A method, system, device and terminal for calculating residual stress in micro grinding
By introducing equivalent thermal moving loads and elastic-plastic contact mechanics theory in fine grinding, the inaccuracy problem of residual stress calculation of fine grinding in the prior art is solved, and effective analysis and quantitative calculation of the fine grinding process are realized .
Patent Information
- Application Number
- CN202111395965.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-11-23
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2041-11-23
AI Technical Summary
The prior art is difficult to accurately calculate residual stress during fine grinding. The macroscopic method ignores the contact stress concentration of a single abrasive grain, and the microscopic method ignores the influence of multiple cuttings and other abrasive grains, resulting in the inreliability of the analysis results.
The calculation method based on micro-grinding equivalent thermal moving load was proposed. By determining the distribution and effect of micro-grinding and macro-heat load, combined with the theory of elastic-plastic contact mechanics, the internal stress of the workpiece under the action of micro-grinding equivalent thermal load was calculated and Residual stress.
Effective calculation and quantitative analysis of residual stress of fine grinding is realized, and more reliable analysis tools are provided, which can accurately reflect the complex contact characteristics of force and heat load during fine grinding.
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Figure CN114091262B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of micro-grinding technology, and in particular relates to a micro-grinding residual stress calculation method, system, equipment and terminal. Background Art
[0002] At present, the calculation methods of grinding residual stress can be summarized into two types, namely macroscopic method and microscopic method. The macroscopic method loads the grinding force and heat load onto the contact arc area as a whole, and then uses analytical modeling or numerical analysis methods to solve the grinding residual stress. However, since grinding is the contact loading of many randomly distributed single abrasives on the grinding arc area, the contact area between the single abrasive and the grinding arc area is small, and the contact stress concentration is much greater than the stress concentration during the overall loading. It can be seen that the macroscopic method greatly weakens the effect of force load on residual stress, so this method is usually used to calculate conventional grinding or high-force grinding residual stress dominated by thermal load. The microscopic method simulates the material removal process of a single abrasive by constructing a finite element model of single abrasive cutting. After the cutting is completed, the residual stress is obtained after the necessary constraint conversion and cooling. However, since it only considers the effect of single abrasive cutting, and ignores the influence of multiple cutting of the same abrasive in the grinding arc area and the participation of other abrasives in the grinding arc area in the actual grinding process on the residual stress, it can generally only make a qualitative analysis of the grinding residual stress. Moreover, the microscopic method is based on the single abrasive-workpiece contact constraint and the fracture removal of chips. In order to improve the solution efficiency, the finite element model size of the workpiece is generally much smaller than the actual size of the workpiece, and the shape and structure are also very different from the actual workpiece, which further affects the reliability of the microscopic method to analyze residual stress. Therefore, the concept of micro-grinding equivalent thermal transfer load is proposed, and then the theoretical analysis method of micro-grinding residual stress based on equivalent thermal transfer load is given, which lays a theoretical foundation for the calculation model of micro-grinding residual stress of the thin neck of the flexible joint.
[0003] Through the above analysis, the problems and defects of the prior art are as follows:
[0004] (1) Since grinding is the contact loading of many randomly distributed single abrasive particles on the grinding arc zone, the contact area between the single abrasive particle and the grinding arc zone is small, and the degree of contact stress concentration is much greater than the stress concentration during overall loading. It can be seen that the macro method greatly weakens the effect of force load on residual stress.
[0005] (2) Since the microscopic method only considers the cutting effect of a single abrasive grain, and ignores the influence of multiple cutting of the same abrasive grain in the grinding arc zone and the influence of other abrasive grains participating in cutting in the grinding arc zone on the residual stress during the actual grinding process, it can generally only make a qualitative analysis of the grinding residual stress.
[0006] The difficulty of solving the above problems and defects is:
[0007] (1) The micro-grinding process is a contact loading process of many randomly distributed single abrasive particles on the grinding arc zone. The contact area between a single abrasive particle and the grinding arc zone is small, and the degree of contact stress concentration is much greater than the stress concentration during overall loading. Therefore, the force load acting on the surface of the workpiece being ground is a micro-scale contact load.
[0008] (2) Regarding grinding heat, existing research results show that since the contact time between the abrasive and the workpiece in the grinding arc zone is extremely short, the heat generated by the cutting of a single abrasive is a transient load, and the grinding heat load cannot be obtained by superimposing the heat load of a single abrasive. Grinding heat is the comprehensive effect generated by the contact between many abrasives and the workpiece, so the grinding heat load is a macro-scale contact load. Due to the macroscopic contact characteristics of the grinding heat load, unlike the multiple cyclic loading of the force load, the grinding heat load on the workpiece is an overall one-time loading within the contact arc length.
[0009] (3) During the micro-grinding process, the microscopic multiple loading of the force load and the macroscopic single loading of the thermal load exist simultaneously and couple with each other to form the contact characteristics of the micro-grinding load.
[0010] The above makes the calculation of micro-grinding residual stress different from other processing residual stress calculation methods. Therefore, a new method must be adopted to achieve reliable calculation of micro-grinding residual stress.
[0011] The significance of solving the above problems and defects is:
[0012] The micro-grinding residual stress calculation method based on the micro-grinding equivalent effective thermal transfer load can realize the effective calculation of micro-grinding residual stress and provide a tool for the quantitative analysis of micro-grinding residual stress. Summary of the invention
[0013] In view of the problems existing in the prior art, the present invention provides a method, system, device and terminal for calculating residual stress in micro-grinding, and more particularly, relates to a method, system, device and terminal for calculating residual stress in micro-grinding based on micro-grinding equivalent effective thermal transfer load.
[0014] The present invention is implemented as follows: a method for calculating residual stress in micro-grinding, the method comprising the following steps:
[0015] Step 1, determine the equivalent thermal transfer load of micro grinding;
[0016] Step 2: Calculate the internal stress of the workpiece under the action of micro-grinding equivalent thermal load;
[0017] Step three, calculate the residual stress in the workpiece under the action of micro-grinding equivalent thermal load.
[0018] Furthermore, in step one, the micro-grinding equivalent force heat transfer load refers to a number of microscopic force loads and a single macroscopic heat load that move along the grinding direction and at the workpiece speed; wherein the microscopic force load refers to the grinding force of a single abrasive particle, and the macroscopic heat load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece; a certain distance is maintained between each microscopic force load to ensure that the stress area generated by the load in the workpiece is not superimposed.
[0019] Further, in step 1, determining the micro-grinding equivalent thermal transfer load includes:
[0020] (1) Determine the distribution of microscopic force loads
[0021] The normal and tangential distributions of the microscopic force load are p g (s) and q g (s), and there is:
[0022]
[0023]
[0024] In the formula, l g is the contact length of a single abrasive particle, which is a function of the abrasive particle radius, the length of the wear plane and the thickness of the undeformed chip.
[0025] Normal load density and tangential load density p of a single abrasive particle g0 and q g0 It is found by the following formula:
[0026]
[0027] (2) Determine the macroscopic heat load distribution
[0028]
[0029] Where, q0 = F t v s / l c w.
[0030] (3) Determine the number of microscopic force loads
[0031] The number of microscopic force loads is calculated by the following formula:
[0032] n load =(l c / l0)((v s +v w ) / v w ).
[0033] Further, in step 2, the calculation of the stress in the workpiece under the micro-grinding equivalent thermal load includes:
[0034] After calculating the stress components generated by the microscopic force load and the macroscopic heat load in the micro-grinding equivalent force heat load respectively, the two are superimposed to finally obtain the internal stress of the workpiece under the action of the micro-grinding equivalent force heat load.
[0035] (1) Analysis of stress generated in the workpiece by microscopic force load under micro-grinding equivalent force and heat load
[0036] The Boussinesq solution of stress distribution under normal and tangential point loads is integrated over the contact area to obtain the stress distribution in the workpiece under the micro-force load. Therefore, under the action of the micro-grinding equivalent thermal transfer load, the stress components generated by the kth micro-force load at point P are calculated by the following formula:
[0037]
[0038] In the formula, p g (k,s) and q g (k, s) are the kth normal micro-force load and tangential micro-force load distribution respectively.
[0039] (2) Analysis of stress generated by thermal load in the workpiece under the action of micro-grinding equivalent thermal transfer load
[0040] The stress caused by thermal load under the action of effective thermal transfer load in micro-grinding is solved according to Duhamel similarity theorem; this theorem simultaneously considers the thermal stress effects of body force, surface force and hydrostatic pressure, and calculates the total thermal stress by superposition of the three stresses.
[0041] (3) Workpiece stress analysis under micro-grinding equivalent thermal transfer load
[0042] The stress generated by the kth microscopic force load and thermal load in the micro-grinding equivalent force and thermal transfer load is expressed as:
[0043]
[0044] In the formula, σ xx R (k-1,x,z) and σ yy R (k-1, x, z) are the residual stresses in the grinding direction x and in the vertical grinding direction y at point P in the workpiece after the k-1 microscopic force loads in the micro-grinding equivalent force heat transfer load are unloaded. Since the workpiece is subjected to stress relief heat treatment before grinding, the residual stress before the first load is considered to be 0.
[0045] Furthermore, in step (2), the stress analysis of the thermal load generated in the workpiece under the micro-grinding equivalent thermal transfer load includes:
[0046] ① Stress component generated by body force
[0047] In the workpiece coordinate system X w O w Z w Under this condition, the grinding temperature T of point P in the workpiece is obtained by constructing a grinding temperature calculation model based on the double adiabatic boundary assumption. Then the body force component X caused by the temperature at this point is T and Z T It is expressed by the following formula:
[0048]
[0049] The thermal stress component due to body force is expressed as follows:
[0050]
[0051] In the formula, G xh , G xh and G xh is the Green's function.
[0052] ②Stress component generated by surface force
[0053] The surface force generated by the grinding temperature is α w E w T / (1-2ν w ), the thermal stress component generated by the surface force at point P in the workpiece is expressed by the following formula:
[0054]
[0055] Where p(t) = α w E w T(x,z=0) / (1-2ν w ).
[0056] ③Influence of hydrostatic pressure
[0057] Hydrostatic pressure is expressed as -α w E w T / (1-2ν w );
[0058] By superimposing the stresses generated by body force, surface force and hydrostatic pressure, the thermal stress components generated by the thermal load at the point P in the workpiece in the micro-grinding equivalent thermal transfer load are obtained as follows:
[0059]
[0060] Further, in step three, the calculation of the residual stress in the workpiece under the micro-grinding equivalent thermal load includes:
[0061] Under the action of effective thermal transfer load equivalent to micro-grinding, the residual stress distribution in the workpiece is obtained by using the theory of increment and unloading in elastic-plastic contact mechanics.
[0062] (1) Elastic-plastic loading analysis
[0063] Under the action of micro-grinding equivalent force and heat transfer load, the kth micro-force load and heat load first elastically load point P in the workpiece, and calculate the elastic stress component generated. After a period of time, when the kth micro-force load reaches point B, the material at point P in the workpiece begins to produce plastic deformation. The basis for determining the transition from elastic loading to plastic loading is the von Mises yield criterion, and the yield function is expressed as:
[0064]
[0065] In the formula, K w is the shear yield strength, S ij and α ij are the deviatoric stress tensor and the passive stress tensor respectively, and we have:
[0066]
[0067] Where n ij is the unit vector in the normal direction of the plastic strain rate.
[0068] For the elastic-plastic loading process, a mixed function is used to calculate the stress-strain increment generated by load loading. The expression of the mixed function is as follows:
[0069]
[0070] Where κ is the mixing function constant, h w is the plastic modulus of the material, G w is the elastic shear modulus of the material. Applying the mixed function, the strain increment dε in the grinding direction xx It is expressed as:
[0071]
[0072] Strain increment dε perpendicular to the grinding direction under plane strain conditions yy is 0 and is represented by:
[0073]
[0074] By combining the equations, we can get the stress increment dσ corresponding to the grinding direction and perpendicular to the grinding direction: xx and dσ yyBefore the loading is completed, the elastic-plastic incremental loading will continue, and the judgment method of loading and unloading is given as follows:
[0075]
[0076] (2) Stress release analysis
[0077] After the kth microscopic force load in the micro-grinding equivalent thermal transfer load is loaded, in order to meet the boundary conditions of plane strain, the stress and strain components in the following formula are gradually released until σ zz , τ xz and ε xx When the release is 0, the stress release ends, and the residual stress after the kth loading is obtained:
[0078]
[0079] Under the action of micro-grinding equivalent thermal transfer load, if k = n pass When all elastic stress and strain components of the load are released, if k < n pass When the stress is released, the elastic stress and strain components generated by the thermal load are not involved. Only the stress generated by the kth load and the residual stress generated by the previous k-1 loads are released. pass , expressed as:
[0080]
[0081] Assuming that the release process is implemented in N steps, the release increment per step for stress and strain components with a value of 0 is:
[0082]
[0083] For non-zero stress components σ xx (k) and σ yy (k) Different release increments are used according to the elastic-plastic state of the workpiece material. When only elastic deformation occurs at a point in the workpiece, that is, F < 0 or F = 0 and n ij (k)dS ij When σ<0, xx (k) and σ yy The elastic release increment of (k) is expressed as:
[0084]
[0085] For the case where the workpiece undergoes elastic-plastic deformation, it is necessary to satisfy F = 0 and n ij (k)dS ij ≥0, σ xx (k) and σyy The elastic release increment of (k) is expressed as:
[0086]
[0087] In the formula, C and D are expressed as:
[0088]
[0089] Another object of the present invention is to provide a micro-grinding residual stress calculation system using the micro-grinding residual stress calculation method, the micro-grinding residual stress calculation system comprising:
[0090] Thermal transfer load determination module, used to determine the equivalent thermal transfer load of micro-grinding;
[0091] Stress calculation module, used to calculate the stress in the workpiece under the effect of effective thermal load equivalent to micro-grinding;
[0092] The residual stress calculation module is used to calculate the residual stress in the workpiece under the action of effective thermal load equivalent to micro-grinding.
[0093] Another object of the present invention is to provide a computer device, the computer device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor performs the following steps:
[0094] Determine the micro-grinding equivalent thermal transfer load; wherein the micro-grinding equivalent thermal transfer load refers to a number of microscopic force loads and a single macroscopic thermal load that move along the grinding direction and at the workpiece speed, the microscopic force load refers to the grinding force of a single abrasive grain, the macroscopic thermal load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece, and a certain distance is maintained between each microscopic force load;
[0095] By superimposing the internal stresses generated by several microscopic force loads and the internal stress generated by a single macroscopic thermal load, the stress in the workpiece under the action of effective thermal load equivalent to micro-grinding is calculated; under the action of effective thermal movement load equivalent to micro-grinding, the theory of increment and unloading in elastic-plastic contact mechanics is used to calculate the residual stress in the workpiece under the action of effective thermal load equivalent to micro-grinding.
[0096] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the following steps:
[0097] Determine the micro-grinding equivalent thermal transfer load; wherein the micro-grinding equivalent thermal transfer load refers to a number of microscopic force loads and a single macroscopic thermal load that move along the grinding direction and at the workpiece speed, the microscopic force load refers to the grinding force of a single abrasive grain, the macroscopic thermal load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece, and a certain distance is maintained between each microscopic force load;
[0098] By superimposing the internal stresses generated by several microscopic force loads and the internal stress generated by a single macroscopic thermal load, the stress in the workpiece under the action of effective thermal load equivalent to micro-grinding is calculated; under the action of effective thermal movement load equivalent to micro-grinding, the theory of increment and unloading in elastic-plastic contact mechanics is used to calculate the residual stress in the workpiece under the action of effective thermal load equivalent to micro-grinding.
[0099] Another object of the present invention is to provide an information data processing terminal, which is used to implement the micro-grinding residual stress calculation system.
[0100] In combination with all the above technical solutions, the advantages and positive effects of the present invention are as follows: the micro-grinding residual stress calculation method provided by the present invention specifically relates to a micro-grinding residual stress calculation method based on micro-grinding equivalent effective thermal transfer load, which can realize the effective calculation of micro-grinding residual stress and provide a tool for the quantitative analysis of micro-grinding residual stress.
[0101] In the present invention, the micro-grinding equivalent effective heat moving load refers to a number of microscopic force loads and a single macroscopic heat load that move along the grinding direction and at the workpiece speed. In particular, the microscopic force load refers to the grinding force of a single abrasive particle, and the macroscopic heat load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece; a certain distance must be maintained between each microscopic force load to ensure that the stress area generated by the load in the workpiece is not superimposed; the internal stress of the workpiece under the action of the micro-grinding equivalent effective heat load is obtained by superimposing the internal stress generated by a number of microscopic force loads and the internal stress generated by the single macroscopic heat load; the residual stress in the workpiece under the action of the micro-grinding equivalent effective heat load is calculated based on the theory of increment and unloading in elastic-plastic contact mechanics. BRIEF DESCRIPTION OF THE DRAWINGS
[0102] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0103] Figure 1 It is a flow chart of a method for calculating residual stress in micro-grinding provided by an embodiment of the present invention.
[0104] Figure 2 is a structural block diagram of a micro-grinding residual stress calculation system provided by an embodiment of the present invention;
[0105] In the figure: 1. Thermal transfer load determination module; 2. Stress calculation module; 3. Residual stress calculation module.
[0106] Figure 3 It is a schematic diagram of loading and unloading analysis of the effective thermal transfer load of micro-grinding provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0107] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0108] In view of the problems existing in the prior art, the present invention provides a method, system, device and terminal for calculating residual stress in micro-grinding. The present invention is described in detail below in conjunction with the accompanying drawings.
[0109] like Figure 1 As shown, the micro-grinding residual stress calculation method provided by the embodiment of the present invention includes the following steps:
[0110] S101, determine the equivalent effective thermal transfer load of micro-grinding;
[0111] S102, calculate the internal stress of the workpiece under the effect of micro-grinding equivalent thermal load;
[0112] S103, calculating the residual stress in the workpiece under the effect of micro-grinding equivalent thermal load.
[0113] like Figure 2 As shown, the micro-grinding residual stress calculation system provided by the embodiment of the present invention includes:
[0114] Thermal transfer load determination module 1, used to determine the thermal transfer load equivalent to micro-grinding;
[0115] Stress calculation module 2, used to calculate the stress in the workpiece under the effect of micro-grinding equivalent thermal load;
[0116] The residual stress calculation module 3 is used to calculate the residual stress in the workpiece under the effect of thermal load equivalent to micro-grinding.
[0117] The technical solution of the present invention is further described below in conjunction with specific embodiments.
[0118] To calculate the residual stress of micro grinding, first determine the equivalent effective thermal movement load of micro grinding, then calculate the internal stress of the workpiece under the equivalent effective thermal load of micro grinding, and finally calculate the residual stress in the workpiece under the equivalent effective thermal load of micro grinding.
[0119] The micro-grinding residual stress calculation method based on the micro-grinding equivalent effective thermal transfer load of the present invention is:
[0120] S1. Determine the equivalent thermal transfer load of micro grinding;
[0121] (1) Determine the distribution of microscopic force loads
[0122] Combination Figure 3 , the normal and tangential distributions of the microscopic load are p g (s) and q g (s), and there is:
[0123]
[0124]
[0125] In the formula, l g is the contact length of a single abrasive particle, which is a function of the abrasive particle radius, the length of the wear plane and the thickness of the undeformed chip. Normal load density and tangential load density p of a single abrasive particle g0 and q g0 It can be obtained by formula (3).
[0126]
[0127] (2) Determine the macroscopic heat load distribution
[0128]
[0129] Where, q0 = F t v s / l c w
[0130] (3) Determine the number of microscopic force loads
[0131] The number of microscopic force loads can be calculated using formula (5).
[0132] n load =(l c / l0)((v s +v w ) / v w ) (5)
[0133] The micro-grinding equivalent force heat transfer load in step S1 refers to a number of microscopic force loads and a single macroscopic heat load that move along the grinding direction and at the workpiece speed. In particular, the microscopic force load refers to the grinding force of a single abrasive grain, and the macroscopic heat load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece. A certain distance must be maintained between each microscopic force load to ensure that the stress area generated by the load in the workpiece does not overlap.
[0134] S2. Calculate the internal stress of the workpiece under the effect of thermal load equivalent to micro-grinding;
[0135] The stress components generated by the microscopic force load and the macroscopic heat load in the micro-grinding equivalent force heat load can be calculated separately, and then the two can be superimposed to finally obtain the internal stress of the workpiece under the action of the micro-grinding equivalent force heat load.
[0136] (1) Analysis of stress generated in the workpiece by microscopic force load under micro-grinding equivalent force and heat load
[0137] The Boussinesq solution of stress distribution under normal and tangential point loads is integrated over the contact area to obtain the stress distribution in the workpiece under microscopic force load. Therefore, under the action of micro-grinding equivalent force and heat transfer load, Figure 3 The stress components generated by the kth microscopic force load at point P can be calculated using formula (6).
[0138]
[0139] In formula (6): p g (k,s) and q g (k, s) are the kth normal micro-force load and tangential micro-force load distribution respectively.
[0140] (2) Analysis of stress generated by thermal load in the workpiece under the action of micro-grinding equivalent thermal transfer load
[0141] The stress caused by thermal load under the action of effective thermal transfer load in micro-grinding can be solved according to Duhamel similarity theorem. This theorem considers the thermal stress effects of body force, surface force and hydrostatic pressure at the same time, and calculates the total thermal stress by superposition of the three stresses.
[0142] ① Stress component generated by body force
[0143] exist Figure 3 Workpiece coordinate system X w O w Z w Under this condition, the grinding temperature T of point P in the workpiece is obtained by the grinding temperature calculation model based on the double adiabatic boundary assumption constructed by the present invention, then the body force component X caused by the temperature at this point T and Z TIt can be expressed by formula (7), and the thermal stress component generated by body force can be expressed by formula (8).
[0144]
[0145]
[0146] In the formula, G xh , G xh and G xh is the Green's function.
[0147] ②Stress component generated by surface force
[0148] The surface force generated by the grinding temperature is α w E w T / (1-2ν w ), therefore, the thermal stress component generated by the surface force at point P inside the workpiece can be expressed by formula (9):
[0149]
[0150] Where p(t) = α w E w T(x,z=0) / (1-2ν w ).
[0151] ③Influence of hydrostatic pressure
[0152] The hydrostatic pressure can be expressed as -α w E w T / (1-2ν w )
[0153] By superimposing the stresses generated by body force, surface force and hydrostatic pressure, the thermal stress components generated by the thermal load at the point P in the workpiece in the micro-grinding equivalent thermal transfer load can be obtained as follows:
[0154]
[0155] (3) Workpiece stress analysis under micro-grinding equivalent thermal transfer load
[0156] The stress generated by the kth microscopic force load and thermal load in the micro-grinding equivalent force and thermal transfer load can be expressed as:
[0157]
[0158] In formula (11), xx R (k-1,x,z) and σ yy R(k-1, x, z) are the residual stresses in the x direction (grinding direction) and y direction (vertical to the grinding direction) at point P in the workpiece after the k-1 microscopic force loads in the micro-grinding equivalent force heat transfer loads are unloaded. Since the workpiece is subjected to stress relief heat treatment before grinding, the residual stress before the first load can be considered to be 0.
[0159] In step S2, the internal stress of the workpiece under the action of the micro-grinding equivalent force and heat load is obtained by superimposing the internal stress generated by a plurality of microscopic force loads and the internal stress generated by a single macroscopic heat load.
[0160] S3. Calculate the residual stress in the workpiece under the effect of thermal load equivalent to micro-grinding;
[0161] Under the action of thermal transfer load equivalent to micro-grinding, the residual stress distribution in the workpiece can be obtained by using the theory of increment and unloading in elastic-plastic contact mechanics.
[0162] (1) Elastic-plastic loading analysis
[0163] Under the action of thermal transfer load equivalent to micro-grinding, Figure 3 In the equation, the kth micro-force load and thermal load first elastically load point P in the workpiece, and the elastic stress component generated is calculated by equation (6). After a period of time, when the kth micro-force load reaches point B, the material at point P in the workpiece begins to produce plastic deformation. The basis for determining whether the elastic loading is transformed into plastic loading is the von Mises yield criterion, and its yield function is expressed as:
[0164]
[0165] Where K w is the shear yield strength, S ij and α ij are the deviatoric stress tensor and the passive stress tensor respectively, and we have:
[0166]
[0167] Where n ij is the unit vector in the normal direction of the plastic strain rate.
[0168] For the elastic-plastic loading process, a mixed function is used to calculate the stress-strain increment generated by load loading. The expression of the mixed function is as follows:
[0169]
[0170] In formula (14), κ is the mixing function constant, h w is the plastic modulus of the material, G w is the elastic shear modulus of the material. Applying the mixed function, the strain increment dε in the grinding directionxx It can be shown as:
[0171]
[0172] Similarly, the strain increment dε perpendicular to the grinding direction under plane strain conditions is yy is 0 and can be expressed as:
[0173]
[0174] By combining equations (15) and (16), we can obtain the stress increment dσ corresponding to the grinding direction and perpendicular to the grinding direction: xx and dσ yy Before the loading is completed, the above-mentioned elastic-plastic incremental loading will continue in unison. Equation (17) gives the method for distinguishing loading and unloading:
[0175]
[0176] (2) Stress release analysis
[0177] After the kth microscopic force load in the micro-grinding equivalent thermal transfer load is loaded, in order to meet the boundary conditions of plane strain, the stress and strain components in equation (18) need to be gradually released until σ zz , τ xz and ε xx When the release is 0, the stress release ends, and the residual stress after the kth loading is obtained.
[0178]
[0179] It is worth mentioning that under the action of micro-grinding equivalent thermal transfer load, if k = n pass When all elastic stress and strain components of the load are released, if k < n pass When , the release of the above stress does not involve the elastic stress and strain components generated by the thermal load, but only releases the stress generated by the kth load and the residual stress generated by the previous k-1 loads. pass , formula (19) can be further expressed as:
[0180]
[0181] Assuming that the above release process is implemented in N steps, the release increment per step for the stress and strain components with a value of 0 in equation (18) is:
[0182]
[0183] For the non-zero stress component σ in equation (18), xx(k) and σ yy (k) Different release increments are used according to the elastic-plastic state of the workpiece material. When only elastic deformation occurs at a point in the workpiece, that is, F < 0 or F = 0 and n ij (k)dS ij When <0 condition, σ xx (k) and σ yy The elastic release increment of (k) is expressed as:
[0184]
[0185] For the case where the workpiece undergoes elastic-plastic deformation, it is necessary to satisfy F = 0 and n ij (k)dS ij ≥0, σ xx (k) and σ yy The elastic release increment of (k) is expressed as:
[0186]
[0187] Where C and D are expressed as:
[0188]
[0189] The residual stress in the workpiece under the action of the effective thermal load equivalent to micro-grinding calculated in step S3 is obtained based on the theory of increment and unloading in elastic-plastic contact mechanics.
[0190] The positive effects of the present invention are further described below in conjunction with specific experimental data.
[0191] The combinations of grinding wheel speed, workpiece speed and grinding depth for two sets of micro-grinding are v s =9.42m / s, v w =19.6mm / s, a p =2μm and v s =12.56m / s, v w =13.1mm / s, a p =3μm, the workpiece material is 3J33, for example. The calculation results of the micro-grinding residual stress calculation method and the experimental results are compared as shown in Table 1. It can be found that the residual stress distribution of the two has good consistency, and the reliable calculation of micro-grinding residual stress is achieved.
[0192] Table 1 Results comparison
[0193]
[0194] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When the use is implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL) or wireless (e.g., infrared, wireless, microwave, etc.) mode) to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state hard disk Solid State Disk (SSD)), etc.
[0195] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.
Claims
1. A method for calculating residual stress in micro grinding, characterized in that: The micro-grinding residual stress calculation method comprises the following steps: Step 1, determine the equivalent thermal transfer load of micro grinding; Step 2: Calculate the internal stress of the workpiece under the action of micro-grinding equivalent thermal load; Step 3, calculate the residual stress in the workpiece under the action of micro-grinding equivalent thermal load; In step 1, the micro-grinding equivalent force heat transfer load refers to a number of microscopic force loads and a single macroscopic heat load that move along the grinding direction and at the workpiece speed; the microscopic force load refers to the grinding force of a single abrasive particle, and the macroscopic heat load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece; a certain distance is maintained between each microscopic force load so that the stress area generated by the load in the workpiece does not overlap; In step 3, the calculation of the residual stress in the workpiece under the micro-grinding equivalent thermal load includes: Under the action of thermal transfer load equivalent to micro-grinding, the residual stress distribution in the workpiece is obtained by using the theory of increment and unloading in elastic-plastic contact mechanics. (1) Elastic-plastic loading analysis Under the action of the micro-grinding equivalent force and heat transfer load, the kth micro-force load and heat load first elastically load the point P in the workpiece, and calculate the elastic stress component generated; after a period of time, when the kth micro-force load reaches point B, the material at point P in the workpiece begins to produce plastic deformation. The basis for determining the transition from elastic loading to plastic loading is the von Mises yield criterion, and the yield function is expressed as: In the formula, K w is the shear yield strength, S ij and α ij are the deviatoric stress tensor and the passive stress tensor respectively, and we have: Where n ij is the unit vector in the normal direction of the plastic strain rate; For the elastic-plastic loading process, a mixed function is used to calculate the stress-strain increment generated by load loading. The expression of the mixed function is as follows: Where κ is the mixing function constant, h w is the plastic modulus of the material, G w is the elastic shear modulus of the material; the strain increment dε in the grinding direction is applied with the mixed function xx It is expressed as: Strain increment dε perpendicular to the grinding direction under plane strain conditions yy is 0 and is represented by: By combining the equations, we can get the stress increment dσ corresponding to the grinding direction and perpendicular to the grinding direction: xx and dσ yy ; Before the loading is completed, the elastic-plastic incremental loading will continue, and the judgment method of loading and unloading is given as shown in the following formula: (2) Stress release analysis After the kth microscopic force load in the micro-grinding equivalent thermal transfer load is loaded, in order to meet the boundary conditions of plane strain, the stress and strain components in the following formula are gradually released until σ zz , τ xz and ε xx When the release is 0, the stress release ends, and the residual stress after the kth loading is obtained: Under the action of micro-grinding equivalent thermal transfer load, if k = n pass When all elastic stress and strain components of the load are released, if k < n pass When the stress is released, the elastic stress-strain component generated by the thermal load is not involved. It only releases the stress generated by the kth load and the residual stress generated by the previous k-1 loads. pass , expressed as: Assuming that the release process is implemented in N steps, the release increment per step for stress and strain components with a value of 0 is: For non-zero stress components σ xx (k) and σ yy (k) Different release increments are used according to the elastic-plastic state of the workpiece material; when only elastic deformation occurs at a point in the workpiece, that is, F < 0 or F = 0 and n ij (k)dS ij When σ<0, xx (k) and σ yy The elastic release increment of (k) is expressed as: For the case where the workpiece undergoes elastic-plastic deformation, it is necessary to satisfy F = 0 and n ij (k)dS ij ≥0, σ xx (k) and σ yy The elastic release increment of (k) is expressed as: In the formula, C and D are expressed as:
2. The micro-grinding residual stress calculation method according to claim 1, characterized in that: In step 1, determining the micro-grinding equivalent thermal transfer load includes: (1) Determine the distribution of microscopic force loads The normal and tangential distributions of the microscopic load are p g (s) and q g (s), and there is: In the formula, l g is the contact length of a single abrasive particle, which is a function of the abrasive particle radius, the length of the wear plane and the thickness of the undeformed chip. Normal load density and tangential load density p of a single abrasive particle g0 and q g0 It is found by the following formula: (2) Determine the macroscopic heat load distribution Where, q0 = F t v s / l c w; (3) Determine the number of microscopic force loads The number of microscopic force loads is calculated by the following formula: n load =(l c / l0)((in s +in w ) / in w )。 3. The method for calculating residual stress in micro-grinding according to claim 1, characterized in that: In step 2, the calculation of the stress in the workpiece under the micro-grinding equivalent thermal load includes: After calculating the stress components generated by the microscopic force load and the macroscopic heat load in the micro-grinding equivalent force heat load respectively, the two are superimposed to finally obtain the internal stress of the workpiece under the micro-grinding equivalent force heat load; (1) Analysis of stress generated in the workpiece by microscopic force load under micro-grinding equivalent force and heat load The Boussinesq solution of stress distribution under normal and tangential point loads is integrated over the contact area to obtain the stress distribution in the workpiece under the micro-force load. Therefore, under the action of the micro-grinding equivalent thermal transfer load, the stress components generated by the kth micro-force load at point P are calculated by the following formula: In the formula, p g (k,s) and q g (k, s) are the kth normal micro-force load and tangential micro-force load distribution, respectively; (2) Analysis of stress generated by thermal load in the workpiece under the action of micro-grinding equivalent thermal transfer load The stress caused by thermal load under the action of micro-grinding equivalent thermal transfer load is solved according to Duhamel similarity theorem; at the same time, the total thermal stress is calculated by combining the thermal stress superposition of body force, surface force and hydrostatic pressure; (3) Workpiece stress analysis under micro-grinding equivalent thermal transfer load The stress generated by the kth microscopic force load and thermal load in the micro-grinding equivalent force and thermal transfer load is expressed as: In the formula, σ xx R (k-1,x,z) and σ yy R (k-1, x, z) are the residual stresses in the grinding direction x and in the vertical grinding direction y at point P in the workpiece after unloading k-1 microscopic force loads in the micro-grinding equivalent thermal transfer load; since the workpiece is subjected to stress relief heat treatment before grinding, the residual stress before the first load is considered to be 0.
4. The method for calculating residual stress in micro-grinding according to claim 3, characterized in that: In step (2), the stress analysis of the thermal load generated in the workpiece under the micro-grinding equivalent thermal transfer load includes: ① Stress component generated by body force In the workpiece coordinate system X w O w Z w Under this condition, the grinding temperature T of point P in the workpiece is obtained by constructing a grinding temperature calculation model based on the double adiabatic boundary assumption. Then the body force component X caused by the temperature at this point is T and Z T It is expressed by the following formula: The thermal stress component due to body force is expressed as follows: In the formula, G xh , G zh and G xzh is the Green’s function; ②Stress component generated by surface force The surface force generated by the grinding temperature is α w E w T / (1-2ν w ), the thermal stress component generated by the surface force at point P in the workpiece is expressed by the following formula: where p(t) = α w E w T(x, z = 0) / (1 - 2ν w ) ③Influence of hydrostatic pressure Hydrostatic pressure is expressed as -α w E w T / (1-2ν w ); By superimposing the stresses generated by body force, surface force and hydrostatic pressure, the thermal stress components generated by the thermal load at the point P inside the workpiece in the micro-grinding equivalent thermal transfer load are obtained as follows:
5. A micro-grinding residual stress calculation system using the micro-grinding residual stress calculation method according to any one of claims 1 to 4, characterized in that: The micro-grinding residual stress calculation system comprises: Mechanical and thermal transfer load determination module, used to determine the equivalent mechanical and thermal transfer load of micro-grinding; Stress calculation module, used to calculate the stress in the workpiece under the effect of effective thermal load equivalent to micro-grinding; The residual stress calculation module is used to calculate the residual stress in the workpiece under the action of effective thermal load equivalent to micro-grinding.
6. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the micro-grinding residual stress calculation method according to any one of claims 1 to 4, including the following steps: Determine the micro-grinding equivalent thermal transfer load; wherein the micro-grinding equivalent thermal transfer load refers to a number of microscopic force loads and a single macroscopic thermal load that move along the grinding direction and at the workpiece speed, the microscopic force load refers to the grinding force of a single abrasive grain, the macroscopic thermal load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece, and a certain distance is maintained between each microscopic force load; The stress in the workpiece under the equivalent effective thermal load of micro-grinding is calculated by superimposing the internal stress generated by several microscopic force loads and the internal stress generated by a single macroscopic thermal load. Under the equivalent effective thermal movement load of micro-grinding, the theory of increment and unloading in elastic-plastic contact mechanics is used to calculate the residual stress in the workpiece under the equivalent effective thermal load of micro-grinding.
7. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the micro-grinding residual stress calculation method according to any one of claims 1 to 4, comprising the following steps: Determine the equivalent thermal transfer load of micro-grinding; where, The micro-grinding equivalent force heat transfer load refers to a number of microscopic force loads and a single macroscopic heat load that move along the grinding direction and at the workpiece speed. The microscopic force load refers to the grinding force of a single abrasive grain, and the macroscopic heat load refers to the grinding heat generated by the contact between the grinding wheel and the workpiece. A certain distance is maintained between each microscopic force load; By superimposing the internal stress generated by several microscopic force loads and the internal stress generated by a single macroscopic thermal load, the stress inside the workpiece under the action of micro-grinding equivalent force thermal load is calculated. Under the action of effective thermal transfer load equivalent to micro-grinding, the residual stress in the workpiece under the action of effective thermal load equivalent to micro-grinding is calculated by using the theory of increment and unloading in elastic-plastic contact mechanics.
8. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the micro-grinding residual stress calculation system as claimed in claim 5.