] 3. Reduce reliance on experimental calibration, lowering development costs and time. Traditional heat source models based on experimental inverse calculations typically require extensive temperature measurements and parameter inverse calculations under various operating conditions, resulting in high costs and long cycles. This embodiment, based on limited experimental data, utilizes the NSGA-II multi-objective optimization algorithm to intelligently optimize the heat source shape parameters, unifying multiple objectives such as "temperature matching, energy conservation, distribution smoothing, high-temperature region control, and temperature peak constraint" into a single optimization framework. A set of heat source parameters with good generalization ability can be obtained with a small amount of temperature measurement data, significantly reducing reliance on large-scale experimental calibration and lowering the time and economic costs of model establishment and verification.

[0364] 4. Balancing computational accuracy and numerical efficiency. This embodiment employs a three-dimensional transient heat conduction numerical solution method combining the Ritz method and finite element discretization, and achieves intelligent adjustment by coupling the optimization process of the heat source model parameters with the temperature field simulation. During the NSGA-II iteration process, rapid temperature field calculations can be performed based on the macroscopic heat source, and microscopic perturbations are superimposed after convergence to finely correct local temperature rises, thereby effectively controlling the computational load while ensuring computational accuracy. Compared with traditional simulation methods that rely entirely on fine meshes and fully nonlinear solutions, this embodiment achieves higher computational efficiency with the same computing resources, making it suitable for parameter scanning and process optimization in engineering scenarios.

[0365] 5. Wide applicability and high engineering application value. Because this embodiment systematically considers multiple disturbance factors in the model, such as ultrasonic vibration parameters, random distribution of abrasive particles, dressing conditions, and different cooling conditions, the proposed temperature field calculation method is applicable to gear grinding processes under dry grinding, wet grinding, and various cooling modes. It is also applicable to both ordinary grinding and ultrasonic vibration-assisted grinding. By appropriately modifying the material thermophysical parameters and grinding wheel characteristic parameters, this method can be extended to different gear materials and different grinding wheel types, providing a unified temperature field prediction and thermal damage prevention method for various gear processing scenarios.

[0366] In summary, this embodiment effectively overcomes the problems of insufficient accuracy, weak generalization ability, and heavy dependence on experiments in the existing technology for grinding temperature prediction by organically integrating the multi-source perturbation intelligent optimization heat source model with three-dimensional transient thermal conduction numerical simulation. It can significantly reduce the risk of tooth surface thermal damage and improve the quality and efficiency of gear grinding in industrial applications, and has important engineering application value.

[0367] Reference Figure 7 This application also provides a temperature field calculation device for gear ultrasonic vibration grinding, the device comprising:

[0368] The first calculation unit 701 is used to calculate the grinding wheel linear velocity and equivalent contact arc length based on the involute parametric equation, and to calculate the total heat flux intensity in the discrete grinding region based on the grinding wheel linear velocity and equivalent contact arc length.

[0369] The first building unit 702 is used to determine the heat flow intensity flowing into the gear tooth surface based on the total heat flow intensity, and to build the heat flow intensity flowing into the gear tooth surface into a nonlinear macroscopic heat source model;

[0370] The first correction unit 703 is used to correct the shape parameters in the nonlinear macro heat source model by ultrasonic amplitude and frequency, and construct shape correction parameters; add micro-perturbation terms to the nonlinear macro heat source model, and correct the micro-perturbation terms by calculating the perturbation correlation length and perturbation variance, and obtain the corrected micro-perturbation terms.

[0371] The second correction unit 704 is used to correct the nonlinear macro heat source model by using the corrected micro-perturbation term and shape correction parameter to obtain the corrected nonlinear macro heat source model.

[0372] The second building unit 705 is used to build the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition based on the modified nonlinear macroscopic heat source model.

[0373] The parameter optimization unit 706 is used to construct a functional from the constructed three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition, and to calculate the initial temperature field based on the functional; based on the initial temperature field, the shape correction parameters are iteratively optimized to obtain the target shape parameters.

[0374] The third building unit 707 is used to modify the modified nonlinear macro heat source model through the target shape parameters to obtain the target nonlinear macro heat source model, and to construct the target boundary conditions based on the target nonlinear macro heat source model.

[0375] The temperature field calculation unit 708 is used to construct the target functional from the constructed three-dimensional heat conduction partial differential equation, target boundary conditions, second boundary conditions, third boundary conditions and initial conditions, and to calculate the target temperature field based on the target functional.

[0376] It should be noted that since the temperature field calculation device in the ultrasonic vibration grinding of gears in this embodiment is based on the same inventive concept as the temperature field calculation method in the ultrasonic vibration grinding of gears described above, the corresponding content in the method embodiment is also applicable to this system embodiment, and will not be described in detail here.

[0377] This application also provides an electronic device, including: at least one control processor and a memory for communicatively connecting to at least one control processor.

[0378] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0379] The non-transient software program and instructions required to implement the temperature field calculation method in ultrasonic vibration grinding of gears according to the above embodiments are stored in the memory. When executed by the processor, the temperature field calculation method in ultrasonic vibration grinding of gears according to the above embodiments is executed.

[0380] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0381] This application also provides a computer-readable storage medium storing computer-executable instructions that are executed by one or more control processors, enabling the one or more control processors to perform a method for calculating the temperature field in ultrasonic vibration grinding of gears as described in the above method embodiments.

[0382] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0383] The above is a detailed description of the preferred embodiments of this application. However, the embodiments of this application are not limited to the above-described implementation methods. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the embodiments of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of the embodiments of this application.

Claims

1. A method for calculating the temperature field in ultrasonic vibration grinding of gears, characterized in that, The method includes: Based on the involute parametric equation, the grinding wheel linear velocity and equivalent contact arc length are calculated, and the total heat flux intensity in the discrete grinding region is calculated according to the grinding wheel linear velocity and the equivalent contact arc length. Based on the total heat flux intensity, the heat flux intensity flowing into the gear tooth surface is determined, and the heat flux intensity flowing into the gear tooth surface is constructed as a nonlinear macroscopic heat source model; The shape parameters in the nonlinear macroscopic heat source model are corrected by ultrasonic amplitude and frequency to construct shape correction parameters; micro-perturbation terms are added to the nonlinear macroscopic heat source model, and the micro-perturbation terms are corrected by the calculated perturbation correlation length and perturbation variance to obtain the corrected micro-perturbation terms. The nonlinear macroscopic heat source model is corrected by the modified microscopic perturbation term and the shape correction parameter to obtain the modified nonlinear macroscopic heat source model. Based on the modified nonlinear macroscopic heat source model, a first boundary condition is constructed, and second boundary conditions, third boundary conditions, and initial conditions are also constructed, including: The gear surface is delineated by boundary and mesh to determine the adiabatic boundary surface, the convective heat transfer boundary surface, and the grinding heat source input boundary surface. For the grinding heat source input boundary surface, a first boundary condition is constructed based on the modified nonlinear macroscopic heat source model; For the aforementioned adiabatic boundary surface, a second boundary condition is constructed; For the convective heat transfer boundary surface, a third boundary condition is constructed; The initial temperature of the workpiece at the beginning of grinding is used as the initial condition; The constructed three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition are used to construct a functional, and the initial temperature field is calculated based on the functional. Based on the initial temperature field, the shape correction parameters are iteratively optimized to obtain the target shape parameters. The modified nonlinear macroscopic heat source model is corrected by the target shape parameters to obtain the target nonlinear macroscopic heat source model. Based on the target nonlinear macroscopic heat source model, the target boundary conditions are constructed. The constructed three-dimensional heat conduction partial differential equation, the target boundary condition, the second boundary condition, the third boundary condition, and the initial condition are used to construct a target functional, and the target temperature field is calculated based on the target functional.

2. The method for calculating the temperature field in ultrasonic vibration grinding of gears according to claim 1, characterized in that, The step of constructing a nonlinear macroscopic heat source model for the heat flow intensity flowing into the gear tooth surface includes: Calculate the heat flux density at any roll angle position on the contact surface between the grinding wheel and the gear; Construct multiple heat source distribution expressions along the contact arc length direction, including piecewise triangular distribution expressions, trapezoidal distribution expressions, and parabolic distribution expressions; Based on the heat flux density and the expression for each heat source distribution, a classical heat source distribution model is constructed; Using the normalized coordinates of the contact arc length as the independent variable, the classical heat source distribution model is constructed into a nonlinear macroscopic heat source model.

3. The method for calculating the temperature field in ultrasonic vibration grinding of gears according to claim 1, characterized in that, The method of correcting the shape parameters in the nonlinear macroscopic heat source model by using ultrasonic amplitude and frequency to construct shape correction parameters includes: The ultrasonic amplitude and frequency are mapped to the shape parameters in the nonlinear macroscopic heat source model through empirical regression, and the shape parameters include the initial thermal intensity, attenuation coefficient, and linear tail weight.

4. The method for calculating the temperature field in ultrasonic vibration grinding of gears according to claim 1, characterized in that, The micro-perturbation term is corrected by calculating the perturbation correlation length and perturbation variance to obtain the corrected micro-perturbation term, including: Obtain the disturbance variance, abrasive particle size, concentration, dressing depth, empirical coefficient, and projected area of ​​the grinding wheel surface under the reference working conditions; The effective number of abrasive grains with cutting capability is calculated based on the abrasive grain size, the concentration, the empirical coefficient, and the projected area of ​​the grinding wheel surface. The average abrasive grain spacing is calculated based on the effective number of abrasive grains and the projected area of ​​the grinding wheel surface. The average abrasive grain spacing is normalized to the contact arc length direction to obtain the disturbance correlation length; Calculate the smoothing coefficient that affects the magnitude of the disturbance variance based on the ultrasonic amplitude and the frequency; The perturbation variance is calculated based on the smoothing coefficient, the dressing depth, the perturbation variance under the reference working condition, and the abrasive grain size. Based on the disturbance correlation length and the disturbance variance, determine the magnitude of the amplitude and the total number of harmonics in the micro-disturbance term; Based on the magnitude of the amplitude and the total number of harmonics in the micro-perturbation term, the micro-perturbation term is corrected to obtain the corrected micro-perturbation term.

5. The method for calculating the temperature field in ultrasonic vibration grinding of gears according to claim 1, characterized in that, The step of iteratively optimizing the shape correction parameters based on the initial temperature field to obtain the target shape parameters includes: Based on the initial temperature field and the nonlinear macroscopic heat source model, a first objective function, a second objective function, a third objective function, a fourth objective function, and a fifth objective function are constructed. Based on the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function, the shape correction parameters are iteratively optimized using a non-dominated sorting genetic method; When the number of iterations does not reach the preset upper limit or the Pareto front does not converge, the shape correction parameters updated in the current iteration are obtained; The nonlinear macroscopic heat source model is repeatedly corrected by the shape correction parameters updated in the current iteration to obtain the repeatedly corrected nonlinear macroscopic heat source model. Based on the repeatedly modified nonlinear macroscopic heat source model, the repeatedly modified first boundary conditions are constructed. The constructed three-dimensional heat conduction partial differential equation, the repeatedly modified first boundary condition, the second boundary condition, the third boundary condition, and the initial condition are used to construct a first functional, and the first temperature field is calculated based on the first functional. Based on the first temperature field, the first objective function, the second objective function, the third objective function, the fourth objective function, and the fifth objective function, the non-dominated sorting genetic method is used to iteratively optimize the shape correction parameters updated in the current iteration until the number of iterations reaches the preset upper limit or the Pareto front converges, thus obtaining the target shape parameters.

6. The method for calculating the temperature field in ultrasonic vibration grinding of gears according to claim 1, characterized in that, The calculation of the target temperature field based on the target functional includes: The solution space domain in the target functional is divided into multiple units, and a functional for each unit is constructed. Each unit is an eight-node hexahedral unit. Based on the extremum conditions of the functional, the Euler equation of the functional for each unit is obtained; Based on the Euler equations of the functional of each element, the element stiffness matrix equation of each element is determined. The time domain corresponding to the element stiffness matrix equation is independently discretized by the finite difference method to obtain the fully discretized element stiffness matrix equation. The fully discretized element stiffness matrix equations corresponding to each element are combined to form the global stiffness matrix equation with nodal temperature as the unknown parameter. By solving the overall stiffness matrix equation, the temperature of each node in each element is obtained, and the temperatures of all nodes in all elements are used to construct the target temperature field.

7. A temperature field calculation device for gear ultrasonic vibration grinding, characterized in that, The device includes: The first calculation unit is used to calculate the grinding wheel linear velocity and equivalent contact arc length based on the involute parametric equation, and to calculate the total heat flux intensity in the discrete grinding region based on the grinding wheel linear velocity and the equivalent contact arc length. The first construction unit is used to determine the heat flow intensity flowing into the gear tooth surface based on the total heat flow intensity, and to construct the heat flow intensity flowing into the gear tooth surface as a nonlinear macroscopic heat source model; The first correction unit is used to correct the shape parameters in the nonlinear macro heat source model by ultrasonic amplitude and frequency, and construct shape correction parameters; add micro-perturbation terms to the nonlinear macro heat source model, and correct the micro-perturbation terms by calculating the perturbation correlation length and perturbation variance, to obtain the corrected micro-perturbation terms. The second correction unit is used to correct the nonlinear macroscopic heat source model using the corrected microscopic perturbation term and the shape correction parameter to obtain the corrected nonlinear macroscopic heat source model. The second construction unit is used to construct the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition based on the modified nonlinear macroscopic heat source model, including: The gear surface is delineated by boundary and mesh to determine the adiabatic boundary surface, the convective heat transfer boundary surface, and the grinding heat source input boundary surface. For the grinding heat source input boundary surface, a first boundary condition is constructed based on the modified nonlinear macroscopic heat source model; For the aforementioned adiabatic boundary surface, a second boundary condition is constructed; For the convective heat transfer boundary surface, a third boundary condition is constructed; The initial temperature of the workpiece at the beginning of grinding is used as the initial condition; The parameter optimization unit is used to construct a functional from the constructed three-dimensional heat conduction partial differential equation, the first boundary condition, the second boundary condition, the third boundary condition, and the initial condition, and to calculate the initial temperature field based on the functional; and to iteratively optimize the shape correction parameters based on the initial temperature field to obtain the target shape parameters. The third construction unit is used to modify the modified nonlinear macroscopic heat source model through the target shape parameters to obtain the target nonlinear macroscopic heat source model, and to construct the target boundary conditions based on the target nonlinear macroscopic heat source model. The temperature field calculation unit is used to construct a target functional from the constructed three-dimensional heat conduction partial differential equation, the target boundary condition, the second boundary condition, the third boundary condition, and the initial condition, and to calculate the target temperature field based on the target functional.

8. An electronic device, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform the temperature field calculation method for gear ultrasonic vibration grinding as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the temperature field calculation method in ultrasonic vibration grinding of gears as described in any one of claims 1 to 6.

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