Bevel gear forming grinding temperature prediction method and system and storage medium

Abstract

The invention discloses a bevel gear forming grinding temperature prediction method and system and a storage medium, and the method comprises the steps: analyzing a bevel gear heat treatment process, and building a multi-field coupling finite element simulation model of a gear heat treatment process including carburizing, quenching and tempering; and calculating non-uniform tooth surface deformation caused by thermal stress, structural stress and inconsistent surface hardening layer depth. Taking a gear model after heat treatment as an initial model of a gear forming and grinding process, taking a grinding heat flux density three-dimensional distribution result as a thermal load, and combining with a gear forming and grinding geometric contact relationship to establish a helical gear forming and grinding continuous finite element simulation model considering the influence of initial tooth surface non-uniform deformation; and calculating to obtain the temperature distribution of the ground workpiece. According to the method, the influence of the heat treatment process on gear forming grinding can be comprehensively considered, the tooth surface temperature distribution of forming grinding machining is accurately predicted, and the method is crucial for analyzing the influence of the heat treatment process on grinding quality and optimizing process parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of gear processing, and relates to a method, a system and a storage medium for predicting the forming grinding temperature of a helical gear. Background Art

[0002] As an important component of mechanical transmission systems, involute helical gears are widely used in many industrial fields such as aircraft, ships, machine tools and defense equipment. The manufacturing accuracy and processing quality of helical gears directly affect the transmission accuracy, load-bearing capacity and service life of helical gears. In order to meet the growing demand for gear load-bearing capacity and fatigue life, the comprehensive physical and mechanical properties of the surface material of the tooth surface after grinding need to be strictly controlled. Gear grinding is a complex, dynamic and multivariable coupled nonlinear process. During this process, due to the direct effect of thermal-mechanical coupling, high grinding temperature will cause changes in the microstructure of the tooth surface, increase tooth shape errors, reduce tooth surface hardness, and generate residual tensile stress on the tooth surface, and reduce the contact fatigue strength of the gear. Therefore, the analysis and prediction of grinding temperature has always been the focus of attention in the field of gear processing.

[0003] The existing common finite element simulation method only considers a single grinding process when predicting the grinding temperature of helical gears, and ignores the influence of heat treatment processes such as carburizing and quenching before grinding. In fact, for most heavy-duty gear steels, if the residual stress distribution after heat treatment is uneven, it will affect the stress release of the gear during grinding, resulting in uncoordinated deformation of each part, which directly affects the temperature distribution during subsequent gear grinding. At the same time, the heat treatment process will significantly change the hardness of the gear, and higher hardness requires higher grinding force and grinding temperature. Therefore, it is crucial to comprehensively consider the influence of the helical gear heat treatment process on the grinding temperature in order to analyze the grinding quality and optimize the process parameters. Summary of the invention

[0004] The purpose of the present invention is to provide a method, system and storage medium for predicting the temperature of helical gear forming grinding, so as to solve the problems of low precision and poor accuracy of existing finite element simulation prediction methods.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A method for predicting the temperature of helical gear forming grinding comprises the following steps:

[0007] S01: Finite element modeling of the carburizing process of helical gears;

[0008] S02: Calculate the carbon concentration distribution of helical gears;

[0009] S03: Finite element modeling of the quenching and tempering process of helical gears;

[0010] S04: Based on the influence of carbon concentration distribution on organizational transformation, combined with temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship, the tooth surface deformation of the helical gear after heat treatment is calculated;

[0011] S05: Modeling of helical gear profile grinding based on the calculated tooth surface deformation model;

[0012] S06: The helical gear forming grinding temperature is calculated by combining the geometric contact relationship, moving heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model.

[0013] In the preferred technical solution, the method of performing finite element modeling on the carburizing process of the helical gear in step S01 includes:

[0014] S11: according to the actual geometric parameters of the helical gear, a three-dimensional model of the helical gear is established using a three-dimensional design software, and the model is saved as a solid model output format and then imported into a finite element simulation software;

[0015] S12: Input the material performance parameters of the helical gear. According to the carburizing process requirements, the material performance parameters include density, carbon diffusion coefficient, specific heat capacity and thermal conductivity;

[0016] S13: Meshing and element type selection for the three-dimensional model of the helical gear;

[0017] S14: The mass diffusion module is used to set the analysis steps for the initial stage, strong carburizing stage and diffusion stage in the carburizing process.

[0018] In the preferred technical solution, step S02 also includes setting boundary conditions for the carburizing process, and the boundary conditions include the initial carbon concentration and the material exchange conditions between the carburizing medium and the workpiece surface, wherein the initial carbon concentration is a uniform carbon concentration field, and the material exchange conditions are calculated according to the following formula:

[0019] J=β(C e -C s )

[0020] Where J is the diffusion flux of carbon atoms, β is the carbon atom transfer coefficient, C e is the carbon concentration of the atmosphere in the carburizing furnace, C s is the carbon concentration on the surface of the part.

[0021] In the preferred technical solution, step S03 specifically includes:

[0022] S31: According to the quenching and tempering process requirements, the input material performance parameters include thermophysical parameters, structural transformation parameters and mechanical performance parameters;

[0023] S32: Perform meshing and use the thermal-mechanical coupling unit to calculate the quenching and tempering processes;

[0024] S33: Set up analysis steps for the four stages of heating, heat preservation, quenching cooling and tempering involved in the quenching and tempering process of gears.

[0025] In the preferred technical solution, step S04 specifically includes:

[0026] S41: importing the carbon concentration of the carburizing process simulation result into the quenching and tempering simulation model for corresponding calculation;

[0027] S42: setting boundary conditions during quenching and tempering, including convection heat transfer boundary conditions and displacement boundary conditions;

[0028] The convection heat transfer boundary conditions of the gear quenching heat transfer model are:

[0029]

[0030] Where λ is the thermal conductivity of the gear material, represents the gradient operator, h is the convective heat transfer coefficient between the part and the quenching medium, T and T f Represent the gear surface temperature and quenching medium temperature respectively;

[0031] The displacement boundary condition is to select the intersection points with different coordinate planes on the inner hole surface of the gear to constrain the symmetry surface;

[0032] S43: Treat the phase change latent heat generated inside each finite element as the internal heat source of the element, and calculate the phase change latent heat generated when the structure transforms during the heat treatment process;

[0033] S44: The organizational transformation model is established based on the TTT curve, phase change kinetics and Scheil superposition principle, and the phase change latent heat and organizational stress are calculated through the phase change products and phase variables at different times during the phase change process;

[0034] S45: The strain increment of each time step at any point inside the workpiece is calculated using the thermoelastic-plastic incremental model. The thermoelastic-plastic incremental model is:

[0035]

[0036] in, is the elastic strain increment, is the plastic strain increment, is the thermal strain increment, is the phase change strain increment, dε tp ij is the phase transformation plastic strain increment, is the creep increment.

[0037] In the preferred technical solution, the method of calculating the phase change latent heat and tissue stress in step S44 includes:

[0038] For diffusion-type transformation, the transformation amount from austenite to pearlite, ferrite and bainite under isothermal transformation conditions is:

[0039] V=1-exp(-bt n )

[0040] Where V represents the transformation amount, t is the isothermal time; b and n represent the coefficient and index related to temperature and material respectively;

[0041] For the gear quenching process with rapid and continuous cooling, the transformation variable V needs to be expanded according to the Scheil superposition principle. By discretizing the time of the continuous cooling process, a certain time interval is approximated as an isothermal transformation process, and the inoculation rate and transformation variable are superimposed and calculated.

[0042] The transition variable V of step i i for:

[0043]

[0044] Among them, b i represents the temperature-dependent coefficient of the i-th step, represents virtual time, Δt i represents the time step of the i-th step, n i represents the index related to the material at step i;

[0045] For non-diffusion transformation, the amount of organizational transformation has nothing to do with time and is only determined by the degree of supercooling. Therefore, the amount of transformation from austenite to martensite V M It is expressed as:

[0046] V M =1-exp(-α M (M s -T))

[0047] Among them, α M Represents the coefficient reflecting the martensitic transformation rate, M s represents the martensite transformation start temperature, and T represents temperature.

[0048] In the preferred technical solution, the calculation method of the elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment, phase change plastic strain increment and creep increment in step S45 is:

[0049]

[0050]

[0051] Where E is the elastic modulus, μ is Poisson's ratio, dσ ij is the stress tensor increment, dσ i is the equivalent stress increment, σ i is the equivalent stress, σ ij is the stress tensor, H is the hardening exponent, ξ m represents the coefficient of thermal expansion, f m is the transfer variable, dT is the temperature increment, β m is the phase expansion coefficient related to the tissue composition, df m is the transformation increment, K is the phase transformation plasticity coefficient, S is the deviatoric stress tensor, A is the material constant, σ is the stress, k is the stress sensitivity coefficient, m is the time sensitivity coefficient, t is the time, and dt is the time increment.

[0052] In the preferred technical solution, step S06 specifically includes:

[0053] S61: importing the deformation model of the helical gear after heat treatment as the initial model of the helical gear for grinding;

[0054] S62: Calculate the normal grinding depth, grinding wheel equivalent radius and grinding speed based on the geometric contact model of helical gear profile grinding;

[0055] S63: The heat flow shape of the grinding arc zone is assumed to be a triangle to simulate the forming grinding process of the helical gear. That is, the heat source is distributed in a triangular shape along the involute extension direction and the grinding width direction. The heat flux density of the helical gear forming grinding arc zone is expressed as:

[0056]

[0057] Where q is the total heat flux density in the grinding arc zone; z i Indicates the distance along the grinding width; represents the rolling angle along the extension direction of the involute, is the maximum rolling angle at the tooth top; l c is the grinding contact arc length between the grinding wheel and the gear;

[0058] S64: Calculate the heat flux distribution ratio flowing into the tooth surface based on the energy conservation principle and the single abrasive particle sliding hypothesis theory;

[0059] S65: Based on the thermo-elastoplastic constitutive model and the heat conduction equation, the grinding temperature of the helical gear is obtained.

[0060] The present invention also discloses a helical gear forming grinding temperature prediction system, comprising:

[0061] Carburizing process modeling module, which performs finite element modeling of the carburizing process of helical gears;

[0062] Carbon concentration calculation module, calculates the carbon concentration distribution of helical gears;

[0063] The quenching and tempering process modeling module performs finite element modeling on the quenching and tempering process of helical gears;

[0064] The stress / strain field calculation module calculates the deformation of the tooth surface after heat treatment of the helical gear based on the influence of the obtained carbon concentration distribution on the organizational transformation, combined with the temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship;

[0065] Helical gear profile grinding modeling module, which performs helical gear profile grinding modeling based on the calculated tooth surface deformation model;

[0066] The helical gear forming grinding temperature calculation module combines the helical gear forming grinding geometric contact relationship, mobile heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model to calculate the helical gear forming grinding temperature.

[0067] The present invention further discloses a computer storage medium on which a computer program is stored. When the computer program is executed, the above-mentioned helical gear forming grinding temperature prediction method is realized.

[0068] Compared with the prior art, the present invention has the following significant advantages:

[0069] The present invention proposes a new method for predicting the forming grinding temperature of helical gears by comprehensively considering the influence of the initial stress field of the gear after heat treatment and the uneven deformation of the tooth surface on the grinding process of the helical gear. The method can effectively predict the influence of the highly nonlinear changes of the temperature, structure, and stress / strain that interact with each other during the gear heat treatment process on various state quantities in the grinding, so as to ensure that the forming grinding temperature distribution of the helical gear tooth surface is obtained more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a flow chart of the helical gear forming grinding temperature prediction method of the present invention;

[0071] Figure 2 It is the mesh diagram of the finite element model of a single tooth of a helical gear;

[0072] Figure 3a-3b is the carbon concentration distribution diagram after carburizing treatment;

[0073] Figure 4 It is the geometric contact diagram of helical gear profile grinding;

[0074] Figure 5 It is a schematic diagram of triangle heat source loading;

[0075] Figure 6a-6b It is the temperature distribution diagram of helical gear form grinding. DETAILED DESCRIPTION

[0076] The principle of the present invention is: by comprehensively considering the influence of the initial stress field of the gear after heat treatment and the uneven deformation of the tooth surface on the grinding process of the helical gear, a new method for predicting the forming grinding temperature of the helical gear is proposed, which can effectively predict the influence of the highly nonlinear changes of the temperature, structure, and stress / strain in the gear heat treatment process on various state quantities in the grinding, so as to ensure that the forming grinding temperature distribution of the helical gear tooth surface is obtained more accurately.

[0077] Embodiment 1:

[0078] like Figure 1 As shown, a method for predicting the temperature of helical gear forming grinding comprises the following steps:

[0079] S01: Finite element modeling of the carburizing process of helical gears;

[0080] S02: Calculate the carbon concentration distribution of helical gears;

[0081] S03: Finite element modeling of the quenching and tempering process of helical gears;

[0082] S04: Based on the influence of carbon concentration distribution on organizational transformation, combined with temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship, the tooth surface deformation of the helical gear after heat treatment is calculated;

[0083] S05: Modeling of helical gear profile grinding based on the calculated tooth surface deformation model;

[0084] S06: The helical gear forming grinding temperature is calculated by combining the geometric contact relationship, moving heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model.

[0085] In a preferred embodiment, the method of performing finite element modeling on the carburizing process of the helical gear in step S01 includes:

[0086] S11: according to the actual geometric parameters of the helical gear, a three-dimensional model of the helical gear is established using a three-dimensional design software, and the model is saved as a solid model output format and then imported into a finite element simulation software;

[0087] S12: Input the material performance parameters of the helical gear. According to the carburizing process requirements, the material performance parameters include density, carbon diffusion coefficient, specific heat capacity and thermal conductivity;

[0088] S13: Meshing and element type selection for the three-dimensional model of the helical gear;

[0089] S14: The mass diffusion module is used to set the analysis steps for the initial stage, strong carburizing stage and diffusion stage in the carburizing process.

[0090] In a preferred embodiment, step S02 also includes setting boundary conditions of the carburizing process, and the boundary conditions include the initial carbon concentration and the material exchange conditions between the carburizing medium and the workpiece surface, wherein the initial carbon concentration is a uniform carbon concentration field, and the material exchange conditions are calculated according to the following formula:

[0091] J=β(C e -C s )

[0092] Where J is the diffusion flux of carbon atoms, β is the carbon atom transfer coefficient, C e is the carbon concentration of the atmosphere in the carburizing furnace, C s is the carbon concentration on the surface of the part.

[0093] In a preferred embodiment, step S03 specifically includes:

[0094] S31: According to the quenching and tempering process requirements, the input material performance parameters include thermophysical parameters, structural transformation parameters and mechanical performance parameters;

[0095] S32: Perform meshing and use the thermal-mechanical coupling unit to calculate the quenching and tempering process;

[0096] S33: Set up analysis steps for the four stages of heating, heat preservation, quenching cooling and tempering involved in the quenching and tempering process of gears.

[0097] In a preferred embodiment, step S04 specifically includes:

[0098] S41: importing the carbon concentration of the carburizing process simulation result into the quenching and tempering simulation model for corresponding calculation;

[0099] S42: setting boundary conditions during quenching and tempering, including convection heat transfer boundary conditions and displacement boundary conditions;

[0100] The convection heat transfer boundary conditions of the gear quenching heat transfer model are:

[0101]

[0102] Where λ is the thermal conductivity of the gear material, represents the gradient operator, h is the convective heat transfer coefficient between the part and the quenching medium, T and T f Represent the gear surface temperature and quenching medium temperature respectively;

[0103] The displacement boundary condition is to select the intersection points with different coordinate planes on the inner hole surface of the gear to constrain the symmetry surface;

[0104] S43: Treat the phase change latent heat generated inside each finite element as the internal heat source of the element, and calculate the phase change latent heat generated when the structure transforms during the heat treatment process;

[0105] S44: The organizational transformation model is established based on the TTT curve, phase change kinetics and Scheil superposition principle, and the phase change latent heat and organizational stress are calculated through the phase change products and phase variables at different times during the phase change process;

[0106] S45: The strain increment of each time step at any point inside the workpiece is calculated using the thermoelastic-plastic incremental model. The thermoelastic-plastic incremental model is:

[0107]

[0108] in, is the elastic strain increment, is the plastic strain increment, is the thermal strain increment, is the phase transformation strain increment, is the phase transformation plastic strain increment, is the creep increment.

[0109] In a preferred embodiment, the method of calculating the phase change latent heat and tissue stress in step S44 includes:

[0110] For diffusion-type transformation, the transformation amount from austenite to pearlite, ferrite and bainite under isothermal transformation conditions is:

[0111] V=1-exp(-bt n )

[0112] Where V represents the transformation amount, t is the isothermal time; b and n represent the coefficient and index related to temperature and material respectively;

[0113] For the gear quenching process with rapid and continuous cooling, the transformation variable V needs to be expanded according to the Scheil superposition principle. By discretizing the time of the continuous cooling process, a certain time interval is approximated as an isothermal transformation process, and the inoculation rate and transformation variable are superimposed and calculated.

[0114] The transition variable V of step i i for:

[0115]

[0116] Among them, b i represents the temperature-dependent coefficient of the i-th step, represents virtual time, Δt i represents the time step of the i-th step, n i Represents the material-related index of the i-th step.

[0117] For non-diffusion transformation, the amount of organizational transformation has nothing to do with time and is only determined by the degree of supercooling. Therefore, the amount of transformation from austenite to martensite V M It is expressed as:

[0118] V M =1-exp(-α M (M s -T))

[0119] Among them, α M Represents the coefficient reflecting the martensitic transformation rate, M s represents the martensite transformation start temperature, and T represents temperature.

[0120] In a preferred embodiment, the calculation method of the elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment, phase change plastic strain increment and creep increment in step S45 is:

[0121]

[0122] Where E is the elastic modulus, μ is Poisson's ratio, dσ ij is the stress tensor increment, dσ i is the equivalent stress increment, σ i is the equivalent stress, σ ij is the stress tensor, H is the hardening exponent, ξ m represents the coefficient of thermal expansion, f m is the transfer variable, dT is the temperature increment, β m is the phase expansion coefficient related to the tissue composition, df m is the transformation increment, K is the phase transformation plasticity coefficient, S is the deviatoric stress tensor, A is the material constant, σ is the stress, k is the stress sensitivity coefficient, m is the time sensitivity coefficient, t is the time, and dt is the time increment.

[0123] In a preferred embodiment, step S06 specifically includes:

[0124] S61: importing the deformation model of the helical gear after heat treatment as the initial model of the helical gear for grinding;

[0125] S62: Calculate the normal grinding depth, grinding wheel equivalent radius and grinding speed based on the geometric contact model of helical gear profile grinding;

[0126] S63: The heat flow shape of the grinding arc zone is assumed to be a triangle to simulate the forming grinding process of the helical gear. That is, the heat source is distributed in a triangular shape along the involute extension direction and the grinding width direction. The heat flux density of the helical gear forming grinding arc zone is expressed as:

[0127]

[0128] Where q is the total heat flux density in the grinding arc zone; z i Indicates the distance along the grinding width; represents the rolling angle along the extension direction of the involute, is the maximum rolling angle at the tooth top; l c is the grinding contact arc length between the grinding wheel and the gear;

[0129] S64: Calculate the heat flux distribution ratio flowing into the tooth surface based on the energy conservation principle and the single abrasive particle sliding hypothesis theory;

[0130] S65: Based on the thermo-elastoplastic constitutive model and the heat conduction equation, the grinding temperature of the helical gear is obtained.

[0131] In another embodiment, a computer storage medium stores a computer program, and when the computer program is executed, the above-mentioned helical gear profile grinding temperature prediction method is implemented. The above-mentioned temperature prediction method is adopted and will not be described in detail here.

[0132] In yet another embodiment, a helical gear profile grinding temperature prediction system includes:

[0133] Carburizing process modeling module, which performs finite element modeling of the carburizing process of helical gears;

[0134] Carbon concentration calculation module, calculates the carbon concentration distribution of helical gears;

[0135] The quenching and tempering process modeling module performs finite element modeling on the quenching and tempering process of helical gears;

[0136] The stress / strain field calculation module calculates the deformation of the tooth surface after heat treatment of the helical gear based on the influence of the obtained carbon concentration distribution on the organizational transformation, combined with the temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship;

[0137] Helical gear profile grinding modeling module, which performs helical gear profile grinding modeling based on the calculated tooth surface deformation model;

[0138] The helical gear forming grinding temperature calculation module combines the helical gear forming grinding geometric contact relationship, mobile heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model to calculate the helical gear forming grinding temperature.

[0139] Specifically, the working process of the helical gear forming grinding temperature prediction system is described as follows by taking a preferred embodiment as an example:

[0140] The following steps are involved:

[0141] (1) Finite element simulation analysis of helical gear carburizing process

[0142] (1.1) According to the actual geometric parameters of the helical gear, the gear model is established using the 3D mechanical design software SolidWorks. The gear parameters of this example are: normal module is 9.5mm, number of teeth is 20, normal pressure angle is 20°, helix angle is 16°, tooth width is 40mm, and hand direction is right-handed. At the same time, the gear model is saved as a solid model output format, namely Parasolid (.X_t) format, and imported into the finite element analysis software Abaqus.

[0143] (1.2) Assignment of gear material properties. The gear material is 17CrNiMo6. According to the carburizing process requirements, the material density, carbon diffusion coefficient, specific heat capacity and thermal conductivity coefficient need to be set.

[0144] (1.3) The gear 3D model is meshed using a hexahedral mesh sweeping method, such as Figure 2 As shown in the figure, for the selection of unit type, DC3D8, an 8-node linear heat transfer solid unit, is used to calculate the carburizing process.

[0145] (1.4) Use the Mass diffusion module to set the analysis steps for the carburizing process. The simulation file of the carburizing process is set with three analysis steps, namely the initial stage, the strong diffusion stage and the diffusion stage.

[0146] (2) Boundary condition setting and gear carbon concentration distribution calculation

[0147] For the carburizing process, the boundary conditions include the initial carbon concentration and the material exchange conditions between the carburizing medium and the workpiece surface. The initial carbon concentration is defined as a uniform carbon concentration field with a concentration of 0.18%, which can be directly set in Abaqus. The material exchange conditions are calculated according to Fick's first law shown in formula (1) and implemented through the secondary development of the subroutine DFLUX.

[0148] J=β(C e -C s ) (1)

[0149] The carbon transfer coefficient β is 0.0001; the carbon concentration C in the atmosphere of the carburizing furnace during the intensive and diffusion stages is e The carbon concentration C of the part surface at the current time and integration point is 1.03% and 0.75% respectively, and the process time is 420 and 180 minutes respectively. s Can be read in real time via DFLUX.

[0150] (3) Finite element modeling of helical gear quenching and tempering process

[0151] (3.1) The establishment of the three-dimensional model of the helical gear is similar to step (1.1).

[0152] (3.2) Since the quenching process involves multi-field coupling calculations, the required material performance parameters include thermophysical parameters, microstructure transformation parameters and mechanical performance parameters, which can be calculated using the linear mixing law of the mixed phase. According to the quenching and tempering process requirements, the material density, specific heat capacity, thermal conductivity, Young's modulus, Poisson's ratio, thermal expansion coefficient, yield stress and creep properties need to be set.

[0153] (3.3) The mesh is divided and the C3D8T thermal-mechanical coupling unit is used to calculate the quenching and tempering processes.

[0154] (3.4) According to the process flow of the quenching and tempering of the helical gear, after carburizing, the gear is heated to 820℃ and then kept warm for a period of time and then cooled in quenching oil at a temperature of 50℃. The gear is then tempered for 960 minutes at a tempering temperature of 180℃. The analysis steps are set for the four stages of heating, heat preservation, quenching cooling and tempering involved in the above process flow. Among them, the quenching simulation uses the thermal-mechanical coupling analysis step, and the simulation of the tempering process uses the visco analysis step.

[0155] (4) Calculation of stress / strain field of gear after heat treatment

[0156] (4.1) The martensitic transformation temperature M shown in formula (2) s The calculation shows that the influence of the carbon concentration distribution of the workpiece after carburizing on the martensitic phase transition temperature of the workpiece material cannot be ignored. Therefore, the carbon concentration distribution of the workpiece after carburizing needs to be considered when calculating the influence of the microstructure change on the stress field during quenching and tempering. By importing the carbon concentration distribution results of the carburizing process simulation as shown in Figure 3 into the predefined field of the quenching and tempering simulation, Figure 3a Carbon concentration distribution after strong penetration, Figure 3b The carbon concentration distribution after diffusion is combined with the subroutines USDFLD and HETVAL for corresponding calculations.

[0157] M s =561-474C-33Mn-17Ni-17Cr-21Mo (2)

[0158] The chemical composition of the gear material 17CrNiMo6 can be selected according to the mass fraction in Table 1.

[0159] Table 1 Chemical composition of 17CrNiMo6 steel (mass fraction, %)

[0160]

[0161]

[0162] (4.2) The boundary conditions during quenching and tempering include convection heat transfer boundary conditions and displacement boundary conditions. The convection heat transfer boundary conditions of the gear quenching heat transfer model are:

[0163]

[0164] The displacement boundary condition is to constrain the symmetry surface by selecting the intersection points with different coordinate planes on the inner hole surface of the gear.

[0165] (4.3) During the heating or cooling process of the gear, the transformation of the structure will absorb or release latent heat. This method treats the latent heat of phase change generated inside each finite element unit as the internal heat source of the unit, and adds a subroutine HETVAL to calculate the transformation amount and phase change latent heat between the structures during the quenching process. The phase change latent heat can be defined as:

[0166] Q=ΔH F ΔV F +ΔH P ΔV P +ΔH B ΔV B +ΔH M ΔV M (4)

[0167] Where ΔH and ΔV are the corresponding enthalpy and volume when austenite per unit volume decomposes into different structures, and the subscripts F, P, B, and M represent martensite, pearlite, bainite, and ferrite, respectively.

[0168] The corresponding enthalpy values ​​when austenite per unit volume decomposes into martensite, pearlite, bainite and ferrite are shown in Table 2.

[0169] Table 2 Enthalpy values ​​of austenite decomposition into different structures

[0170]

[0171] (4.4) In order to simulate the specific gear heat treatment phase transformation process, it is necessary to obtain the phase transformation products and phase variables at different times in the phase transformation process to calculate the phase transformation latent heat and structural stress. For diffusion-type transformation, the transformation variables from austenite to pearlite, ferrite and bainite under isothermal transformation conditions are:

[0172] V=1-exp(-bt n ) (5)

[0173] Where V represents the transformation amount; t is the isothermal time; b and n represent the coefficients and exponents related to temperature and material, respectively. For the fast and continuous cooling gear quenching process, equation (5) needs to be expanded according to the Scheil superposition principle. By discretizing the time of the continuous cooling process, each small time interval is approximated as an isothermal transformation process, and the inoculation rate and transformation amount are superimposed and calculated. The transformation amount of the i-th step can be defined as:

[0174]

[0175] For non-diffusion transformation, the amount of organizational transformation has nothing to do with time and is only determined by the degree of supercooling. Therefore, the amount of transformation from austenite to martensite can be expressed as:

[0176] V M =1-exp(-α M (M s -T)) (7)

[0177] (4.5) The quenching process is a typical thermoelastic-plastic problem. The thermoelastic-plastic incremental model shown in formula (8) is used to calculate the strain increment of any point inside the workpiece at each time step:

[0178]

[0179] For elastic strain and plastic strain Subroutine USDFLD is required for secondary development and calculation by equations (9) and (10). Phase change strain and phase transformation plastic strain It should be defined in the subroutine UEXPAN and calculated using equations (11), (12) and (13).

[0180]

[0181]

[0182] Where E is the elastic modulus, μ is Poisson's ratio, dσ ij is the stress tensor increment, dσ i is the equivalent stress increment, σ i is the equivalent stress, σ ij is the stress tensor, H is the hardening exponent, ξ m represents the coefficient of thermal expansion, f m is the transfer variable, dT is the temperature increment, β m is the phase expansion coefficient related to the tissue composition, df m is the transformation increment, K is the phase transformation plasticity coefficient, and S is the deviatoric stress tensor.

[0183] For the tempering process, the time-hardening model shown below is used to describe the tempering creep model of steel:

[0184]

[0185] Where A is the material constant, σ is stress, k is the stress sensitivity coefficient, m is the time sensitivity coefficient, t is time, and dt is the time increment.

[0186] (5) Helical gear profile grinding modeling

[0187] (5.1) For the form grinding process, the establishment of the three-dimensional model of the helical gear is similar to step (1.1).

[0188] (5.2) Input of helical gear material performance parameters, including density, specific heat capacity, thermal conductivity, Young's modulus, Poisson's ratio, thermal expansion coefficient and yield stress.

[0189] (5.3) The mesh is divided and the C3D8T thermal-mechanical coupling unit is used to calculate the helical gear forming grinding process.

[0190] (5.4) The thermomechanical coupling module is used to set the analysis steps of the grinding process, and the grinding time is determined based on the tooth width and workpiece feed speed.

[0191] (6) Calculation of helical gear grinding temperature

[0192] (6.1) Considering the influence of the initial stress distribution state before gear forming grinding on the grinding process, the deformation model of the helical gear after heat treatment is introduced as the initial model of the helical gear for grinding.

[0193] (6.2) During the gear profile grinding process, the working section of the grinding wheel is trimmed into an involute tooth profile that matches the tooth profile shape between the workpiece teeth. Grinding is performed by using radial feed motion and axial reciprocating motion of the grinding wheel, and indexing is performed after each tooth is ground. Due to the change in curvature of the involute tooth profile, the grinding motion parameters of each grinding contact point are different. According to Figure 4 The geometric contact model of gear profile grinding, normal grinding depth a n , Grinding wheel equivalent radius r e and grinding speed v s Can be expressed as:

[0194]

[0195] Where a r is the radial grinding depth; is the rolling angle at the grinding contact point K; σ b r is the half angle of the base circle tooth groove; s Indicates the initial radius of the grinding wheel, rb and r f Respectively represent the base circle radius and tooth root radius; θ k is the development angle; α k is the pressure angle at any point on the involute of the tooth profile; n s is the grinding wheel speed.

[0196] (6.3) In order to simulate the grinding wheel movement during gear forming grinding, the heat flow shape of the grinding arc area is assumed to be a triangle for heat flow loading, such as Figure 5 As shown. The heat flux density in the gear shaping grinding arc zone can be expressed as:

[0197]

[0198] The grinding contact arc length between the grinding wheel and the gear is l c It is related to the equivalent radius of the grinding wheel and the normal grinding depth, and can be calculated according to step (6.2).

[0199] (6.4) According to the energy conservation principle and the single abrasive sliding hypothesis theory, calculate the heat flux distribution ratio flowing into the tooth surface.

[0200] (6.5) Based on the thermoelastic-plastic constitutive model and the heat conduction equation, the helical gear forming grinding temperature is obtained. The finite element simulation calculation results of the helical gear forming grinding temperature are shown in Figure 6. Figure 6a is the grinding temperature distribution along the tooth profile direction, Figure 6b is the grinding temperature distribution along the tooth thickness direction, where the grinding parameter is the radial grinding depth a r =0.01mm, grinding wheel linear speed v s =30m / s, feed speed v w =1000mm / min, workpiece speed n g =20rad / min.

[0201] In order to verify the accuracy of the calculation results of the proposed helical gear forming grinding temperature simulation method, gear heat treatment and forming grinding related experiments were carried out. The heat-treated helical gears were ground using the American Gleason-PFAUTE P600 / 800G forming gear grinding machine, a high-speed precision grinding center. A microcrystalline corundum grinding wheel (Φ350×32×127mm, 3SG70GHV50) was used as a grinding tool. During the grinding process, a semi-artificial thermocouple was used to measure the grinding temperature. In order to improve the accuracy and uniformity of the test data, measurements were taken at different positions along the involute tooth profile and tooth width direction, and the average value was used for analysis. The results show that the helical gear forming grinding temperature simulation method and the experimental measurement results have good consistency, proving that the prediction method is effective.

[0202] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principles of the present invention shall be equivalent replacement modes and shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the temperature of helical gear forming grinding, characterized in that: The following steps are involved: S01: Finite element modeling of the carburizing process of helical gears; S02: Calculate the carbon concentration distribution of helical gears; S03: Finite element modeling of the quenching and tempering process of helical gears; S04: Based on the influence of carbon concentration distribution on organizational transformation, combined with temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship, the tooth surface deformation of the helical gear after heat treatment is calculated; S05: Modeling of helical gear profile grinding based on the calculated tooth surface deformation model; S06: The helical gear forming grinding temperature is calculated by combining the geometric contact relationship, moving heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model.

2. The helical gear shaping grinding temperature prediction method according to claim 1, characterized in that: Step S01: The method for performing finite element modeling on the carburizing process of the helical gear includes: S11: according to the actual geometric parameters of the helical gear, a three-dimensional model of the helical gear is established using a three-dimensional design software, and the model is saved as a solid model output format and then imported into a finite element simulation software; S12: Input the material performance parameters of the helical gear. According to the carburizing process requirements, the material performance parameters include density, carbon diffusion coefficient, specific heat capacity and thermal conductivity; S13: Meshing and element type selection for the three-dimensional model of the helical gear; S14: The mass diffusion module is used to set the analysis steps for the initial stage, strong carburizing stage and diffusion stage in the carburizing process.

3. The helical gear profile grinding temperature prediction method according to claim 1, characterized in that: Step S02 also includes setting boundary conditions for the carburizing process, which include initial carbon concentration and material exchange conditions between the carburizing medium and the workpiece surface, wherein the initial carbon concentration is a uniform carbon concentration field, and the material exchange conditions are calculated according to the following formula: J=β(C e -C s ) Where J is the diffusion flux of carbon atoms, β is the carbon atom transfer coefficient, C e is the carbon concentration of the atmosphere in the carburizing furnace, C s is the carbon concentration on the surface of the part.

4. The method for predicting the temperature of helical gear forming grinding according to claim 1, characterized in that: Step S03 specifically includes: S31: According to the quenching and tempering process requirements, the input material performance parameters include thermophysical parameters, structural transformation parameters and mechanical performance parameters; S32: Perform meshing and use the thermal-mechanical coupling unit to calculate the quenching and tempering process; S33: Set up analysis steps for the four stages of heating, heat preservation, quenching cooling and tempering involved in the quenching and tempering process of gears.

5. The method for predicting the temperature of helical gear profile grinding according to claim 1, characterized in that: Step S04 specifically includes: S41: importing the carbon concentration of the carburizing process simulation result into the quenching and tempering simulation model for corresponding calculation; S42: setting boundary conditions during quenching and tempering, including convection heat transfer boundary conditions and displacement boundary conditions; The convection heat transfer boundary conditions of the gear quenching heat transfer model are: Where λ is the thermal conductivity of the gear material, represents the gradient operator, h is the convective heat transfer coefficient between the part and the quenching medium, T and T f Represent the gear surface temperature and quenching medium temperature respectively; The displacement boundary condition is to select the intersection points with different coordinate planes on the inner hole surface of the gear to constrain the symmetry surface; S43: Treat the phase change latent heat generated inside each finite element as the internal heat source of the element, and calculate the phase change latent heat generated when the structure transforms during the heat treatment process; S44: The organizational transformation model is established based on the TTT curve, phase change kinetics and Scheil superposition principle, and the phase change latent heat and organizational stress are calculated through the phase change products and phase variables at different times during the phase change process; S45: The strain increment of each time step at any point inside the workpiece is calculated using the thermoelastic-plastic incremental model. The thermoelastic-plastic incremental model is: in, is the elastic strain increment, is the plastic strain increment, is the thermal strain increment, is the phase transformation strain increment, is the phase transformation plastic strain increment, is the creep increment.

6. The method for predicting the temperature of helical gear profile grinding according to claim 1, characterized in that: The method of calculating the phase change latent heat and tissue stress in step S44 includes: For diffusion-type transformation, the transformation amount from austenite to pearlite, ferrite and bainite under isothermal transformation conditions is: V=1-exp(-bt n ) Where V represents the transformation amount, t is the isothermal time; b and n represent the coefficient and index related to temperature and material respectively; For the gear quenching process with rapid and continuous cooling, the transformation variable V needs to be expanded according to the Scheil superposition principle. By discretizing the time of the continuous cooling process, a certain time interval is approximated as an isothermal transformation process, and the inoculation rate and transformation variable are superimposed and calculated. The transition variable V of step i i for: Among them, b i represents the temperature-dependent coefficient of the i-th step, represents virtual time, Δt i represents the time step of the i-th step, n i represents the index related to the material at step i; For non-diffusion transformation, the amount of organizational transformation has nothing to do with time and is only determined by the degree of supercooling. Therefore, the amount of transformation from austenite to martensite V M It is expressed as: In M =1-exp(-α M (M s -T)) Among them, α M Represents the coefficient reflecting the martensitic transformation rate, M s represents the martensite transformation start temperature, and T represents temperature.

7. The method for predicting the temperature of helical gear profile grinding according to claim 1, characterized in that: The calculation method of the elastic strain increment, plastic strain increment, thermal strain increment, phase change strain increment, phase change plastic strain increment and creep increment in step S45 is: Where E is the elastic modulus, μ is Poisson's ratio, dσ ij is the stress tensor increment, dσ i is the equivalent stress increment, σ i is the equivalent stress, σ ij is the stress tensor, H is the hardening exponent, ξ m represents the coefficient of thermal expansion, f m is the transfer variable, dT is the temperature increment, β m is the phase expansion coefficient related to the tissue composition, df m is the transformation increment, K is the phase transformation plasticity coefficient, S is the deviatoric stress tensor, A is the material constant, σ is the stress, k is the stress sensitivity coefficient, m is the time sensitivity coefficient, t is the time, and dt is the time increment.

8. The method for predicting the temperature of helical gear profile grinding according to claim 1, characterized in that: Step S06 specifically includes: S61: importing the deformation model of the helical gear after heat treatment as the initial model of the helical gear for grinding; S62: Calculate the normal grinding depth, grinding wheel equivalent radius and grinding speed based on the geometric contact model of helical gear profile grinding; S63: The heat flow shape of the grinding arc zone is assumed to be a triangle to simulate the form grinding process of the helical gear. That is, the heat source is distributed in a triangular shape along the involute extension direction and the grinding width direction. The heat flux density of the helical gear form grinding arc zone is expressed as: Where q is the total heat flux density in the grinding arc zone; z i Indicates the distance along the grinding width; represents the rolling angle along the extension direction of the involute, is the maximum rolling angle at the tooth top; l c is the grinding contact arc length between the grinding wheel and the gear; S64: Calculate the heat flux distribution ratio flowing into the tooth surface based on the energy conservation principle and the single abrasive particle sliding hypothesis theory; S65: Based on the thermo-elastoplastic constitutive model and the heat conduction equation, the grinding temperature of the helical gear is obtained.

9. A helical gear forming grinding temperature prediction system, characterized in that: include: Carburizing process modeling module, which performs finite element modeling of the carburizing process of helical gears; Carbon concentration calculation module, calculates the carbon concentration distribution of helical gears; The quenching and tempering process modeling module performs finite element modeling on the quenching and tempering process of helical gears; The stress / strain field calculation module calculates the deformation of the tooth surface after heat treatment of the helical gear based on the influence of the obtained carbon concentration distribution on the organizational transformation, combined with the temperature field heat transfer calculation, phase change dynamics and thermoelastic-plastic constitutive relationship; Helical gear profile grinding modeling module, which performs helical gear profile grinding modeling based on the calculated tooth surface deformation model; The helical gear forming grinding temperature calculation module combines the helical gear forming grinding geometric contact relationship, mobile heat source theory, heat flow distribution ratio and thermal elastic-plastic constitutive model to calculate the helical gear forming grinding temperature.

10. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the helical gear forming grinding temperature prediction method according to any one of claims 1 to 8 is implemented.

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