On-machine measurement method of face gear pitch error based on CNC worm wheel gear grinding machine

Abstract

The present invention discloses an on-machine measurement method for the pitch error of a face gear based on a numerically controlled worm wheel gear grinding machine, comprising the following steps: Step 1: planning of gear tooth surface measurement points: 11) establishing the tooth surface equation of the face gear: constructing the tooth surface equation of the face gear according to the homogeneous transformation matrix between the gear cutter coordinate system and the face gear coordinate system and the meshing relationship between the gear cutter and the face gear; 12) planning the tooth surface measurement points with the center point of the tooth surface of the face gear according to the constructed tooth surface equation of the face gear; 13) solving the coordinates and normal direction of each tooth surface measurement point; Step 2: on-machine measurement of the face gear: measuring all side measurement points on the machine. The present invention is based on the on-machine measurement method for the pitch error of a face gear based on a numerically controlled worm wheel gear grinding machine. By measuring the pitch error of the face gear on the machine, it is possible to avoid repeated installation of the face gear due to detection, and changes in the installation reference affecting the tooth surface measurement accuracy, tooth surface processing accuracy and tooth surface processing efficiency.

Description

Technical Field

[0001] The invention belongs to the technical field of gear detection, and specifically relates to an on-machine measurement method for a face gear pitch error based on a numerically controlled worm wheel gear grinding machine. Background Art

[0002] The face gear transmission system has many advantages such as no axial force, strong load-bearing capacity and high overlap, and is called "the hope of rotorcraft transmission in the 21st century" by Western countries. The face gear transmission structure is compact and greatly reduces the quality of the main reducer, but the promotion of face gears in China is still very challenging, mainly reflected in the immature processing technology of face gears, low processing efficiency and low processing accuracy. The manufacturing accuracy of face gears directly affects the transmission accuracy, noise, efficiency and service life of the corresponding products.

[0003] In order to measure the tooth surface error of face gears, some scholars in China have measured the coordinate points of face gears to reflect the overall tooth surface error of face gears. Wang Yanzhong from Beijing University of Aeronautics and Astronautics proposed a method to obtain the normal deviation of the tooth surface of face gears based on coordinate measurement, and conducted experimental verification at the gear measurement center; Lin Chao from Chongqing University proposed a method to measure the normal deviation of the tooth surface of orthogonal variable transmission ratio face gears based on the gear measurement center, and completed the tooth surface measurement of face gears at the gear measurement center; Gao Feng from Xi'an University of Technology realized the research on the on-machine measurement method of CNC forming grinding wheel gear grinding machine, and verified it on the YK73125 CNC forming grinding wheel gear grinding machine. At present, the on-machine measurement of face gear tooth surface error is still in its infancy, and no unified standard has been formed. The tooth surface error is mainly judged by measuring the coordinate points of the tooth surface. In addition, since the tooth surface of face gears is a complex spatial surface, the tooth surface measurement of face gears is mainly offline measurement, and there is no research on the on-machine measurement of face gears. Compared with off-line measurement, on-machine measurement can detect the tooth surface error of the face gear online, which can avoid the influence of repeated installation of the workpiece due to detection on the measurement accuracy, measurement efficiency, processing accuracy and processing efficiency. Summary of the invention

[0004] In view of this, an object of the present invention is to provide an on-machine measurement method for face gear pitch error based on a CNC worm wheel gear grinding machine, which can perform on-machine measurement on the face gear tooth surface.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine comprises the following steps:

[0007] Step 1: Planning of gear tooth surface measurement points:

[0008] 11) Establishing the tooth surface equation of the face gear: According to the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system and the meshing relationship between the gear shaping cutter and the face gear, the tooth surface equation of the face gear is constructed;

[0009] 12) According to the constructed face gear tooth surface equation, the tooth surface measurement points are planned with the center point of the face gear tooth surface;

[0010] 13) Solve the coordinates and direction of each tooth surface measurement point;

[0011] Step 2: Face gear measurement on machine:

[0012] 21) Face gear alignment: align the center of the face gear tooth groove with the feed direction of the X axis;

[0013] 22) Establish measurement coordinate system: Establish measurement coordinate system based on the center point of face gear tooth surface;

[0014] 23) Input the coordinates (x, y, z) and normal direction (i, j, k) of the target tooth surface measurement point, call the MOVE subroutine, and move the probe to a safe area;

[0015] 24) Move the measuring head to the normal direction of the target tooth surface measuring point, and the distance from the target tooth surface measuring point is the set distance d;

[0016] 25) driving the measuring head to move a distance d along the normal direction of the target tooth surface measuring point to obtain the measurement coordinates, and moving the measuring head along the normal direction of the target tooth surface measuring point to a position at a distance d from the target tooth surface measuring point;

[0017] 26) Determine whether the number of measurements of the target tooth surface measurement point reaches a preset number; if not, execute step 24); if so, execute step 27);

[0018] 27) Determine whether all tooth surface measurement points on the tooth surface have been measured; if so, execute step 28); if not, execute step 23);

[0019] 28) Fitting the coordinate measurement values ​​of all tooth surface measurement points on the tooth surface into a surface to construct a tooth surface error topological surface; the coordinate measurement value is the average value of the measurement coordinates obtained by multiple measurements of the tooth surface measurement points.

[0020] Further, in step 11), the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system is:

[0021]

[0022] Among them, M fs Represents the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system; Indicates the face gear rotation angle; Indicates the gear shaping cutter angle.

[0023] Furthermore, the meshing relationship between the gear shaping cutter and the face gear is as follows:

[0024] The gear shaping cutter rotates the coordinate system S s In the figure, the angular velocity of the gear shaping tool is expressed by the vector express:

[0025]

[0026] The gear shaping cutter rotates the coordinate system S f In the figure, the angular velocity of the gear shaping tool is expressed by the vector express:

[0027]

[0028] in:

[0029] w f =q fs ·w s

[0030]

[0031] Among them, w s represents the angular velocity of the gear shaping cutter; w f represents the angular velocity of the face gear; q fs Indicates the gear ratio between the gear shaping cutter and the face gear; N s Indicates the number of teeth on the gear shaping cutter, N f Indicates the number of teeth on the face gear;

[0032] Gear shaping cutter rotation coordinate system S s The relative speed of motion is:

[0033]

[0034] The meshing equation between the face gear and the gear shaping cutter is obtained as follows:

[0035]

[0036] in, Indicates the gear shaping cutter rotation coordinate system S s The relative motion speed; F represents the meshing equation between the face gear and the gear shaping cutter; Indicates the gear shaping cutter rotation coordinate system S s The relative angular velocity of Represents the unit normal of the gear shaping cutter tooth surface.

[0037] Furthermore, the tooth surface equation of the face gear is constructed as follows:

[0038]

[0039] in, represents the gear tooth surface equation; r s (u s ,θ s ) represents the tooth surface equation of the gear shaping cutter.

[0040] Furthermore, in step 12), the method of planning the tooth surface measurement points using the tooth surface equation of the face gear is:

[0041] 121) Determine the tooth surface measurement area: divide the tooth surface of the face gear into a working tooth surface and a transition tooth surface, the transition tooth surface is the area where the transition curved surface is located, the top profile of the working tooth surface is the intersection line between the tooth surface and the tooth top surface, and the bottom profile is the upper boundary line of the transition tooth surface;

[0042] The top profile is translated downward by a distance ΔL to obtain a top contraction profile, and ΔL = αH v , where α is the shrinkage ratio of the top contour, H v is the tooth addendum height of the face gear;

[0043] Move any point k on the bottom contour upward by a distance ΔL 2-k Then the bottom contraction profile is obtained, and ΔL 2-k =βH k , where β is the shrinkage ratio of the bottom profile, H k is the height distance from any point k on the bottom profile to the tooth top surface;

[0044] 122) Determine the tooth surface measurement points:

[0045] (1) Determine the center point P' of the working tooth surface;

[0046] (2) Using the principle of rotational projection, the working tooth surface is projected onto the tooth groove center plane zOx to obtain a top contraction projection profile obtained by projecting the top contraction profile, a bottom contraction projection profile obtained by projecting the bottom contraction profile, and a reference point P obtained by projecting the center point P'; wherein the z-axis in the tooth groove center plane zOx is perpendicular to the top contraction projection profile, and the x-axis is parallel to the top contraction projection profile;

[0047] (3) Using reference point P as reference, solve for plane point p ij =(x i ,z j ), where x i represents a plane point p ij The horizontal axis; z j represents a plane point p ij The vertical coordinate of ; and:

[0048]

[0049]

[0050] Among them, x (m,n) and z (m,n) Respectively represent the horizontal and vertical coordinates of the reference point P; M represents the number of plane points set along the tooth width direction, and M is an odd number, M = 2m + 1; N represents the number of plane points set along the tooth height direction, and N is an odd number, N = 2n + 1; R1 and R2 represent half of the inner diameter and outer diameter of the face gear respectively; s1 represents the contraction ratio in the tooth width direction; z a Indicates the coordinate value of the top contraction projection contour on the z-axis; ij Indicates that the horizontal coordinate of the bottom contraction projection contour is equal to x i The coordinate value of the point on the z-axis;

[0051] (4) Using the principle of rotational projection, the plane point p ij =(x i ,z j ) is projected onto the tooth surface of the face gear to obtain the tooth surface measurement point p' ij =(x' i ,z' j ).

[0052] Further, in step 122), the method for determining the center point P' of the working tooth surface is: fitting M' straight lines at equal intervals along the tooth width direction on the working tooth surface, and fitting N' curves at equal intervals between the top contraction profile and the bottom contraction profile; wherein M' and N' are both odd numbers, then the first The straight line and The point where the two curves intersect is taken as the center point P' of the working tooth surface.

[0053] Further, in step 122), the plane point p ij =(x i ,z j ) and tooth surface measuring point p i ' j =(x i ',z' j ) is as follows:

[0054]

[0055] in, Indicates the face gear rotation angle, θ s Represents the gear cutter tooth profile parameters.

[0056] Further, the method further includes step 29), determining whether all tooth surfaces of the face gear have been measured. If not, the face gear is driven to rotate 360°*M+360° / N around its axis. f , M is a positive integer greater than or equal to 0, execute step 23); if so, end the measurement.

[0057] The beneficial effects of the present invention are:

[0058] The present invention is based on an on-machine measurement method for the pitch error of a face gear of a numerically controlled worm wheel gear grinding machine, uses a gear shaping cutter to construct a tooth surface equation of the face gear, uses the tooth surface equation to plan tooth surface measurement points, and obtains the coordinates and normal direction of each tooth surface measurement point; during the machine measurement process, the normal direction of each tooth surface measurement point is used as the feed direction of the measurement pair, so that the target tooth surface measurement point can be accurately aligned, and the same tooth surface measurement point is measured multiple times and then the average is calculated to reduce the measurement error; in this way, the on-machine measurement of the pitch error of the face gear can be achieved, and repeated installation of the face gear due to detection and changes in the installation reference that affect the tooth surface measurement accuracy, tooth surface processing accuracy and tooth surface processing efficiency can be avoided, and the measurement cost is low.

[0059] The tooth surface of the face gear is divided into a working tooth surface and a transition tooth surface, thereby obtaining the working tooth surface of the face gear tooth surface, and finding the center point P' of the working tooth surface; then the working tooth surface and the center point P' are projected onto the center plane zOx of the tooth groove to obtain the projection area of ​​the working tooth surface and the reference point P obtained by the projection of the center point P', and the reference point P is used to solve the plane point p ij , plane point p ij Plane points p are set at equal intervals in the tooth width direction and are located on the same straight line in the tooth height direction. ij The spacing between them is equal, so that all plane points p distributed in the projection area of ​​the working tooth surface are obtained. ij ; Finally, the plane point p ij Projected onto the tooth surface of the face gear, the tooth surface measurement point p' is obtained ij ; In summary, after projecting the working tooth surface onto the tooth groove center plane zOx, the reference point P is used to solve other plane points p according to the set rules. ij , and then through the back projection method, the plane point p ij Project it onto the working surface to get the tooth surface measurement point p i ' j , which can better match the working tooth surface into a spatial curved surface, make the distribution of measuring points more uniform and closer to the real tooth surface, and can accurately reflect the error of the entire tooth surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0061] Figure 1 This is a simplified motion diagram of a CNC worm wheel gear grinding machine;

[0062] Figure 2 It is the face gear machining coordinate system;

[0063] Figure 3 It is a structural schematic diagram of the tooth surface measurement area obtained after the working tooth surface is shrunk;

[0064] Figure 4 It is a structural schematic diagram after the working tooth surface is projected onto the center plane of the tooth groove;

[0065] Figure 5 The simulation diagram of the tooth surface measurement points obtained by solving the problem;

[0066] Figure 6 This is a schematic diagram of using MATLAB to calculate the normal vector direction of the side measurement point;

[0067] Figure 7 This is the flow chart of on-machine measurement;

[0068] Figure 8 This is a comparison diagram between the measured surface and the theoretical surface;

[0069] Fig. 9 is the pitch error topological surface obtained by fitting. DETAILED DESCRIPTION

[0070] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0071] The on-machine measurement method of the face gear pitch error based on the CNC worm wheel gear grinding machine of this embodiment comprises the following steps:

[0072] Step 1: Gear tooth surface measurement point planning

[0073] 11) Establish the tooth surface equation of the face gear: According to the homogeneous transformation matrix between the gear cutter coordinate system and the face gear coordinate system and the meshing relationship between the gear cutter and the face gear, the tooth surface equation of the face gear is constructed.

[0074] like Figure 1 The above is a CNC. A simplified diagram of the machine tool motion of a worm wheel gear grinder. The face gear is mounted on the C axis, and the probe is mounted on the Y axis through a mechanical arm; the probe can move in the Y axis direction through the movement of the Y axis, in the tooth direction through the movement of the X axis, in the tooth height direction through the movement of the Z axis, and in the normal direction through the rotation of the C axis and the A axis. The workpiece coordinate system of the face gear is established with the C axis.

[0075] In order to facilitate the derivation of the gear tooth surface equation, the following is established: Figure 2 The gear cutter envelope shown in the figure generates the machining coordinate system of the face gear tooth surface, where S s (x s ,y s ,z s ) and S f (x f ,y f ,z f ) are the fixed moving coordinate systems of the gear shaping cutter and the face gear, S s0 (x s0 ,y s0 ,z s0 ) is the fixed coordinate system that connects the gear shaping cutter to the machine tool base, S f0 (x f0 ,y f0 ,z f0 ) is the fixed coordinate system of the face gear and the C axis; the gear cutter rotation angle Angle of face gear Satisfaction relationship: Where N s Indicates the number of teeth on the gear shaping cutter, N f Indicates the number of teeth on the face gear. According to the homogeneous transformation theory, solve the gear cutter rotation coordinate system S s To the face gear rotation coordinate system S f The transformation matrix.

[0076] (1) Coordinate system S s (x s ,y s ,z s ) to coordinate system S s0 (x s0 ,y s0 ,z s0 )’s transformation matrix M s0s for:

[0077]

[0078] (2) Coordinate system S f0 (x f0 ,y f0 ,z f0 ) to coordinate system S f (xf,yf,z f ) is the transformation matrix M ff0 for:

[0079]

[0080] (3) Coordinate system S s0 (x s0 ,y s0 ,zs0 ) to coordinate system S f0 (x f0 ,y f0 ,z f0 )’s transformation matrix M f0s0 for:

[0081]

[0082] Finally, the gear shaping cutter coordinate system S is obtained. s With face gear coordinate system S f The homogeneous transformation matrix between is:

[0083]

[0084] Among them, N fs Represents the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system; Indicates the face gear rotation angle; Indicates the gear shaping cutter angle.

[0085] The meshing relationship between the gear shaping cutter and the face gear is as follows:

[0086] The gear shaping cutter rotates the coordinate system S s In the figure, the angular velocity of the gear shaping tool is expressed by the vector express:

[0087]

[0088] The gear shaping cutter rotates the coordinate system S f In the figure, the angular velocity of the gear shaping tool is expressed by the vector express:

[0089]

[0090] in:

[0091] w f =q fs ·w s

[0092]

[0093] Among them, w s represents the angular velocity of the gear shaping cutter; w f represents the angular velocity of the face gear; q fs Indicates the gear ratio between the gear shaping cutter and the face gear; N s Indicates the number of teeth on the gear shaping cutter, N f Indicates the number of teeth on the face gear;

[0094] Gear shaping cutter rotation coordinate system S s The relative speed of motion is:

[0095]

[0096] The meshing equation between the face gear and the gear shaping cutter is obtained as follows:

[0097]

[0098] in, Indicates the gear shaping cutter rotation coordinate system S s The relative motion speed; F represents the meshing equation between the face gear and the gear shaping cutter; Indicates the gear shaping cutter rotation coordinate system S s The relative angular velocity of Represents the unit normal of the gear shaping cutter tooth surface.

[0099] The constructed tooth surface equation of the face gear is:

[0100]

[0101] in, represents the gear tooth surface equation; r s (u s ,θ s ) represents the tooth surface equation of the gear shaping cutter.

[0102] 12) According to the constructed face gear tooth surface equation, the tooth surface measurement points are planned with the center point of the face gear tooth surface. Specifically, the method is as follows:

[0103] 121) Determine the tooth surface measurement area: The tooth surface of the face gear is divided into a working tooth surface and a transition tooth surface. The transition tooth surface is the area where the transition surface is located. The top contour line of the working tooth surface is the intersection line between the tooth surface and the tooth top surface, and the bottom contour line is the upper boundary line of the transition tooth surface. Specifically, the face gear transition surface is a spatial surface formed by the generatrix of the tooth top circle of the gear shaping cutter during the generating motion, that is, the equation of the face gear transition surface can be obtained by multiplying the tooth top circle of the gear shaping cutter by the fixed coordinate system of the gear shaping cutter to the fixed coordinate system of the face gear, such as Figure 2 As shown in the figure, the transition surface equation of the face gear is:

[0104]

[0105] Among them, M f→s represents the transformation matrix between the gear shaping cutter solidification coordinate system and the face gear solidification coordinate system; r s (u s ,θ smax ) represents the face gear tooth addendum generatrix, θ smax is the addendum circle parameter of the face gear, and:

[0106]

[0107] Among them, r as is the tip circle radius of the gear shaping cutter, r bs is the base circle radius of the gear shaping cutter.

[0108] The top profile is translated downward by a distance ΔL to obtain a top contraction profile, and ΔL = αH v , where α is the shrinkage ratio of the top contour, H v is the tooth top height of the face gear. Move any point k on the bottom profile upward by a distance ΔL 2-k Then the bottom contraction profile is obtained, and ΔL 2-k =βH k , where β is the shrinkage ratio of the bottom profile, H k is the height distance from any point k on the bottom profile to the tooth top surface.

[0109] Specifically, in the process of measuring the coordinate points of the face gear, a suitable tooth surface area should be selected for measurement; since there is no unified standard for the selection of the tooth surface area of ​​the face gear, the tooth surface area of ​​the face gear is selected with reference to the standard for selecting the tooth surface area of ​​the bevel gear. The tooth surface of the face gear is divided into a working tooth surface and a transition tooth surface. In the process of the face gear, the accuracy of the working tooth surface is mainly guaranteed. Therefore, the measurement of the face gear is mainly to measure the working tooth surface, while the transition tooth surface is ignored. In addition, in order to avoid interference between the probe and the tooth surface at the tooth top and the tooth root, normal measurement cannot be performed; the tooth top direction is shrunk downward by 5%, that is, in this embodiment, α=5%; the transition arc in the tooth root direction is shrunk upward by 5%, that is, in this embodiment, β=5%. In some embodiments, it is also possible to shrink in the tooth width direction, such as shrinking inward by 10% in the tooth width direction. The planning of the tooth surface measurement area obtained after shrinkage is as follows: Figure 3 As shown, W h is the face gear tooth width.

[0110] 122) Determine the tooth surface measurement points:

[0111] Specifically, the method for determining the center point P' of the working tooth surface is as follows: M' straight lines are fitted at equal intervals along the tooth width direction on the working tooth surface, and N' curves are fitted at equal intervals between the top contraction profile and the bottom contraction profile; where M' and N' are both odd numbers, then The straight line and The point where the two curves intersect is taken as the center point P' of the working tooth surface.

[0112] In order to make the tooth surface measurement closer to the real tooth surface, and only through a limited number of measurements, the tooth surface measurement points need to be planned. In this embodiment, the number of grid points in the tooth surface measurement area is: 9×5, that is, 9 grid points are determined in the tooth width direction and 5 grid points are determined in the tooth height direction. That is, M'=9, N'=5.

[0113] (2) In order to obtain more evenly distributed measurement points, it is necessary to further determine the position of the grid points and obtain the theoretical coordinates of each measurement point. To this end, in this embodiment, the principle of rotational projection is used to project the working tooth surface onto the tooth groove center plane zOx, and obtain the top contraction projection contour obtained by projecting the top contraction contour, the bottom contraction projection contour obtained by projecting the bottom contraction contour, and the reference point P projected from the center point P'; wherein the z-axis in the tooth groove center plane zOx is perpendicular to the top contraction projection contour, and the x-axis is parallel to the top contraction projection contour. The projection area obtained after projection is as follows: Figure 4 As shown in the figure, the projection area of ​​the face gear tooth surface at zOx is ∑, the projection area of ​​the tooth surface measurement area at zOx is A'B'C'D', the top contraction projection profile is the straight line A'D', and the bottom contraction projection profile is the curve C'.

[0114] (3) Using reference point P as reference, solve for plane point p ij =(x i ,z j ), where x i represents a plane point p ij The horizontal axis; z j represents a plane point p ij The vertical coordinate of ; and:

[0115]

[0116]

[0117] Among them, x (m,n) and z (m,n) Respectively represent the horizontal and vertical coordinates of the reference point P; M represents the number of plane points set along the tooth width direction, and M is an odd number, M = 2m + 1, i = 1, 2, ..., M; N represents the number of plane points set along the tooth height direction, and N is an odd number, N = 2n + 1, j = 1, 2, ..., N; R1 and R2 represent half of the inner diameter and outer diameter of the face gear respectively; s1 represents the contraction ratio in the tooth width direction, in this embodiment, s1 = 10%; z a Indicates the coordinate value of the top contraction projection contour on the z-axis; ij Indicates that the horizontal coordinate of the bottom contraction projection contour is equal to x i The coordinate value of the point on the z-axis; in this embodiment, M=9, N=5.

[0118] (4) Using the principle of rotational projection, the plane point p ij =(x i ,z j ) is projected onto the tooth surface of the face gear to obtain the tooth surface measurement point p' ij =(x' i ,z' j). Specifically, the plane point p ij =(x i ,z j ) and tooth surface measuring point p' ij =(x' i ,z' j ) is as follows:

[0119]

[0120] in, Indicates the rotation angle of the face gear, θ s Represents the gear cutter tooth profile parameters.

[0121] After calculation by MATLAB, we can get Figure 5 Measuring points on the tooth flank are shown.

[0122] 13) Solve the coordinates and direction of each tooth surface measurement point;

[0123] Use MATLAB to calculate the measuring points on the tooth surface of the face gear and the direction of the normal vector, such as Figure 6 In one implementation of this embodiment, the tooth surface measurement points and normal vector direction data are shown in Table 1:

[0124] Table 1 Theoretical measurement point data of tooth surface

[0125]

[0126] Step 2: Face gear measurement on machine:

[0127] According to GB / T10095.1-2008, the pitch of a cylindrical gear is defined as: the length of the arc between the tooth profiles of two adjacent teeth on the same side of any circle is called the pitch on the circle, that is, on the same circle, the pitch is equal to the sum of the tooth thickness and the tooth width; the gear deviation of a cylindrical gear is defined as: the difference between the theoretical pitch and the actual pitch. However, for face gears, the definition of the pitch deviation of a cylindrical gear is obviously inappropriate. The tooth surface of a face gear is a spatial curved surface, and the pitch of each point on the tooth surface is not equal. Therefore, referring to the definition of the pitch of a cylindrical gear, the pitch of a face gear is defined as: select 5*9 tooth surface points on the same tooth surface, and measure the pitch deviation of 45 points to reflect the pitch deviation of the entire tooth surface. The tooth surface point measurement point planning is as follows: Figure 4 As shown in Figure 2, the distribution of tooth surface points and normal direction are calculated by MATLAB, as shown in Figure 2. Figure 6 The distribution of tooth surface points and normal direction data are shown in Table 1. Different from the traditional measurement method, the pitch error of the entire tooth surface can be reflected by measuring a limited number of points, which can greatly improve the measurement efficiency of the face gear pitch error.

[0128] like Figure 7 As shown, the on-machine measurement process of the face gear in this embodiment is as follows:

[0129] 21) Face gear alignment: align the center of the face gear tooth groove with the feed direction of the X axis;

[0130] 22) Establish measurement coordinate system: Establish measurement coordinate system based on the center point of face gear tooth surface;

[0131] 23) Input the coordinates (x, y, z) and normal direction (i, j, k) of the target tooth surface measurement point, call the MOVE subroutine, and move the probe to a safe area;

[0132] 24) Move the measuring head to the normal direction of the target tooth surface measuring point, and the distance from the target tooth surface measuring point is set to a distance d. In this embodiment, d=0.5 mm;

[0133] 25) driving the measuring head to move a distance d along the normal direction of the target tooth surface measuring point to obtain the measurement coordinates, and moving the measuring head along the normal direction of the target tooth surface measuring point to a position at a distance d from the target tooth surface measuring point;

[0134] 26) Determine whether the number of measurements of the target tooth surface measurement point reaches a preset number; if not, execute step 24); if so, execute step 27);

[0135] 27) Determine whether all tooth surface measurement points on the tooth surface have been measured; if so, execute step 28); if not, execute step 23);

[0136] 28) Fitting the coordinate measurement values ​​of all tooth surface measurement points on the tooth surface into a surface to construct a tooth surface error topology surface; the coordinate measurement value is the average value of the measurement coordinates obtained by multiple measurements of the tooth surface measurement points. Specifically, Figure 8 As shown in the figure, the measured surface and the theoretical surface are fitted in MATLAB, the pitch error of 45 points is analyzed, and the pitch error topological surface is fitted based on the center of the face gear, as shown in Fig. 9 shown.

[0137] 29) Determine whether all tooth surfaces of the face gear have been measured. If not, drive the face gear to rotate 360°*M+360° / N around its axis. f , M is a positive integer greater than or equal to 0, * represents a product operation, and step 23 is executed; if yes, the measurement is terminated.

[0138] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine, characterized in that: The steps include: Step 1: Gear tooth surface measurement point planning: 11) Establishing the tooth surface equation of the face gear: According to the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system and the meshing relationship between the gear shaping cutter and the face gear, the tooth surface equation of the face gear is constructed; 12) According to the constructed face gear tooth surface equation, the tooth surface measurement points are planned with the center point of the face gear tooth surface; The method of planning the tooth surface measurement points based on the tooth surface equation of the face gear is: 121) Determine the tooth surface measurement area: divide the tooth surface of the face gear into a working tooth surface and a transition tooth surface, the transition tooth surface is the area where the transition curved surface is located, the top profile of the working tooth surface is the intersection line between the tooth surface and the tooth top surface, and the bottom profile is the upper boundary line of the transition tooth surface; The top profile is translated downward by a distance ΔL to obtain a top contraction profile, and ΔL = αH v , where α is the shrinkage ratio of the top contour, H v is the tooth addendum height of the face gear; Move any point k on the bottom contour upward by a distance ΔL 2-k Then the bottom contraction profile is obtained, and ΔL 2-k =βH k , where β is the shrinkage ratio of the bottom profile, H k is the height distance from any point k on the bottom profile to the tooth top surface; 122) Determine the tooth surface measurement point: (1) Determine the center point P' of the working tooth surface; (2) Using the principle of rotational projection, the working tooth surface is projected onto the tooth groove center plane zOx to obtain a top contraction projection profile obtained by projecting the top contraction profile, a bottom contraction projection profile obtained by projecting the bottom contraction profile, and a reference point P obtained by projecting the center point P'; wherein the z-axis in the tooth groove center plane zOx is perpendicular to the top contraction projection profile, and the x-axis is parallel to the top contraction projection profile; (3) Using reference point P as reference, solve for plane point p ij =(x i ,z j ), where x i Represents a plane point p ij The horizontal axis; z j Represents a plane point p ij The vertical coordinate of ; and: Among them, x (m,n) and z (m,n) Respectively represent the horizontal and vertical coordinates of the reference point P; M represents the number of plane points set along the tooth width direction, and M is an odd number, M = 2m + 1; N represents the number of plane points set along the tooth height direction, and N is an odd number, N = 2n + 1; R1 and R2 represent half of the inner diameter and outer diameter of the face gear respectively; s1 represents the contraction ratio in the tooth width direction; z a Indicates the coordinate value of the top contraction projection contour on the z-axis; ij Indicates that the horizontal coordinate of the bottom contraction projection contour is equal to x i The coordinate value of the point on the z-axis; (4) Using the principle of rotational projection, the plane point p ij =(x i ,z j ) is projected onto the tooth surface of the face gear to obtain the tooth surface measurement point p i ' j =(x i ',z' j ); 13) Solve the coordinates and normal vector direction of each tooth surface measurement point; Step 2: Face gear measurement on machine: 21) Face gear alignment: align the center of the face gear tooth groove with the feed direction of the X axis; 22) Establish measurement coordinate system: Establish measurement coordinate system based on the center point of face gear tooth surface; 23) Input the coordinates (x, y, z) and normal direction (i, j, k) of the target tooth surface measurement point, call the MOVE subroutine, and move the probe to a safe area; 24) Move the measuring head to the normal direction of the target tooth surface measuring point, and the distance from the target tooth surface measuring point is the set distance d; 25) driving the measuring head to move a distance d along the normal direction of the target tooth surface measuring point to obtain the measurement coordinates, and moving the measuring head along the normal direction of the target tooth surface measuring point to a position at a distance d from the target tooth surface measuring point; 26) Determine whether the number of measurements of the target tooth surface measurement point reaches a preset number; if not, execute step 24); if so, execute step 27); 27) Determine whether all tooth surface measurement points on the tooth surface have been measured; if so, execute step 28); if not, execute step 23); 28) Fitting the coordinate measurement values ​​of all tooth surface measurement points on the tooth surface into a surface to construct a tooth surface error topological surface; the coordinate measurement value is the average value of the measurement coordinates obtained by multiple measurements of the tooth surface measurement points.

2. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to claim 1, characterized in that: In step 11), the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system is: Among them, M fs Represents the homogeneous transformation matrix between the gear shaping cutter coordinate system and the face gear coordinate system; Indicates the face gear rotation angle; Indicates the gear shaping cutter angle.

3. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to claim 2, characterized in that: The meshing relationship between the gear shaping cutter and the face gear is as follows: The gear shaping cutter rotates the coordinate system S s In the figure, the angular velocity of the gear shaping tool is expressed by the vector express: The gear shaping cutter rotates the coordinate system S f In the figure, the angular velocity of the gear shaping tool is expressed by the vector express: in: w f =q fs ·w s Among them, w s represents the angular velocity of the gear shaping cutter; w f represents the angular velocity of the face gear; q fs Indicates the gear ratio between the gear shaping cutter and the face gear; N s Indicates the number of teeth on the gear shaping cutter, N f Indicates the number of teeth on the face gear; Gear shaping cutter rotation coordinate system S s The relative speed of motion is: The meshing equation between the face gear and the gear shaping cutter is obtained as follows: in, Indicates the gear shaping cutter rotation coordinate system S s The relative motion speed; F represents the meshing equation between the face gear and the gear shaping cutter; Indicates the gear shaping cutter rotation coordinate system S s The relative angular velocity of Represents the unit normal of the gear shaping cutter tooth surface.

4. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to claim 3, characterized in that: The constructed tooth surface equation of the face gear is: in, represents the gear tooth surface equation; r s (u s ,θ s ) represents the tooth surface equation of the gear shaping cutter.

5. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to claim 1, characterized in that: In the step 122), the method for determining the center point P' of the working tooth surface is: fitting M' straight lines at equal intervals along the tooth width direction on the working tooth surface, and fitting N' curves at equal intervals between the top contraction profile and the bottom contraction profile; wherein M' and N' are both odd numbers, then the first The straight line and The point where the two curves intersect is taken as the center point P' of the working tooth surface.

6. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to claim 1, characterized in that: In step 122), the plane point p ij =(x i ,z j ) and tooth surface measuring point p' ij =(x' i ,z' j ) is as follows: in, Indicates the rotation angle of the face gear, θ s Represents the gear cutter tooth profile parameters.

7. The method for measuring the pitch error of a face gear on a CNC worm wheel gear grinding machine according to any one of claims 1 to 6, characterized in that: The method also includes step 29), determining whether all tooth surfaces of the face gear have been measured. If not, the face gear is driven to rotate 360°*M+360° / N around its axis. f , M is a positive integer greater than or equal to 0, execute step 23); if so, end the measurement.

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