Gear forming grinding contact area temperature field calculation method based on single-abrasive-particle cutting heat production mechanism

Abstract

The invention discloses a gear forming grinding contact area temperature field calculation method based on a single-abrasive-particle cutting heat production mechanism, and the method comprises the steps: firstly, calculating the undeformed cutting thickness according to the geometric contact relation between abrasive particles and a tooth surface, and judging that the abrasive particles are in a scraping, ploughing or cutting stage; then, the heat flux density generated by each abrasive particle is calculated in stages, the proportion of heat transmitted into the workpiece is determined according to a dynamic heat distribution mechanism, and then the heat flux density distribution of a contact area is obtained through fitting; and finally, on the basis of a moving heat source model and a point heat source superposition method, a temperature field of the gear forming grinding contact area is constructed and solved. According to the method, the limitation that a traditional model adopts fixed heat flow distribution is overcome, accurate prediction of the grinding temperature field is achieved from the physical mechanism level, and a key theoretical basis is provided for effectively controlling tooth surface heat damage and improving gear machining quality.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gear form grinding, and particularly relates to a gear form grinding contact area temperature field calculation method based on a single abrasive grain cutting heat generation mechanism. BACKGROUND

[0002] Gears are widely used in key fields such as aerospace, automobiles, high-end numerical control machine tools and engineering machinery as key components in mechanical transmission. In actual production, grinding is usually used as the last finishing process to ensure the machining quality of gears. However, as a high-energy input machining method, 70% to 80% of the input energy is converted into heat during the machining process. Moreover, due to the complexity of the contact area, the grinding fluid is difficult to enter, hindering the dissipation of heat in the grinding area, and thermal damage is easily caused on the gear surface.

[0003] Therefore, accurately predicting the grinding contact area temperature field is of great significance to improve the machining quality. However, the existing research generally adopts a relatively traditional and fixed triangular heat flux density distribution form when building the form grinding contact area temperature field model, which is difficult to cope with the complex and variable grinding contact form, greatly limiting the improvement of the form grinding surface quality. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a gear form grinding contact area temperature field calculation method based on a single abrasive grain cutting heat generation mechanism, which can accurately predict the gear form grinding contact area temperature field under given machining process parameters.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical solutions: A gear form grinding contact area temperature field calculation method based on a single abrasive grain cutting heat generation mechanism, comprising the following steps: Step one: single abrasive grain cutting mechanism analysis and stage determination: based on the geometric contact relationship between the abrasive grain and the gear surface during form grinding, the undeformed cutting thickness of each abrasive grain in the grinding contact area is calculated, and the cutting stage of each abrasive grain is determined according to the comparison between the undeformed cutting thickness and the critical depth, the cutting stage including the scraping stage, the plowing stage and the cutting stage; Step two: heat generation calculation of abrasive grains in each stage: according to the determination result of step one, the heat flux density generated by the abrasive grains in the scraping stage, the plowing stage and the cutting stage in the grinding contact area is calculated respectively; Step three: heat flux density distribution and fitting: according to the heat flux density distribution mechanism of each grinding stage, the proportion of the heat flux density transmitted to the workpiece in the grinding contact area is determined, and the heat flux density generated by all the abrasive grains participating in grinding and transmitted to the workpiece is integrated and fitted to obtain the heat flux density distribution model in the grinding contact area; Step four: temperature field modeling and solving: based on the heat flux density distribution model obtained in step three, the grinding contact area is equivalent to a surface heat source moving on the gear tooth surface, and the temperature field model of the gear forming grinding contact area is established and solved by the point heat source superposition method.

[0006] Further, in the step one, based on the geometric contact relationship between the abrasive particles and the tooth surface during the forming grinding, the contact arc length of the abrasive particles is obtained as follows: wherein: is the normal depth of cut of the abrasive particle; is the equivalent diameter of the abrasive particle; is the protrusion height of the abrasive particle; is the maximum protrusion height of all abrasive particles of the grinding wheel; is the normal depth of cut during the forming grinding; is the corresponding grinding wheel radius of the abrasive particle; is the corresponding rolling angle of the tooth surface of the abrasive particle; is half of the central angle corresponding to the gear base circle pitch. Further, the maximum undeformed cutting thickness of the abrasive particle is: wherein: is the number of cutting edges per unit area;

[0007] is the ratio of the chip width and height; is the feed speed of the grinding wheel; is the linear speed of the abrasive particle; and: wherein: is the linear speed of the outermost periphery of the grinding wheel; is the radius of the outermost periphery of the grinding wheel; is the corresponding grinding wheel radius of the abrasive particle. Further, in the step one, the critical depth of ploughing and cutting is represented as: wherein: is the critical depth of ploughing; is the critical depth of cutting.

[0008] Further, in the step one, the critical depth of ploughing and cutting is represented as: the critical depth of scraping and ploughing​​​​​​​​ is represented as: wherein: is the Brinell hardness of the workpiece material; is the equivalent elastic modulus of the grinding wheel and the gear; is the protrusion height of the abrasive grain when the undeformed cutting thickness of the abrasive grain is less than the protrusion height of the abrasive grain, it is determined that the abrasive grain is in the scraping stage; when the undeformed cutting thickness of the abrasive grain is greater than the protrusion height of the abrasive grain, it is determined that the abrasive grain is in the plowing stage; when the undeformed cutting thickness of the abrasive grain is greater than the protrusion height of the abrasive grain, it is determined that the abrasive grain is in the cutting stage.

[0009] Further, in the step two, when the abrasive grain is in the scraping stage, the heat flux generated by the abrasive grain is represented as: wherein: is the scraping cutting power; is the scraping contact area; is the contact radius of the abrasive grain with the gear; is the tangential scraping force generated by the abrasive grain when it is in contact with the gear surface; is the linear velocity of the abrasive grain when the abrasive grain is in the plowing stage, the heat flux generated by the abrasive grain is represented as: wherein: is the tangential plowing force generated by the abrasive grain when it is in contact with the gear surface; is the contact area of the plowing stage; when the abrasive grain is in the cutting stage, the heat flux generated by the abrasive grain is represented as: wherein: is the tangential grinding force received by the abrasive grain

[0010] Further, in the step three, the heat flux distribution mechanism includes: when the abrasive grain is in the cutting stage, the total heat is generated in the contact area of the abrasive grain and the gear surface, and is distributed according to ​​​​​​the heat flux density distribution ratio into the workpiece in the grinding contact zone calculated by a model containing the convective heat transfer coefficient of the grinding fluid, the workpiece thermal conductivity factor and the Peclet number; When the abrasive particles are in the ploughing and scraping stages, heat is distributed to the workpiece, the grinding wheel and the grinding fluid, and in the chip and workpiece system, the distribution ratio into the workpiece .

[0011] Further, the heat flux density distribution ratio into the workpiece in the grinding contact zone is expressed as: where: is the convective heat transfer coefficient of the grinding fluid; is the workpiece thermal conductivity factor; is the heat flux density distribution ratio into the workpiece in the grinding wheel and workpiece system; is the heat distribution ratio into the workpiece in the chip and workpiece system in the grinding contact zone; and: the heat flux density distribution ratio into the workpiece in the grinding wheel and workpiece system is: where: is the effective contact radius of the abrasive particle with the tooth surface; is the thermal conductivity of the abrasive particle; , and are the thermal conductivity, density and specific heat capacity of the gear, respectively.

[0012] the heat distribution ratio into the workpiece in the chip and workpiece system in the grinding contact zone is: where: is the thermal diffusivity of the chip; is the average undeformed chip thickness; is the shear strain in the chip formation zone.

[0013] Further, the heat flux density distribution ratio into the workpiece in the ploughing and scraping stages is expressed as: where: is the heat flux density into the workpiece in the scraping and ploughing stages; is the heat flux density generated in the scraping and ploughing stages; the heat flux density distribution ratio into the grinding wheel and the grinding fluid can be expressed as: where: assigning a ratio to the heat flux density of the incoming grinding wheel; assigning a ratio to the heat flux density of the incoming grinding fluid.

[0014] Further, in the step three, the heat flux density of each position in the grinding contact zone is integrated and fitted to the workpiece The fitting is a function of the position , and the heat flux density distribution model is obtained: wherein: represents the rolling angle corresponding to the involute tooth profile; is between 0 and the contact arc length .

[0015] Further, in the step four, the method for establishing the temperature field model by the point heat source superposition method is that the temperature field of the contact zone is equivalent to a surface heat source moving along the feed direction; Suppose that a transient point heat source is located at , and the point heat source emits heat at the time ; then the temperature rise at the point is: wherein: is the temperature rise; is the distance between the point heat source and the point ; and are the thermal diffusivity and the density of the heat conduction body respectively; is the specific heat capacity of the gear; The point heat source is superposed in the gear forming grinding contact zone to obtain the temperature field of the grinding contact zone: wherein: represents the base circle radius of the gear; represents the rolling angle of the integral infinitesimal; represents the time interval; represents the feed speed of the grinding wheel spindle; represents the actual contact position of the integral infinitesimal; and represent the upper and lower limits of the rolling angle respectively; represents the contact arc length of the integral infinitesimal; represents the observation time.

[0016] The present application has the beneficial effects that: The application is based on a gear forming grinding contact area temperature field calculation method of single abrasive grain cutting heat generation mechanism, realizes more scientific and more accurate prediction of the gear forming grinding contact area temperature, and achieves the following technical effects: (1) The accuracy and scientificity of temperature field prediction are significantly improved: the traditional model adopts fixed triangular heat flow distribution, which is difficult to reflect the complex and changeable heat generation in the real contact area; the application accurately calculates the undeformed cutting thickness by analyzing the geometric relationship between single abrasive grain and gear surface, and determines the scraping, plowing or cutting stage of the abrasive grain, thereby more truly revealing the heat generation mechanism at different stages from the physical mechanism, laying a theoretical foundation for accurate calculation of heat flux density; (2) Dynamic and fine modeling of heat flux density generation and distribution is realized: the application not only calculates the heat generation of each abrasive grain in stages, but also further considers the dynamic distribution proportion of heat to the workpiece, grinding wheel, grinding dust and grinding fluid, which changes with process parameters and gear surface position, so that the finally fitted heat flux density distribution model can better fit the heat input in the actual grinding process; (3) It has important engineering guiding value: by equivalent to moving surface heat source and using point heat source superposition method, the temperature field which can accurately reflect the actual working condition is finally obtained; this provides a reliable theoretical tool for optimizing process parameters before production, predicting and controlling gear surface thermal damage (such as burn, residual stress), and directly serves to improve gear machining quality and qualification rate. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to make the purpose, technical scheme and beneficial effects of the application clearer, the application provides the following drawings for illustration: Figure 1 The flow chart of the gear forming grinding contact area temperature field calculation method based on single abrasive grain cutting heat generation mechanism of the application; Figure 2 The schematic diagram of the grinding contact area of the grinding wheel and the gear; Figure 3 The schematic diagram of the undeformed cutting thickness; Figure 4 The schematic diagram of the elastic deformation of the gear surface in the scraping stage; Figure 5 The schematic diagram of the plastic deformation of the gear surface in the plowing stage; Figure 6 The schematic diagram of the cutting of the gear surface in the cutting stage; Figure 7 The schematic diagram of the fitted heat flux density distribution model; Figure 8 The schematic diagram of the temperature rise of a point heat source to an infinite heat conductor. DETAILED DESCRIPTION

[0018] The application will be further described below in connection with the drawings and specific embodiments so that those skilled in the art can better understand the application and implement it, but the embodiments are not intended to limit the application.

[0019] As shown in the figure, the embodiment is based on the tooth forming grinding contact area temperature field calculation method of gear forming grinding heat generation mechanism of single abrasive grain, which includes the following steps. Figure 1

[0020] Step one: single abrasive grain cutting mechanism analysis and stage determination: based on the geometric contact relationship between abrasive grain and gear surface during forming grinding, the undeformed cutting thickness of each abrasive grain in the grinding contact area is calculated, and according to the comparison between the undeformed cutting thickness and the critical depth, the cutting stage of each abrasive grain is determined, which includes the scraping stage, the plowing stage and the cutting stage.

[0021] (1) undeformed cutting thickness During gear forming grinding, the material removal of gear surface is realized through the rotation of the grinding wheel spindle and the feed movement of the grinding wheel along the axial direction of the gear. However, due to the differences in the corresponding rotation radius, protrusion height and other factors of each abrasive grain, the trajectory of its cutting and removal will be more complex than that of plane grinding. For the whole grinding wheel, the grinding contact area with the gear is also more irregular, as shown in the figure. Figure 2 Since material removal only occurs in the contact area, it is necessary to calculate the contact length of each abrasive grain in the grinding area, that is, the contact arc length of each abrasive grain.

[0022] The contact arc length of abrasive grain can be represented as: Wherein: is the equivalent diameter of abrasive grain ; is the normal depth of cut of abrasive grain . Since the protrusion height of abrasive grain is randomly assigned by experimental measurement during the reshaping of grinding wheel, there is a height difference between abrasive grains. The actual normal depth of cut of each abrasive grain is not consistent, so the actual depth of cut of abrasive grain can be represented as: Wherein: is the protrusion height of abrasive grain ; is the maximum value of protrusion height among all abrasive grains of grinding wheel; is the normal depth of cut during forming grinding.

[0023] The equivalent diameter of abrasive grain ​​​ For: where: is the abrasive grain corresponding to the radius of the grinding wheel; is the abrasive grain corresponding to the rolling angle on the tooth surface; is half of the base circle pitch angle of the gear corresponding to the center angle, which can be expressed as: where: is the number of teeth; is the pressure angle.

[0024] By combining the above equations, the contact arc length can be expressed as: When the abrasive grain is located in the contact zone and the protrusion height is sufficient, it will participate in cutting. As shown in Figure 3 , the abrasive grain begins to participate in cutting at the cutting-in point, at which time the undeformed cutting thickness is 0. When reaching the cutting-out point, the undeformed cutting thickness will reach the maximum. The maximum undeformed cutting thickness of the abrasive grain is: where: is the number of cutting edges per unit area, which is measured by experiment; is the ratio of the width to the height of the chip; is the feed speed of the grinding wheel; is the linear speed of the abrasive grain , and: where: is the linear speed of the outermost periphery of the grinding wheel, which is set according to the processing requirements; is the radius of the outermost periphery of the grinding wheel; is the corresponding radius of the grinding wheel.

[0025] (2) Cutting stage judgment ​​Grinding consists of three stages: scraping, plowing, and cutting. During the scraping stage, the workpiece material undergoes only elastic deformation. During the plowing stage, the workpiece material undergoes elastoplastic deformation. Only during the cutting stage is the workpiece material removed. The different states of the workpiece material at each stage lead to different grinding force calculations and varying heat flux densities. The plowing stage occurs when the contact stress between the abrasive grain and the gear exceeds half the Brinell hardness of the material. The cutting stage occurs when the contact stress exceeds the Brinell hardness of the material.

[0026] Specifically, the critical depth for plowing and cutting. Represented as: Critical depth for scraping and plowing Represented as: in: The Brinell hardness of the workpiece material; This represents the equivalent elastic modulus of the grinding wheel and gear. abrasive grains Its prominent height; When the undeformed cutting thickness of the abrasive grains At that time, it is determined that the abrasive grains are in the scraping stage; When the undeformed cutting thickness of the abrasive grains At that time, it was determined that the abrasive particles were in the plowing stage; When the undeformed cutting thickness of the abrasive grains At that time, it is determined that the abrasive grains are in the cutting stage.

[0027] Step 2: Calculation of heat generation of abrasive grains at each stage: Based on the judgment results of Step 1, calculate the heat flux density generated by abrasive grains in the grinding contact area during the scraping stage, plowing stage and cutting stage respectively.

[0028] (1) Calculation of heat flux density during the scraping stage When the undeformed cutting thickness of the abrasive grains At this stage, the abrasive grains are in the scraping phase. During this time, the abrasive grains slide on the gear surface, causing elastic deformation of the surface material. The surface material will rebound after scraping ends, and no material is removed, such as... Figure 4 As shown.

[0029] When the abrasive grains are in the scraping stage, the abrasive grains The generated heat flux density Represented as: in: For scraping cutting power; This refers to the area of ​​the scratch contact zone; abrasive grains The contact radius with the gear; abrasive grains The tangential scraping force generated when in contact with the tooth surface; abrasive grains The linear velocity.

[0030] abrasive grains Contact radius with gear Represented as: in: abrasive grains The corresponding pressure angle.

[0031] abrasive grains Tangential scraping force generated when in contact with the tooth surface Represented as: in: abrasive grains Normal scraping force: This represents the coefficient of friction during the scraping phase.

[0032] Specifically, abrasive grains normal scraping force Represented as: in: Indicates abrasive grains The average stress generated on the contact tooth surface; Abrasive particles during the scraping stage The contact area with the gear.

[0033] (2) Calculation of heat flux density during plowing stage When the undeformed cutting thickness of the abrasive grains At this stage, the abrasive grains are in the plowing phase. During this time, the material on the gear surface undergoes plastic deformation under the pushing force of the abrasive grains, accumulating on both sides of the grains and the rake face. After the abrasive grains pass through, they leave scratches on the tooth surface, but no material is removed, such as... Figure 5 As shown.

[0034] When the abrasive grains are in the plowing stage, the abrasive grains The generated heat flux density Represented as: in: abrasive grains The tangential plowing force generated by contact with the tooth surface; This refers to the area of ​​the contact zone during the plowing stage.

[0035] abrasive particle tangential ploughing force generated by the contact with the tooth surface is expressed as: wherein: is the normal ploughing force of the abrasive particle . represents the scraping coefficient of the material.

[0036] abrasive particle normal ploughing force of the abrasive particle is expressed as: wherein: is the average stress suffered by the ploughing contact zone.

[0037] (3) Calculation of heat flux density in the cutting phase When the undeformed cutting thickness of the abrasive particle , the abrasive particle is in the cutting phase. Under the push of the abrasive particle, the tooth surface material will be plastically deformed and a chip will be generated. There will still be scraping and ploughing phenomena in the positions with depth located in , only the positions with depth located in will have cutting phenomena. In the cutting position, the abrasive particle will suffer the force generated by the material to resist the generation of the chip, as shown in Figure 6 .

[0038] When the abrasive particle is in the cutting phase, the heat flux density generated by the abrasive particle is expressed as: wherein: is the tangential grinding force suffered by the abrasive particle .

[0039] Specifically, the grinding force suffered by the abrasive particle can be obtained through the shear stress of the material: wherein: is the normal grinding force suffered by the abrasive particle ; is the corresponding rake angle of the abrasive particle when cutting; is the friction angle of the abrasive particle when cutting; is the shear strength of the machined material; and are the upper and lower limits of the rake angle of the abrasive particle , respectively.

[0040] Step three: Heat flux density distribution and fitting: According to the heat flux density distribution mechanism of grinding cutting, the proportion of the heat flux density transmitted into the workpiece in the grinding contact area is determined, and the heat flux density transmitted into the workpiece generated by all the grinding particles involved in grinding is integrated and fitted to obtain the heat flux density distribution model in the grinding contact area.

[0041] In the process of gear form grinding, 70%~80% of the spindle power will be converted into heat energy in the grinding area, except for a small part of the grinding energy consumed in the surface energy and residual strain energy generated by the new surface. This heat energy will be distributed to the workpiece, grinding fluid, grinding wheel and grinding dust in a certain proportion. And the distribution ratio is dynamic: ① affected by process parameters: changes in process parameters such as grinding wheel speed, grinding depth, feed speed, etc. will change the heat distribution ratio between the workpiece, grinding fluid, grinding wheel and grinding dust. ② Changes along the tooth profile (rolling angle): due to the differences in the geometric shape of the grinding wheel-workpiece contact area at different rolling angles on the gear tooth profile, the heat distribution ratio is not constant in the entire tooth profile direction, but shows a continuous change trend. Therefore, in order to accurately predict and calculate the temperature rise in the grinding area, it is necessary to solve the corresponding heat flux density distribution ratio for different process parameter combinations and at different positions on the tooth profile.

[0042] (1) Heat flux density distribution model in cutting stage When the grinding particles are in the cutting stage, the total heat is generated in the contact area between the grinding particles and the tooth surface, and is distributed to the workpiece, grinding wheel, grinding dust and grinding fluid in a certain proportion, which is expressed as: wherein: , , and are the heat flux densities transmitted into the workpiece, grinding wheel, grinding dust and grinding fluid during grinding, respectively.

[0043] Heat flux density distribution ratio transmitted into the workpiece It is calculated by a model containing the convective heat transfer coefficient of the grinding fluid, the workpiece thermal conductivity factor and the Prandtl number. Specifically, the heat flux density distribution ratio transmitted into the workpiece in the grinding contact area is expressed as: wherein: is the convective heat transfer coefficient of the grinding fluid; is the thermal conductivity factor of the workpiece; is the heat flux density distribution ratio of the workpiece in the grinding wheel and workpiece system; is the heat distribution ratio of the workpiece in the grinding dust and workpiece system in the grinding contact area.

[0044] Heat flux density distribution ratio of the workpiece in the grinding wheel and workpiece system​ is: where: is the effective contact radius of the abrasive particle and the tooth surface; is the thermal conductivity of the abrasive particle; , and are the thermal conductivity, density and specific heat capacity of the gear, respectively.

[0045] Both grinding parameters and abrasive particle types have an impact on the heat conduction in the chip formation process in the grinding zone. The thermal partition of the chips and the workpiece in the grinding contact zone is: where: is the thermal diffusivity of the chip; is the average undeformed chip thickness; is the shear strain in the chip formation zone.

[0046] (2) Heat flux density distribution model in the scraping and ploughing stage When the abrasive particle is in the ploughing and scraping stage, the abrasive particle only passes through the tooth surface and does not produce a chip. The heat generated by the contact between the abrasive particle and the tooth surface is only transmitted into the workpiece, the grinding fluid and the grinding wheel. At this time, in the chip and workpiece system, the distribution ratio of the heat transmitted into the workpiece . The distribution ratio of the heat flow density flowing into the workpiece in the ploughing and scraping stage can be expressed as: where: is the heat flow density transmitted into the workpiece in the scraping and ploughing stage; is the heat flow density generated in the scraping and ploughing stage; The distribution ratio of the heat flow density transmitted into the grinding wheel and the grinding fluid at this time can be expressed as: where: is the heat flow density distribution ratio transmitted into the grinding wheel; is the heat flow density distribution ratio transmitted into the grinding fluid.

[0047] (3) Heat flow density distribution model The heat generated by each grinding abrasive particle participating in the grinding is integrated by analyzing the contact relationship between the abrasive particle and the tooth surface, and the heat flow density distribution in the grinding contact zone is solved.

[0048] The heat flow density transmitted into the workpiece when the abrasive particle is in the scraping, ploughing and cutting stage can be expressed as: where: , and are the heat fluxes transmitted into the workpiece during the scraping, ploughing and cutting phases of the abrasive particles, respectively; , and are the heat fluxes generated during the scraping, ploughing and cutting phases, respectively.

[0049] The heat fluxes transmitted into the workpiece at each position in the grinding contact zone are integrated and fitted to a function of the position , as shown in Fig. 2, to obtain a heat flux distribution model: Figure 7 where: is the rolling angle corresponding to the involute tooth profile; is between 0 and the contact arc length .

[0050] Step four: temperature field modeling and solving: based on the heat flux distribution model obtained in step three, the grinding contact zone is equivalent to a surface heat source moving on the gear tooth surface, and the temperature field model of the gear forming grinding contact zone is established and solved by the point heat source superposition method.

[0051] During gear forming grinding, the contact relationship between the grinding wheel and the gear tooth surface, the depth of cut, etc. are relatively stable in the gear axial direction. The temperature field of the contact zone can be equivalent to a relatively stable surface heat source moving on the tooth surface in the feed direction, and the temperature rise generated by the gear in the moving time period. This surface heat source can be equivalent to the superposition of an infinite number of point heat sources. Therefore, the basis of the modeling of the grinding contact zone temperature field is the temperature rise generated by a point heat source on an infinite heat conductor, as shown in Fig. 3. Figure 8

[0052] Assuming that a point heat source is located at at time , the point heat source emits heat ; then the temperature rise at point is: where: is the temperature rise; is the distance between the point heat source and point ; and are the thermal diffusivity and density of the heat conductor, respectively; is the specific heat capacity of the gear.

[0053] The point heat source is superimposed in the gear forming grinding contact zone to obtain the grinding contact zone temperature field: ​​ wherein: denotes the gear base circle radius; denotes the rolling angle of the integration infinitesimal; denotes the time interval; denotes the feed speed of the grinding wheel spindle; denotes the actual contact position of the integration infinitesimal; and denote the upper and lower limits of the rolling angle, respectively; denotes the contact arc length of the integration infinitesimal; denotes the observation time.

[0054] The above-described embodiments are merely preferred embodiments of the present application, and the scope of the present application is not limited thereto. Any equivalent replacement or transformation made by those skilled in the art based on the present application shall fall within the scope of the present application. The scope of the present application is defined by the claims.

Claims

1. A method for calculating the temperature field of the contact zone in gear form grinding based on the heat generation mechanism of single abrasive grain cutting, characterized in that: The method comprises the following steps: Step one: single abrasive grain cutting mechanism analysis and stage determination: based on the geometric contact relationship between the abrasive grains and the tooth surface during the forming grinding, the undeformed cutting thickness of each abrasive grain in the grinding contact area is calculated, and according to the comparison between the undeformed cutting thickness and the critical depth, the cutting stage of each abrasive grain is determined, the cutting stage includes the scraping stage, the plowing stage and the cutting stage; Step two: heat production calculation of abrasive grains in each stage: according to the determination result of step one, the heat flux density generated by the abrasive grains in the scraping stage, the plowing stage and the cutting stage in the grinding contact area is calculated respectively; Step three: heat flux density distribution and distribution fitting: according to the heat flux density distribution mechanism of each grinding stage, the proportion of the heat flux density transmitted to the workpiece in the grinding contact area is determined, and the heat flux density generated by all the abrasive grains participating in the grinding and transmitted to the workpiece is integrated and fitted to obtain the heat flux density distribution model in the grinding contact area; Step four: temperature field modeling and solving: based on the heat flux density distribution model obtained in step three, the grinding contact area is equivalent to a surface heat source moving on the gear tooth surface, and the temperature field model of the gear forming grinding contact area is established and solved by point heat source superposition method.

2. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 1, characterized in that: In step one, the abrasive grains are obtained based on the geometric contact relationship between the abrasive grains and the tooth surface during profile grinding. Contact arc length : in: abrasive grains Normal depth of cut; abrasive grains Equivalent diameter; abrasive grains Its prominent height; This represents the maximum protrusion height among all abrasive grains on the grinding wheel. This refers to the normal depth of cut during form grinding; abrasive grains The corresponding grinding wheel radius; abrasive grains The rolling angle corresponding to the tooth surface; It is half of the central angle corresponding to the tooth pitch of the gear base circle.

3. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 2, characterized in that: Abrasive particles Maximum undeformed cutting thickness of the abrasive particle is: wherein: is the number of cutting edges per unit area; is the ratio of the chip width to the chip height; is the feed speed of the grinding wheel; is the linear speed of the abrasive particles; and: is the linear speed of the abrasive particles; and: wherein: is the linear speed of the outermost periphery of the grinding wheel; is the radius of the outermost periphery of the grinding wheel; is the abrasive grain corresponding to the radius of the grinding wheel.

4. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 1, characterized in that: The critical depth of ploughing and cutting in step one is represented as: Critical depth of scraping and plowing is represented as: wherein: is the Brinell hardness of the workpiece material; is the equivalent elastic modulus of the grinding wheel and the gear; is the protrusion height of the abrasive particles . When the undeformed cutting thickness of the abrasive particle is determined to be in the scraping stage; When the undeformed cutting thickness of the abrasive particle is determined to be in the plowing stage; When the undeformed cutting thickness of the abrasive particle is determined to be in the cutting stage.

5. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 1, characterized in that: In step two, when the abrasive particle is in the scraping phase, the abrasive particle Heat flux generated is represented as: wherein: is the scraping chip removal power; is the scraping contact area; is the abrasive grain is the contact radius with the gear; is the abrasive grain is the tangential scraping force generated when in contact with the tooth surface; is the abrasive grain is the linear velocity of the When the abrasive particles are in the plowing stage, the abrasive particles Heat flux density generated is represented as: wherein: is an abrasive grain is the tangential ploughing force generated by the contact with the tooth surface; is the area of the contact zone in the ploughing phase When the abrasive particles are in the cutting stage, the abrasive particles Heat flux density generated is represented as: wherein: abrasive particles experienced tangential grinding force.

6. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 1, characterized in that: In step three, the heat flux density distribution mechanism comprises: When the abrasive grain is in the cutting stage, the total heat is generated in the contact area between the abrasive grain and the tooth surface, and is distributed to the workpiece, the grinding wheel, the grinding dust and the grinding fluid, wherein the heat flux density transmitted to the workpiece is distributed in proportion to The heat flux density transmitted to the workpiece is distributed in proportion to The model is calculated by including the convection heat transfer coefficient of the grinding fluid, the workpiece thermal conductivity factor and the Prandtl number. When the abrasive particles are in the plowing and scraping stages, heat is distributed to the workpiece, the grinding wheel, and the grinding fluid, and in the swarf and workpiece system, the distribution to the workpiece is greater than .

7. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 6, characterized in that: Distribution of heat flux into a workpiece at a grinding contact zone is represented as: wherein: is the convective heat transfer coefficient for the grinding fluid; is the thermal conductivity factor for the workpiece; is the heat flux density partition ratio for the workpiece in the grinding wheel and workpiece system; is the thermal partition ratio for the swarf in the grinding contact zone and the workpiece in the workpiece system; and: Heat flux density distribution ratio of workpiece in grinding wheel and workpiece system is: wherein: is the effective contact radius of the abrasive particles with the tooth surface; is the thermal conductivity of the abrasive particles; , and are the thermal conductivity, density and specific heat capacity of the gear, respectively; Thermal matching of workpiece in a system of grinding dust and workpiece in a grinding contact zone To: where: is the thermal diffusivity of the swarf; is the average undeformed chip thickness; is the shear strain in the chip formation zone.

8. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 6, characterized in that: Distribution ratio of heat flux into a workpiece during plowing and scraping is represented as: wherein: is the heat flux density transmitted to the workpiece for the scraping and ploughing phase; is the heat flux density generated for the scraping and ploughing phase; The distribution ratio of the heat flux density transmitted to the grinding wheel and the grinding fluid can be expressed as: wherein: a fraction of the heat flux transmitted into the grinding wheel; a fraction of the heat flux transmitted into the grinding fluid.

9. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 1, characterized in that: In the third step, the heat flux density is integrated and fitted to obtain the heat flux density at each position in the grinding contact zone The fitting is a function of the position and the heat flux density distribution model is obtained wherein: is the rolling angle corresponding to the involute profile; is between 0 and the contact arc length .

10. The method for calculating the temperature field of the contact zone in the gear forming grinding according to the heat generation mechanism of single abrasive grain cutting according to claim 6, characterized in that: In step four, the method for establishing the temperature field model by point heat source superposition method is to equivalent the temperature field of the contact area to a surface heat source moving along the feed direction; Assume that at an instant point in time the heat source is located at , at time the point heat source emits heat ; then the temperature rise generated at point is: wherein: is the temperature rise; is the point heat source is the distance between the point ; and are the thermal diffusivity and density of the heat conductor, respectively; is the specific heat capacity of the gear; The point heat sources are superimposed in the gear forming grinding contact area to obtain the grinding contact area temperature field: wherein: denotes the gear base circle radius; denotes the rolling angle of the integration infinitesimal; denotes the time interval; denotes the feed speed of the grinding wheel spindle; denotes the actual contact position of the integration infinitesimal; and denote the upper and lower limits of the rolling angle, respectively; denotes the contact arc length of the integration infinitesimal; denotes the observation time instant.

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