Spiral bevel gear tooth profile and pitch measurement method, device and equipment and storage medium

Abstract

The invention discloses a spiral bevel gear tooth profile and pitch measuring method, device and equipment and a storage medium, and the spiral bevel gear tooth profile and pitch measuring method comprises the steps: obtaining to-be-measured tooth profile data and to-be-measured pitch data of a to-be-measured spiral bevel gear, the to-be-measured tooth profile data and the to-be-measured tooth pitch data are measured by a measuring head of the spiral bevel gear machine tool based on a pre-constructed measuring coordinate system; according to the to-be-measured tooth profile data, obtaining a tooth profile error of the to-be-measured spiral bevel gear; according to the to-be-measured tooth pitch data, the tooth pitch error of the to-be-measured spiral bevel gear is obtained; wherein the measurement coordinate system is obtained through the following steps: obtaining a plurality of pieces of accurate sphere center position information corresponding to a plurality of sphere center points; according to the multiple pieces of accurate sphere center position information, axis position information of the axis of the workpiece spindle is obtained; and establishing a measurement coordinate system of the spiral bevel gear machine tool based on the axis position information. According to the invention, the tooth profile and pitch measurement precision of the spiral bevel gear can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of machining, and in particular, to a method, device, equipment and storage medium for measuring the tooth profile and pitch of spiral bevel gears. Background Art

[0002] For high-precision spiral bevel gears, it is difficult to achieve the required accuracy through a single gear grinding process. It is often necessary to measure the tooth profile and pitch of the spiral bevel gear, obtain the tooth profile and pitch error of the gear, and then, based on the previous measurement results once or multiple times, adjust and correct the machining parameters in reverse before a product that meets the accuracy requirements can be machined. This process is called the closed-loop machining of spiral bevel gears.

[0003] In the closed-loop machining process of spiral bevel gears, offline measurement technology is mainly used. The gear generally needs to go through processes such as gear grinding, disassembly, inspection, clamping, secondary gear grinding, disassembly, and reinspection. The measurement processes of inspection and reinspection are operated by dedicated measuring equipment. At the same time, the measurement process is based on a measurement coordinate system established relying on the geometric features of the gear blank. The machining processes of gear grinding and secondary gear grinding are operated by an electric control machine tool. At the same time, the machining process is based on the machine tool coordinate system determined according to the machine tool spindle. There is a lack of rigid connection between the two, resulting in inconsistent measurement coordinate system and machining coordinate system, which affects the measurement accuracy of the tooth profile and pitch in the gear grinding of spiral bevel gears. Summary of the Invention

[0004] The present application aims to propose a method, device, equipment and storage medium for measuring the tooth profile and pitch of spiral bevel gears, which can improve the measurement accuracy of the tooth profile and pitch of spiral bevel gears.

[0005] The method for measuring the tooth profile and pitch of spiral bevel gears according to the first aspect embodiment of the present application includes: Obtaining the to-be-measured tooth profile data and to-be-measured pitch data of the to-be-measured spiral bevel gear, wherein the to-be-measured spiral bevel gear is clamped on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the to-be-measured tooth profile data and the to-be-measured pitch data are measured by a probe of the spiral bevel gear machine tool based on a pre-constructed measurement coordinate system; Obtaining the tooth profile error of the to-be-measured spiral bevel gear according to the to-be-measured tooth profile data; Obtaining the pitch error of the to-be-measured spiral bevel gear according to the to-be-measured pitch data; Wherein, the measurement coordinate system is obtained through the following steps: Obtaining the accurate position information of multiple corresponding center points of the balls, the multiple center points of the balls being the center points of the standard ball in different spatial positions, the number of the center points of the balls being greater than or equal to three, the standard ball being arranged on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the workpiece spindle being used to rotate the standard ball to different spatial positions; Based on the multiple pieces of accurate ball center position information, obtain the axis position information of the axis of the workpiece spindle; Based on the axis position information, establish a measurement coordinate system for the spiral bevel gear machine tool, where the measurement coordinate system has a plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

[0006] According to some embodiments of the present application, the multiple pieces of accurate ball center position information corresponding to multiple ball center points are obtained, where the accurate ball center position information corresponding to each ball center point is obtained through the following steps: Control the probe to randomly contact the surface of the standard ball to obtain the position information of multiple random contact points located on the surface of the standard ball, where the number of random contact points is greater than or equal to three; Based on the least squares method, obtain the rough ball center position information of the standard ball according to the position information of multiple random contact points; Set multiple preset contact points located on the surface of the standard ball, and plan a preset movement path for the probe to contact the multiple preset contact points. Among them, the multiple preset contact points include multiple first preset contact points and one second preset contact point. The number of the first preset contact points is greater than or equal to three. The multiple first preset contact points are in the same plane and the plane where they are located passes through the center of the standard ball. The connection line between the second preset contact point and the center of the standard ball is perpendicular to the plane where the multiple first preset contact points are located; According to the rough ball center position information and the preset movement path, obtain the movement constraint equation that the probe needs to satisfy when moving along the preset movement path; Control the probe to move along the preset movement path and contact the multiple preset contact points to obtain the position information of the multiple preset contact points; Based on the least squares method, obtain the accurate ball center position information of the standard ball according to the position information of the multiple preset contact points and the movement constraint equation.

[0007] According to some embodiments of the present application, the obtaining the axis position information of the axis of the workpiece spindle according to the multiple pieces of accurate ball center position information includes: According to the multiple pieces of accurate ball center position information, fit the multiple ball center points to obtain a first fitted circle, and determine the first center position information of the first fitted circle; According to the multiple pieces of accurate ball center position information and the first center position information of the first fitted circle, obtain a deviation matrix, where the deviation matrix characterizes the position deviation of the multiple pieces of accurate ball center position information relative to the first center position information of the first fitted circle; Calculate the covariance matrix of the deviation matrix and obtain the eigenvector corresponding to the minimum eigenvalue of the covariance matrix; Determine the direction information of the axis of the workpiece spindle according to the eigenvector; Determine the plane where the fitted circle is located according to the eigenvector, and select two orthogonal basis vectors in the plane; Project the multiple center point of the balls onto the plane where the fitted circle is located according to the two orthogonal basis vectors, and obtain multiple two-dimensional coordinate information corresponding to the multiple center point of the balls; Based on the least squares method, fit the multiple center point of the balls according to the multiple two-dimensional coordinate information corresponding to the multiple center point of the balls, obtain a second fitted circle, and determine the second center position information of the second fitted circle; Obtain the axis position information of the axis of the workpiece spindle according to the second center position information of the second fitted circle and the direction information of the axis of the workpiece spindle;

[0008] According to some embodiments of the present application, establishing the measurement coordinate system of the spiral bevel gear machine tool based on the axis position information includes: Determine the Z axis of the measurement coordinate system according to the axis position information; Control the probe to randomly contact the end face of the workpiece spindle to obtain the position information of multiple random plane contact points located on the end face of the workpiece spindle, wherein the number of the random plane contact points is greater than or equal to three; Obtain the end plane position information of the end face of the workpiece spindle according to the position information of the multiple random plane contact points; Determine the XY plane of the measurement coordinate system according to the end plane position information, the blank height and the mounting distance of the spiral bevel gear to be measured, and determine the origin O of the measurement coordinate system according to the determined Z axis and the XY plane; Control the probe to contact the middle area of the tooth surface of the spiral bevel gear to obtain the position information of the rough measurement point of the tooth surface midpoint located in the middle area of the tooth surface; Determine the rough X axis of the measurement coordinate system passing through the rough measurement point of the tooth surface midpoint and the origin O according to the position information of the rough measurement point of the tooth surface midpoint; Obtain a rough measurement coordinate system according to the determined Z axis, the origin O and the rough X axis; Based on the tooth surface equation of the spiral bevel gear, obtain the first theoretical tooth surface midpoint coordinate and the unit normal vector corresponding to a tooth surface midpoint of the spiral bevel gear to be measured; Based on the rough measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system, and continuously correct the rough measurement coordinate system by comparing the rough tooth surface midpoint coordinates with the first theoretical tooth surface midpoint coordinates to obtain the measurement coordinate system.

[0009] According to some embodiments of the present application, the method of based on the rough measurement coordinate system, controlling the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, obtaining the rough tooth surface midpoint coordinates in the rough measurement coordinate system, and continuously correcting the rough measurement coordinate system by comparing the rough tooth surface midpoint coordinates with the first theoretical tooth surface midpoint coordinates to obtain the measurement coordinate system includes: Based on the rough measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, and obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system; Determine a first radius according to the rough tooth surface midpoint coordinates, where the first radius is the distance between the rough tooth surface midpoint corresponding to the rough tooth surface midpoint coordinates and the workpiece spindle; Obtain the absolute value of the difference between the first radius and the theoretical radius, where the theoretical radius is the distance between the first theoretical tooth surface midpoint and the workpiece spindle, and the theoretical radius is determined according to the first theoretical tooth surface midpoint coordinates; When the absolute value is greater than a preset precision value, rotate and adjust the current rough measurement coordinate system by an adjustment angle around the workpiece spindle to obtain an updated rough measurement coordinate system, and jump to the step of based on the rough measurement coordinate system, controlling the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system; When the absolute value is less than the preset precision value, determine the current rough measurement coordinate system as the measurement coordinate system.

[0010] According to some embodiments of the present application, the to-be-measured tooth profile data includes the measured tooth surface coordinates of multiple tooth points of the spiral bevel gear to be measured. The method for obtaining the to-be-measured tooth profile data of the spiral bevel gear to be measured includes: Based on the measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured, and measure the measured tooth surface coordinates of the multiple tooth points; The method for obtaining the tooth profile error of the spiral bevel gear to be measured according to the to-be-measured tooth profile data includes: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, obtain the theoretical tooth surface coordinates of the multiple tooth points of the spiral bevel gear to be measured; Based on the theoretical tooth surface coordinates and the measured tooth surface coordinates of the multiple tooth surface points, the tooth profile error is obtained.

[0011] According to some embodiments of the present application, the tooth pitch data to be measured includes multiple individual tooth pitches and cumulative tooth pitches of the spiral bevel gear to be measured, and the tooth pitch error includes individual tooth pitch error and cumulative tooth pitch error; The multiple individual tooth pitches include the individual tooth pitches between all adjacent tooth surfaces, and obtaining the tooth pitch data to be measured of the spiral bevel gear to be measured includes: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, the second theoretical tooth surface midpoint coordinate corresponding to a tooth surface midpoint of the spiral bevel gear to be measured is obtained; Performing a tooth pitch measurement strategy according to the second theoretical tooth surface midpoint coordinate to obtain the multiple individual tooth pitches; Wherein, the tooth pitch measurement strategy includes: Placing the probe between the Nth group of adjacent tooth surfaces of the spiral bevel gear to be measured; Controlling the probe to be located at the second theoretical tooth surface midpoint coordinate; Controlling the spiral bevel gear to be measured to rotate in a first direction so that the left tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the left rotation angle value between the Nth group of adjacent tooth surfaces; Controlling the spiral bevel gear to be measured to rotate in a second direction so that the right tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the right rotation angle value between the Nth group of adjacent tooth surfaces; Obtaining the individual tooth pitch corresponding to the Nth group of adjacent tooth surfaces according to the left rotation angle value and the right rotation angle value, and assigning N + 1 to N; When the individual tooth pitch errors between all adjacent tooth surfaces have not been obtained, jumping to the step of placing the probe between the Nth group of adjacent tooth surfaces of the spiral bevel gear to be measured; The obtaining the tooth pitch error of the spiral bevel gear to be measured according to the tooth pitch data to be measured includes: Obtaining the multiple individual tooth pitch errors corresponding to the multiple individual tooth pitches according to the theoretical tooth pitch of the spiral bevel gear to be measured and the multiple individual tooth pitches; Summing the multiple individual tooth pitch errors to obtain the cumulative tooth pitch error.

[0012] According to the spiral bevel gear tooth profile and tooth pitch measurement device of the second aspect embodiment of the present application, the device includes: An acquisition module, configured to acquire measured tooth profile data and measured pitch data of a spiral bevel gear to be measured, wherein the spiral bevel gear to be measured is clamped on the end face of a workpiece spindle of a spiral bevel gear machine tool, and the measured tooth profile data and the measured pitch data are measured by a probe of the spiral bevel gear machine tool based on a pre-constructed measurement coordinate system; A first obtaining module, configured to obtain a tooth profile error of the spiral bevel gear to be measured according to the measured tooth profile data; A second obtaining module, configured to obtain a pitch error of the spiral bevel gear to be measured according to the measured pitch data; Wherein, the measurement coordinate system is obtained through the following steps: Obtain a plurality of accurate ball center position information corresponding to a plurality of ball center points. The plurality of ball center points are the ball centers of a standard ball in different spatial positions. The number of the ball center points is greater than or equal to three. The standard ball is arranged on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the workpiece spindle is used to rotate the standard ball to different spatial positions; According to the plurality of accurate ball center position information, obtain the axis position information of the axis of the workpiece spindle; Based on the axis position information, establish the measurement coordinate system of the spiral bevel gear machine tool, wherein the measurement coordinate system uses a plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

[0013] An electronic device according to an embodiment of the third aspect of the present application includes a processor and a memory. The memory stores a program or instruction that can run on the processor. When the program or instruction is executed by the processor, the steps of the spiral bevel gear tooth profile and pitch measurement method according to any one of the embodiments of the first aspect are implemented.

[0014] A computer-readable storage medium according to an embodiment of the fourth aspect of the present application stores computer-executable instructions, and the computer-executable instructions are used to execute the spiral bevel gear tooth profile and pitch measurement method according to the embodiment of the first aspect.

[0015] In the embodiments of the present application, based on a pre-constructed measurement coordinate system, the tooth profile and pitch data of the spiral bevel gear to be measured are obtained by measuring with a probe of a spiral bevel gear machine tool, and then the tooth profile and pitch error conditions are obtained. The present application adopts the in-machine measurement technology of a trigger probe, integrating measurement and machining. After the spiral bevel gear to be measured is measured to obtain the error conditions, if machining is required, it does not need to be disassembled and reinstalled, which can effectively avoid multiple installation errors caused by repeated clamping of the spiral bevel gear to be measured during the clamping process. At the same time, a unified coordinate system is established, that is, a measurement coordinate system with the end face parallel to the workpiece spindle of the spiral bevel gear machine tool as the XY plane and the axis of the workpiece spindle as the Z axis, which is used as both the measurement reference and the machining reference, so that the measurement and machining processes use the same coordinate system, which can effectively eliminate the tooth blank reference error caused by problems such as low tooth blank reference accuracy, blank deformation, or uneven heat treatment of the spiral bevel gear to be measured. In summary, the present application constructs a measurement-machining homologous reference system, which can obtain the tooth profile and pitch measurement results separated from the installation error and the tooth blank reference error, improve the measurement accuracy, and also help to improve the subsequent machining accuracy.

[0016] Other features and advantages of the present application will be described in the following specification, and part of them will become obvious from the specification or be understood by implementing the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and / or additional aspects and advantages of the present application will become obvious and easy to understand from the description of the embodiments in conjunction with the following drawings, where: Figure 1 is a schematic flow chart of an embodiment of the method for measuring the tooth profile and pitch of a spiral bevel gear of the present application; Figure 2 is a schematic diagram of the off-line measurement process; Figure 3 is a schematic diagram of the in-machine measurement process; Figure 4 is a schematic structural diagram of the in-machine measurement system of a spiral bevel gear of the present application; Figure 5 is a schematic diagram of the probe in the in-machine measurement system of a spiral bevel gear of the present application; Figure 6 is a schematic structural diagram of the coordinate system of the machine tool of the present application; Figure 7 is a schematic diagram of the machine tool motion chain for measuring a gear of the present application; Figure 8 is a schematic diagram of the machine tool motion chain for measuring a standard ball of the present application; Figure 9 is a schematic diagram of randomly touched points on the surface of the standard ball of the present application; Figure 10 is a schematic diagram of the preset touched points and the preset movement path of the present application; Figure 11 It is a schematic diagram of multiple accurate ball center position information of the present application; Figure 12 It is a schematic diagram of the measurement coordinate system of the present application; Figure 13 It is a schematic diagram of the process of iteratively and accurately establishing a measurement coordinate system from a rough measurement coordinate system in the present application; Figure 14 It is a schematic diagram of the tooth surface of the spiral bevel gear to be measured in the present application; Figure 15 It is a schematic diagram of the measurement path of the tooth profile error in the present application; Figure 16 It is a schematic diagram of the structure of an embodiment of the spiral bevel gear tooth profile and pitch measurement device of the present application; Figure 17 It is a schematic diagram of the hardware structure of an embodiment of the electronic device of the present application. Detailed implementation manners

[0018] The embodiments of the present application will be described in detail below. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application, and should not be construed as a limitation to the present application.

[0019] In the description of the present application, if the first, second, etc. are described, it is only for the purpose of distinguishing technical features, and should not be construed as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features or implicitly indicating the sequence relationship of the indicated technical features.

[0020] In the description of the present application, it should be understood that the orientation descriptions such as up, down, etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present application.

[0021] In the description of the present application, it should be noted that unless otherwise clearly defined, words such as setting, installing, connecting, etc. should be understood in a broad sense, and those skilled in the technical field can reasonably determine the specific meanings of the above words in the present application in combination with the specific content of the technical solution.

[0022] The technical solutions of the present application will be described clearly and completely below with reference to the drawings. Obviously, the following described embodiments are part of the embodiments of the present application, not all embodiments.

[0023] Figure 1The flowchart of the spiral bevel gear tooth profile and pitch measurement method for the embodiments provided in this application is shown below. Next, refer to Figure 1 to further elaborate on the embodiments of this application.

[0024] The embodiments of this application propose a spiral bevel gear tooth profile and pitch measurement method, which includes the following steps: Step 101: Obtain the tooth profile data and pitch data of the spiral bevel gear to be measured. Among them, the spiral bevel gear to be measured is clamped on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the tooth profile data and pitch data to be measured are obtained by the probe of the spiral bevel gear machine tool based on a pre-constructed measurement coordinate system; Step 102: Obtain the tooth profile error of the spiral bevel gear to be measured according to the tooth profile data to be measured; Step 103: Obtain the pitch error of the spiral bevel gear to be measured according to the pitch data to be measured; Among them, the measurement coordinate system is obtained through the following steps: Obtain the accurate position information of multiple ball center points corresponding to multiple ball center points. The multiple ball center points are the ball centers of the standard ball in different spatial positions. The number of ball center points is greater than or equal to three. The standard ball is arranged on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the workpiece spindle is used to rotate the standard ball to different spatial positions through rotation; According to the accurate position information of multiple ball center points, obtain the axis position information of the axis of the workpiece spindle; Based on the axis position information, establish the measurement coordinate system of the spiral bevel gear machine tool. Among them, the measurement coordinate system takes the plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

[0025] In the embodiments of this application, based on the pre-constructed measurement coordinate system, the tooth profile and pitch data of the spiral bevel gear to be measured are measured by the probe of the spiral bevel gear machine tool, and then the tooth profile and pitch error conditions are obtained. This application adopts the trigger probe in-machine measurement technology, which integrates measurement and processing. After the spiral bevel gear to be measured completes the measurement and obtains the error conditions, if processing is required, there is no need to disassemble and assemble, which can effectively avoid the multiple installation errors caused by repeated clamping of the spiral bevel gear to be measured during the clamping process; at the same time, a unified coordinate system is established, that is, the measurement coordinate system with the plane parallel to the end face of the workpiece spindle of the spiral bevel gear machine tool as the XY plane and the axis of the workpiece spindle as the Z axis is used as both the measurement reference and the processing reference, so that the measurement and processing processes use the same coordinate system, which can effectively eliminate the tooth blank reference error caused by problems such as low tooth blank reference accuracy, blank deformation, or uneven heat treatment of the spiral bevel gear to be measured. In summary, this application constructs a measurement-processing homologous reference system, which can obtain the tooth profile and pitch measurement results that separate the installation error and the tooth blank reference error, improve the measurement accuracy, and also help to improve the subsequent processing accuracy.

[0026] In addition, by adopting the on-machine measurement technology with a trigger probe, online compensation of machining errors can be achieved, the machining cycle time can be shortened by more than 60%, expensive special measurement equipment such as coordinate measuring machines and gear measuring centers can be omitted, and machining costs can be saved. For example, Figure 2 and Figure 3 as shown, Figure 2 is a schematic diagram of the off-line measurement process, Figure 3 and is a schematic diagram of the on-machine measurement process.

[0027] It should be noted that this application is applied to the on-machine measurement system of spiral bevel gears for a six-axis five-linkage spiral bevel gear machine tool. Here, for the convenience of elaborating the tooth profile and pitch measurement method of the spiral bevel gears in this application, a brief description of the on-machine measurement system of spiral bevel gears is given here.

[0028] As Figure 4 shown, the X-axis of the spiral bevel gear machine tool is the horizontal axis of the machine tool, the Y-axis is the vertical axis of the machine tool, the Z-axis is the bed axis of the machine tool, the A-axis is the workpiece spindle, the B-axis is the rotary table spindle, and the C-axis is the tool spindle. The A-axis and the C-axis can achieve arbitrary circumferential rotation. The X-axis and the Z-axis are perpendicular and located in the same horizontal plane of the bed. The Y-axis is located on the column and perpendicular to the plane formed by the X-axis and the Z-axis. The workpiece box is located on the rotary table and can rotate around the B-axis.

[0029] As Figure 4 shown, the probe is an on-machine measurement probe and is a trigger probe, which is installed beside the C-axis. During the measurement process, the relative position between the probe and the center of the C-axis remains unchanged. As Figure 5 shown, the center point of the probe O P and the center point of the C-axis O C in the XY plane of the machine tool coordinate system is as shown in Figure 2 shown. The offset amounts of the two center points in the X and Y directions are respectively set as ΔPb_X , ΔPb_Y . When measuring, the probe extends out to avoid interference between the worm grinding wheel and the gear during measurement.

[0030] As Figure 4 shown, the spiral bevel gear to be measured is installed on the A-axis. It should be noted that when a standard ball is needed, the standard ball can be adsorbed to the edge position on the end face of the A-axis, that is, the edge position on the gear rotary table, through a magnetic base. The standard ball will rotate along with the rotation of the A-axis. When measuring the gear on the machine, the A-axis serves as the rotating axis, similar to the rotary table of a gear measuring center. The B-axis rotates to the spiral bevel gear pitch cone angle and then remains stationary to avoid interference between the probe and the tooth surface during measurement.

[0031] The machine tool kinematic chain model established based on the above on-machine measurement system of spiral bevel gears is as shown in Figure 6 and Figure 7As shown Figure 6 is a schematic diagram of the coordinate system structure of the machine tool Figure 7 is a schematic diagram of the machine tool motion chain for measuring gears. From the machine tool bed to the workpiece, i.e., the spiral bevel gear to be measured, and from the machine tool bed to the probe respectively belong to two motion chains. From the machine tool bed to the spiral bevel gear to be measured, i.e., from the machine tool coordinate system (Machine Coordinate System, MCS) to the workpiece coordinate system (Workpiece Coordinate System, WCS). It should be noted that this workpiece coordinate system is also the measurement coordinate system in this application; from the machine tool bed to the probe, i.e., from the machine tool coordinate system to the tool / probe coordinate system (Tool Coordinate System, TCS). Figure 6 In it, r m1 is the position vector from the A-axis coordinate system to the workpiece coordinate system, r m2 is the position vector from the Y-axis coordinate system to the probe coordinate system, r p is the position vector from the probe coordinate system to the workpiece coordinate system, S Y is the Y-axis coordinate system, S A is the A-axis coordinate system., S P is the probe coordinate system, S W is the measurement coordinate system, S F is the machine tool coordinate system Figure 7 In it, o F is the origin of the machine tool coordinate system, S P is the probe coordinate system, S W is the measurement coordinate system, R2 is the distance between the center point of the B-axis and the workpiece installation end face in the same XZ plane, θ2 is the B-axis phase, ω2 is the A-axis phase, Workpiece_H represents the workpiece height DX represents the position of the center point of the machine tool B-axis on the X-axis in the machine tool coordinate system DY represents the distance from the A-axis end face to the XZ plane of the machine tool coordinate system DZ represents the distance from the probe installation surface to the XY plane of the machine tool coordinate system, Pb_long represents the distance from the center point of the probe to the probe installation surface ΔPb_X 、 ΔPb_Y are the offset amounts of the probe and the tool center point in the X and Y directions respectively

[0032] The above-mentioned measurement coordinate system needs to be pre-constructed first. Subsequently, the tooth profile and pitch measurement of the spiral bevel gear to be measured are all based on this measurement coordinate system, and if the gear needs to be processed later, this unified coordinate system is still used. This is because during offline measurement, the machining coordinate system is based on the machine tool's rotary axis, and the measurement coordinate system depends on the blank geometry. There is no rigid connection between the two, and the blank reference errors, including reference accuracy, blank deformation, uneven heat treatment, etc., will also cause the measurement coordinate system to be inconsistent with the machining coordinate system, thus affecting the tooth profile and pitch measurement accuracy in the grinding process of spiral bevel gears. In this application, the A-axis of the workpiece spindle of the spiral bevel gear machine tool is used as the reference to establish the measurement coordinate system, thereby separating the blank reference error.

[0033] The above-mentioned spiral bevel gear machine tool is a numerically controlled machine tool.

[0034] In some embodiments, the machine tool motion chain for measuring the standard ball is as Figure 8 shown, where S B is the standard ball coordinate system, and the standard ball coordinate system takes the center of the standard ball as the coordinate origin. d wx , d wy , d wz respectively represent the distances of the center of the standard ball relative to the center point of the end face of the A-axis of the machine tool in the X-axis, Y-axis, and Z-axis directions of the machine tool coordinate system.

[0035] The homogeneous coordinate transformation matrix from the machine tool coordinate system S F to the probe coordinate system S P can be expressed as: (1); where is the coordinate transformation matrix from the probe holder to the tip of the probe, is the coordinate transformation matrix from the C-axis to the probe holder, is the coordinate transformation matrix from the Y-axis to the C-axis, is the coordinate transformation matrix from the X-axis to the Y-axis, is the coordinate transformation matrix from the machine tool body to the X-axis, X is the machine tool X-axis coordinate, Y is the machine tool Y-axis coordinate, DZ represents the distance from the probe mounting surface to the XY plane of the machine tool coordinate system, Pb_long represents the distance from the center point of the probe to the probe mounting surface, ΔPb_X 、 ΔPb_Y are the offset amounts of the probe and the tool center point in the X and Y axis directions respectively.

[0036] The transformation matrix from the machine tool coordinate system S F to the standard ball coordinate system S B can be expressed as: (2); Among them, is the coordinate transformation matrix from the A-axis to the standard spherical coordinate system, is the coordinate transformation matrix from the Y-axis to the A-axis coordinate system, is the coordinate transformation matrix from the Z-axis to the Y-axis coordinate system, is the coordinate transformation matrix from the X-axis to the Z-axis coordinate system, is the coordinate transformation matrix from the Y-axis to the X-axis coordinate system, DX represents the position of the center point of the B-axis of the machine tool on the X-axis in the machine tool coordinate system, DY represents the position of the center point of the A-axis of the machine tool on the Y-axis in the machine tool coordinate system, Z represents the Z-axis coordinate of the machine tool, B represents the B-axis coordinate of the machine tool, and R2 represents the distance between the center point of the B-axis and the workpiece mounting end face in the same XZ plane.

[0037] In some embodiments, multiple accurate spherical center position information corresponding to multiple spherical center points is obtained. Among them, the accurate spherical center position information corresponding to each spherical center point is obtained through the following steps: Control the probe to randomly contact the surface of the standard sphere to obtain the position information of multiple random contact points located on the surface of the standard sphere, where the number of random contact points is greater than or equal to three; Based on the least squares method, according to the position information of multiple random contact points, obtain the rough spherical center position information of the standard sphere; Set multiple preset contact points located on the surface of the standard sphere, and plan a preset movement path for the probe to contact multiple preset contact points. Among them, the multiple preset contact points include multiple first preset contact points and one second preset contact point. The number of first preset contact points is greater than or equal to three. The multiple first preset contact points are in the same plane and the plane where they are located passes through the center of the standard sphere. The line connecting the second preset contact point and the center of the standard sphere is perpendicular to the plane where the multiple first preset contact points are located; According to the rough spherical center position information and the preset movement path, obtain the movement constraint equation that the probe needs to satisfy when moving along the preset movement path; Control the probe to move along the preset movement path and contact multiple preset contact points to obtain the position information of multiple preset contact points; Based on the least squares method, according to the position information of multiple preset contact points and the movement constraint equation, obtain the accurate spherical center position information of the standard sphere.

[0038] In this embodiment, by calculating the accurate spherical center position information again on the basis of obtaining the rough spherical center position information of the standard sphere, a more accurate spherical center position can be obtained.

[0039] The above control probe randomly contacts the surface of the standard ball to obtain the position information of multiple random touch points located on the surface of the standard ball. The control probe can be moved to make the probe randomly contact the surface of the standard ball. In some cases, the probe can also be moved by a handwheel to make the probe randomly contact the surface of the standard ball, and then record the position of each axis of the machine tool at this moment after each contact. ,( i = 1, 2, …, n , n > 3), that is n the coordinates of the random touch points in the machine tool coordinate system, as Figure 9 shown.

[0040] The rough coordinates of the midpoint of the end face of the A-axis of the machine tool are given in the machine tool factory inspection report, or the probe can be moved to the midpoint of the end face of the A-axis of the machine tool, and the machine tool reading is recorded, that is, the coordinate point in the machine tool coordinate system is (X AM , Y AM , Z AM ). Through coordinate transformation, the corresponding coordinates of each random touch point P i in the standard ball coordinate system S B (x B , y B , z B ) are calculated. This coordinate is the position information of the above-mentioned multiple random touch points. Among them, the coordinate transformation process is restricted by the following expression: (3); where can be obtained according to formula (2), can be obtained by inverse transformation according to formula (1) , d wx , d wy , d wz are unknowns, respectively representing the distances of the position of the center point of the standard ball relative to the center point of the end face of the A-axis of the machine tool in the X-axis, Y-axis, and Z-axis directions of the machine tool coordinate system, as Figure 8 shown.

[0041] The above-mentioned process of obtaining the rough center position information of the standard ball based on the least squares method according to the position information of multiple random touch points can be as follows.

[0042] Given the corresponding coordinates of P i in the standard ball coordinate system S B (x B , y B , z B ), since P iis a point on the equidistant surface of a standard sphere, so it satisfies the spherical equation and contains unknown position parameters d wx , d wy , d wz , that is, the position of the center of the standard sphere relative to the center point of the end face of the machine tool A-axis. Therefore, an optimization model can be established by the least squares method to initially calculate the position of the center of the standard sphere, that is, the rough center position information of the above standard sphere ( ), and the optimization model is restricted by the following expressions: (4); wherein, R in the formula b is the radius of the standard sphere, r m is the radius of the probe, P ix , P iy , P iz are the coordinate values in the standard spherical coordinate system corresponding to P i obtained according to formula (3).

[0043] The above-mentioned sets a plurality of preset touch points on the surface of the standard sphere, and plans a preset movement path for the probe to contact the plurality of preset touch points.

[0044] Specifically, as shown in FIG. 10, five preset touch points to be measured can be planned and set on the standard sphere. Specifically, the four intersection points a, b, c, and d of the standard sphere with the X-axis and Y-axis of the standard spherical coordinate system are set as the first preset touch points, and these four first preset touch points are all in the XY plane of the standard spherical coordinate system. The intersection point e of the standard sphere with the positive half-axis of the Z-axis is set as the second preset touch point, and the preset movement path is as Figure 10 shown, and the five preset touch points a, b, c, d, and e are measured in sequence.

[0045] The above-mentioned obtains the movement constraint equation that the probe needs to satisfy according to the rough center position information and the preset movement path; Control the probe to move according to the preset movement path and contact the plurality of preset touch points to obtain the position information of the plurality of preset touch points.

[0046] Specifically, since the plurality of preset touch points are self-preset, the corresponding coordinates of the theoretical positions of the plurality of preset touch points in the machine tool coordinate system can be obtained. It should be noted that when the plurality of preset touch points are on the X-axis, Y-axis, and Z-axis of the standard spherical coordinate system, it is easier to determine the corresponding coordinates of the theoretical positions.

[0047] Assume that in the standard spherical coordinate system, the corresponding coordinates of the preparation positions of the plurality of preset touch points are P bi , (i = 1, 2, 3, 4, 5), and the normal vector corresponding to each point is nbi , when measuring the standard ball, the positions of each axis of the machine tool can be calculated by the following movement constraint equations: (5); Where, d off_set is the offset distance, which is to avoid interference during the measurement process and failure to measure the ideal point to be measured due to the inaccuracy of the rough center position of the ball calculated previously ( ). Therefore, when planning the preparation position of the preset touch point, it is still necessary to offset a certain distance inward along its normal vector d off_set , o m = [0, 0, 0, 1] T represents the coordinates of the center point of the probe in the S p (x p , y p , z p ) coordinate system.

[0048] Substitute the coordinates P of the point to be measured bi and its unit normal vector n bi as well as the probe radius r m and the determined offset distance d off_set into Equation (5), and then combine it with Equation (3), the positions of each axis of the machine tool when the probe is located at the preparation positions of multiple preset touch points can be calculated, that is, the corresponding coordinates of the preparation positions of multiple preset touch points in the machine tool coordinate system are obtained. Subsequently, by controlling the positions of each axis of the machine tool, the probe can be controlled to move to the corresponding preparation positions.

[0049] According to the principle of in-machine measurement: in the machine tool coordinate system, when the coordinates of a certain point on the probe are the same as those of the measured point, it means that the center point of the probe is located at the position where the measured point is offset by the probe radius along its normal vector.

[0050] After calculating the corresponding coordinates of the theoretical positions and preparation positions of the center points of the probe for measuring multiple preset touch points in the machine tool coordinate system, for each preset touch point, by controlling the linkage of the X-axis, Y-axis, and Z-axis of the machine tool, the probe is made to approach the corresponding coordinates of the theoretical position along the normal direction of the point to be measured from the corresponding coordinates of the preparation position, and the measurement operation is performed on the preset touch point to be measured. That is, when the probe touches the standard ball during the approaching process, the actual measurement coordinates of the preset touch point are recorded, that is, the position information of the above-mentioned multiple preset touch points.

[0051] Based on the least squares method, according to the position information of multiple preset touch points and the movement constraint equations, the accurate center position information of the standard ball is obtained.

[0052] Specifically, after the actual measurement coordinates of multiple preset touch points, that is, the position information of the above-mentioned multiple preset touch points is measured, the measurement data is substituted into the above-mentioned movement constraint equation, that is, Equation (5), to obtain the corresponding coordinates of multiple preset touch points in the standard spherical coordinate system containing unknown position parameters d wx , d wy , d wz . Through the least squares method, an optimization model is established. The optimization model is constrained by Equation (4), and the unknown position parameters d wx , d wy , d wz are calculated and used to represent the position of the center of the standard sphere. Therefore, the position of the center of the standard sphere can be expressed as (d wx ,d wy ,d wz ) , that is, the accurate position information of the center of the above-mentioned standard sphere.

[0053] In some embodiments, according to the position information of multiple accurate sphere centers, the axis position information of the workpiece spindle is obtained, including: According to the position information of multiple accurate sphere centers, multiple sphere center points are fitted to obtain a first fitted circle, and the first center position information of the first fitted circle is determined; According to the position information of multiple accurate sphere centers and the first center position information of the first fitted circle, a deviation matrix is obtained, where the deviation matrix characterizes the position deviation of multiple accurate sphere center positions relative to the first center position information of the first fitted circle; Calculate the covariance matrix of the deviation matrix and obtain the eigenvector corresponding to the minimum eigenvalue of the covariance matrix; According to the eigenvector, determine the direction information of the axis of the workpiece spindle; According to the eigenvector, determine the plane where the fitted circle is located and select two orthogonal basis vectors in the plane; According to the two orthogonal basis vectors, project multiple sphere center points onto the plane where the fitted circle is located to obtain multiple two-dimensional coordinate information corresponding to the multiple sphere center points; Based on the least squares method, according to the multiple two-dimensional coordinate information corresponding to the multiple sphere center points, the multiple sphere center points are fitted to obtain a second fitted circle, and the second center position information of the second fitted circle is determined; According to the second center position information of the second fitted circle and the direction information of the axis of the workpiece spindle, the axis position information of the axis of the workpiece spindle is obtained.

[0054] In this embodiment, the axial position information of the axis of the workpiece spindle A can be accurately determined.

[0055] Based on the above-mentioned multiple accurate sphere center position information, multiple sphere center points are fitted to obtain a first fitted circle, and the first center position information of the first fitted circle is determined.

[0056] Specifically, the accurate sphere center coordinates of the standard sphere obtained in the previous step (d wx ,d wy ,d wz ) After that, it rotates α° around the axis of the A axis, repeats the measurement step, and obtains the second accurate sphere center coordinates (d wx2 ,d wy2 ,d wz2 ) , and so on to obtain (d wxi ,d wyi ,d wzi ) , ( i = 1, 2, …, n , n > 3), that is, the above-mentioned multiple accurate sphere center position information is obtained, as Figure 11 shown.

[0057] Suppose the accurate sphere center coordinates of multiple standard spheres of the A axis measured at n different angles in the previous step are: (6); Then the coordinates of the first center O1 of the first fitted circle fitted by these points are (7); Based on the above-mentioned multiple accurate sphere center position information and the first center position information of the first fitted circle, a deviation matrix is obtained.

[0058] Specifically, the deviation matrix B calculated for each accurate sphere center coordinate point relative to the coordinates of the first center O1 is: (8); Calculate the covariance matrix of the above-mentioned deviation matrix, and obtain the eigenvector corresponding to the minimum eigenvalue of the covariance matrix; based on the eigenvector, determine the direction information of the axis of the workpiece spindle.

[0059] Specifically, the covariance matrix M is: (9); When the A-axis rotates, the trajectory of the standard ball center is approximately a circle in a plane, and the variance of the data points along the plane normal direction (i.e., the A-axis axis direction) is the smallest. Therefore, the eigenvalues of the covariance matrix M are solved. λ 1 ,λ 2 ,λ 3 and the corresponding unit eigenvectors ν 1 ,ν 2 , ν 3. The eigenvector corresponding to the smallest eigenvalue ν=(a,b,c) is the axis direction.

[0060] Based on the eigenvector, determine the plane where the fitting circle is located, and select two orthogonal basis vectors in the plane; according to the two orthogonal basis vectors, project multiple ball center points onto the plane where the fitting circle is located to obtain multiple two-dimensional coordinate information corresponding to the multiple ball center points.

[0061] Specifically, the plane equation where the standard ball center trajectory is located can be obtained as: (10); Select two orthogonal basis vectors in the plane , Project each point onto this plane to obtain the two-dimensional coordinates ( , ): ; Based on the least squares method, according to the multiple two-dimensional coordinate information corresponding to multiple ball center points, fit the multiple ball center points to obtain a second fitting circle, and determine the second center position information of the second fitting circle; according to the second center position information of the second fitting circle and the direction information of the axis of the workpiece spindle, obtain the axis position information of the axis of the workpiece spindle.

[0062] Specifically, use the least squares method to fit a two-dimensional circle to obtain the center O2(u c ,v c ), and the radius r.

[0063] (11); Finally, obtain the actual position of the A-axis, that is, the straight line passing through the center O2 and in the direction of v, expressed as: (12); That is, obtain the axis position information of the axis of the workpiece spindle.

[0064] In some embodiments, based on the axis position information, establish a measurement coordinate system for the spiral bevel gear machine tool, including: According to the axis position information, determine the Z-axis of the measurement coordinate system; The control probe randomly contacts the end face of the workpiece spindle to obtain the position information of a plurality of randomly located plane contact points on the end face of the workpiece spindle, where the number of randomly located plane contact points is greater than or equal to three; Based on the position information of the plurality of randomly located plane contact points, the end plane position information of the end face of the workpiece spindle is obtained; Based on the end plane position information, the blank height of the spiral bevel gear to be measured, and the mounting distance, the XY plane of the measurement coordinate system is determined. Based on the determined Z axis and XY plane, the origin O of the measurement coordinate system is determined; The control probe contacts the middle area of the tooth surface of the spiral bevel gear to obtain the position information of the rough tooth surface midpoint located in the middle area of the tooth surface; Based on the position information of the rough tooth surface midpoint, the rough X axis of the measurement coordinate system passing through the rough tooth surface midpoint and the origin O is determined; Based on the determined Z axis, origin O, and rough X axis, the rough measurement coordinate system is obtained; Based on the tooth surface equation of the spiral bevel gear, the first theoretical tooth surface midpoint coordinates and the unit normal vector corresponding to a tooth surface midpoint of the spiral bevel gear to be measured are obtained; Based on the rough measurement coordinate system, the control probe contacts the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, and the rough tooth surface midpoint coordinates in the rough measurement coordinate system are obtained. By comparing the rough tooth surface midpoint coordinates with the first theoretical tooth surface midpoint coordinates, the rough measurement coordinate system is continuously corrected to obtain the measurement coordinate system.

[0065] In this embodiment, establishing a measurement coordinate system based on the axis position information of the A axis can achieve the unity of the coordinate systems used in the measurement and machining processes. At the same time, by first establishing a rough coordinate system and then continuously correcting it, a more accurate measurement coordinate system can be obtained. The established measurement coordinate system is as Figure 12 shown.

[0066] In some embodiments, establishing the measurement coordinate system of a spiral bevel gear machine tool includes the following steps.

[0067] The first step is to determine the actual position of the A axis as the Z WCS axis of the gear measurement coordinate system. At this time, the coordinate origin O of the measurement coordinate system WCS is obtained w in the x coordinate O wx and y coordinate O wy of the machine tool, as well as the direction of Z WCS , but the O wz , as well as the directions of X WCS and Y WCS still need to be further determined. The second step is to determine the coordinate O wz of the measurement coordinate system origin. Z WCSAfter the axis direction is determined, control the probe to measure at least 3 points on the end face of the workpiece spindle. Take the average value of the z coordinates of these points and add the blank height and the mounting distance h caused by the clamping of the spiral bevel gear to obtain the position O of the XY plane of the measurement coordinate system in the machine tool coordinate system. wz , combined with the measurement coordinate system Z WCS axis direction and position determined in the previous step, the origin O w of the measurement coordinate system can be determined. In addition, the position O of the XY plane of the measurement coordinate system in the machine tool coordinate system can also be obtained by directly controlling the probe to measure at least 3 points on the top plane of the teeth of the spiral bevel gear to be measured and taking the average value of the z coordinates of these points. wz .

[0068] The third step is the preliminary establishment of the X WCS axis of the measurement coordinate system. By controlling the probe to touch the midpoint area of the tooth surface, capture the spatial coordinates of the tooth surface midpoint P 5,3 ([[]] x p5,3 , y p5,3 , z p5,3 ). The position of the machine tool A axis and the position of the reference plane have been determined previously. Here, it is the coordinate of the feature point relative to the axis of the machine tool A axis. The directions of the X, Y, and Z axes are still the X, Y, and Z axes in the machine tool coordinate system, but the coordinate origin becomes the intersection of the machine tool A axis and the reference plane. Since the X WCS axis of the measurement coordinate system should pass through the tooth surface midpoint and the coordinate origin O WCS simultaneously, the angle β between the X WCS axis of the measurement coordinate system and the X axis of the machine tool can be calculated based on the measured point coordinates: (13); Therefore, rotating the X axis in the machine tool coordinate system by the angle β can determine the X WCS axis of the measurement coordinate system, and then using the right-hand rule can determine the direction of the Y WCS axis of the measurement coordinate system. After determining the position of the origin O WCS of the measurement coordinate system, the direction of the X WCS axis, the direction of the Y WCS axis, and the direction of the Z WCS axis, the measurement coordinate system is preliminarily aligned. It should be noted that since the accuracy of the tooth surface midpoint coordinates captured in this step is relatively general, only a rough X WCS axis can be initially determined.

[0069] It should be noted that generally 5×9 tooth surface points are evenly discretized in the working area of the spiral bevel gear tooth surface to obtain a total of 45 tooth surface points in 5 rows and 9 columns. As Figure 14 shown, where (5, 3) is the tooth surface midpoint.

[0070] The fourth step is the precise establishment of the X WCS axis. For the systematic errors existing in the initial positioning, an iterative optimization algorithm is adopted for compensation and correction. This process gradually reduces the coordinate system deviation by repeatedly comparing the measured coordinates and the theoretical coordinate data of the center point of the tooth surface. The specific iterative process is as Figure 13 shown. Through multiple rounds of data collection and parameter correction, the high-precision alignment of the X WCS axis is realized, and finally the measurement coordinate system is precisely established.

[0071] In some embodiments, as Figure 13 shown, based on the rough measurement coordinate system, the probe is controlled to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, and the rough tooth surface midpoint coordinates in the rough measurement coordinate system are obtained. By comparing the rough tooth surface midpoint coordinates with the first theoretical tooth surface midpoint coordinates, the rough measurement coordinate system is continuously corrected to obtain the measurement coordinate system, including: Based on the rough measurement coordinate system, the probe is controlled to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector, and the rough tooth surface midpoint coordinates in the rough measurement coordinate system are obtained; According to the rough tooth surface midpoint coordinates, the first radius is determined, where the first radius is the distance between the rough tooth surface midpoint corresponding to the rough tooth surface midpoint coordinates and the workpiece spindle; The absolute value of the difference between the first radius and the theoretical radius is obtained, where the theoretical radius is the distance between the first theoretical tooth surface midpoint and the workpiece spindle, and the theoretical radius is determined according to the first theoretical tooth surface midpoint coordinates; When the absolute value is greater than the preset precision value, the current rough measurement coordinate system is rotated by an adjustment angle around the workpiece spindle to obtain an updated rough measurement coordinate system, and then it jumps to the step of controlling the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector based on the rough measurement coordinate system to obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system; When the absolute value is less than the preset precision value, the current rough measurement coordinate system is determined as the measurement coordinate system.

[0072] In this embodiment, by repeatedly adjusting the rotation adjustment angle of the current rough measurement coordinate system around the workpiece spindle until the accuracy requirement is met, a measurement coordinate system with higher accuracy can be obtained.

[0073] Since the tooth surface equation of the spiral bevel gear is known, the theoretical coordinates of the center point of the tooth surface P 5,3 in the ideal measurement coordinate system and the unit normal vector of this point can be obtained n 5,3 , and along n 5,3 the contact point P 5,3, output the measurement result PM 5,3 = ([[]]END] x m5,3 , y m5,3 , z m5,3 ), and at this time the radius of this point is: (14); The intersection angle with the X WCS axis β k is obtained from the following formula: (15); Subsequently, the radius of the measurement point R M5,3 is compared with the theoretical radius R 5,3 . If the set accuracy ε requirement is not met, the current coordinate system is rotated around the Z WCS axis by β k , and then the midpoint of the tooth surface is re-measured in the rotated measurement coordinate system. Repeat the above process until | R M5,3 - R 5,3 | meets the accuracy requirement, then the current coordinate system is used as the final measurement coordinate system, and subsequent in-machine measurements are all based on the data of this measurement coordinate system.

[0074] In some embodiments, the tooth profile data to be measured includes the measured tooth surface coordinates of multiple tooth surface points of the spiral bevel gear to be measured. Obtaining the tooth profile data of the spiral bevel gear to be measured includes: Based on the measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured, and measure the measured tooth surface coordinates of multiple tooth surface points; According to the tooth profile data to be measured, obtain the tooth profile error of the spiral bevel gear to be measured, including: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, obtain the theoretical tooth surface coordinates of multiple tooth surface points of the spiral bevel gear to be measured; According to the theoretical tooth surface coordinates and measured tooth surface coordinates of multiple tooth surface points, obtain the tooth profile error.

[0075] In this embodiment, tooth profile data is measured based on the established measurement coordinate system, and the tooth profile error is obtained, which is convenient for subsequent accurate machining based on the unified coordinate system on the basis of this data.

[0076] The above-mentioned multiple tooth surface points can be 45 tooth surface points that are evenly discretized in the working area of the tooth surface of the spiral bevel gear obtained by the projection method. Among them, (5, 3) is the midpoint of the tooth surface, such as Figure 14As shown, for these 45 tooth surface points, the theoretical tooth surface coordinates of each tooth surface point can be calculated according to the tooth surface equation of the spiral bevel gear, and then by controlling the probe to measure these 45 tooth surface points in sequence along the tooth profile error measurement path as shown in Figure 15 the measured tooth surface coordinates of each tooth surface point can be obtained. By subtracting the theoretical tooth surface points from the measured tooth surface points of each tooth surface point, the tooth surface error of each tooth surface point can be obtained.

[0077] The tooth profile error of the spiral bevel gear is reflected by the difference surface. Select the tooth surface midpoint (5, 3) as the reference point, assuming that the tooth surface error of this point is 0. Subtracting the tooth surface error of the tooth surface midpoint from the errors of the other points, the relative tooth surface error of each tooth surface point can be obtained. The difference surface can be made through the relative tooth surface error, as shown in the following formula: (16); It should be noted that during the measurement of the tooth profile, generally multiple tooth surfaces at equal intervals can be selected, and the tooth profile error can be obtained according to the 45 tooth surface points on each tooth surface. Specifically, four tooth surfaces can be selected for tooth profile measurement.

[0078] In some embodiments, the to-be-measured pitch data includes multiple individual pitches and cumulative pitches of the to-be-measured spiral bevel gear, and the pitch error includes individual pitch error and cumulative pitch error; The multiple individual pitches include the individual pitches between all adjacent tooth surfaces. Obtaining the to-be-measured pitch data of the to-be-measured spiral bevel gear includes: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, obtaining the second theoretical tooth surface midpoint coordinates corresponding to a tooth surface midpoint of the to-be-measured spiral bevel gear; Executing a pitch measurement strategy according to the second theoretical tooth surface midpoint coordinates to obtain multiple individual pitches; Among them, the pitch measurement strategy includes: Making the probe be between the Nth group of adjacent tooth surfaces of the to-be-measured spiral bevel gear; Controlling the probe to be located at the second theoretical tooth surface midpoint coordinates; Controlling the to-be-measured spiral bevel gear to rotate around the first direction so that the left tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the left rotation angle value between the Nth group of adjacent tooth surfaces; Controlling the to-be-measured spiral bevel gear to rotate around the second direction so that the right tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the right rotation angle value between the Nth group of adjacent tooth surfaces; Obtaining the individual pitch corresponding to the Nth group of adjacent tooth surfaces according to the left rotation angle value and the right rotation angle value, and assigning N + 1 to N; In the case of not obtaining the individual pitch errors between all adjacent tooth surfaces, jumping to making the probe be between the Nth group of adjacent tooth surfaces of the to-be-measured spiral bevel gear; According to the pitch data to be measured, the pitch error of the spiral bevel gear to be measured is obtained, including: According to the theoretical pitch and multiple individual pitches of the spiral bevel gear to be measured, multiple individual pitch errors corresponding to the multiple individual pitches are obtained; Sum the multiple individual pitch errors to obtain the cumulative pitch error.

[0079] In this embodiment, the pitch data is measured based on the established measurement coordinate system, and the pitch error is obtained, which is convenient for subsequent accurate machining based on the unified coordinate system on the basis of this data.

[0080] The rotation directions of the above-mentioned first direction and the second direction are opposite. Specifically, the rotation around the first direction can be counterclockwise rotation, and the rotation around the second direction can be clockwise rotation.

[0081] The difference between the measured value and the theoretical value reflects the actual pitch error. The individual pitch deviation can be expressed as: (17); Wherein, A sta represents the theoretical angular difference between adjacent tooth surfaces, and the value is equal to the central angle corresponding to a single tooth, A N1 and A N2 represent the left rotation angle value and the right rotation angle value between the Nth group of adjacent tooth surfaces, R p represents the pitch radius at the measurement point, and N is less than or equal to Z, where Z is the number of teeth of the spiral bevel gear to be measured. Summing the individual pitch errors can obtain the cumulative pitch error, as shown below: (18); The pitch error of the spiral bevel gear to be measured can be obtained.

[0082] In some embodiments, for the spiral bevel gear that has completed one gear grinding process, the tooth profile pitch data is measured based on the measurement coordinate system, and then the tooth surface error and the pitch error are obtained. Then, based on this measurement coordinate system, the spiral bevel gear is subjected to a second gear grinding process. Therefore, the entire machining process of the spiral bevel gear does not require repeated disassembly and assembly, the installation error is separated, and the measurement and machining processes use the same coordinate system, separating the tooth blank reference error. Finally, the required high-precision spiral bevel gear can be machined to meet the machining accuracy requirements.

[0083] The method for measuring the tooth profile and pitch of a spiral bevel gear provided by an embodiment of the present application may be executed by a spiral bevel gear tooth profile and pitch measuring device 200. In the embodiments of the present application, taking the spiral bevel gear tooth profile and pitch measuring device 200 as an example of executing the spiral bevel gear tooth profile and pitch measuring method, the spiral bevel gear tooth profile and pitch measuring device 200 provided by the embodiments of the present application will be described.

[0084] Please refer to Figure 16 , which is a schematic structural diagram of a spiral bevel gear tooth profile and pitch measuring device 200 provided by an embodiment of the present application. As Figure 16 shown, the spiral bevel gear tooth profile and pitch measuring device 200 includes: An acquisition module 201, configured to acquire the to-be-measured tooth profile data and to-be-measured pitch data of a to-be-measured spiral bevel gear, wherein the to-be-measured spiral bevel gear is clamped on the end face of the workpiece spindle of a spiral bevel gear machine tool, and the to-be-measured tooth profile data and to-be-measured pitch data are measured by a probe of the spiral bevel gear machine tool based on a pre-constructed measurement coordinate system; A first obtaining module 202, configured to obtain the tooth profile error of the to-be-measured spiral bevel gear according to the to-be-measured tooth profile data; A second obtaining module 203, configured to obtain the pitch error of the to-be-measured spiral bevel gear according to the to-be-measured pitch data; Among them, the measurement coordinate system is obtained through the following steps: Obtain a plurality of accurate ball center position information corresponding to a plurality of ball center points. The plurality of ball center points are the ball centers of a standard ball in different spatial positions. The number of ball center points is greater than or equal to three. The standard ball is arranged on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the workpiece spindle is used to rotate the standard ball to different spatial positions; According to the plurality of accurate ball center position information, obtain the axis position information of the axis of the workpiece spindle; Based on the axis position information, establish a measurement coordinate system of the spiral bevel gear machine tool, wherein the measurement coordinate system takes the plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

[0085] In some embodiments, the acquisition module 201 may be configured to: Control the probe to randomly contact the surface of the standard ball to obtain the position information of a plurality of random contact points located on the surface of the standard ball, wherein the number of random contact points is greater than or equal to three; Based on the least squares method, obtain the rough ball center position information of the standard ball according to the position information of the plurality of random contact points; Set a plurality of preset touch points on the surface of a standard sphere, and plan a preset movement path for the probe to contact the plurality of preset touch points. Among them, the plurality of preset touch points include a plurality of first preset touch points and a second preset touch point. The number of the first preset touch points is greater than or equal to three. The plurality of first preset touch points are in the same plane and the plane where they are located passes through the center of the standard sphere. The line connecting the second preset touch point and the center of the standard sphere is perpendicular to the plane where the plurality of first preset touch points are located; According to the rough center position information of the sphere and the preset movement path, obtain the movement constraint equation that the probe needs to satisfy when moving along the preset movement path; Control the probe to move along the preset movement path and contact the plurality of preset touch points to obtain the position information of the plurality of preset touch points; Based on the least squares method, according to the position information of the plurality of preset touch points and the movement constraint equation, obtain the accurate center position information of the standard sphere.

[0086] In some embodiments, the acquisition module 201 can be used for: According to a plurality of accurate center position information of the sphere, fit a plurality of center points of the sphere to obtain a first fitting circle, and determine the first center position information of the first fitting circle; According to a plurality of accurate center position information of the sphere and the first center position information of the first fitting circle, obtain a deviation matrix, where the deviation matrix characterizes the position deviation of the plurality of accurate center position information of the sphere relative to the first center position information of the first fitting circle; Calculate the covariance matrix of the deviation matrix, and obtain the eigenvector corresponding to the minimum eigenvalue of the covariance matrix; According to the eigenvector, determine the direction information of the axis of the workpiece spindle; According to the eigenvector, determine the plane where the fitting circle is located, and select two orthogonal basis vectors in the plane where it is located; According to the two orthogonal basis vectors, project a plurality of center points of the sphere onto the plane where the fitting circle is located to obtain a plurality of two-dimensional coordinate information corresponding to the plurality of center points of the sphere; Based on the least squares method, according to a plurality of two-dimensional coordinate information corresponding to a plurality of center points of the sphere, fit a plurality of center points of the sphere to obtain a second fitting circle, and determine the second center position information of the second fitting circle; According to the second center position information of the second fitting circle and the direction information of the axis of the workpiece spindle, obtain the axis position information of the axis of the workpiece spindle.

[0087] In some embodiments, the acquisition module 201 can be used for: According to the axis position information, determine the Z axis of the measurement coordinate system; Control the probe to randomly contact the end face of the workpiece spindle to obtain the position information of multiple random plane contact points located on the end face of the workpiece spindle, where the number of random plane contact points is greater than or equal to three; Obtain the end plane position information of the end face of the workpiece spindle according to the position information of multiple random plane contact points; Determine the XY plane of the measurement coordinate system according to the end plane position information, the blank height and the mounting distance of the spiral bevel gear to be measured. Determine the origin O of the measurement coordinate system according to the determined Z axis and XY plane; Control the probe to contact the middle area of the tooth surface of the spiral bevel gear to obtain the position information of the rough tooth surface midpoint located in the middle area of the tooth surface; Determine the rough X axis of the measurement coordinate system passing through the rough tooth surface midpoint and the origin O according to the position information of the rough tooth surface midpoint; Obtain the rough measurement coordinate system according to the determined Z axis, origin O and rough X axis; Based on the tooth surface equation of the spiral bevel gear, obtain the first theoretical tooth surface midpoint coordinate and the unit normal vector corresponding to a tooth surface midpoint of the spiral bevel gear to be measured; Based on the rough measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinate in the rough measurement coordinate system. By comparing the rough tooth surface midpoint coordinate and the first theoretical tooth surface midpoint coordinate, continuously correct the rough measurement coordinate system to obtain the measurement coordinate system.

[0088] In some embodiments, the acquisition module 201 can be used for: Based on the rough measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinate in the rough measurement coordinate system; Determine the first radius according to the rough tooth surface midpoint coordinate, where the first radius is the distance between the rough tooth surface midpoint corresponding to the rough tooth surface midpoint coordinate and the workpiece spindle; Obtain the absolute value of the difference between the first radius and the theoretical radius, where the theoretical radius is the distance between the first theoretical tooth surface midpoint and the workpiece spindle, and the theoretical radius is determined according to the first theoretical tooth surface midpoint coordinate; When the absolute value is greater than the preset precision value, rotate and adjust the current rough measurement coordinate system by an angle around the workpiece spindle to obtain the updated rough measurement coordinate system, and jump to control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector based on the rough measurement coordinate system to obtain the rough tooth surface midpoint coordinate in the rough measurement coordinate system; When the absolute value is less than the preset precision value, determine the current rough measurement coordinate system as the measurement coordinate system.

[0089] In some embodiments, the to-be-measured tooth profile data includes the measured tooth surface coordinates of multiple tooth surface points of the to-be-measured spiral bevel gear. The acquisition module 201 can be used for: Based on the measurement coordinate system, control the probe to contact the tooth surface of the to-be-measured spiral bevel gear, and measure the measured tooth surface coordinates of multiple tooth surface points; The first obtaining module 202 can be used for: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, obtain the theoretical tooth surface coordinates of multiple tooth surface points of the to-be-measured spiral bevel gear; According to the theoretical tooth surface coordinates and the measured tooth surface coordinates of multiple tooth surface points, obtain the tooth profile error.

[0090] In some embodiments, the to-be-measured tooth pitch data includes multiple individual tooth pitches and cumulative tooth pitches of the to-be-measured spiral bevel gear, and the tooth pitch error includes individual tooth pitch error and cumulative tooth pitch error; The acquisition module 201 can be used for: Based on the measurement coordinate system, according to the tooth surface equation of the spiral bevel gear, obtain the second theoretical tooth surface midpoint coordinates corresponding to a tooth surface midpoint of the to-be-measured spiral bevel gear; Execute a tooth pitch measurement strategy according to the second theoretical tooth surface midpoint coordinates to obtain multiple individual tooth pitches; Among them, the tooth pitch measurement strategy includes: Make the probe be between the Nth group of adjacent two tooth surfaces of the to-be-measured spiral bevel gear; Control the probe to be located at the second theoretical tooth surface midpoint coordinates; Control the to-be-measured spiral bevel gear to rotate around the first direction, so that the left tooth surface of the Nth group of adjacent two tooth surfaces contacts the probe, in order to obtain the left rotation angle value between the Nth group of adjacent two tooth surfaces; Control the to-be-measured spiral bevel gear to rotate around the second direction, so that the right tooth surface of the Nth group of adjacent two tooth surfaces contacts the probe, in order to obtain the right rotation angle value between the Nth group of adjacent two tooth surfaces; Obtain the individual tooth pitch corresponding to the Nth group of adjacent two tooth surfaces according to the left rotation angle value and the right rotation angle value, and assign N + 1 to N; In the case where the individual tooth pitch errors between all adjacent two tooth surfaces have not been obtained, jump to make the probe be between the Nth group of adjacent two tooth surfaces of the to-be-measured spiral bevel gear; The second obtaining module 203 can be used for: According to the theoretical tooth pitch of the to-be-measured spiral bevel gear and multiple individual tooth pitches, obtain multiple individual tooth pitch errors corresponding to the multiple individual tooth pitches; Sum the multiple individual tooth pitch errors to obtain the cumulative tooth pitch error.

[0091] Since the spiral bevel gear tooth profile and pitch measuring device 200 adopts all the technical solutions of the spiral bevel gear tooth profile and pitch measuring method of the above embodiment, it has at least all the beneficial effects brought by the technical solutions of the above embodiment, and will not be elaborated here.

[0092] Figure 17 The figure is a schematic hardware structure diagram of an electronic device provided by an embodiment of the present application.

[0093] This electronic device may include a processor 301 and a memory 302 storing computer program instructions.

[0094] Specifically, the above-mentioned processor 301 may include a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0095] The memory 302 may include a mass storage for data or instructions. By way of example and not limitation, the memory 302 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disc, a magneto-optical disc, a magnetic tape, or a universal serial bus (USB) drive, or a combination of two or more of these. In a suitable case, the memory 302 may include a removable or non-removable (or fixed) medium. In a suitable case, the memory 302 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, the memory 302 is a non-volatile solid state memory.

[0096] In some embodiments, the memory 302 may include a read only memory (ROM), a random access memory (RAM), a magnetic disk storage media device, an optical storage media device, a flash memory device, an electrical, optical, or other physical / tangible memory storage device. Thus, in general, the 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 in reference to the method according to one aspect of the present disclosure.

[0097] The processor 301 reads and executes the computer program instructions stored in the memory 302 to implement any one of the spiral bevel gear tooth profile and pitch measuring methods in the above embodiments.

[0098] In one example, the electronic device may further include a communication interface 303 and a bus 310. Among them, as Figure 17As shown, a processor 301, a memory 302, and a communication interface 303 are connected via a bus 310 and complete communication with each other.

[0099] The communication interface 303 is mainly used to implement communication between various modules, devices, units, and / or apparatuses in the embodiments of the present application.

[0100] The bus 310 includes hardware, software, or both, and couples the components of the online data flow metering device to each other. By way of example and not limitation, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Extended Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an InfiniBand 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 a combination of two or more of these. In a suitable case, the bus 310 may include one or more buses. Although the embodiments of the present application describe and illustrate specific buses, the present application contemplates any suitable bus or interconnect.

[0101] The electronic device can execute the spiral bevel gear tooth profile and pitch measurement method in the embodiments of the present application, thereby implementing the combination Figure 1 and Figure 16 the spiral bevel gear tooth profile and pitch measurement method and apparatus described.

[0102] In addition, in combination with the spiral bevel gear tooth profile and pitch measurement method in the above embodiments, the embodiments of the present application can be implemented by providing a computer storage medium. Computer program instructions are stored on the computer storage medium; when the computer program instructions are executed by a processor, any one of the spiral bevel gear tooth profile and pitch measurement methods in the above embodiments is implemented.

[0103] It should be clear that the present 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 illustrated as examples. However, the method process of the present application is not limited to the specific steps described and illustrated, and those skilled in the art can make various changes, modifications, and additions, or change the order between steps after understanding the spirit of the present application.

[0104] The functional blocks shown in the above-described structural block diagrams can be implemented as hardware, software, firmware, or a combination thereof. When implemented in hardware, it can be an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a functional card, and so on. When implemented in software, the elements of the present application are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium or transmitted via a data signal carried in a carrier wave over a transmission medium or a communication link. A "machine-readable medium" can include any medium that can store or transmit information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical discs, hard disks, fiber optic media, radio frequency (RF) links, and so on. The code segment can be downloaded via a computer network such as the Internet, an intranet, and so on.

[0105] It should also be noted that the exemplary embodiments mentioned in the present application describe some methods or systems based on a series of steps or devices. However, the present application is not limited to the order of the above steps, that is, the steps can be executed in the order mentioned in the embodiments, can be different from the order in the embodiments, or several steps can be executed simultaneously.

[0106] Aspects of the present disclosure have been described above with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It should be understood that each block in the flowcharts and / or block diagrams, and the combinations of blocks in the flowcharts 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 device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device enable the implementation of the functions / actions specified in one or more blocks of the flowcharts 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 should also be understood that each block in the block diagrams and / or flowcharts, and the combinations of blocks in the block diagrams and / or flowcharts, can also be implemented by dedicated hardware that performs the specified functions or actions, or by a combination of dedicated hardware and computer instructions.

[0107] As described above, this is only the specific implementation manner of the present application. Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, modules, and units described above can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated herein. It should be understood that the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present application.

Claims

1. A method for measuring the tooth profile and pitch of spiral bevel gears, characterized in that, Including: Obtaining the to-be-measured tooth profile data and to-be-measured pitch data of the spiral bevel gear to be measured, wherein the spiral bevel gear to be measured is clamped on the end face of the workpiece spindle of the spiral bevel gear machine tool, and the to-be-measured tooth profile data and the to-be-measured pitch data are measured by the probe of the spiral bevel gear machine tool based on a pre-constructed measurement coordinate system; Obtaining the tooth profile error of the spiral bevel gear to be measured according to the to-be-measured tooth profile data; Obtaining the pitch error of the spiral bevel gear to be measured according to the to-be-measured pitch data; Wherein, the measurement coordinate system is obtained through the following steps: Obtaining multiple accurate ball center position information corresponding to multiple ball center points, the multiple ball center points being the ball centers of the standard ball in different spatial positions, the number of the ball center points being greater than or equal to three, the standard ball being arranged on the end face of the workpiece spindle, and the workpiece spindle being used to rotate the standard ball to different spatial positions; Obtaining the axis position information of the axis of the workpiece spindle according to the multiple accurate ball center position information; Based on the axis position information, establishing the measurement coordinate system of the spiral bevel gear machine tool, wherein the measurement coordinate system takes the plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

2. The method for measuring the tooth profile and pitch of spiral bevel gears according to claim 1, characterized in that The obtaining multiple accurate ball center position information corresponding to multiple ball center points, wherein the accurate ball center position information corresponding to each ball center point is obtained through the following steps: Controlling the probe to randomly contact the surface of the standard ball to obtain the position information of multiple random contact points located on the surface of the standard ball, wherein the number of the random contact points is greater than or equal to three; Based on the least squares method, obtaining the rough ball center position information of the standard ball according to the position information of the multiple random contact points; Setting multiple preset contact points on the surface of the standard ball and planning a preset movement path for the probe to contact the multiple preset contact points, wherein the multiple preset contact points include multiple first preset contact points and one second preset contact point, the number of the first preset contact points being greater than or equal to three, the multiple first preset contact points being in the same plane and the plane passing through the ball center of the standard ball, and the connection line between the second preset contact point and the ball center of the standard ball being perpendicular to the plane where the multiple first preset contact points are located; Obtaining the movement constraint equation that the probe needs to satisfy when moving according to the preset movement path according to the rough ball center position information and the preset movement path; Controlling the probe to move according to the preset movement path and contact the multiple preset contact points to obtain the position information of the multiple preset contact points; Based on the least squares method, obtaining the accurate ball center position information of the standard ball according to the position information of the multiple preset contact points and the movement constraint equation.

3. The method for measuring the tooth profile and pitch of spiral bevel gears according to claim 1, characterized in that The obtaining the axis position information of the axis of the workpiece spindle according to the multiple accurate ball center position information includes: Fitting the multiple ball center points according to the multiple accurate ball center position information to obtain a first fitted circle and determining the first center position information of the first fitted circle; A deviation matrix is obtained based on the multiple accurate ball center position information and the first center position information of the first fitted circle, where the deviation matrix characterizes the position deviation of the multiple accurate ball center position information relative to the first center position information of the first fitted circle; Calculate the covariance matrix of the deviation matrix and obtain the eigenvector corresponding to the minimum eigenvalue of the covariance matrix; Determine the direction information of the axis of the workpiece spindle according to the eigenvector; Determine the plane where the fitted circle is located according to the eigenvector and select two orthogonal basis vectors in the plane; Project the multiple ball center points onto the plane where the fitted circle is located according to the two orthogonal basis vectors to obtain multiple two-dimensional coordinate information corresponding to the multiple ball center points; Based on the least squares method, fit the multiple ball center points according to the multiple two-dimensional coordinate information corresponding to the multiple ball center points to obtain a second fitted circle and determine the second center position information of the second fitted circle; Obtain the axis position information of the axis of the workpiece spindle according to the second center position information of the second fitted circle and the direction information of the axis of the workpiece spindle; 4. The method for measuring the tooth profile and pitch of a spiral bevel gear according to claim 1, wherein Establishing the measurement coordinate system of the spiral bevel gear machine tool based on the axis position information includes: Determine the Z-axis of the measurement coordinate system according to the axis position information; Control the probe to randomly contact the end face of the workpiece spindle to obtain the position information of multiple random plane contact points located on the end face of the workpiece spindle, where the number of the random plane contact points is greater than or equal to three; Obtain the end plane position information of the end face of the workpiece spindle according to the position information of the multiple random plane contact points; Determine the XY plane of the measurement coordinate system according to the end plane position information, the blank height and the mounting distance of the spiral bevel gear to be measured, and determine the origin O of the measurement coordinate system according to the determined Z-axis and the XY plane; Control the probe to contact the middle area of the tooth surface of the spiral bevel gear to obtain the position information of the rough tooth surface midpoint located in the middle area of the tooth surface; Determine the rough X-axis of the measurement coordinate system passing through the rough tooth surface midpoint and the origin O according to the position information of the rough tooth surface midpoint; Obtain the rough measurement coordinate system according to the determined Z-axis, the origin O and the rough X-axis; Based on the tooth surface equation of the spiral bevel gear, obtain the first theoretical tooth surface midpoint coordinate and the unit normal vector corresponding to a tooth surface midpoint of the spiral bevel gear to be measured; Based on the rough measurement coordinate system, control the probe to contact the tooth surface of the spiral bevel gear to be measured along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinate in the rough measurement coordinate system. By comparing the rough tooth surface midpoint coordinate and the first theoretical tooth surface midpoint coordinate, continuously correct the rough measurement coordinate system to obtain the measurement coordinate system.

5. The method for measuring the tooth profile and pitch of spiral bevel gears according to claim 4, characterized in that Based on the rough measurement coordinate system, controlling the probe to contact the tooth surface of the to-be-measured spiral bevel gear along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system, and continuously correcting the rough measurement coordinate system by comparing the rough tooth surface midpoint coordinates with the first theoretical tooth surface midpoint coordinates to obtain the measurement coordinate system, including: Based on the rough measurement coordinate system, controlling the probe to contact the tooth surface of the to-be-measured spiral bevel gear along the direction of the unit normal vector to obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system; Determining a first radius according to the rough tooth surface midpoint coordinates, where the first radius is the distance between the rough tooth surface midpoint corresponding to the rough tooth surface midpoint coordinates and the workpiece spindle; Obtaining the absolute value of the difference between the first radius and the theoretical radius, where the theoretical radius is the distance between the first theoretical tooth surface midpoint and the workpiece spindle, and the theoretical radius is determined according to the first theoretical tooth surface midpoint coordinates; When the absolute value is greater than the preset precision value, rotating the current rough measurement coordinate system around the workpiece spindle by an adjustment angle to obtain an updated rough measurement coordinate system, and jumping to the step of controlling the probe to contact the tooth surface of the to-be-measured spiral bevel gear along the direction of the unit normal vector based on the rough measurement coordinate system to obtain the rough tooth surface midpoint coordinates in the rough measurement coordinate system; When the absolute value is less than the preset precision value, determining the current rough measurement coordinate system as the measurement coordinate system.

6. The method for measuring the tooth profile and pitch of spiral bevel gears according to claim 1, wherein, The to-be-measured tooth profile data includes the measured tooth surface coordinates of multiple tooth points of the to-be-measured spiral bevel gear. Obtaining the to-be-measured tooth profile data of the to-be-measured spiral bevel gear includes: Based on the measurement coordinate system, controlling the probe to contact the tooth surface of the to-be-measured spiral bevel gear to measure and obtain the measured tooth surface coordinates of the multiple tooth points; The obtaining the tooth profile error of the to-be-measured spiral bevel gear according to the to-be-measured tooth profile data includes: Based on the measurement coordinate system, obtaining the theoretical tooth surface coordinates of the multiple tooth points of the to-be-measured spiral bevel gear according to the tooth surface equation of the spiral bevel gear; Obtaining the tooth profile error according to the theoretical tooth surface coordinates and the measured tooth surface coordinates of the multiple tooth points.

7. The method for measuring the tooth profile and pitch of spiral bevel gears according to claim 1, wherein The to-be-measured tooth pitch data includes multiple single tooth pitches and cumulative tooth pitches of the to-be-measured spiral bevel gear, and the tooth pitch error includes single tooth pitch error and cumulative tooth pitch error; The multiple single tooth pitches include the single tooth pitches between all adjacent tooth surfaces. Obtaining the to-be-measured tooth pitch data of the to-be-measured spiral bevel gear includes: Based on the measurement coordinate system, obtaining the second theoretical tooth surface midpoint coordinates corresponding to a tooth surface midpoint of the to-be-measured spiral bevel gear according to the tooth surface equation of the spiral bevel gear; Performing a tooth pitch measurement strategy according to the second theoretical tooth surface midpoint coordinates to obtain the multiple single tooth pitches; Wherein, the tooth pitch measurement strategy includes: Making the probe be between the Nth group of adjacent tooth surfaces of the to-be-measured spiral bevel gear; Controlling the probe to be located at the second theoretical tooth surface midpoint coordinates; Control the bevel gear under test to rotate in the first direction so that the left tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the left rotation angle value between the Nth group of adjacent tooth surfaces; Control the bevel gear under test to rotate in the second direction so that the right tooth surface of the Nth group of adjacent tooth surfaces contacts the probe to obtain the right rotation angle value between the Nth group of adjacent tooth surfaces; Obtain the single pitch corresponding to the Nth group of adjacent tooth surfaces according to the left rotation angle value and the right rotation angle value, and assign N + 1 to N; When the single pitch errors between all adjacent tooth surfaces have not been obtained, jump to the step of making the probe located between the Nth group of adjacent tooth surfaces of the bevel gear under test; The obtaining the pitch error of the bevel gear under test according to the pitch data to be measured includes: Obtain the multiple single pitch errors corresponding to the multiple single pitches according to the theoretical pitch of the bevel gear under test and the multiple single pitches; Sum the multiple single pitch errors to obtain the cumulative pitch error.

8. A measuring device for the tooth profile and pitch of spiral bevel gears, characterized in that, Includes: An acquisition module for acquiring the to-be-measured tooth profile data and to-be-measured pitch data of the bevel gear under test, wherein the bevel gear under test is clamped on the end face of the workpiece spindle of the bevel gear machine tool, and the to-be-measured tooth profile data and the to-be-measured pitch data are measured by the probe of the bevel gear machine tool based on a pre-constructed measurement coordinate system; A first obtaining module for obtaining the tooth profile error of the bevel gear under test according to the to-be-measured tooth profile data; A second obtaining module for obtaining the pitch error of the bevel gear under test according to the to-be-measured pitch data; Wherein, the measurement coordinate system is obtained through the following steps: Obtain the accurate center position information of multiple center points of the balls, the multiple center points of the balls are the center points of the standard ball in different spatial positions, the number of the center points of the balls is greater than or equal to three, the standard ball is arranged on the end face of the workpiece spindle of the bevel gear machine tool, and the workpiece spindle is used to rotate the standard ball to different spatial positions; Obtain the axis position information of the axis of the workpiece spindle according to the accurate center position information of the multiple center points of the balls; Based on the axis position information, establish the measurement coordinate system of the bevel gear machine tool, wherein the measurement coordinate system takes the plane parallel to the end face of the workpiece spindle as the XY plane and the axis of the workpiece spindle as the Z axis.

9. An electronic device, characterized in that, Includes a processor and a memory, the memory stores a program or instruction that can run on the processor, and when the program or instruction is executed by the processor, it implements the steps of the bevel gear tooth profile and pitch measurement method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to execute the bevel gear tooth profile and pitch measurement method according to any one of claims 1 to 7.

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