CN117970866A - Face gear on-machine measurement path planning and error correction method - Google Patents
Face gear on-machine measurement path planning and error correction method Download PDFInfo
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Abstract
The invention discloses a method for planning and correcting errors of on-machine measuring paths of face gears, which comprises the steps of obtaining coordinates and normal vectors of theoretical to-be-measured points of tooth surfaces through building a standard model of the face gears, completing path planning from probe calibration, gear correction to tooth surface measurement on a worm grinding wheel gear grinding machine, obtaining pre-travel errors of probes through ring gauges, building a pre-travel error database, obtaining probe radiuses, correcting planeness and roundness of the face gears, centering tooth grooves on the basis, planning tooth surface measuring paths, correcting the obtained coordinates according to the pre-travel errors and the probe radius error compensation, building an eccentric error correction model to obtain actual coordinate values, multiplying actual coordinate vectors by theoretical coordinate vector differences by theoretical normal vectors to obtain accurate tooth surface errors, and improving on-machine measuring accuracy and efficiency.
Description
Technical Field
The invention belongs to the field of gear detection, and particularly relates to an on-machine measurement path planning and error correction method for face gears.
Technical Field
The face gear transmission is applied to transmission systems of navigation, aviation and helicopters, can realize space intersecting shaft transmission, and has the advantages of large transmission ratio, simple structure, light weight, low noise, no feeding force and the like compared with bevel gear transmission. Meanwhile, the face gear transmission is used as a first-stage gear transmission in the main speed reducer, and has the working characteristics of high contact ratio, strong bearing capacity, compact structure and the like. However, because the tooth thickness of the inner diameter position of the face gear is thinner, the traditional face gear transmission is suitable for lower load transmission, and therefore, higher requirements on transmission performance are required under heavy load working conditions. The domestic face gear processing technology is not mature enough, and the tooth surface processing precision is lower. During the processing of the face gear, the data of the processed tooth surface is required to be processed so as to facilitate the subsequent error calculation and the anti-pitch correction.
The face gear is large in general size and large in number of teeth, and the optimal detection mode during machining is on-machine measurement, so that positioning errors caused by detection can be avoided, and meanwhile, the time for assembling and disassembling workpieces is saved. After measurement, accuracy detection is generally performed, measurement data are processed, and good accuracy of the face gear is guaranteed. In the aspect of face gear tooth surface measurement, beijing industrial university stone shining and the like analyze the influence of the measuring head diameter of the coordinate measuring machine on the measurement error, and an error compensation formula is provided, so that a foundation is laid for face gear coordinate measurement; chongqing university Li Guolong et al adopts a novel point distribution grid to carry out on-machine measurement on the tooth surface precision of the face gear; the Mingxing ancestor of Hubei university uses the shape error of the face gear tooth surface as a research object, establishes a face gear tooth surface mathematical equation, and performs error measurement on the face gear tooth surface through a three-coordinate measuring instrument (CMM). However, the detection data cannot be directly used for the reverse trimming of the tooth surface machining error. Thus, an accurate on-board measurement method was developed.
Disclosure of Invention
Aiming at the defects and shortcomings of the on-machine measuring method of the face gear at the present stage, the invention provides a method for planning an on-machine measuring path of the face gear and correcting errors.
In order to solve the technical problems, the invention adopts the following technical scheme:
A face gear on-machine measuring path planning and error correction method comprises the steps of obtaining coordinates and normal vectors of theoretical to-be-measured points of a tooth face through building a face gear standard model, completing path planning from probe calibration and gear correction to tooth face measurement on a worm grinding wheel gear grinding machine, obtaining a pre-stroke error of a probe through a ring gauge, building a pre-stroke error database, obtaining a probe radius, carrying out flatness and roundness correction on the face gear, carrying out tooth socket centering on the basis, planning a tooth face measuring path, correcting the obtained coordinates according to the pre-stroke error and the probe radius error compensation, building an eccentric error correction model to obtain actual coordinate values, and multiplying an actual coordinate vector by a theoretical coordinate vector difference by the theoretical normal vector to obtain an accurate tooth face error.
The method comprises the steps of firstly obtaining coordinates of a to-be-measured point of a tooth surface of a face gear through a meshing principle, wherein a coordinate conversion process is a gear shaper cutter motion coordinate system-a face gear motion coordinate system-a mounting distance offset-a tooth space centering rotation coordinate system, and providing a reference model for obtaining theoretical coordinates and calculating tooth surface errors. The face gear tooth surface can be expressed in tooth space centering rotation coordinates by coordinate conversion as follows:
,φθ＝φs+θos+θs,φ2＝m2sφs,H＝0.5*mz-ha*m+h＝58.96mm,"+" in the equation corresponds to the right tooth face of the face gear and "-" corresponds to the left tooth face of the face gear. And 45 theoretical coordinates of the tooth surface can be obtained by assigning the variables.
For convenience of representation, let 45 coordinates of points to be measured of the tooth surface at this time and normal vector be (left tooth surface):
The probe pre-travel error data is then acquired with the ring gauge at a time other than the on-machine measurement. The probe is internally provided with a trigger device, when the probe is contacted with an object, the numerical control system can send a time random error t 1 during an interrupt request to the CPU after receiving a trigger signal, if the system error t 2 caused by the field protection indispensable to an interrupt program is considered, the measurement speed is set to be v when the probe is contacted with a workpiece, the pre-travel error from sending a signal to the response of the numerical control system is:
The polar coordinate system is built by the ring gauge center, the probe measures 180 points at intervals of 2 degrees on the ring gauge, the pre-travel error omega of each point is recorded, an error database is built, the error database can be directly called in the machine measurement process, the time of on-machine measurement is greatly saved, and meanwhile, the obtained measurement point coordinates can be corrected in real time.
The probe calibration needs to correct the radius of the probe, firstly, the measuring probe is moved to be close to the position H Z above the center of the ring gauge, then the probe is moved into the ring gauge, the probe is completely lowered into the ring gauge, the position is set as X 0,Y0, the X axis is controlled, firstly, the probe is moved to be in positive direction to touch the ring gauge to obtain a coordinate (X 1,Y1), the probe is moved to be in negative direction to touch the ring gauge to obtain the coordinate (X 2,Y2), and the probe returns to the original position after the measurement is completed. Similarly, moving the Y-axis yields two coordinates (X 3,Y3) and (X 4,Y4) in the forward and reverse directions, respectively, and then back to the position (X 0,Y0) where the probe position is offset relative (X 0,Y0) for accurate measurement of the radius of the probe, and the remaining four different positions are measured in the same manner. Then obtaining the center coordinates of the ring gauge through eight points:
Thus, the radius of the probe can be accurately obtained:
And finally, transmitting the obtained probe radius into a numerical control system, lifting the Z-axis coordinate to H Z, returning to the original measurement position, and completing the probe calibration. Wherein R G is the ring gauge inner diameter.
Performing face gear correction, firstly performing flatness correction, moving a probe to the upper part (x 0,0,z0) of a face gear, wherein x 0 = (D-b)/2, D is the outer diameter of the face gear, b is the tooth width, then descending the probe, setting a height threshold value as z by adopting a numerical control code MEAS function, enabling the probe to move downwards to obtain a measured height, if the height is lower than z, enabling the probe to touch a tooth surface, recording the workpiece shaft rotation angle M 1 at the moment, reversely touching the other tooth surface to obtain a rotation angle M 2, rotating the workpiece shaft to (M 1+M2)/2, ascending the probe to z 0, rotating the workpiece pi/N, and descending the probe to obtain a tooth top height value; if the height value is higher than or equal to the threshold value, directly touching the tooth top to obtain a height value, then rotating the workpiece shaft by 120 degrees to sequentially obtain three coordinates, thereby obtaining the normal vector according to the least square fitting plane:
Calculating an included angle between the algorithm vector and the Z axis:
Setting the angle threshold and if the deviation is large, reinstalling the workpiece is required. Secondly, roundness correction is carried out, the probe is moved to (X 4,0,z4),x4＝D/2+5,z4 =z-h, h is tooth height, a numerical control code MEAS function is adopted, the probe is measured along the negative direction of the X axis, the outer circle of the face gear is touched to obtain point coordinates, then the workpiece is retracted to (X 4,0,z4), the workpiece axis is rotated for 60 degrees, 6 points of the outer circumference are obtained according to the same step, and the roundness correction is carried out by least square circumference fitting to obtain an actual rotation center.
And then tooth slot centering is carried out, and firstly, a measurement mode is planned to be that the probe is positioned at a fixed coordinate of an XOZ plane, and the C-axis rotation quantity is obtained by rotating the C-axis touch tooth surface. In the measuring process, when the workpiece is near to the probe, a certain buffer area is arranged, and after entering the area, the rotation rate is reduced until the workpiece touches the tooth surface. The buffer interval size (rotation arc length) is thus set in the measurement program:
The rotation angle of the C axis is expressed as K, wherein the K can take the value of 0.5-1. (Angle system)
The fixed coordinate position of the probe is calculated, taking the left tooth surface as an example, the position of the theoretical tooth surface to be measured point and the normal vector are known, and a rotation matrix is added
Obtaining a fixed coordinate of the probe theoretical tooth surface during touch according to the coordinate relation:
Wherein r is the radius of the probe, and the coordinates of the center of the probe at the moment are as follows ri＝90+i(i＝1,2,…9)，Is a rotation matrix. The probe is fixed on an XOZ plane in advance in the measuring process, the face gear rotates the C shaft clockwise and anticlockwise respectively to measure to obtain rotation quantity, an S-shaped measuring path is adopted to sequentially obtain 45 groups of rotation angles, and a statistical formula is utilized to determine the rotation quantity in tooth slot centering:
C 1i and C 2i are respectively the rotation amounts of the C shaft when the probe is touched clockwise and anticlockwise, and C is the rotation amount of the tooth slot when the probe is centered.
After tooth slot centering, planning a probe measurement path according to coordinates of a tooth surface to-be-measured point, and firstly calculating coordinates of a probe sphere center touched by the probe and a workpiece to-be-measured point:
Then, a workpiece is fixed, the probe is fed in the Y direction, a proper back-off point is set for avoiding interference between the probe and the workpiece, the maximum Y value is-1.3 through the coordinates of the spherical center of the probe, a buffer area is set, and finally the back-off point is set as Y= -1. Firstly, the probe descends to the height of a first measuring point, then the probe is fed along the Y direction to touch the tooth surface to obtain a first measuring point coordinate, then the probe is retracted to a position Y= -1, the probe descends to the height of a second measuring point, the probe is fed along the Y direction to obtain a second measuring point coordinate, and 45 measuring point coordinates are sequentially obtained according to the same operation from the outer diameter to the inner diameter of the face gear in an S-shaped measuring track.
And correcting the obtained coordinates by utilizing the pre-stroke error and the probe radius error compensation.
Because the actual measurement points are different from the theoretical measurement points, the theoretical tooth surface is divided into dense grids, the coordinates of the sphere center are utilized to find three nearest grid points, and the weighted unit normal vector of the actual measurement points is obtained through the distance between the three grid points and the normal vector of each point
Wherein the method comprises the steps ofIs the normal vector of three grid points,/>D i is the center-to-grid point distance.
Because the design coordinate system is not coincident with the measurement coordinate system, rotation offset can be generated between the design coordinate system and the measurement coordinate system, and therefore an eccentric error correction model is established. Firstly, establishing coordinates of a point to be measured after rotation offset through a tooth surface theoretical point:
wherein:
Establishing an eccentric error model:
Wherein, u=x c-x'a,V＝yc-y'a,W＝zc-z'a, by bringing the actual point coordinates, iterating δ by using a coordinate rotation method, obtaining the optimal eccentric amounts Δx, Δy, Δz, Δθ, and correcting the measured point coordinates by using an inverse matrix:
finally, the corrected tooth surface error is obtained:
σ＝(x'c-xa)·nxa+(y'c-ya)·nya+(z'c-za)·nza.
The beneficial effects of the invention are as follows:
1. And (3) according to the actual condition of on-machine measurement, carrying out probe calibration and planning a path from gear correction to tooth surface measurement. The tooth slot centering adopts a mode that the probe is fixed and the C shaft rotates, so that the operation is simple and convenient, when the tooth surface is measured, the workpiece is fixed, the probe adopts a measurement mode of Y-direction feeding, the number of transmission shafts is reduced, and the transmission error can be effectively reduced.
2. And when the measurement is out of the machine measurement, a probe pre-travel error online database is established by using the ring gauge, the measurement time is saved by calling at any time in the measurement process, and a weighted unit normal vector is calculated for compensating the probe radius error, so that the accurate measurement point coordinate is obtained. And finally, establishing an eccentric error correction model, and accurately calculating the eccentric amount, so that the measurement coordinate system is overlapped with the design coordinate system. Through the above steps, the coordinate is corrected, so that a more accurate tooth surface error is obtained, and the on-machine measurement precision and efficiency are improved.
Drawings
FIG. 1 is a flow chart of a face gear on-machine measurement path planning and error correction method;
FIG. 2 is a face gear theoretical model diagram;
FIG. 3 is a modeling diagram of 45 theoretical points of a theoretical tooth surface;
FIG. 4 is an on-machine measurement physical diagram of the worm grinding wheel gear grinding machine;
FIG. 5 is a schematic diagram of probe calibration performed by the calibration ring gauge;
FIG. 6 is a schematic illustration of tooth slot alignment;
FIG. 7 is an on-machine measurement spline centering probe trajectory;
FIG. 8 is a schematic diagram of an on-machine measurement feed and retract mode;
FIG. 9 is a schematic diagram of correction of measured coordinates according to pre-stroke error coordinates;
Fig. 10 is a diagram of an eccentricity correction model.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description. The specific parameters are shown in table 1.
TABLE 1
The on-machine measurement path planning and error correction method of the face gear is shown in fig. 1, the specific operation is as follows, firstly, the face gear tooth surface to be measured point is obtained through the meshing principle, the coordinate conversion process is as shown in fig. 2, which is a gear shaper cutter motion coordinate system O S-XsYsZs -a gear shaper cutter fixed coordinate system O G-XGYGZG -a face gear fixed coordinate system O M-XmYmZm -a face gear motion coordinate system O 2-X2Y2Z2 -a mounting distance offset O H-XHYHZH -a tooth slot centering rotation coordinate system O B-XBYBZB, the tooth slot centering rotation coordinate system O B-XBYBZB is used as a design coordinate system, and at the moment, the tooth slot center of the theoretical tooth surface is located on the XOZ plane, a reference model is provided for obtaining theoretical coordinates and tooth surface error calculation later, and the face gear tooth surface can be expressed in the tooth slot centering rotation coordinate through coordinate conversion:
,φθ＝φs+θos+θs,φ2＝m2sφs,H＝0.5*mz-ha*m+h＝58.96mm,"+" in the equation corresponds to the right tooth face of the face gear and "-" corresponds to the left tooth face of the face gear. As shown in fig. 3, 45 theoretical coordinates of the left and right tooth surfaces can be obtained by assigning values to the variables.
For convenience of representation, let the tooth surface coordinates and theoretical normal vector at this time be (left tooth surface):
On the worm grinding wheel gear grinding machine YS7323, the positions of the trigger type probe and the face gear are shown in fig. 4, and the probe pre-stroke error data is acquired by adopting a ring gauge at a time out of on-machine measurement. The specific acquisition method is that a trigger device is arranged in the probe, when the probe is contacted with an object, a numerical control system can send a time random error t 1 during an interrupt request to a CPU after receiving a trigger signal, if the system error t 2 caused by the field protection indispensable to an interrupt program is considered, the measurement speed when the probe touches a workpiece is set as v, and the pre-travel error from sending a signal to the response of the numerical control system is as follows:
A polar coordinate system is established by using the center of the ring gauge, a probe measures 180 points at intervals of 2 degrees on the ring gauge, the pre-travel error omega of each point is recorded, then an error database is established and stored in a numerical control system, and the error database can be directly called in the on-machine measurement process, so that the on-machine measurement time is greatly saved, and meanwhile, the obtained coordinates are continuously corrected.
Then correcting the radius of the probe, wherein the theoretical radius of the known ring gauge is 20.5mm, as shown in fig. 5, firstly moving the measuring probe to the position close to the position above the center of the ring gauge, H Z, moving the probe into the ring gauge, completely descending the probe into the ring gauge, controlling the X and Y axes respectively, touching the ring gauge respectively to obtain four points, and then performing offset to obtain four points, wherein the coordinates of the measuring points are shown in table 2:
TABLE 2
The ring gauge center coordinates can be obtained from the above coordinates:
the probe radius can then be accurately obtained:
And finally, transmitting the obtained probe radius into a numerical control system, and simultaneously lifting the Z-axis coordinate to H Z and returning to the original measurement position. The probe calibration is completed. Wherein R G is the ring gauge inner diameter.
The face gear correction steps are as follows, firstly, flatness correction is carried out, a probe is moved to the upper part (x 0,0,z0) of the face gear, wherein x 0 = (D-b)/2=95, D is the outer diameter of the face gear, then the probe descends, a numerical control code MEAS function is adopted, a height threshold value is set to be z 1, the probe moves downwards to obtain a measured height, if the measured height is lower than z 1, the probe touches a tooth surface, a workpiece shaft rotation angle M 1 at the moment is recorded, the other tooth surface is reversely touched to obtain a rotation angle M 2, the workpiece shaft is rotated to (M 1+M2)/2, the probe ascends to z 0, the workpiece pi/N=3.75 is rotated, and the probe descends to obtain a tooth top height value; if the height value is higher than or equal to the threshold value, directly touching the tooth top to obtain a height value, then rotating the workpiece shaft by 120 degrees to sequentially obtain three coordinates, thereby obtaining the normal vector according to the least square fitting plane:
Calculating an included angle between the algorithm vector and the Z axis:
Setting the angle threshold and if the deviation is large, reinstalling the workpiece is required. Secondly, roundness correction is carried out, the probe is moved to (X 4,0,z4),x4＝D/2+5＝105,z4 =z-h=10, h is tooth height, numerical control code MEAS function is adopted, the probe is measured along the negative direction of the X axis, the outer circle of the face gear is touched to obtain point coordinates, then the workpiece is retracted to (X 4,0,z4), the workpiece axis is rotated for 60 degrees, 6 points of the outer circumference are obtained according to the same step, and the roundness correction is carried out by least square circumference fitting to obtain the actual rotation center.
And then tooth slot centering is carried out, as shown in fig. 6, the measurement mode is planned to be that the probe is positioned at the fixed coordinate of the XOZ plane, and the rotation C axis touches the tooth surface to obtain the rotation quantity. And in the measuring process, when the workpiece is near to the probe, a certain buffer area is arranged, and after entering the area, the rotation speed is reduced until the workpiece touches the tooth surface. The buffer interval size (rotation arc length) is thus set in the measurement program:
The rotation angle of the C axis is expressed as K, wherein the K can take the value of 0.5-1. (Angle system)
Firstly, calculating the fixed coordinate position of the probe, taking the left tooth surface as an example, knowing the position of a theoretical tooth surface to be measured point and a normal vector, and adding a rotation matrix
Obtaining a fixed coordinate when the probe touches the theoretical tooth surface according to the coordinate relation:
Wherein r is the radius of the probe after correction, and the coordinates of the probe center at the moment are as follows R i =90+i (i=1, 2, … 9) is face gear radius,/>A workpiece rotation matrix. The Z coordinate of the probe at this time is shown in table 3,
TABLE 3 Table 3
The probe is fixed on an XOZ plane in advance in the measuring process, the face gear rotates the C shaft clockwise and anticlockwise respectively to measure to obtain rotation quantity, an S-shaped measuring path is adopted from the inner diameter to the outer diameter of the face gear as shown in fig. 7, 45 groups of rotation angles are obtained in sequence, and the rotation quantity in tooth slot centering is determined by utilizing a statistical formula:
C 1i and C 2i are respectively clockwise rotation and anticlockwise rotation of the C shaft, and C is rotation during tooth slot centering.
Then, a probe measurement path is planned, as shown in fig. 8, first, the coordinates of the sphere center of the probe, where the probe touches the workpiece to be measured, are calculated:
The workpiece is fixed, the probe is fed in the Y direction, a proper back-off point is set for avoiding interference between the probe and the workpiece, the maximum Y value is-1.3 through the coordinates of the spherical center of the probe, and meanwhile, a buffer area is set, so that the back-off point is set to be Y= -1. The specific measuring path is that a probe is positioned to the upper end near the center of a tooth socket in the first step, the probe descends to the height of a first measuring point in the second step, the tooth surface is touched along the Y direction to obtain a first measuring point coordinate in the third step, the probe retreats to the position Y= -1 in the fourth step, the probe descends to the height of a second measuring point in the fifth step, the probe descends to obtain a second measuring point coordinate along the Y direction, and 45 measuring point coordinates of the tooth surface are sequentially measured according to the same operation from the outer diameter to the inner diameter of the face gear in an S-shaped measuring track.
As shown in fig. 9, the coordinates of the measurement points obtained by compensation correction based on the pre-stroke error and the probe radius error:
Since the actual measurement point is not the same as the theoretical measurement point, the normal vector In order to obtain accurate actual measurement point coordinates, the theoretical face gear tooth surface is meshed and thinned into a certain amount of meshes, and three closest mesh points are searched through the spherical center coordinates to obtain a weighted unit normal vector/>
Wherein the method comprises the steps ofIs the normal vector of three grid points,/>D i is the center-to-grid point distance.
Since the design coordinate system and the workpiece coordinate system do not coincide in practice, as shown in fig. 10, rotational offset occurs between the two, and the eccentric amounts are Δx, Δy, Δz, and Δθ, respectively, so that an eccentric error correction model is established.
The specific correction steps are as follows, firstly, the coordinates of the point to be measured after the rotational offset is established through the theoretical point of the tooth surface:
[x'b y'b z'b 1]T＝MP(Δx,Δy,Δz)·MX(Δθ)·[xa ya za 1]T
wherein the offset rotation matrix is:
Establishing an eccentric error model:
Wherein, u=x c-x'a,V＝yc-y'a,W＝zc-z'a, by bringing the actual point coordinates, iterating δ by using a coordinate rotation method, obtaining the optimal eccentric amounts Δx, Δy, Δz, Δθ, and correcting the measured point coordinates by using an inverse matrix:
then, the corrected tooth surface error is obtained:
σ＝(x'c-xa)·nxa+(y'c-ya)·nya+(z'c-za)·nza
As shown in table 4, the face gear had tooth face errors (μm) before and after the mechanical measurement error correction.
TABLE 4 Table 4
The two groups of data can find that the maximum error and the minimum error of the tooth surface after correction all show a reduction trend, so that the measurement efficiency can be improved by establishing reasonable probe calibration and gear correction to tooth surface measurement path planning, and errors generated by pre-stroke errors, probe radius error compensation, eccentric design coordinate system and measurement coordinate system are comprehensively considered, and the coordinates obtained by on-machine measurement are corrected, so that more accurate tooth surface errors can be obtained, and the measurement precision is greatly improved.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (7)
1. A face gear on-machine measuring path planning and error correction method is characterized in that the method comprises the steps of obtaining coordinates and normal vectors of theoretical to-be-measured points of a tooth face through building a face gear standard model, completing path planning from probe calibration and gear correction to tooth face measurement on a worm grinding wheel gear grinding machine, obtaining a pre-stroke error of a probe through a ring gauge, building a pre-stroke error database, obtaining a probe radius at the same time, correcting flatness and roundness of the face gear, carrying out tooth socket centering on the basis, planning a tooth face measuring path, correcting the obtained coordinates according to the pre-stroke error and the probe radius error compensation, building an eccentric error correction model to obtain actual coordinate values, and multiplying an actual coordinate vector with a theoretical coordinate vector difference value by the theoretical normal vector to obtain the tooth face error.
2. The on-machine measurement path planning and error correction method of face gear according to claim 1, characterized in that the pre-stroke error database is constructed by planning proper measurement points on each angle of the ring gauge at a time other than on-machine measurement, measuring the probe inside the ring gauge along the Y axis, obtaining pre-stroke error omega of each direction according to the pre-stroke error generation mechanism, and directly calling the database to correct the obtained coordinates when measuring tooth surface coordinates.
3. The method for planning and correcting the on-machine measuring path of the face gear according to claim 1, wherein the flatness correction is characterized in that firstly, a probe is moved to the upper part of the face gear (x 0,0,z0), wherein x 0 = (D-b)/2, D is the outer diameter of the face gear, b is the tooth width, then the probe descends, a numerical control code MEAS function is adopted, a height threshold value is set as z, the probe moves downwards to obtain the measured height, if the measured height is lower than z, the probe touches a tooth surface, the rotation angle M 1 of a workpiece shaft at the moment is recorded, the rotation angle M 2 is obtained by reversely touching the other tooth surface, the workpiece shaft is rotated to (M 1+M2)/2, the probe is lifted to z 0, the workpiece pi/N is rotated, and the probe is descended to obtain the tooth top height value; if the measured height is higher than or equal to the threshold value, directly touching the tooth top to obtain a height value, then rotating the workpiece shaft by 120 degrees to sequentially obtain three coordinates, and accordingly obtaining the normal vector and the Z-axis angle according to the least square fitting plane, and if the difference between the normal vector and the Z-axis angle is larger than the set angle threshold value, adjusting the position of the workpiece.
4. The method for planning on-machine measurement path and correcting error according to claim 1, wherein the roundness correction is performed by moving a probe to (X 4,0,z4),x4＝D/2+5,z4 =z-h, h is tooth height, adopting numerical control code MEAS function, measuring the probe along the negative direction of the X axis, touching the outer circle of the face gear to obtain point coordinates, then backing to (X 4,0,z4), rotating the workpiece axis by 60 degrees, obtaining 6 point coordinates of the outer circumference according to the same step, performing least square circumference fitting to perform roundness correction, and obtaining the rotation center coordinates of the workpiece.
5. The method for planning and correcting errors of on-machine measuring paths of face gears according to claim 1, wherein the tooth space centering is performed in a mode of probe immobility and workpiece rotation, and fixed coordinates of the probe when the probe touches a theoretical tooth surface point are calculated:
Wherein r is the radius of the probe, And/>For the coordinate vectors and normal vectors of 45 points to be detected of the tooth surface, the coordinates of the probe sphere center at the moment are/>ri＝90+i(i＝1,2,…9)，/>Is a rotation matrix. The probe is fixed on an XOZ plane in advance in the measurement process, the gear tooth surface of the C-axis touch surface gear is rotated clockwise and anticlockwise respectively to obtain the rotation quantity of the workpiece, a buffer area is added in the touch area to prevent firing pins, and the rotation quantity in tooth slot centering is determined by using a statistical formula:
C 1i and C 2i are respectively clockwise rotation and anticlockwise rotation of the C shaft, and C is rotation during tooth slot centering.
6. The method for planning and correcting errors of on-machine measurement paths of face gears according to claim 1, wherein the measurement path planning calculates the positions of measurement points of the probe:
setting a proper back-off point, wherein in the measuring process, the workpiece is motionless, the probe obtains coordinates in a Y-direction feeding mode, and the obtained coordinates are corrected according to the pre-stroke error and the probe radius error compensation, so that corrected tooth surface coordinates are obtained:
because the actual measurement point is different from the theoretical measurement point in the process of machine measurement, the normal vector In order to obtain accurate actual measurement point coordinates, the theoretical face gear tooth surface is meshed and thinned into a certain amount of meshes, and three closest mesh points are searched through the spherical center coordinates to obtain a weighted unit normal vector/>
Wherein the method comprises the steps ofIs the normal vector of three grid points,/>D i is the center-to-grid point distance.
7. The on-machine measurement path planning and error correction method of claim 1, wherein the eccentric error correction model is characterized in that a theoretical model design coordinate system is not coincident with a measurement coordinate system, theoretical point coordinates to be measured after rotational offset is established through theoretical points of tooth surfaces, and an eccentric error model is established:
,U＝xc-x'a,V＝yc-y'a,W＝zc-z'a,xc,yc,zc is a theoretical coordinate of a point to be measured, the coordinate is brought into an actual coordinate of a measured point, delta is iterated by a coordinate rotation method, optimal offset delta x, delta y, delta z and delta theta are obtained, the coordinate of the measured point is corrected by an inverse matrix, and the corrected coordinate vector of the measured point and the theoretical coordinate vector of the point are subjected to difference and dot product with a theoretical normal vector to obtain a tooth surface error.
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