Method for calculating spindle thermal error control domain of spiral bevel gear grinding machine tool

Abstract

The application discloses a main shaft thermal error control domain calculation method of a spiral bevel gear grinding machine tool, and the main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool comprises the following steps: calculating a first conversion matrix of a workpiece coordinate system and a tool coordinate system; calculating first tooth surface point coordinates and corresponding first tooth surface point normal vectors based on a blank shaft section and the first conversion matrix; calculating second tooth surface point coordinates based on a first main shaft thermal error boundary, the blank shaft section and the first conversion matrix; calculating a tooth surface deviation value based on the first tooth surface point coordinates, the first tooth surface point normal vectors and the second tooth surface point coordinates; and when the tooth surface deviation value is greater than a preset tooth surface deviation value and half of a first step length is less than a preset minimum step length, taking an initial main shaft thermal error boundary as a main shaft thermal error control boundary, so that enough tooth surface precision can be ensured in the prediction under various working conditions.

Description

Technical Field

[0001] This application relates to the technical field of spindle thermal error control domain calculation for spiral bevel gear grinding machine tools, and in particular to a method for calculating the spindle thermal error control domain for spiral bevel gear grinding machine tools. Background Technology

[0002] Numerous factors influence CNC machine tool errors, including machine tool geometric errors, thermal, mechanical, installation, and machine tool vibration. These errors significantly affect the machining accuracy of spiral bevel gears, generally requiring reverse machining to improve tooth surface precision. Among these error factors, thermal errors account for a high proportion, and due to their time-varying characteristics, their impact on spiral bevel gear machining is constantly changing. Therefore, during batch processing, this can cause insufficient and unstable machining accuracy of spiral bevel gears, which is difficult to resolve through reverse machining. Generally, it is necessary to predict and compensate for machine tool thermal errors.

[0003] Currently, the modeling and compensation of thermal errors in CNC machine tools mainly focuses on continuously reducing prediction deviations through modeling algorithms and improving algorithm performance in order to pursue infinitesimal modeling and prediction errors. However, there is no clear target for the required accuracy of various thermal errors, making it difficult to guarantee that the tooth surface accuracy requirements can be met after error compensation. Summary of the Invention

[0004] This application aims to at least address the technical problems existing in the prior art. To this end, this application proposes a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine, which can provide a clear prediction accuracy target for thermal error modeling and ensure sufficient tooth surface accuracy in predictions under various working conditions.

[0005] The first aspect of this application provides a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool, comprising the following steps:

[0006] Obtain the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expand the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0007] Construct a workpiece coordinate system and a tool coordinate system, and calculate the first transformation matrix between the workpiece coordinate system and the tool coordinate system;

[0008] Calculate the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the cross section of the tooth blank and the first transformation matrix;

[0009] Based on the first spindle thermal error boundary, the gear blank axial section and the first transformation matrix, calculate the coordinates of the second tooth surface point;

[0010] The tooth surface deviation value is calculated based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point.

[0011] When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is taken as the spindle thermal error control boundary.

[0012] The control method according to the embodiments of this application has at least the following beneficial effects:

[0013] This method obtains the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expands the initial spindle thermal error boundary based on the first step length to obtain the first spindle thermal error boundary; constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix between the workpiece coordinate system and the tool coordinate system; calculates the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the gear blank shaft section and the first transformation matrix; calculates the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank shaft section, and the first transformation matrix; calculates the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by preset tooth surface deviation value, providing a clear prediction accuracy target for thermal error modeling, and ensuring sufficient tooth surface accuracy in predictions under various working conditions.

[0014] According to some embodiments of this application, the step of calculating the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the gear blank shaft section and the first transformation matrix includes:

[0015] Based on the first transformation matrix, the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector are calculated using the following formulas:

[0016] ;

[0017] in, Let the position vector of the origin of the tool coordinate system in the tool coordinate system be denoted as . Let Z be the unit vector basis of the tool coordinate system. Let be the unit normal vector of the surface of revolution at point p. for and The angle of formation Let be the rotation angle of a point on the cutting edge about the tool axis to a point on the rotating surface. Let point p and point The distance between them Where is the radius of the cutter head. The distance between the blade tips. For the profile pressure angle, The origin and point of the tool coordinate system The distance between them for and The intersection, + corresponds to the concave surface of the tool and - corresponds to the convex surface of the tool. Let be the position vector of a point on the rotating surface in the tool coordinate system. This is the first transformation matrix. The tool axis vector in the workpiece coordinate system. This is the position vector of the origin of the tool coordinate system in the workpiece coordinate system. For the corner of the rocking platform, The normal vector of the gear tooth surface. Let be the normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system. The position vector of the small gear tooth surface. It is the relative velocity;

[0018] The coordinates of the first tooth surface point are calculated based on the pinion tooth surface normal vector, the pinion tooth surface position vector, and the relative velocity using the following formula:

[0019] ;

[0020] in, Let Q be the X-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. Let Q be the Z-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. The distance between the outer cones. These are the discrete parameters of the projection surface along the tooth direction. These are the discrete parameters of the projection plane along the tooth height direction. It is the cone angle. For tooth width, For the tooth tip corresponding to parameter f, For the tooth root corresponding to parameter f, Let be the discrete quantity in the tooth direction. Let be the discrete quantity in the tooth height direction. For the first tooth direction discrete points, For the first tooth in the tooth height direction discrete points, For tooth tip height, For tooth root height, It is the cone angle. The root cone angle, Let X be the X coordinate of the first tooth surface point. The Y-coordinate of the first tooth surface point The Z-coordinate of the first tooth surface point;

[0021] Based on the normal vector of the pinion tooth surface, calculate the normal vector of the first tooth surface point corresponding to the coordinates of the first tooth surface point.

[0022] According to some embodiments of this application, calculating the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank axial section, and the first transformation matrix includes:

[0023] A spindle coordinate system is constructed with the intersection of the grinding wheel mounting surface and the spindle axis as the origin.

[0024] The thermal error boundary of the first spindle is downsampled to obtain the offset of the origin of the spindle coordinate system along the X-axis, the offset of the origin of the spindle coordinate system along the Y-axis, the offset of the origin of the spindle coordinate system along the Z-axis, the deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and the deflection angle of the Z-axis of the spindle coordinate system around the Y-axis.

[0025] Based on the offset of the origin of the principal axis coordinate system along the X-axis, the offset of the origin of the principal axis coordinate system along the Y-axis, the offset of the origin of the principal axis coordinate system along the Z-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the X-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the Y-axis, the gear blank axial section, and the first transformation matrix, the pinion tooth surface error position vector is calculated using the following formula:

[0026] ;

[0027] in, The main spindle thermal error matrix, The offset of the origin of the principal coordinate system along the X-axis. The offset of the origin of the main coordinate system along the Y-axis. The offset of the origin of the main axis coordinate system along the Z-axis. Let be the angle of deviation of the Z-axis of the principal coordinate system about the X-axis. Let be the angle of deviation of the Z-axis of the principal coordinate system about the Y-axis. This is the second transformation matrix. The error tool axis vector in the workpiece coordinate system. This is the error position vector of the tool coordinate system origin in the workpiece coordinate system. This is the normal vector of the gear tooth surface error. For the error relative velocity, For the error of the rocking table angle, The error rotation angle is the angle of rotation of a point on the cutting edge about the tool axis to a point on the rotating surface. The origin and point of the tool coordinate system The error distance between them Let the position vector be the error vector of the small gear tooth surface. For error distance, This is the error normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system;

[0028] The coordinates of the second tooth surface point are calculated based on the pinion tooth surface error vector using the following formula:

[0029] ;

[0030] in, The X coordinate of the second tooth surface point is... The Y-coordinate of the second tooth surface point. Here is the Z-coordinate of the second tooth surface point.

[0031] According to some embodiments of this application, the tooth surface deviation value includes an average tooth surface deviation value and a maximum tooth surface deviation value. The calculation of the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point includes:

[0032] Obtain the coordinates of the first center point of the first tooth surface composed of the coordinates of the first tooth surface points; obtain the coordinates of the second center point of the second tooth surface composed of the coordinates of the second tooth surface points.

[0033] The phase angle is calculated based on the Y and Z coordinates of the first center point and the Y and Z coordinates of the second center point. The phase angle is used to rotate the Y and Z coordinates of the first center point around the workpiece axis by the phase angle so that they coincide with the Y and Z coordinates of the second center point.

[0034] The coordinates of the second tooth surface point are obtained by rotating the phase angle around the workpiece axis by the second tooth surface point coordinates;

[0035] The normal deviation value is calculated based on the coordinates of the first tooth surface point and the coordinates of the third tooth surface point using the following formula:

[0036] ;

[0037] in, For the first The tooth direction direction Normal deviation value in the tooth height direction For the first The tooth direction direction The coordinates of the third tooth surface point in the tooth height direction. For the first The tooth direction direction Coordinates of the first tooth surface point in the tooth height direction. For the first The tooth direction direction The normal vector of the first tooth surface point in the tooth height direction;

[0038] The tooth surface deviation value is calculated based on the normal deviation value using the following formula:

[0039] ;

[0040] in, The average deviation value of the tooth surface is the tooth surface deviation value. The maximum deviation value of the tooth surface is the tooth surface deviation value.

[0041] According to some embodiments of this application, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0042] When the tooth surface deviation value is less than the preset tooth surface deviation value, the first spindle thermal error boundary is expanded based on the first step length to obtain the second spindle thermal error boundary;

[0043] When the second spindle thermal error boundary is greater than the preset maximum error boundary, the second spindle thermal error boundary is used as the spindle thermal error control boundary.

[0044] When the second spindle thermal error boundary is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the second spindle thermal error boundary. This process is repeated until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length. Then, the (K-1)th spindle thermal error boundary is taken as the spindle thermal error control boundary, where K is the iteration number.

[0045] According to some embodiments of this application, the method for calculating the spindle thermal error control domain of the spiral bevel gear grinding machine tool further includes:

[0046] If the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, then the first step length is halved to obtain the second step length.

[0047] Based on the first step length, the first spindle thermal error boundary is expanded to obtain the second step length spindle thermal error boundary;

[0048] When the second step size spindle thermal error boundary is greater than the preset maximum error boundary, the second step size spindle thermal error boundary is used as the spindle thermal error control boundary.

[0049] When the second step size spindle thermal error boundary is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the second step size spindle thermal error boundary. This process is repeated until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step size is less than the preset minimum step size. Then, the Q-1th spindle thermal error boundary is taken as the spindle thermal error control boundary, where Q is the iteration number.

[0050] According to some embodiments of this application, calculating the first transformation matrix between the workpiece coordinate system and the tool coordinate system includes:

[0051] Construct the machine tool coordinate system, the workpiece axis fixed coordinate system, the machine tool fixed coordinate system, the rocking table fixed coordinate system, and the tool rotation coordinate system;

[0052] The first transformation matrix is ​​calculated using the following formula based on the workpiece coordinate system, the tool coordinate system, the machine tool coordinate system, the workpiece axis fixed coordinate system, the machine tool fixed coordinate system, the rocker table fixed coordinate system, and the tool rotation coordinate system:

[0053] ;

[0054] ;

[0055] in, This is the first transformation matrix. Let be the transformation matrix from the workpiece axis-fixed coordinate system to the workpiece coordinate system. This is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system. This is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system. Let be the transformation matrix from the fixed coordinate system of the rocking table to the machine tool coordinate system. Let be the transformation matrix from the tool-rotating coordinate system to the fixed coordinate system of the rocking table. This is the transformation matrix from the tool coordinate system to the tool rotation coordinate system. For vertical wheel positions, For beds, For horizontal wheel positions, For angular tool position, For radial tool position, For installation angle, For the angle of the knife, For the knife to turn the corner, For the wheel blank rotation angle, For the corner of the rocking platform, For rolling ratio, is the helical coefficient.

[0056] A second aspect of this application provides a spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool, the spindle thermal error control domain calculation system comprising:

[0057] The data acquisition module is used to acquire the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expand the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0058] The first transformation matrix calculation module is used to construct the workpiece coordinate system and the tool coordinate system, and to calculate the first transformation matrix between the workpiece coordinate system and the tool coordinate system;

[0059] The first tooth surface point coordinate calculation module is used to calculate the coordinates of the first tooth surface point and the corresponding first tooth surface point normal vector based on the tooth blank axial section and the first transformation matrix.

[0060] The second tooth surface point coordinate calculation module is used to calculate the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the tooth blank axial section and the first transformation matrix;

[0061] The tooth surface deviation value calculation module is used to calculate the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point.

[0062] The spindle thermal error control boundary calculation module is used to take the initial spindle thermal error boundary as the spindle thermal error control boundary when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length.

[0063] This system obtains the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expands the initial spindle thermal error boundary based on the first step length to obtain the first spindle thermal error boundary; it constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix between the workpiece coordinate system and the tool coordinate system; it calculates the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the gear blank shaft section and the first transformation matrix; it calculates the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank shaft section, and the first transformation matrix; it calculates the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by preset tooth surface deviation value, providing a clear prediction accuracy target for thermal error modeling, and ensuring sufficient tooth surface accuracy in predictions under various working conditions.

[0064] A third aspect of this application provides an electronic device for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions that can be executed by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to execute the above-described method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine.

[0065] In a fourth aspect, this application provides a computer-readable storage medium storing computer-executable instructions for causing a computer to execute the aforementioned method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine.

[0066] It should be noted that the beneficial effects of the second to fourth aspects of this application with respect to the prior art are the same as the beneficial effects of the above-mentioned spindle thermal error control domain calculation system for a spiral bevel gear grinding machine tool with respect to the prior art, and will not be described in detail here.

[0067] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0068] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0069] Figure 1 This is a flowchart illustrating a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine according to an embodiment of this application;

[0070] Figure 2 This is a schematic diagram of the spindle thermal error structure of a spindle thermal error control domain calculation method for a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0071] Figure 3 This is a schematic diagram of the spindle thermal error coordinates of a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine according to an embodiment of this application;

[0072] Figure 4 This is a schematic diagram of the cutting edge of a tool in a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine according to an embodiment of this application;

[0073] Figure 5 This is a schematic diagram of the coordinate system for machining the small spiral bevel gear in accordance with the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0074] Figure 6 This is a schematic diagram of the spindle cross-section of a spiral bevel gear grinding machine tool according to an embodiment of this application, wherein (a) is a three-dimensional schematic diagram of the spindle cross-section of the gear blank, and (b) is a planar schematic diagram of the spindle cross-section of the gear blank.

[0075] Figure 7 This is a schematic diagram of the tooth surface error of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0076] Figure 8 This is a topology diagram of concave tooth surface error when δx equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0077] Figure 9This is a topology diagram of the convex tooth surface error when δx equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0078] Figure 10 This is a topology diagram of the concave tooth surface error when δy equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0079] Figure 11 This is a topology diagram of the convex tooth surface error when δy equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0080] Figure 12 This is a topology diagram of concave tooth surface error when δz equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0081] Figure 13 This is a topology diagram of the convex tooth surface error when δz equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0082] Figure 14 This is a topology diagram of the concave tooth surface error when εx is equal to 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0083] Figure 15 This is a topology diagram of the convex tooth surface error when εx is equal to 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0084] Figure 16 This is a topology diagram of concave tooth surface error when εy equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0085] Figure 17 This is a topology diagram of the convex tooth surface error when εy equals 1µm, based on the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0086] Figure 18 This is a schematic diagram showing the normal deviation change result of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0087] Figure 19 This is a schematic diagram showing the normal deviation change result of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0088] Figure 20This is a schematic diagram showing the normal deviation change result of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0089] Figure 21 This is a schematic diagram showing the change in normal deviation due to the influence of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application.

[0090] Figure 22 This is a schematic diagram showing the normal deviation change result of the spindle thermal error control domain calculation method of a spiral bevel gear grinding machine tool according to an embodiment of this application;

[0091] Figure 23 This is a schematic diagram of an embodiment of the spindle thermal error control domain calculation system for the spiral bevel gear grinding machine provided in this application;

[0092] Figure 24 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application. Detailed Implementation

[0093] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0094] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0095] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0096] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0097] To address the aforementioned technical deficiencies, this application provides a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine.

[0098] Please see Figure 1 This is a flowchart illustrating a method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool, provided in an embodiment of this application. This method is applied to electronic devices, such as servers. Figure 1 As shown, the calculation method for the spindle thermal error control domain of this spiral bevel gear grinding machine includes:

[0099] Step S101: Obtain the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expand the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0100] Step S102: Construct the workpiece coordinate system and the tool coordinate system, and calculate the first transformation matrix between the workpiece coordinate system and the tool coordinate system;

[0101] Step S103: Calculate the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the cross section of the tooth blank and the first transformation matrix;

[0102] Step S104: Calculate the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the tooth blank axial section, and the first transformation matrix;

[0103] Step S105: Calculate the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point;

[0104] Step S106: When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is taken as the spindle thermal error control boundary.

[0105] This method obtains the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expands the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary; constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix between the workpiece coordinate system and the tool coordinate system; calculates the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the gear blank shaft section and the first transformation matrix; calculates the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank shaft section, and the first transformation matrix; calculates the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by preset tooth surface deviation value, providing a clear prediction accuracy target for thermal error modeling, and ensuring sufficient tooth surface accuracy in predictions under various working conditions.

[0106] In some embodiments, refer to Figures 2 to 5In step S103, the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point are calculated based on the tooth blank shaft section and the first transformation matrix, including:

[0107] Step S201: Based on the first transformation matrix, calculate the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector using the following formula:

[0108] ;

[0109] in, Let the position vector of the origin of the tool coordinate system in the tool coordinate system be denoted as . Let Z be the unit vector basis of the tool coordinate system. Let be the unit normal vector of the surface of revolution at point p. for and The angle of formation Let be the rotation angle of a point on the cutting edge about the tool axis to a point on the rotating surface. Let point p and point The distance between them Where is the radius of the cutter head. The distance between the blade tips. For the profile pressure angle, The origin and point of the tool coordinate system The distance between them for and The intersection, + corresponds to the concave surface of the tool and - corresponds to the convex surface of the tool. Let be the position vector of a point on the rotating surface in the tool coordinate system. This is the first transformation matrix. The tool axis vector in the workpiece coordinate system. This is the position vector of the origin of the tool coordinate system in the workpiece coordinate system. For the corner of the rocking platform, The normal vector of the gear tooth surface. Let be the normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system. The position vector of the small gear tooth surface. It is the relative velocity;

[0110] Step S202: Calculate the coordinates of the first tooth surface point based on the pinion tooth surface normal vector, pinion tooth surface position vector, and relative velocity using the following formula:

[0111] ;

[0112] in, Let Q be the X-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. Let Q be the Z-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. The distance between the outer cones. These are the discrete parameters of the projection surface along the tooth direction. These are the discrete parameters of the projection plane along the tooth height direction. It is the cone angle. For tooth width, For the tooth tip corresponding to parameter f, For the tooth root corresponding to parameter f, Let be the discrete quantity in the tooth direction. Let be the discrete quantity in the tooth height direction. For the first tooth direction discrete points, For the first tooth in the tooth height direction discrete points, For tooth tip height, For tooth root height, It is the cone angle. The root cone angle, Let X be the X coordinate of the first tooth surface point. The Y-coordinate of the first tooth surface point The Z-coordinate of the first tooth surface point;

[0113] Step S203: Based on the normal vector of the pinion tooth surface, calculate the normal vector of the first tooth surface point corresponding to the coordinates of the first tooth surface point.

[0114] In some embodiments, refer to Figures 6 to 22 In step S104, based on the first spindle thermal error boundary, the gear blank axial section, and the first transformation matrix, the coordinates of the second tooth surface point are calculated, including:

[0115] Step S301: Construct a spindle coordinate system with the intersection of the grinding wheel mounting surface and the spindle axis as the origin;

[0116] Step S302: Downsample the thermal error boundary of the first spindle to obtain the offset of the origin of the spindle coordinate system along the X-axis, the offset of the origin of the spindle coordinate system along the Y-axis, the offset of the origin of the spindle coordinate system along the Z-axis, the deflection angle of the Z-axis of the spindle coordinate system around the X-axis, and the deflection angle of the Z-axis of the spindle coordinate system around the Y-axis.

[0117] Step S303: Based on the offset of the origin of the principal axis coordinate system along the X-axis, the offset of the origin of the principal axis coordinate system along the Y-axis, the offset of the origin of the principal axis coordinate system along the Z-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the X-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the Y-axis, the gear blank axial section, and the first transformation matrix, calculate the pinion tooth surface error position vector using the following formula:

[0118] ;

[0119] in, The main spindle thermal error matrix, The offset of the origin of the principal coordinate system along the X-axis. The offset of the origin of the main coordinate system along the Y-axis. The offset of the origin of the main axis coordinate system along the Z-axis. The angle of deviation of the Z-axis around the X-axis in the principal coordinate system. The angle of deviation of the Z-axis around the Y-axis in the principal coordinate system. This is the second transformation matrix. The error tool axis vector in the workpiece coordinate system. This is the error position vector of the tool coordinate system origin in the workpiece coordinate system. This is the normal vector of the gear tooth surface error. For the error relative velocity, For the error of the rocking table angle, The error rotation angle is the angle of rotation of a point on the cutting edge about the tool axis to a point on the rotating surface. The origin and point of the tool coordinate system The error distance between them Let the position vector be the error vector of the small gear tooth surface. For error distance, This is the error normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system;

[0120] Step S304: Calculate the coordinates of the second tooth surface point based on the pinion tooth surface error position vector using the following formula:

[0121] ;

[0122] in, The X coordinate of the second tooth surface point is... The Y-coordinate of the second tooth surface point. Here is the Z-coordinate of the second tooth surface point.

[0123] A spindle coordinate system is established with the intersection of the grinding wheel mounting surface and the spindle axis as the origin. Therefore, the spindle thermal error can be quantitatively expressed as the deviation between the ideal and actual positions of the spindle coordinate system after thermal deformation of the machine tool, containing error components of six degrees of freedom. Indexing errors around the Z-axis have no impact on machining and are not considered. Specifically, this refers to the offset of the spindle coordinate system origin along the X, Y, and Z axes. , , The deflection angles of the Z-axis of the principal coordinate system around the X-axis and Y-axis, respectively. , In the experiment, the five spindle thermal errors can be measured and decomposed by arranging five eddy current sensors using the "five-point method".

[0124] In some embodiments, the tooth surface deviation value in step S105 includes the average tooth surface deviation value and the maximum tooth surface deviation value. The tooth surface deviation value is calculated based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point, including:

[0125] Step S401: Obtain the coordinates of the first center point of the first tooth surface composed of the coordinates of the first tooth surface points; obtain the coordinates of the second center point of the second tooth surface composed of the coordinates of the second tooth surface points;

[0126] Step S402: Calculate the phase angle based on the Y and Z coordinates of the first center point and the Y and Z coordinates of the second center point. The phase angle is used to rotate the Y and Z coordinates of the first center point around the workpiece axis so that they coincide with the Y and Z coordinates of the second center point.

[0127] Step S403: Rotate the coordinates of the second tooth surface point around the workpiece axis by a phase angle to obtain the coordinates of the third tooth surface point;

[0128] Step S404: Calculate the normal deviation value based on the coordinates of the first tooth surface point and the third tooth surface point using the following formula:

[0129] ;

[0130] in, For the first The tooth direction direction Normal deviation value in the tooth height direction For the first The tooth direction direction The coordinates of the third tooth surface point in the tooth height direction. For the first The tooth direction direction Coordinates of the first tooth surface point in the tooth height direction. For the first The tooth direction direction The normal vector of the first tooth surface point in the tooth height direction;

[0131] Step S405: Calculate the tooth surface deviation value based on the normal deviation value using the following formula:

[0132] ;

[0133] in, The average deviation value of the tooth surface is the tooth surface deviation value. This represents the maximum deviation value of the tooth surface.

[0134] In some embodiments, the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool further includes:

[0135] Step S501: When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the first spindle thermal error boundary is expanded to obtain the second spindle thermal error boundary;

[0136] Step S502: When the thermal error boundary of the second spindle is greater than the preset maximum error boundary, the thermal error boundary of the second spindle is used as the thermal error control boundary of the spindle.

[0137] Step S503: When the thermal error boundary of the second spindle is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the thermal error boundary of the second spindle. This process is repeated until the deviation value of the Kth tooth surface is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length. Then, the thermal error boundary of the (K-1)th spindle is taken as the thermal error control boundary of the spindle, where K is the iteration number.

[0138] In some embodiments, the method for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool further includes:

[0139] Step S601: When the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain the second step length.

[0140] Step S602: Based on the second step size, expand the first spindle thermal error boundary to obtain the second step size spindle thermal error boundary;

[0141] Step S603: When the thermal error boundary of the second step spindle is greater than the preset maximum error boundary, the thermal error boundary of the second step spindle is taken as the thermal error control boundary of the spindle.

[0142] Step S604: When the spindle thermal error boundary of the second step length is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated according to the spindle thermal error boundary of the second step length. This process is repeated until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step length is less than the preset minimum step length. Then, the Q-1th spindle thermal error boundary is taken as the spindle thermal error control boundary, where Q is the iteration number.

[0143] Taking a pair of 23 / 43 tooth spiral bevel gears as an example, this study investigates the influence of single spindle thermal error on spiral bevel gear error. The basic parameters of the gear pair are shown in Tables 1 and 2 below. Table 1 shows the parameters of the gear pair blank, and Table 2 shows the parameters of the gear pair machining.

[0144] Table 1

[0145]

[0146] Table 2

[0147]

[0148] Specifically, using the maximum absolute deviation and average absolute deviation of the tooth surface as constraints, the normal deviation at each tooth surface point is calculated. The maximum absolute deviation and average absolute deviation of the tooth surface can then be expressed as:

[0149]

[0150] Among them, E1 and E2 are the corresponding control targets.

[0151] By optimizing the solution algorithm, we search for the maximum allowable boundaries of various spindle thermal errors that can meet the requirements of E1 and E2.

[0152]

[0153] in, , , , , These are the control boundaries for various thermal errors.

[0154] This application provides a prediction accuracy target for spindle thermal error modeling, ensuring that when the prediction accuracy meets the requirements, the machining accuracy of the tooth surface after thermal error compensation can meet the given accuracy requirements. In the boundary search algorithm, a boundary search strategy is formulated based on the influence law of various spindle thermal errors on tooth surface errors, namely, symmetrical search to the left and right boundaries, and using the same boundary when the prediction difficulty of various errors is similar, which can significantly improve the boundary solution efficiency and reduce the computation time.

[0155] In some embodiments, calculating the first transformation matrix between the workpiece coordinate system and the tool coordinate system in step S102 includes:

[0156] Step S701: Construct the machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, rocker table fixed coordinate system, and tool rotation coordinate system;

[0157] Step S702: Calculate the first transformation matrix using the following formula based on the workpiece coordinate system, tool coordinate system, machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, rocker table fixed coordinate system, and tool rotation coordinate system:

[0158] ;

[0159] in, This is the first transformation matrix. Let be the transformation matrix from the workpiece axis-fixed coordinate system to the workpiece coordinate system. This is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system. This is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system. Let be the transformation matrix from the fixed coordinate system of the rocking table to the machine tool coordinate system. Let be the transformation matrix from the tool-rotating coordinate system to the fixed coordinate system of the rocking table. This is the transformation matrix from the tool coordinate system to the tool rotation coordinate system. For vertical wheel positions, For beds, For horizontal wheel positions, For angular tool position, For radial tool position, For installation angle, For the angle of the knife, For the knife to turn the corner, For the wheel blank rotation angle, For the corner of the rocking platform, For rolling ratio, is the helical coefficient.

[0160] Specifically, for the convenience of those skilled in the art, a set of preferred embodiments is provided below:

[0161] I. Data Acquisition:

[0162] Obtain the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expand the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0163] II. Calculation of the first transformation matrix:

[0164] Construct the workpiece coordinate system and the tool coordinate system, and calculate the first transformation matrix between the workpiece coordinate system and the tool coordinate system, specifically:

[0165] Construct the machine tool coordinate system, the workpiece axis fixed coordinate system, the machine tool fixed coordinate system, the rocking table fixed coordinate system, and the tool rotation coordinate system;

[0166] The first transformation matrix is ​​calculated using the following formula based on the workpiece coordinate system, tool coordinate system, machine tool coordinate system, workpiece axis fixed coordinate system, machine tool fixed coordinate system, rocker table fixed coordinate system, and tool rotation coordinate system:

[0167] ;

[0168] ;

[0169] in, This is the first transformation matrix. Let be the transformation matrix from the workpiece axis-fixed coordinate system to the workpiece coordinate system. This is the transformation matrix from the machine tool fixed coordinate system to the workpiece axis fixed coordinate system. This is the transformation matrix from the machine tool coordinate system to the machine tool fixed coordinate system. Let be the transformation matrix from the fixed coordinate system of the rocking table to the machine tool coordinate system. Let be the transformation matrix from the tool-rotating coordinate system to the fixed coordinate system of the rocking table. This is the transformation matrix from the tool coordinate system to the tool rotation coordinate system. For vertical wheel positions, For beds, For horizontal wheel positions, For angular tool position, For radial tool position, For installation angle, For the angle of the knife, For the knife to turn the corner, For the wheel blank rotation angle, For the corner of the rocking platform, For rolling ratio, is the helical coefficient.

[0170] III. Calculation of the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point:

[0171] The coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point are calculated based on the axial section of the gear blank and the first transformation matrix, specifically as follows:

[0172] Based on the first transformation matrix, the pinion tooth surface normal vector, relative velocity, and pinion tooth surface position vector are calculated using the following formula:

[0173] ;

[0174] in, Let the position vector of the origin of the tool coordinate system in the tool coordinate system be denoted as . Let Z be the unit vector basis of the tool coordinate system. Let be the unit normal vector of the surface of revolution at point p. for and The angle of formation Let be the rotation angle of a point on the cutting edge about the tool axis to a point on the rotating surface. Let point p and point The distance between them Where is the radius of the cutter head. The distance between the blade tips. For the profile pressure angle, The origin and point of the tool coordinate system The distance between them for and The intersection, + corresponds to the concave surface of the tool and - corresponds to the convex surface of the tool. Let be the position vector of a point on the rotating surface in the tool coordinate system. This is the first transformation matrix. The tool axis vector in the workpiece coordinate system. This is the position vector of the origin of the tool coordinate system in the workpiece coordinate system. For the corner of the rocking platform, The normal vector of the gear tooth surface. Let be the normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system. The position vector of the small gear tooth surface. It is the relative velocity;

[0175] The coordinates of the first tooth surface point are calculated using the following formula based on the pinion tooth surface normal vector, pinion tooth surface position vector, and relative velocity:

[0176]

[0177] in, Let Q be the X-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. Let Q be the Z-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. The distance between the outer cones. These are the discrete parameters of the projection surface along the tooth direction. These are the discrete parameters of the projection plane along the tooth height direction. It is the cone angle. For tooth width, For the tooth tip corresponding to parameter f, For the tooth root corresponding to parameter f, Let be the discrete quantity in the tooth direction. Let be the discrete quantity in the tooth height direction. For the first tooth direction discrete points, For the first tooth in the tooth height direction discrete points, For tooth tip height, For tooth root height, It is the cone angle. The root cone angle, Let X be the X coordinate of the first tooth surface point. The Y-coordinate of the first tooth surface point The Z-coordinate of the first tooth surface point;

[0178] Based on the normal vector of the pinion tooth surface, calculate the normal vector of the first tooth surface point corresponding to the coordinates of the first tooth surface point.

[0179] IV. Calculation of the coordinates of the second tooth surface point:

[0180] Based on the thermal error boundary of the first main spindle, the axial section of the gear blank, and the first transformation matrix, the coordinates of the second tooth surface point are calculated as follows:

[0181] A spindle coordinate system is constructed with the intersection of the grinding wheel mounting surface and the spindle axis as the origin.

[0182] The thermal error boundary of the first principal axis is downsampled to obtain the offset of the origin of the principal axis coordinate system along the X-axis, the offset of the origin of the principal axis coordinate system along the Y-axis, the offset of the origin of the principal axis coordinate system along the Z-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the X-axis, and the deflection angle of the Z-axis of the principal axis coordinate system around the Y-axis.

[0183] Based on the offset of the origin of the principal axis coordinate system along the X-axis, the offset of the origin of the principal axis coordinate system along the Y-axis, the offset of the origin of the principal axis coordinate system along the Z-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the X-axis, the deflection angle of the Z-axis of the principal axis coordinate system around the Y-axis, the axial section of the gear blank, and the first transformation matrix, the pinion tooth surface error position vector is calculated using the following formula:

[0184] ;

[0185] in, The main spindle thermal error matrix, The offset of the origin of the principal coordinate system along the X-axis. The offset of the origin of the main coordinate system along the Y-axis. The offset of the origin of the main axis coordinate system along the Z-axis. The angle of deviation of the Z-axis around the X-axis in the principal coordinate system. The angle of deviation of the Z-axis around the Y-axis in the principal coordinate system. This is the second transformation matrix. The error tool axis vector in the workpiece coordinate system. This is the error position vector of the tool coordinate system origin in the workpiece coordinate system. This is the normal vector of the gear tooth surface error. For the error relative velocity, For the error of the rocking table angle, The error rotation angle is the angle of rotation of a point on the cutting edge about the tool axis to a point on the rotating surface. The origin and point of the tool coordinate system The error distance between them Let the position vector be the error vector of the small gear tooth surface. For error distance, This is the error normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system;

[0186] The coordinates of the second tooth surface point are calculated based on the pinion tooth surface error vector using the following formula:

[0187] ;

[0188] in, The X coordinate of the second tooth surface point is... The Y-coordinate of the second tooth surface point. Here is the Z-coordinate of the second tooth surface point.

[0189] V. Calculation of tooth surface deviation:

[0190] The tooth surface deviation value is calculated based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point. The tooth surface deviation value includes the average tooth surface deviation value and the maximum tooth surface deviation value, specifically:

[0191] Obtain the coordinates of the first center point of the first tooth surface composed of the coordinates of the first tooth surface points; obtain the coordinates of the second center point of the second tooth surface composed of the coordinates of the second tooth surface points.

[0192] The phase angle is calculated based on the Y and Z coordinates of the first center point and the Y and Z coordinates of the second center point. The phase angle is used to rotate the Y and Z coordinates of the first center point around the workpiece axis by a phase angle so that they coincide with the Y and Z coordinates of the second center point.

[0193] Rotate the coordinates of the second tooth surface point around the workpiece axis by a phase angle to obtain the coordinates of the third tooth surface point;

[0194] The normal deviation value is calculated based on the coordinates of the first tooth surface point and the third tooth surface point using the following formula:

[0195] ;

[0196] in, For the first The tooth direction direction Normal deviation value in the tooth height direction For the first The tooth direction direction The coordinates of the third tooth surface point in the tooth height direction. For the first The tooth direction direction Coordinates of the first tooth surface point in the tooth height direction. For the first The tooth direction direction The normal vector of the first tooth surface point in the tooth height direction;

[0197] The tooth surface deviation value is calculated based on the normal deviation value using the following formula:

[0198] ;

[0199] in, The average deviation value of the tooth surface is the tooth surface deviation value. This represents the maximum deviation value of the tooth surface.

[0200] VI. Calculation of spindle thermal error control boundary:

[0201] When the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary.

[0202] When the tooth surface deviation value is less than the preset tooth surface deviation value, the first spindle thermal error boundary is expanded based on the first step length to obtain the second spindle thermal error boundary;

[0203] When the thermal error boundary of the second spindle is greater than the preset maximum error boundary, the thermal error boundary of the second spindle is used as the thermal error control boundary of the spindle.

[0204] When the thermal error boundary of the second spindle is less than the preset maximum error boundary, the second tooth surface deviation value is calculated based on the thermal error boundary of the second spindle. This process is repeated until the deviation value of the Kth tooth surface is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length. Then, the thermal error boundary of the (K-1)th spindle is taken as the thermal error control boundary of the spindle, where K is the iteration number.

[0205] If the tooth surface deviation value is greater than the preset tooth surface deviation value, but half of the first step length is greater than the preset minimum step length, then the first step length is halved to obtain the second step length.

[0206] Based on the second step size, the thermal error boundary of the first spindle is expanded to obtain the thermal error boundary of the second step size spindle;

[0207] If the second step spindle thermal error boundary is greater than the preset maximum error boundary, then the second step spindle thermal error boundary shall be used as the spindle thermal error control boundary.

[0208] When the spindle thermal error boundary of the second step is less than the preset maximum error boundary, the corresponding tooth surface deviation value is calculated based on the spindle thermal error boundary of the second step. This process is repeated until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step is less than the preset minimum step. Then, the Q-1th spindle thermal error boundary is taken as the spindle thermal error control boundary, where Q is the iteration number.

[0209] This application analyzes the influence of spindle thermal error on tooth surface normal deviation and develops a spindle thermal error control boundary solution algorithm driven by tooth surface accuracy. Using tooth surface machining requirements as constraints, it solves the feasible domain of various spindle thermal errors, determines the error control boundary, and provides a predicted accuracy target under a given tooth surface accuracy requirement for spindle thermal error modeling and compensation, ensuring that the tooth surface accuracy can meet the requirements after the control target is achieved.

[0210] Additionally, refer to Figure 23One embodiment of this application provides a spindle thermal error control domain calculation system for a spiral bevel gear grinding machine, including a data acquisition module 1100, a first transformation matrix calculation module 1200, a first tooth surface point coordinate calculation module 1300, a second tooth surface point coordinate calculation module 1400, a tooth surface deviation value calculation module 1500, and a spindle thermal error control boundary calculation module 1600, wherein:

[0211] The data acquisition module 1100 is used to acquire the initial spindle thermal error boundary, the gear blank shaft section and the first step length, and expand the initial spindle thermal error boundary according to the first step length to obtain the first spindle thermal error boundary;

[0212] The first transformation matrix calculation module 1200 is used to construct the workpiece coordinate system and the tool coordinate system, and to calculate the first transformation matrix between the workpiece coordinate system and the tool coordinate system;

[0213] The first tooth surface point coordinate calculation module calculates the first tooth surface point coordinates and the corresponding first tooth surface point normal vector using the 1300 tooth blank shaft section and the first transformation matrix;

[0214] The second tooth surface point coordinate calculation module 1400 is used to calculate the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the tooth blank axial section and the first transformation matrix;

[0215] The tooth surface deviation calculation module 1500 is used to calculate the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point.

[0216] The spindle thermal error control boundary calculation module 1600 is used to take the initial spindle thermal error boundary as the spindle thermal error control boundary when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length.

[0217] This system obtains the initial spindle thermal error boundary, the gear blank shaft section, and the first step length, and expands the initial spindle thermal error boundary based on the first step length to obtain the first spindle thermal error boundary; it constructs the workpiece coordinate system and the tool coordinate system, and calculates the first transformation matrix between the workpiece coordinate system and the tool coordinate system; it calculates the coordinates of the first tooth surface point and the corresponding normal vector of the first tooth surface point based on the gear blank shaft section and the first transformation matrix; it calculates the coordinates of the second tooth surface point based on the first spindle thermal error boundary, the gear blank shaft section, and the first transformation matrix; it calculates the tooth surface deviation value based on the coordinates of the first tooth surface point, the normal vector of the first tooth surface point, and the coordinates of the second tooth surface point; when the tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, the initial spindle thermal error boundary is used as the spindle thermal error control boundary. This application calculates the spindle thermal error control boundary by preset tooth surface deviation value, providing a clear prediction accuracy target for thermal error modeling, and ensuring sufficient tooth surface accuracy in predictions under various working conditions.

[0218] It should be noted that the system embodiments described above are based on the same inventive concept as the method embodiments described above. Therefore, the relevant content of the method embodiments described above is also applicable to the system embodiments described above, and will not be repeated here.

[0219] Figure 24 A schematic diagram of the hardware structure for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine tool provided in an embodiment of this application is shown.

[0220] The computing device for the spindle thermal error control domain of a spiral bevel gear grinding machine tool may include a processor 301 and a memory 302 storing computer program instructions.

[0221] Specifically, the processor 301 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0222] Memory 302 may include mass storage for data or instructions. For example, and not limitingly, memory 302 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 302 may include removable or non-removable (or fixed) media. Where appropriate, memory 302 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 302 is non-volatile solid-state memory.

[0223] In some embodiments, memory 302 may include read-only memory (ROM), random access memory (RAM), disk storage media device, optical storage media device, flash memory device, electrical, optical, or other physical / tangible memory storage device. Thus, generally, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to one aspect of this disclosure.

[0224] The processor 301 reads and executes the computer program instructions stored in the memory 302 to implement any of the spindle thermal error control domain calculation methods for spiral bevel gear grinding machines in the above embodiments.

[0225] In one example, the spindle thermal error control domain calculation device of a spiral bevel gear grinding machine may also include a communication interface 303 and a bus 310. For example, Figure 24 As shown, the processor 301, memory 302, and communication interface 303 are connected through bus 310 and complete communication with each other.

[0226] The communication interface 303 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0227] Bus 310 includes hardware, software, or both, that couples components of the spindle thermal error control domain computing device of a spiral bevel gear grinding machine together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 310 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, any suitable bus or interconnect is contemplated herein.

[0228] The spindle thermal error control domain calculation device of the spiral bevel gear grinding machine can execute the spindle thermal error control domain calculation method of the spiral bevel gear grinding machine in this application embodiment based on a three-dimensional design model, thereby achieving a combination of Figure 1 and Figure 8 The method and system for calculating the spindle thermal error control domain of a spiral bevel gear grinding machine are described.

[0229] Furthermore, in conjunction with the spindle thermal error control domain calculation method for the spiral bevel gear grinding machine tool described in the above embodiments, this application embodiment can provide a computer storage medium for implementation. This computer storage medium stores computer program instructions; when these computer program instructions are executed by a processor, they implement any of the spindle thermal error control domain calculation methods for the spiral bevel gear grinding machine tool described in the above embodiments.

[0230] It should be clarified that this application is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of this application is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of this application.

[0231] The functional blocks shown in the above block diagram can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, they can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this application are programs or code segments used to perform the required tasks. Programs or code segments can be stored on a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried on a carrier wave. "Machine-readable medium" can include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. Code segments can be downloaded via computer networks such as the Internet, intranets, etc.

[0232] It should also be noted that the exemplary embodiments mentioned in this application describe methods or systems based on a series of steps or apparatus. However, this application is not limited to the order of the above steps; that is, the steps can be performed in the order mentioned in the embodiments, or in a different order, or several steps can be performed simultaneously.

[0233] The aspects of this disclosure have been described above with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block in the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that these instructions, executable via the processor of the computer or other programmable data processing apparatus, enable the implementation of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Such a processor can be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field-programmable logic circuit. It is also understood that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by special-purpose hardware performing the specified functions or actions, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0234] The above description is merely a specific implementation of this application. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, modules, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. It should be understood that the protection scope of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the protection scope of this application.

Claims

1. A method for calculating the thermal error control field of the main shaft of a spiral bevel gear grinding machine, characterized in that, The main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool comprises: Obtaining an initial main shaft thermal error boundary, a blank shaft section, and a first step, and expanding the initial main shaft thermal error boundary according to the first step to obtain a first main shaft thermal error boundary; Building a workpiece coordinate system and a tool coordinate system, and calculating a first conversion matrix of the workpiece coordinate system and the tool coordinate system; Calculating a first tooth surface point coordinate and a corresponding first tooth surface point normal vector based on the blank shaft section and the first conversion matrix; Calculating a second tooth surface point coordinate based on the first main shaft thermal error boundary, the blank shaft section, and the first conversion matrix; Calculating a tooth surface deviation value based on the first tooth surface point coordinate, the first tooth surface point normal vector, and the second tooth surface point coordinate, wherein the tooth surface deviation value comprises a tooth surface average deviation value and a tooth surface maximum deviation value, and specifically: Obtaining a first center point coordinate of a first tooth surface composed of a first tooth surface point coordinate; obtaining a second center point coordinate of a second tooth surface composed of a second tooth surface point coordinate; Calculating a phase angle based on Y and Z coordinates of the first center point coordinate and Y and Z coordinates of the second center point coordinate, wherein the phase angle is used to rotate the Y and Z coordinates of the first center point coordinate around a workpiece axis by the phase angle, so as to coincide with the Y and Z coordinates of the second center point coordinate; Rotating the second tooth surface point coordinate around the workpiece axis by the phase angle to obtain a third tooth surface point coordinate; Calculating a normal deviation value based on the first tooth surface point coordinate and the third tooth surface point coordinate by the following formula: ； in, For the first The tooth direction direction Normal deviation value in the tooth height direction For the first The tooth direction direction The coordinates of the third tooth surface point in the tooth height direction. For the first The tooth direction direction Coordinates of the first tooth surface point in the tooth height direction. For the first The tooth direction direction The normal vector of the first tooth surface point in the tooth height direction; Calculating the tooth surface deviation value based on the normal deviation value by the following formula: ； wherein is the mean deviation of the tooth face deviation values, is the maximum deviation of the tooth face deviation values, is the offset of the origin of the main axis coordinate system along the X axis, is the offset of the origin of the main axis coordinate system along the Y axis, is the offset of the origin of the main axis coordinate system along the Z axis, is the angle of the Z axis of the main axis coordinate system around the X axis, is the angle of the Z axis of the main axis coordinate system around the Y axis; When the tooth surface deviation value is greater than a preset tooth surface deviation value and half of the first step is less than a preset minimum step, the initial main shaft thermal error boundary is taken as a main shaft thermal error control boundary.

2. The method according to claim 1, wherein, The calculation of the first tooth surface point coordinate and the corresponding first tooth surface point normal vector based on the blank shaft section and the first conversion matrix comprises: Calculating a pinion tooth surface normal vector, a relative velocity, and a pinion tooth surface position vector based on the first conversion matrix by the following formula: ； in, Let the position vector of the origin of the tool coordinate system in the tool coordinate system be denoted as . Let Z be the unit vector basis of the tool coordinate system. Let be the unit normal vector of the surface of revolution at point p. for and The angle of formation Let be the rotation angle of a point on the cutting edge about the tool axis to a point on the rotating surface. Let point p and point The distance between them Where is the radius of the cutter head. The distance between the blade tips. For the profile pressure angle, The origin and point of the tool coordinate system The distance between them for and The intersection, + corresponds to the concave surface of the tool and - corresponds to the convex surface of the tool. Let be the position vector of a point on the rotating surface in the tool coordinate system. This is the first transformation matrix. The tool axis vector in the workpiece coordinate system. This is the position vector of the origin of the tool coordinate system in the workpiece coordinate system. For the corner of the rocking platform, The normal vector of the gear tooth surface. Let be the normal vector of the rotating surface of the tool's straight cutting edge in the tool coordinate system. The position vector of the small gear tooth surface. It is the relative velocity; Calculating the first tooth surface point coordinate based on the pinion tooth surface normal vector, the pinion tooth surface position vector, and the relative velocity by the following formula: ； in, Let Q be the X-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. Let Q be the Z-coordinate of the grid point Q in the axial section of the gear blank in the workpiece coordinate system. The distance between the outer cones. These are the discrete parameters of the projection plane along the tooth direction. These are the discrete parameters of the projection plane along the tooth height direction. It is the pitch cone angle. For tooth width, For the tooth tip corresponding to parameter f, For the tooth root corresponding to parameter f, Let be the discrete quantity in the tooth direction. Let be the discrete quantity in the tooth height direction. For the first tooth direction discrete points, For the first tooth in the tooth height direction discrete points, For tooth tip height, For tooth root height, It is the cone angle. The root cone angle, Let X be the X coordinate of the first tooth surface point. The Y-coordinate of the first tooth surface point The Z-coordinate of the first tooth surface point; Calculating the first tooth surface point normal vector corresponding to the first tooth surface point coordinate based on the pinion tooth surface normal vector.

3. The method of claim 2, wherein the method further comprises: determining a thermal error control field of the main shaft of the spiral bevel gear grinding machine based on the thermal error control field of the main shaft of the spiral bevel gear grinding machine and the thermal error control field of the main shaft of the spiral bevel gear grinding machine. The calculation of the second tooth surface point coordinate based on the first main shaft thermal error boundary, the blank shaft section, and the first conversion matrix comprises: Building a main shaft coordinate system with an intersection point of a grinding wheel mounting surface and a main shaft axis as a coordinate origin; Down-sampling the first main shaft thermal error boundary to obtain a shift of a main shaft coordinate system origin along an X axis, a shift of the main shaft coordinate system origin along a Y axis, a shift of the main shaft coordinate system origin along a Z axis, a deflection angle of a Z axis of the main shaft coordinate system around the X axis, and a deflection angle of the Z axis of the main shaft coordinate system around the Y axis; Based on the offset of the origin of the main shaft coordinate system along the X axis, the offset of the origin of the main shaft coordinate system along the Y axis, the offset of the origin of the main shaft coordinate system along the Z axis, the deflection angle of the Z axis of the main shaft coordinate system around the X axis, the deflection angle of the Z axis of the main shaft coordinate system around the Y axis, the gear blank shaft section and the first conversion matrix, the pinion tooth surface error vector is calculated by the following formula: ； wherein, is a spindle thermal error matrix, is an offset of the spindle coordinate system origin along the X-axis, is an offset of the spindle coordinate system origin along the Y-axis, is an offset of the spindle coordinate system origin along the Z-axis, is an offset angle of the Z-axis of the spindle coordinate system around the X-axis, is an offset angle of the Z-axis of the spindle coordinate system around the Y-axis, is a second conversion matrix, is an error tool axis vector in the workpiece coordinate system, is an error position vector of the tool coordinate system origin in the workpiece coordinate system, is a pinion tooth surface error normal vector, is an error relative velocity, is an error swivel angle, is an error rotation angle of a point on the cutting edge around the tool axis to the point of the rotary surface, is an error distance between the tool coordinate system origin and the point on the rotary surface, is a pinion tooth surface error position vector, is an error distance, is an error normal vector of the tool linear edge rotary surface in the tool coordinate system; Based on the pinion tooth surface error vector, the second tooth surface point coordinates are calculated by the following formula: ； wherein is the X coordinate of the second tooth surface point, is the Y coordinate of the second tooth surface point, is the Z coordinate of the second tooth surface point.

4. The method of claim 1, wherein the method further comprises: determining a thermal error control field of the main shaft of the spiral bevel gear grinding machine based on the thermal error control field of the main shaft of the spiral bevel gear grinding machine. The main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool further comprises: When the tooth surface deviation value is less than the preset tooth surface deviation value, based on the first step length, the first main shaft thermal error boundary is expanded to obtain a second main shaft thermal error boundary; When the second main shaft thermal error boundary is greater than the preset maximum error boundary, the second main shaft thermal error boundary is taken as the main shaft thermal error control boundary; When the second main shaft thermal error boundary is less than the preset maximum error boundary, a second tooth surface deviation value is calculated according to the second main shaft thermal error boundary, and the process is sequentially repeated until the Kth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the first step length is less than the preset minimum step length, and the K-1th main shaft thermal error boundary is taken as the main shaft thermal error control boundary, wherein K is the iteration number.

5. The method of claim 1, wherein, The main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool further comprises: When the tooth surface deviation value is greater than the preset tooth surface deviation value but half of the first step length is greater than the preset minimum step length, the first step length is halved to obtain a second step length; Based on the second step length, the first main shaft thermal error boundary is expanded to obtain a second step length main shaft thermal error boundary; When the second step length main shaft thermal error boundary is greater than the preset maximum error boundary, the second step length main shaft thermal error boundary is taken as the main shaft thermal error control boundary; When the second step length main shaft thermal error boundary is less than the preset maximum error boundary, a corresponding tooth surface deviation value is calculated according to the second step length main shaft thermal error boundary, and the process is sequentially repeated until the Qth tooth surface deviation value is greater than the preset tooth surface deviation value and half of the Qth step length is less than the preset minimum step length, and the Q-1th main shaft thermal error boundary is taken as the main shaft thermal error control boundary, wherein Q is the iteration number.

6. The method of claim 1, wherein the method further comprises: The calculation of the first conversion matrix of the workpiece coordinate system and the tool coordinate system comprises: constructing a machine tool coordinate system, a workpiece shaft fixed coordinate system, a machine tool fixed coordinate system, a turret fixed coordinate system and a tool rotation coordinate system; calculating the first conversion matrix according to the workpiece coordinate system, the tool coordinate system, the machine tool coordinate system, the workpiece shaft fixed coordinate system, the machine tool fixed coordinate system, the turret fixed coordinate system and the tool rotation coordinate system by the following formula: ； ； wherein is a first transformation matrix, is a transformation matrix of the workpiece axis-fixed coordinate system to the workpiece coordinate system, is a transformation matrix of the machine tool-fixed coordinate system to the workpiece axis-fixed coordinate system, is a transformation matrix of the machine tool coordinate system to the machine tool-fixed coordinate system, is a transformation matrix of the table-fixed coordinate system to the machine tool coordinate system, is a transformation matrix of the tool rotation coordinate system to the table-fixed coordinate system, is a transformation matrix of the tool coordinate system to the tool rotation coordinate system, is a vertical wheel position, is a bed position, is a horizontal wheel position, is an angular tool position, is a radial tool position, is an installation angle, is a tool inclination angle, is a tool rotation angle, is a wheel blank rotation angle, is a table rotation angle, is a rolling ratio, is a helix coefficient.

7. A spindle thermal error control domain computing system for a spiral bevel gear grinding machine, characterized by, The main shaft thermal error control domain calculation system of the spiral bevel gear grinding machine tool comprises: a data acquisition module configured to acquire an initial main shaft thermal error boundary, a gear blank shaft section and a first step length, and expand the initial main shaft thermal error boundary according to the first step length to obtain a first main shaft thermal error boundary; a first conversion matrix calculation module configured to construct a workpiece coordinate system and a tool coordinate system, and calculate a first conversion matrix of the workpiece coordinate system and the tool coordinate system; a second conversion matrix calculation module configured to calculate a second conversion matrix of the workpiece coordinate system and the tool coordinate system according to the first conversion matrix and a tooth surface deviation value; The first tooth surface point coordinate calculation module is configured to calculate first tooth surface point coordinates and corresponding first tooth surface point normal vectors based on the blank shaft section and the first conversion matrix. The second tooth surface point coordinate calculation module is configured to calculate second tooth surface point coordinates based on the first main shaft thermal error boundary, the blank shaft section and the first conversion matrix. The tooth surface deviation value calculation module is configured to calculate tooth surface deviation values based on the first tooth surface point coordinates, the first tooth surface point normal vectors and the second tooth surface point coordinates, wherein the tooth surface deviation values include tooth surface average deviation values and tooth surface maximum deviation values, and specifically: The first center point coordinates of a first tooth surface composed of the first tooth surface point coordinates are obtained, and the second center point coordinates of a second tooth surface composed of the second tooth surface point coordinates are obtained. The phase angle is calculated based on the Y coordinate and the Z coordinate of the first center point coordinates, and the Y coordinate and the Z coordinate of the second center point coordinates, wherein the phase angle is used to rotate the Y coordinate and the Z coordinate of the first center point coordinates around the workpiece axis by the phase angle, so as to coincide with the Y coordinate and the Z coordinate of the second center point coordinates. The second tooth surface point coordinates are rotated around the workpiece axis by the phase angle to obtain third tooth surface point coordinates. The normal deviation value is calculated based on the first tooth surface point coordinates and the third tooth surface point coordinates by the following formula: ； in, For the first The tooth direction direction Normal deviation value in the tooth height direction For the first The tooth direction direction The coordinates of the third tooth surface point in the tooth height direction. For the first The tooth direction direction Coordinates of the first tooth surface point in the tooth height direction. For the first The tooth direction direction The normal vector of the first tooth surface point in the tooth height direction; The tooth surface deviation value is calculated based on the normal deviation value by the following formula: ； wherein is the mean deviation of the tooth face deviation values, is the maximum deviation of the tooth face deviation values, is the offset of the origin of the main axis coordinate system along the X axis, is the offset of the origin of the main axis coordinate system along the Y axis, is the offset of the origin of the main axis coordinate system along the Z axis, is the angle of deviation of the Z axis of the main axis coordinate system around the X axis, is the angle of deviation of the Z axis of the main axis coordinate system around the Y axis; The main shaft thermal error control boundary calculation module is configured to, when the tooth surface deviation value is greater than a preset tooth surface deviation value and half of the first step length is less than a preset minimum step length, take the initial main shaft thermal error boundary as a main shaft thermal error control boundary.

8. A main shaft thermal error control field computing device for a spiral bevel gear grinding machine, characterized by, The at least one control processor and a memory connected in communication with the at least one control processor; the memory stores instructions executable by the at least one control processor, and the instructions are executed by the at least one control processor to enable the at least one control processor to perform the main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer readable storage medium stores computer executable instructions for enabling a computer to perform the main shaft thermal error control domain calculation method of the spiral bevel gear grinding machine tool according to any one of claims 1 to 6.

Images