Method for predicting forming grinding force of involute helical gear

Abstract

The invention discloses an involute helical gear forming grinding force prediction method, which comprises the following steps: firstly, based on a helical gear forming grinding space motion relationship, establishing a helical tooth surface model comprising an involute surface and a tooth root transition curved surface, and constructing a geometric contact model of a grinding wheel and a gear; then, tooth surface deformation data obtained after heat treatment are obtained through a three-coordinate measuring machine, coordinate mapping is carried out, and the grinding depth and contact parameters are corrected; on the basis, a grinding force integral model considering the heat treatment influence is established by combining a plane grinding mechanism, and integral calculation is carried out on tangential and normal grinding force of a tooth surface involute section, a transition arc section and a tooth bottom section; finally, actual measurement data are obtained through a grinding experiment, and model parameter calibration is completed. According to the method, dynamic and accurate prediction of tangential and normal grinding force in the bevel gear forming and grinding process can be achieved, and a reliable basis is provided for mechanical behavior analysis and process optimization in the gear machining process.

Description

Technical Field

[0001] This invention belongs to the field of gear grinding, specifically relating to a method for predicting the grinding force of involute helical gears. Background Technology

[0002] Grinding force is a key parameter in the gear forming grinding process, directly affecting the surface quality of the machined gear teeth, the distribution of the heat-affected layer, and the service performance of the gear. Currently, modeling research on involute gear grinding forces mainly focuses on spur gears and surface grinding scenarios, employing simplified geometric contact relationships and idealized material removal models. These studies typically neglect the complex spatial meshing characteristics of helical gears and cannot accurately describe the grinding force distribution during their forming grinding process.

[0003] For the forming grinding process of involute helical gears, the grinding contact line is a spatial curve. As the grinding point moves on the tooth surface, it constantly changes, resulting in non-uniform variations in the curvature, grinding depth, equivalent diameter, and grinding wheel linear velocity at the contact point. This leads to a dynamic distribution of grinding force on the tooth profile. Furthermore, after heat treatment, the helical gear tooth surface undergoes varying degrees of morphological distortion and residual stress field changes due to microstructural transformation and thermal stress release. This makes the initial grinding contact state less than ideal, further causing changes in the local depth of cut and contact stiffness in the grinding contact area.

[0004] However, existing technologies generally neglect the influence of uneven deformation of the tooth surface after heat treatment on the forming grinding force, specifically presenting the following technical problems: They ignore the modeling requirements for non-ideal deformation of the tooth surface after heat treatment; existing models are mostly based on ideal tooth surfaces and cannot reflect the influence of tooth profile errors after heat treatment on grinding contact depth and mechanical response; they lack grinding force modeling methods that consider the dynamic coupling relationship between heat treatment deformation and grinding wheel contact position, making it impossible to explain abrupt changes or local fluctuations in grinding force in different areas of the tooth profile; and they cannot reveal how micro-geometric deviations caused by heat treatment are amplified through the grinding process and affect the grinding force distribution, making effective compensation difficult in high-precision grinding applications.

[0005] Therefore, a grinding force prediction method is needed that can integrate information on uneven deformation of the tooth surface after heat treatment, spatial contact geometry of helical gears, and metal grinding mechanism to achieve accurate modeling and dynamic prediction of the actual grinding force during the forming grinding process of helical gears, thereby improving the processing quality control and modeling practicality. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems existing in the related art.

[0007] The purpose of this invention is to provide a method for predicting the grinding force of involute helical gears that can integrate information on uneven deformation of the tooth surface after heat treatment, establish a spatial grinding contact model and a mechanical response model driven by thermal history factors, and realize the dynamic and accurate prediction of tangential and normal grinding forces during the grinding process.

[0008] To achieve the above objectives, the present invention provides a method for predicting the forming grinding force of involute helical gears, comprising the following steps:

[0009] S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface;

[0010] S2. Calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel.

[0011] S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field.

[0012] S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field;

[0013] S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of helical gear forming grinding force that incorporates the influence of heat treatment.

[0014] S6. Conduct grinding experiments and calibrate the parameters of the integral model of the helical gear forming grinding force. Use the integral model of the helical gear forming grinding force after parameter calibration to predict the forming grinding force of involute helical gears.

[0015] A further preferred technical solution of the present invention is that, in step S1, a helical tooth surface model including an involute surface and a tooth root transition surface is established based on the spatial motion relationship of helical gear forming grinding; specifically, it includes:

[0016] S11. For a right-hand involute helical gear, the involute helical surface model of the right tooth surface is represented as:

[0017] ;

[0018] in, , and These are the involute helical surfaces of the right-hand tooth surface. coordinate, coordinates and coordinate; The radius of the base circle, For the base circle tooth groove half angle, The roll angle, The rotation angle of the spiral motion, These are the parameters for helical motion;

[0019] S12. For the tooth root transition surface, the right tooth surface transition circular arc spiral surface model is represented as:

[0020] ;

[0021] in, , and These are the right-hand tooth surface transition arc spiral surfaces. coordinate, coordinates and coordinate; and The centers of the transition arcs are respectively coordinates and coordinate; The radius of the tooth root circle, The radius of the transition arc. For the transition arc angle;

[0022] S13. For the tooth root transition surface, the right tooth surface root helical surface model is represented as:

[0023] ;

[0024] in, , and These are the right tooth surface and tooth root helical surfaces, respectively. coordinate, coordinates and coordinate.

[0025] Preferably, step S2 involves calculating the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the grinding wheel profile parameters; specifically including:

[0026] S21. Calculate the grinding depth of the normal tooth profile along the involute segment of the tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] in, Nominal grinding depth The grinding wheel speed is... The helix angle, The initial radius of the grinding wheel;

[0031] S22. Calculate the grinding depth along the transition arc segment of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] S23. Calculate the grinding depth along the tooth root of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0036] ;

[0037] ;

[0038] .

[0039] Preferably, step S3 involves acquiring the tooth surface deformation data after heat treatment and performing coordinate mapping to form a tooth surface deformation correction data field; specifically:

[0040] The tooth profile of the involute helical gear is measured using a coordinate measuring machine, and the deformation of the tooth surface after heat treatment relative to the theoretical tooth profile is extracted. This deformation is then mapped to the coordinates of each helical tooth surface in the helical tooth surface model established in step S1 to form a tooth surface deformation correction data field.

[0041] Preferably, step S4 involves correcting the geometric contact parameters based on the tooth surface deformation correction data field; specifically:

[0042] S41. Based on the tooth surface deformation correction data field from step S3, calculate the corrected radial grinding depth for each contact point, expressed as:

[0043]

[0044] in, This is the corrected radial grinding depth. Nominal grinding depth This is the amount of deformation;

[0045] Based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel, calculate the geometric contact parameters between the grinding wheel and the helical gear during form grinding;

[0046] S42, Adjust the radial grinding depth Substitute the values ​​from step S2 to correct the geometric contact parameters between the grinding wheel and the helical gear during the shape grinding process.

[0047] Preferably, step S5 involves constructing an integral model of the helical gear forming grinding force, incorporating the effects of heat treatment, based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of the helical gear forming grinding process; specifically including:

[0048] S51. The tooth surface region is divided into involute segments, circular arc transition segments, and tooth root segments. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, the entire tooth surface is integrated on the basis of the grinding force distribution per unit width, as shown below:

[0049] ;

[0050] ;

[0051] in, and These are the tangential grinding forces along the involute of the tooth profile, the transition arc, and the root portion, respectively. and These are the normal grinding forces along the involute, transition arc, and root of the tooth profile, respectively. The rolling angle at the tooth tip. Indicates the maximum arc angle. For feed rate, The tooth root round groove half the width, This is the straight line length of the tooth root portion. and These are experimental constants;

[0052] S52. Summing the tangential and normal grinding forces obtained in step S51 along the involute, transition arc, and root of the tooth profile, the final helical gear forming grinding force is calculated as follows:

[0053]

[0054] in, and These are the tangential grinding force and the normal grinding force of the helical gear, respectively.

[0055] Preferably, step S6 involves conducting a grinding experiment and calibrating the parameters of the helical gear forming grinding force integral model; specifically:

[0056] Under different typical grinding parameter combinations, the measured values ​​of tangential and normal grinding forces were obtained using a three-component force gauge. The measured values ​​were then fitted to the integral model of the helical gear forming grinding force using a nonlinear regression method, and the experimental constants of the integral model were calculated in reverse. Complete the model calibration or correction.

[0057] In another aspect, the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, the computer instructions causing a computer to execute the above-described method for predicting the grinding force of involute helical gears.

[0058] In another aspect, the present invention provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the above-mentioned method for predicting the grinding force of involute helical gears.

[0059] In another aspect, the present invention provides a computer program product comprising a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer performs the above-described method for predicting the grinding force of involute helical gears.

[0060] Beneficial Effects: This invention first establishes a helical tooth surface model, including the involute surface and the tooth root transition surface, based on the spatial motion relationship of helical gear forming grinding, and constructs a geometric contact model between the grinding wheel and the gear. It then acquires tooth surface deformation data after heat treatment using a coordinate measuring machine and performs coordinate mapping, correcting the grinding depth and contact parameters. Furthermore, it performs integral calculations of the tangential and normal grinding forces on the involute segment, transition arc segment, and tooth root segment of the tooth surface. This invention incorporates information on the tooth surface distortion after heat treatment into the grinding force modeling, which can more realistically reflect the actual machining state and improve the accuracy and applicability of the prediction model.

[0061] The involute helical gear forming grinding force prediction method of the present invention, compared with the prior art, can combine actual working conditions and propose a helical gear forming grinding force prediction method based on thermal deformation correction and tooth surface spatial contact modeling, which has higher physical accuracy and model adaptability. Attached Figure Description

[0062] Figure 1 This is a flowchart of the involute helical gear forming grinding force prediction method of the present invention.

[0063] Figure 2 This is a graph showing the relationship between the grinding wheel linear velocity and the grinding force in Example 1.

[0064] Figure 3 This is a graph showing the relationship between grinding depth and grinding force in Example 1.

[0065] Figure 4 This is a graph showing the relationship between feed rate and grinding force in Example 1. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0067] The following combination Figure 1-Figure 4 This invention describes the method for predicting the grinding force of involute helical gears during forming.

[0068] Example 1: This example provides a method for predicting the grinding force of involute helical gears during forming, such as... Figure 1 As shown, it includes the following steps:

[0069] S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface. Specifically, this includes:

[0070] S11. For a right-hand involute helical gear, the involute helical surface model of the right tooth surface is represented as:

[0071] ;

[0072] in, , and These are the involute helical surfaces of the right-hand tooth surface. coordinate, coordinates and coordinate; The radius of the base circle, For the base circle tooth groove half angle, The roll angle, The rotation angle of the spiral motion, These are the parameters for helical motion;

[0073] S12. For the tooth root transition surface, the right tooth surface transition circular arc spiral surface model is represented as:

[0074] ;

[0075] in, , and These are the right-hand tooth surface transition arc spiral surfaces. coordinate, coordinates and coordinate; and The centers of the transition arcs are respectively coordinates and coordinate; The radius of the tooth root circle, The radius of the transition arc. For the transition arc angle;

[0076] S13. For the tooth root transition surface, the right tooth surface root helical surface model is represented as:

[0077] ;

[0078] in, , and These are the right tooth surface and tooth root helical surfaces, respectively. coordinate, coordinates and coordinate.

[0079] S2. Based on the normal tooth profile parameters of the helical gear and the grinding wheel profile parameters, calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding. Specifically, this includes:

[0080] S21. Calculate the grinding depth of the normal tooth profile along the involute segment of the tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] in, Nominal grinding depth The grinding wheel speed is... The helix angle, The initial radius of the grinding wheel;

[0085] S22. Calculate the grinding depth along the transition arc segment of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0086] ;

[0087] ;

[0088] ;

[0089] S23. Calculate the grinding depth along the tooth root of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows:

[0090] ;

[0091] ;

[0092] .

[0093] S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field. Specifically:

[0094] The tooth profile of the involute helical gear is measured using a coordinate measuring machine (CMM), and the deformation of the tooth surface after heat treatment relative to the theoretical tooth profile is extracted. This deformation is then mapped to the coordinates of each helical tooth surface in the helical tooth surface model established in step S1 to form a tooth surface deformation correction data field.

[0095] S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field. Specifically:

[0096] S41. Based on the tooth surface deformation correction data field from step S3, calculate the corrected radial grinding depth for each contact point, expressed as:

[0097]

[0098] in, This is the corrected radial grinding depth. Nominal grinding depth This is the amount of deformation;

[0099] Based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel, calculate the geometric contact parameters between the grinding wheel and the helical gear during form grinding;

[0100] S42, Adjust the radial grinding depth Substitute the values ​​from step S2 to correct the geometric contact parameters between the grinding wheel and the helical gear during the shape grinding process.

[0101] S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of the helical gear forming grinding force incorporating the effects of heat treatment. Specifically, this includes:

[0102] S51. The tooth surface region is divided into involute segments, circular arc transition segments, and tooth root segments. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, the entire tooth surface is integrated on the basis of the grinding force distribution per unit width, as shown below:

[0103] ;

[0104] ;

[0105] in, and These are the tangential grinding forces along the involute of the tooth profile, the transition arc, and the root portion, respectively. and These are the normal grinding forces along the involute, transition arc, and root of the tooth profile, respectively. The rolling angle at the tooth tip. Indicates the maximum arc angle. For feed rate, The tooth root round groove half the width, This is the straight line length of the tooth root portion. and These are experimental constants;

[0106] S52. Summing the tangential and normal grinding forces obtained in step S51 along the involute, transition arc, and root of the tooth profile, the final helical gear forming grinding force is calculated as follows:

[0107]

[0108] in, and These are the tangential grinding force and the normal grinding force of the helical gear, respectively.

[0109] S6. Under different typical grinding parameter combinations (grinding wheel linear speed, feed rate, grinding depth), the measured values ​​of tangential and normal grinding forces are obtained using a three-component force gauge. The measured values ​​are then fitted to the integral model of helical gear forming grinding force using a nonlinear regression method, and the experimental constants of the integral model of helical gear forming grinding force are calculated in reverse. Complete the model calibration or correction.

[0110] Then, the involute helical gear forming grinding force is predicted using the integral model of the helical gear forming grinding force after the parameters are calibrated.

[0111] To verify the accuracy of the calculation results of the involute helical gear forming grinding force prediction method in this embodiment, the method was applied to predict the grinding force during forming grinding of a certain type of helical gear. The basic parameters of this gear are: normal module of 10mm, number of teeth of 18, normal pressure angle of 20°, helix angle of 16°, and material of 17CrNiMo6 alloy steel. The grinding wheel used is a ceramic microcrystalline grinding wheel with the following basic parameters: outer diameter of 350 and abrasive grit size of 70#. Before grinding, the gear tooth surface profile was measured using a coordinate measuring machine (CMM) to extract the residual deformation of the tooth surface after heat treatment relative to the theoretical tooth profile. Then, the gear was ground using a Gleason-PFAUTE P600 / 800G CNC forming gear grinding machine. During the grinding process, the grinding force of the helical gear was measured using a KISTLER-9129AA multi-component force gauge. The forming grinding parameters and grinding force measurement results are shown in Table 1.

[0112] Table 1. Grinding parameters and grinding force measurement results for helical gear forming grinding

[0113]

[0114] To verify the accuracy of the helical gear forming grinding force calculation model proposed in this invention, and to further analyze the influence of key process parameters on grinding force, a single-factor experimental method was used for comparative verification. Specifically, while keeping other parameters constant, the grinding wheel linear speed, grinding depth, and feed rate were adjusted respectively to obtain the calculated and measured values ​​of grinding force under different combinations of processing parameters. Figure 2 , Figure 3 and Figure 4 The graphs show the relationship curves between grinding wheel linear velocity, grinding depth, feed rate, and grinding force. As can be seen from the graphs, the calculated values ​​of the grinding force calculation model under various parameter variations agree well with the experimentally measured values, and both exhibit a consistent trend. These results demonstrate that the grinding force model proposed in this invention possesses good accuracy and applicability, and can effectively reflect the variation of grinding force with process parameters during actual machining.

[0115] Example 2: This example provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a method for predicting the grinding force of involute helical gears. The method includes the following steps:

[0116] S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface;

[0117] S2. Calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel.

[0118] S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field.

[0119] S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field;

[0120] S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of helical gear forming grinding force that incorporates the influence of heat treatment.

[0121] S6. Conduct grinding experiments and calibrate the parameters of the integral model of the helical gear forming grinding force. Use the integral model of the helical gear forming grinding force after parameter calibration to predict the forming grinding force of involute helical gears.

[0122] Example 3: This example provides an electronic device that may include a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute a method for predicting the grinding force of involute helical gears. This method includes the following steps:

[0123] S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface;

[0124] S2. Calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel.

[0125] S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field.

[0126] S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field;

[0127] S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of helical gear forming grinding force that incorporates the influence of heat treatment.

[0128] S6. Conduct grinding experiments and calibrate the parameters of the integral model of the helical gear forming grinding force. Use the integral model of the helical gear forming grinding force after parameter calibration to predict the forming grinding force of involute helical gears.

[0129] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0130] Example 4: This example provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a method for predicting the grinding force of involute helical gears. This method includes the following steps:

[0131] S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface;

[0132] S2. Calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel.

[0133] S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field.

[0134] S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field;

[0135] S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of helical gear forming grinding force that incorporates the influence of heat treatment.

[0136] S6. Conduct grinding experiments and calibrate the parameters of the integral model of the helical gear forming grinding force. Use the integral model of the helical gear forming grinding force after parameter calibration to predict the forming grinding force of involute helical gears.

[0137] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0138] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for predicting the grinding force during the forming of involute helical gears, characterized in that, The steps include: S1. Based on the spatial motion relationship of helical gear forming grinding, establish a helical tooth surface model including the involute surface and the tooth root transition surface; S2. Calculate the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel. S3. Obtain the tooth surface deformation data after heat treatment and perform coordinate mapping to form a tooth surface deformation correction data field. S4. Correct the geometric contact parameters based on the tooth surface deformation correction data field; S5. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, construct an integral model of helical gear forming grinding force that incorporates the influence of heat treatment. S6. Conduct grinding experiments and calibrate the parameters of the integral model of the helical gear forming grinding force. Use the integral model of the helical gear forming grinding force after parameter calibration to predict the forming grinding force of involute helical gears.

2. The method for predicting the grinding force of involute helical gears according to claim 1, characterized in that, Step S1 describes establishing a helical tooth surface model, including the involute surface and the tooth root transition surface, based on the spatial motion relationship of helical gear forming grinding; specifically, it includes: S11. For a right-hand involute helical gear, the involute helical surface model of the right tooth surface is represented as: ； in, , and These are the involute helical surfaces of the right-hand tooth surface. coordinate, coordinates and coordinate; The radius of the base circle, For the base circle tooth groove half angle, The roll angle, The rotation angle of the spiral motion, These are the parameters for helical motion; S12. For the tooth root transition surface, the right tooth surface transition circular arc spiral surface model is represented as: ； in, , and These are the right-hand tooth surface transition arc spiral surfaces. coordinate, coordinates and coordinate; and The centers of the transition arcs are respectively coordinates and coordinate; The radius of the tooth root circle, The radius of the transition arc. For the transition arc angle; S13. For the tooth root transition surface, the right tooth surface root helical surface model is represented as: ； in, , and These are the right tooth surface and tooth root helical surfaces, respectively. coordinate, coordinates and coordinate.

3. The method for predicting the grinding force of involute helical gears according to claim 2, characterized in that, Step S2 involves calculating the geometric contact parameters between the grinding wheel and the helical gear during profile grinding based on the normal tooth profile parameters of the helical gear and the grinding wheel profile parameters; specifically, this includes: S21. Calculate the grinding depth of the normal tooth profile along the involute segment of the tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows: ； ； ； in, Nominal grinding depth The grinding wheel speed is... The helix angle, The initial radius of the grinding wheel; S22. Calculate the grinding depth along the transition arc segment of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows: ； ； ； S23. Calculate the grinding depth along the tooth root of the normal tooth profile. Equivalent contact radius and grinding wheel linear velocity The calculation formulas are as follows: ； ； 。 4. The method for predicting the grinding force of involute helical gears according to claim 1, characterized in that, Step S3 involves acquiring the tooth surface deformation data after heat treatment and performing coordinate mapping to form a tooth surface deformation correction data field; specifically: The tooth profile of the involute helical gear is measured using a coordinate measuring machine, and the deformation of the tooth surface after heat treatment relative to the theoretical tooth profile is extracted. This deformation is then mapped to the coordinates of each helical tooth surface in the helical tooth surface model established in step S1 to form a tooth surface deformation correction data field.

5. The method for predicting the grinding force of involute helical gears according to claim 1, characterized in that, Step S4 involves correcting the geometric contact parameters based on the tooth surface deformation correction data field; specifically: S41. Based on the tooth surface deformation correction data field from step S3, calculate the corrected radial grinding depth for each contact point, expressed as: ； in, This is the corrected radial grinding depth. Nominal grinding depth This is the amount of deformation; Based on the normal tooth profile parameters of the helical gear and the profile parameters of the grinding wheel, calculate the geometric contact parameters between the grinding wheel and the helical gear during form grinding; S42, Adjust the radial grinding depth Substitute the values ​​from step S2 to correct the geometric contact parameters between the grinding wheel and the helical gear during the shape grinding process.

6. The method for predicting the grinding force of involute helical gears according to claim 3, characterized in that, Step S5 describes constructing an integral model of the helical gear forming grinding force, incorporating the effects of heat treatment, based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding; specifically, it includes: S51. The tooth surface region is divided into involute segments, circular arc transition segments, and tooth root segments. Based on the spatial motion relationship, geometric contact parameters, and surface grinding mechanism of helical gear forming grinding, the entire tooth surface is integrated on the basis of the grinding force distribution per unit width, as shown below: ； ； in, and These are the tangential grinding forces along the involute of the tooth profile, the transition arc, and the root portion, respectively. and These are the normal grinding forces along the involute, transition arc, and root of the tooth profile, respectively. The rolling angle at the tooth tip. Indicates the maximum arc angle. For feed rate, The tooth root round groove half the width, This is the straight line length of the tooth root portion. and These are experimental constants; S52. Summing the tangential and normal grinding forces obtained in step S51 along the involute, transition arc, and root of the tooth profile, the final helical gear forming grinding force is calculated as follows: ； in, and These are the tangential grinding force and the normal grinding force of the helical gear, respectively.

7. The method for predicting the grinding force of involute helical gears according to claim 6, characterized in that, Step S6 involves conducting grinding experiments and calibrating the parameters of the helical gear forming grinding force integral model; specifically: Under different typical grinding parameter combinations, the measured values ​​of tangential and normal grinding forces were obtained using a three-component force gauge. The measured values ​​were then fitted to the integral model of the helical gear forming grinding force using a nonlinear regression method, and the experimental constants of the integral model were calculated in reverse. Complete the model calibration or correction.

8. A non-transitory computer-readable storage medium, characterized in that, It stores computer instructions that cause the computer to execute the involute helical gear forming grinding force prediction method according to any one of claims 1-7.

9. An electronic device, characterized in that, include: The system includes a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor calls logical instructions from the memory to execute the involute helical gear forming grinding force prediction method according to any one of claims 1-7.

10. A computer program product, characterized in that, The computer program product includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer performs the involute helical gear forming grinding force prediction method according to any one of claims 1-7.

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