A method for predicting surface roughness of involute helical gears during form grinding

Abstract

The present invention discloses a method for predicting the surface roughness of involute helical gears during form grinding. First, a spatial motion model for gear form grinding is established, and a geometric contact model between abrasive particles and gears is established. The motion trajectory of the abrasive particles is then calculated. An effective abrasive screening criterion is constructed to screen out abrasive particles that have a significant impact on the tooth surface roughness. The local maximum response matrix of the normal undeformed chip thickness is extracted from the discrete point matrix of the tooth surface. The roughness of any discrete point on the tooth surface is calculated, and a grinding area roughness prediction model is established. The grinding area roughness is jointly controlled by the peak intensity in the response matrix and the unit normal vector at any position on the tooth surface. The present invention uses the local response matrix of the maximum undeformed chip thickness as the core modeling basis, and can accurately reflect the influence of machine tool motion parameters and grinding process parameters on gear surface roughness. This provides a theoretical basis for optimizing the precision grinding process of gears and can improve the transmission efficiency and service life of gears.

Description

Technical Field

[0001] The invention belongs to the field of gear grinding, and in particular relates to a method for predicting the surface roughness of an involute helical gear during form grinding. Background Art

[0002] As core components of mechanical transmission systems, involute helical gears are widely used in high-precision applications such as automotive, aerospace, and wind power equipment. Surface roughness, a crucial component of surface integrity, directly impacts key performance indicators such as gear contact fatigue life, transmission efficiency, and vibration and noise. Form grinding, as a finishing process for gears, is an effective means of improving tooth surface quality and enhancing transmission accuracy.

[0003] However, the formation mechanism of gear surface roughness during form grinding is complex and influenced by the coupling of multiple process parameters, such as grinding wheel linear speed, grinding depth, feed rate, grinding wheel dressing status, and workpiece material properties. Traditional surface roughness control methods rely primarily on empirical trials or simplified theoretical models. These methods suffer from strong empirical dependence, lack of versatility, and a failure to consider the geometric characteristics of the continuously changing curvature of the involute helicoid surface. This leads to significant deviations between theoretical predictions and actual measurements. Summary of the Invention

[0004] The present invention aims to solve one of the technical problems existing in the related art at least to a certain extent.

[0005] The purpose of the present invention is to provide a method for predicting the surface roughness of involute helical gears during form grinding, so as to solve the problems of low calculation accuracy and poor applicability of existing empirical and analytical methods, and to provide a new theoretical basis for reducing stress concentration on the gear surface and improving gear fatigue life.

[0006] In order to achieve the above-mentioned object, the present invention provides a method for predicting the surface roughness of an involute helical gear during form grinding, comprising the following steps:

[0007] S1. According to the relative motion relationship between the grinding wheel and the gear during grinding, a gear profile grinding spatial motion model is established;

[0008] S2. According to the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established;

[0009] S3, calculating the motion trajectory of the abrasive particles by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear;

[0010] S4. Constructing effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and forming an abrasive particle set;

[0011] S5, extracting the local maximum response matrix of the normal undeformed chip thickness in the discrete point matrix of the tooth surface;

[0012] S6. Calculate the surface roughness values ​​of discrete points along the involute direction and the tooth width direction of the gear tooth surface, integrate the surface roughness values ​​of discrete points in the discrete area, and construct a roughness distribution data set of the tooth surface grinding area as the roughness prediction result of the entire tooth surface grinding area.

[0013] A further preferred technical solution of the present invention is that, in step S1, a gear profile grinding spatial motion model is established based on the relative motion relationship between the grinding wheel and the gear during grinding; specifically comprising:

[0014] S11. Establishing a gear coordinate system, a grinding wheel coordinate system, and a fixed spatial coordinate system based on the spindle motion, tangential feed motion, and radial feed motion during gear profile grinding;

[0015] S12. Calculate the transformation relationship from the gear coordinate system to the fixed space coordinate system, expressed as:

[0016] ;

[0017] in, is the transformation relationship from the gear coordinate system to the fixed space coordinate system, is the rotation matrix around the gear axis, is the rotation angle, is the position vector of the instantaneous meshing point relative to the gear coordinate system, is the spiral motion parameter, is the unit vector of the gear axis;

[0018] S13. Calculate the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, expressed as:

[0019] ;

[0020] in, is the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, is the rotation matrix around the gear radial direction, is the radial displacement of the grinding wheel, is the unit vector along the radial direction of the grinding wheel, is the initial center distance between the grinding wheel and the gear, expressed as:

[0021] ;

[0022] in, is the grinding wheel radius, is the helix angle, is the maximum protrusion height of the abrasive particles, is the gear base circle radius, is the radial grinding depth of the grinding contact point.

[0023] Preferably, step S2 establishes a geometric contact model between the abrasive and the gear according to the gear forming and grinding relationship; specifically includes:

[0024] S21. According to the gear forming grinding relationship, calculate the normal grinding depth of any point of grinding contact, expressed as:

[0025] ;

[0026] in, is the gear involute roll angle, is the abrasive particle radius, is the distance from the abrasive grain to the base circle;

[0027] S22. Establish a geometric contact model between the abrasive particles and the gear, expressed as:

[0028] ;

[0029] in, are the center coordinates of the abrasive particles, are the gear coordinates, is the height of the abrasive protrusion, is the normal grinding depth of the grinding contact point, is the unit normal vector of any point on the tooth profile.

[0030] Preferably, in step S3, the abrasive particle motion trajectory is calculated by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particle and the gear; specifically, the step S3 includes:

[0031] S31. Establish a surface coordinate system with any position on the tooth surface as the origin, and calculate the transformation relationship from the surface coordinate system to the gear coordinate system, which can be expressed as:

[0032] ;

[0033] in, Represents the transformation relationship from the surface coordinate system to the gear coordinate system, is the rotation matrix from the surface coordinate system to the gear coordinate system, Represents the coordinate vector of any point on the tooth surface in the surface coordinate system;

[0034] S32. Based on the geometric contact model between the abrasive grains and the gear, calculate the conversion relationship between the surface coordinate system and the grinding wheel coordinate system, which can be expressed as:

[0035] ;

[0036] in, Indicates the transformation relationship from the surface coordinate system to the grinding wheel coordinate system, Represents the rotation matrix from the gear coordinate system to the grinding wheel coordinate system;

[0037] S33. Calculate the motion trajectory of the abrasive particles in the surface coordinate system through coordinate transformation. Its three-dimensional coordinates are expressed as:

[0038] ;

[0039] in, represents the motion trajectory coordinates of the abrasive particles in the surface coordinate system, represents the coordinates of the abrasive grains in the grinding wheel coordinate system, Use the following formula to calculate:

[0040] ;

[0041] in, represents the radius of rotation of the abrasive particle, Indicates the grinding wheel angle, Indicates the gear feed speed, Indicates the feeding time, Indicates the ordinate of any point on the gear end face, It represents the angle between the abrasive rotating plane and the gear axis.

[0042] Preferably, step S4 constructs an effective abrasive particle screening criterion to screen out abrasive particles that have a significant impact on tooth surface roughness to form an abrasive particle set; specifically, the step S4 includes:

[0043] S41. Calculate the normal undeformed chip thickness of a single abrasive particle entering any point on the gear tooth surface. , expressed as:

[0044] ;

[0045] in, represents the normal undeformed chip thickness, Represents the coordinates of the motion trajectory of the abrasive particles in the surface coordinate system;

[0046] S42. In the surface coordinate system, count the normal undeformed chip thickness of each abrasive grain and the point. , define the threshold , forming a preliminary screening rule: If , the abrasive particles are judged to be effective abrasive particles.

[0047] Preferably, the threshold It is the minimum effective cutting depth value determined based on process experience or simulation tests.

[0048] Preferably, the step S5 of extracting the local maximum response matrix of the normal undeformed chip thickness from the tooth surface discrete point matrix specifically includes:

[0049] S51, discretize the tooth surface along the tooth width direction and the involute direction into Grid points, calculate the coordinate values ​​of discrete points in the gear coordinate system through the rolling angles at different positions on the tooth surface and the angles of the gear's spiral motion;

[0050] S52. Update the final undeformed chip thickness of the tooth surface grid point according to the effective abrasive with the largest undeformed chip thickness at the set position on the tooth surface, and form a local maximum response matrix of the normal undeformed chip thickness.

[0051] Preferably, in step S6, the surface roughness value of any discrete point on the tooth surface is expressed as , the calculation formula is:

[0052] ;

[0053] Where, is the coordinate of any discrete point in the workpiece coordinate system, represents the local maximum of the response matrix, is the unit normal vector at any discrete point on the gear tooth surface, which is related to the gear roll angle and spiral motion angle.

[0054] Another aspect of the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, wherein the computer instructions enable a computer to execute the above-mentioned method for predicting the surface roughness of the involute helical gear during form grinding.

[0055] Another aspect of 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 the logic instructions in the memory to execute the above-mentioned involute helical gear forming grinding surface roughness prediction method.

[0056] Another aspect of the present invention provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer executes the above-mentioned method for predicting the surface roughness of the involute helical gear forming grinding.

[0057] Beneficial effects: The surface roughness prediction method of involute helical gear forming grinding of the present invention establishes a spatial motion model of gear-grinding wheel and a geometric contact model of abrasive-gear for the helical gear forming grinding process; according to the local contact conditions and geometric mapping relationship of gear forming grinding, a spatial spiral cutting motion model of abrasive relative to the workpiece is established, and the motion trajectory of the abrasive in the surface coordinate system is calculated; the normal undeformed chip thickness of a single abrasive is calculated, and by constructing an effective abrasive screening criterion, the abrasive particle set that has a significant impact on the tooth surface roughness is determined; the local maximum response matrix of the normal undeformed chip thickness is extracted in the discrete point matrix of the tooth surface, and a surface roughness prediction model for helical gear forming grinding is established.

[0058] In summary, the roughness prediction method for helical gear forming grinding based on effective abrasive trajectory analysis and local chip thickness response modeling of the present invention accurately reflects the cutting path and action mechanism of abrasive particles in actual processing. Compared with the traditional method based only on empirical formulas or simplified models, the present invention takes the local response matrix of the maximum undeformed chip thickness as the core modeling basis, establishes a joint mapping relationship between tooth surface roughness and spiral motion angle and roll angle, and significantly improves the accuracy of roughness prediction; this method fully considers complex factors such as helix angle and axial feed, and is suitable for the processing process of complex tooth shapes such as helical gears, which makes up for the limitation that traditional models are only applicable to simple tooth shapes; in addition, the present invention can provide theoretical support for grinding process parameter optimization and surface quality control, and has strong engineering practicality and promotion value. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Flowchart of the surface roughness prediction method for form grinding of involute helical gears.

[0060] Figure 2 This is the spatial motion coordinate system diagram for gear forming grinding.

[0061] Figure 3 is a schematic diagram of the discretized tooth surface.

[0062] Figure 4 This is a comparison chart of the tooth surface roughness measurement and calculation results in Example 1. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the embodiments described are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0064] The following combination Figures 1-4 The present invention describes the surface roughness prediction method of involute helical gear form grinding.

[0065] Example 1: This example provides a method for predicting the surface roughness of an involute helical gear during forming grinding. Figure 1 As shown, the following steps are included:

[0066] S1. Based on the relative motion relationship between the grinding wheel and the gear during grinding, a gear profile grinding spatial motion model is established. The specific method is:

[0067] S11. Establish the gear coordinate system according to the spindle motion, tangential feed motion and radial feed motion during gear profile grinding. , Grinding wheel coordinate system and space-fixed coordinate system ;

[0068] S12. Calculate the transformation relationship from the gear coordinate system to the fixed space coordinate system, expressed as:

[0069] ;

[0070] in, is the transformation relationship from the gear coordinate system to the fixed space coordinate system, is the rotation matrix around the gear axis, is the rotation angle, is the position vector of the instantaneous meshing point relative to the gear coordinate system, is the spiral motion parameter, is the unit vector of the gear axis;

[0071] S13. Calculate the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, expressed as:

[0072] ;

[0073] in, is the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, is the rotation matrix around the gear radial direction, is the radial displacement of the grinding wheel, is the unit vector along the radial direction of the grinding wheel, is the initial center distance between the grinding wheel and the gear, expressed as:

[0074] ;

[0075] in, is the grinding wheel radius, is the helix angle, is the maximum protrusion height of the abrasive particles, is the gear base circle radius, is the radial grinding depth of the grinding contact point. The spatial motion coordinate system of helical gear profile grinding is shown in Figure 2.

[0076] S2. According to the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established. The specific method is:

[0077] S21. According to the gear forming grinding relationship, calculate the normal grinding depth of any point of grinding contact, expressed as:

[0078] ;

[0079] in, is the gear involute roll angle, is the abrasive particle radius, is the distance from the abrasive grain to the base circle;

[0080] S22. Establish a geometric contact model between the abrasive particles and the gear, expressed as:

[0081] ;

[0082] in, are the center coordinates of the abrasive particles, are the gear coordinates, is the height of the abrasive protrusion, is the normal grinding depth of the grinding contact point, is the unit normal vector of any point on the tooth profile.

[0083] S3. Calculate the motion trajectory of the abrasive particles by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear. The specific method is:

[0084] S31. Establish a surface coordinate system with any position on the tooth surface as the origin, and calculate the transformation relationship from the surface coordinate system to the gear coordinate system, which can be expressed as:

[0085] ;

[0086] in, Represents the transformation relationship from the surface coordinate system to the gear coordinate system, is the rotation matrix from the surface coordinate system to the gear coordinate system, Represents the coordinate vector of any point on the tooth surface in the surface coordinate system;

[0087] S32. Based on the geometric contact model between the abrasive grains and the gear, calculate the conversion relationship between the surface coordinate system and the grinding wheel coordinate system, which can be expressed as:

[0088] ;

[0089] in, Indicates the transformation relationship from the surface coordinate system to the grinding wheel coordinate system, Represents the rotation matrix from the gear coordinate system to the grinding wheel coordinate system;

[0090] S33. Calculate the motion trajectory of the abrasive particles in the surface coordinate system through coordinate transformation. Its three-dimensional coordinates are expressed as:

[0091] ;

[0092] in, represents the motion trajectory coordinates of the abrasive particles in the surface coordinate system, represents the coordinates of the abrasive grains in the grinding wheel coordinate system, Use the following formula to calculate:

[0093] ;

[0094] in, represents the radius of rotation of the abrasive particle, Indicates the grinding wheel angle, Indicates the gear feed speed, Indicates the feeding time, Indicates the ordinate of any point on the gear end face, It represents the angle between the abrasive rotating plane and the gear axis.

[0095] S4. Construct effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and form an abrasive particle set. The specific method is:

[0096] S41. Calculate the normal undeformed chip thickness of a single abrasive particle entering any point on the gear tooth surface. , expressed as:

[0097] ;

[0098] in, represents the normal undeformed chip thickness, Represents the coordinates of the motion trajectory of the abrasive particles in the surface coordinate system;

[0099] S42. In the surface coordinate system, count the normal undeformed chip thickness of each abrasive grain and the point. , define the threshold , forming a preliminary screening rule: If , the abrasive particles are judged as effective abrasive particles; the threshold It is the minimum effective cutting depth value determined based on process experience or simulation tests.

[0100] S5. Extract the local maximum response matrix of the normal undeformed chip thickness from the discrete point matrix of the tooth surface. Specifically:

[0101] S51, discretize the tooth surface along the tooth width direction and the involute direction into Grid points, such as Figure 3 As shown, the coordinate values ​​of discrete points in the gear coordinate system are calculated by the rolling angles at different positions on the tooth surface and the angles of the gear's spiral motion;

[0102] S52. Update the final undeformed chip thickness of the tooth surface grid point according to the effective abrasive with the largest undeformed chip thickness at the set position on the tooth surface, and form a local maximum response matrix of the normal undeformed chip thickness.

[0103] S6. Calculate the surface roughness values ​​of discrete points along the involute direction and the tooth width direction of the gear tooth surface, integrate the surface roughness values ​​of discrete points in the discrete area, and construct a roughness distribution data set of the tooth surface grinding area as the roughness prediction result of the entire tooth surface grinding area.

[0104] Since the tooth surface roughness is the set of the maximum value of the undeformed chip thickness at discrete points on the tooth surface, the surface roughness value of any discrete point on the tooth surface is , the calculation formula is:

[0105] ;

[0106] Where, is the coordinate of any discrete point in the workpiece coordinate system, represents the local maximum of the response matrix, is the unit normal vector at any discrete point on the gear tooth surface, which is related to the gear roll angle and spiral motion angle.

[0107] To verify the accuracy of the calculation results of the surface roughness prediction method for involute helical gears during form grinding in this embodiment, the above method was applied to predict the tooth surface roughness of a certain type of helical gear during form grinding. 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 20CrMnMo alloy steel. The grinding wheel used is a chrome corundum grinding wheel with basic parameters: outer diameter of 350 and grit size of 50-120. Before grinding, the form grinding wheel is first trimmed with a diamond roller, and then the workpiece is ground using a Gleason-PFAUTE P600 / 800G CNC form grinding machine. The form grinding processing parameters are shown in Table 1.

[0108] Table 1 Processing parameters of helical gear profile grinding

[0109]

[0110] After grinding, single-tooth specimens were prepared: a single tooth was cut along the helix angle. The tooth surface was then subjected to 3D topography measurement using a SENSOFAR S NEOX 3D optical profilometer. Measurements were taken at multiple locations along the involute profile and tooth width of the gear's normal cross-section. The optical profilometer has a measurement area of ​​1.0 x 0.7 mm, a sampling interval of 0.64 μm, and a measurement accuracy of 0.1 μm.

[0111] The tooth surface roughness results obtained under different processing parameters shown in Table 1 are as follows Figure 4 As shown in the figure, by comparing the measurement and calculation results, it can be seen that the maximum relative error between the experimental and simulation results is 7.99%, indicating that the model has a good prediction ability for the tooth surface roughness of helical gear form grinding, and verifies the accuracy of the calculation method.

[0112] Embodiment 2: This embodiment provides a non-transitory computer-readable storage medium having computer instructions stored thereon. The computer instructions enable a computer to execute a method for predicting surface roughness of an involute helical gear during form grinding. The method comprises the following steps:

[0113] S1. According to the relative motion relationship between the grinding wheel and the gear during grinding, a gear profile grinding spatial motion model is established;

[0114] S2. According to the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established;

[0115] S3, calculating the motion trajectory of the abrasive particles by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear;

[0116] S4. Constructing effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and forming an abrasive particle set;

[0117] S5, extracting the local maximum response matrix of the normal undeformed chip thickness in the discrete point matrix of the tooth surface;

[0118] S6. Calculate the roughness of any discrete point on the tooth surface and establish the roughness of the grinding area Prediction model, the grinding area roughness It is controlled jointly by the peak intensity in the response matrix and the unit normal vector at any position on the tooth surface.

[0119] Embodiment 3: This embodiment provides an electronic device, which may include: a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory communicate with each other via the communications bus. The processor may call logic instructions in the memory to execute a method for predicting the surface roughness of an involute helical gear during form grinding, the method comprising the following steps:

[0120] S1. According to the relative motion relationship between the grinding wheel and the gear during grinding, a gear profile grinding spatial motion model is established;

[0121] S2. According to the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established;

[0122] S3, calculating the motion trajectory of the abrasive particles by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear;

[0123] S4. Constructing effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and forming an abrasive particle set;

[0124] S5, extracting the local maximum response matrix of the normal undeformed chip thickness in the discrete point matrix of the tooth surface;

[0125] S6. Calculate the roughness of any discrete point on the tooth surface and establish the roughness of the grinding area Prediction model, the grinding area roughness It is controlled jointly by the peak intensity in the response matrix and the unit normal vector at any position on the tooth surface.

[0126] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion 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 for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media capable of storing program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks.

[0127] Embodiment 4: This embodiment provides a computer program product, which includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can perform a method for predicting the surface roughness of an involute helical gear during form grinding. The method includes the following steps:

[0128] S1. According to the relative motion relationship between the grinding wheel and the gear during grinding, a gear profile grinding spatial motion model is established;

[0129] S2. According to the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established;

[0130] S3, calculating the motion trajectory of the abrasive particles by combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear;

[0131] S4. Constructing effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and forming an abrasive particle set;

[0132] S5, extracting the local maximum response matrix of the normal undeformed chip thickness in the discrete point matrix of the tooth surface;

[0133] S6. Calculate the roughness of any discrete point on the tooth surface and establish the roughness of the grinding area Prediction model, the grinding area roughness It is controlled jointly by the peak intensity in the response matrix and the unit normal vector at any position on the tooth surface.

[0134] 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.

[0135] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion 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, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0136] 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 surface roughness of involute helical gear form grinding, characterized in that: The steps include: S1. Establish a gear profile grinding spatial motion model based on the relative motion relationship between the grinding wheel and the gear during grinding; specifically including: S11. Establishing a gear coordinate system, a grinding wheel coordinate system, and a fixed spatial coordinate system based on the spindle motion, tangential feed motion, and radial feed motion during gear profile grinding; S12. Calculate the transformation relationship from the gear coordinate system to the fixed space coordinate system, expressed as: ； in, is the transformation relationship from the gear coordinate system to the fixed space coordinate system, is the rotation matrix around the gear axis, is the rotation angle, is the position vector of the instantaneous meshing point relative to the gear coordinate system, is the spiral motion parameter, is the unit vector of the gear axis; S13. Calculate the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, expressed as: ； in, is the transformation relationship from the fixed space coordinate system to the grinding wheel coordinate system, is the rotation matrix around the gear radial direction, is the radial displacement of the grinding wheel, is the unit vector along the radial direction of the grinding wheel, is the initial center distance between the grinding wheel and the gear, expressed as: ； in, is the grinding wheel radius, is the helix angle, is the maximum protrusion height of the abrasive particles, is the gear base circle radius, is the radial grinding depth of the grinding contact point; S2. Based on the gear forming and grinding relationship, a geometric contact model between the abrasive and the gear is established; specifically including: S21. According to the gear forming grinding relationship, calculate the normal grinding depth of any point of grinding contact, expressed as: ； in, is the gear involute roll angle, is the abrasive particle radius, is the distance from the abrasive to the base circle; S22. Establish a geometric contact model between the abrasive particles and the gear, expressed as: ； in, are the center coordinates of the abrasive particles, are the gear coordinates, is the height of the abrasive protrusion, is the normal grinding depth of the grinding contact point, is the unit normal vector of any point on the tooth profile; S3, combining the gear shaping grinding spatial motion model and the geometric contact model between the abrasive particles and the gear, calculating the motion trajectory of the abrasive particles; specifically comprising: S31. Establish a surface coordinate system with any position on the tooth surface as the origin, and calculate the transformation relationship from the surface coordinate system to the gear coordinate system, which can be expressed as: ； in, Represents the transformation relationship from the surface coordinate system to the gear coordinate system, is the rotation matrix from the surface coordinate system to the gear coordinate system, Represents the coordinate vector of any point on the tooth surface in the surface coordinate system; S32. Based on the geometric contact model between the abrasive grains and the gear, calculate the conversion relationship between the surface coordinate system and the grinding wheel coordinate system, which can be expressed as: ； in, Indicates the transformation relationship from the surface coordinate system to the grinding wheel coordinate system, Represents the rotation matrix from the gear coordinate system to the grinding wheel coordinate system; S33. Calculate the motion trajectory of the abrasive particles in the surface coordinate system through coordinate transformation. Its three-dimensional coordinates are expressed as: ； in, represents the motion trajectory coordinates of the abrasive particles in the surface coordinate system, represents the coordinates of the abrasive grains in the grinding wheel coordinate system, Use the following formula to calculate: ； in, represents the radius of rotation of the abrasive particle, Indicates the grinding wheel angle, Indicates the gear feed speed, Indicates the feeding time, Indicates the ordinate of any point on the gear end face, It represents the angle between the abrasive particle rotation plane and the gear axis; S4. Constructing effective abrasive particle screening criteria to screen out abrasive particles that have a significant impact on tooth surface roughness and forming an abrasive particle set; S5, extracting the local maximum response matrix of the normal undeformed chip thickness in the discrete point matrix of the tooth surface; S6. Calculate the surface roughness values ​​of the gear tooth surface along the involute direction and the tooth width direction respectively. The surface roughness value of any discrete point on the tooth surface is expressed as , the calculation formula is: ； Where, is the coordinate of any discrete point in the workpiece coordinate system, represents the local maximum of the response matrix, is the unit normal vector at any discrete point on the gear tooth surface, which is related to the gear roll angle and spiral motion angle; The surface roughness values ​​of discrete points in the discrete area are integrated to construct a roughness distribution data set of the tooth surface grinding area as the roughness prediction result of the entire tooth surface grinding area.

2. The method for predicting surface roughness of involute helical gear form grinding according to claim 1, characterized in that: In step S4, effective abrasive particle screening criteria are constructed to screen out abrasive particles that have a significant impact on tooth surface roughness to form an abrasive particle set; Specifically include: S41. Calculate the normal undeformed chip thickness of a single abrasive particle entering any point on the gear tooth surface. , expressed as: ； in, represents the normal undeformed chip thickness, Represents the coordinates of the motion trajectory of the abrasive particles in the surface coordinate system; S42. In the surface coordinate system, count the normal undeformed chip thickness of each abrasive grain and the point. , define the threshold , forming a preliminary screening rule: If , the abrasive particles are judged to be effective abrasive particles.

3. The method for predicting surface roughness of involute helical gear profile grinding according to claim 2, characterized in that: The threshold It is the minimum effective cutting depth value determined based on process experience or simulation tests.

4. The method for predicting surface roughness of involute helical gear form grinding according to claim 1, characterized in that: Step S5 extracts the local maximum response matrix of the normal undeformed chip thickness from the tooth surface discrete point matrix; specifically includes: S51, discretize the tooth surface along the tooth width direction and the involute direction into Grid points, calculate the coordinate values ​​of discrete points in the gear coordinate system through the rolling angles at different positions on the tooth surface and the angles of the gear's spiral motion; S52. Update the final undeformed chip thickness of the tooth surface grid point according to the effective abrasive with the largest undeformed chip thickness at the set position on the tooth surface, and form a local maximum response matrix of the normal undeformed chip thickness.

5. A non-transitory computer-readable storage medium, characterized in that Computer instructions are stored thereon, and the computer instructions enable the computer to execute the method for predicting the surface roughness of the involute helical gear formed grinding according to any one of claims 1 to 4.

6. An electronic device, characterized in that: include: A processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus, and the processor calls the logic instructions in the memory to execute the surface roughness prediction method for the forming grinding of involute helical gears according to any one of claims 1 to 4.

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