CN113639682A - On-machine detection method for face gear - Google Patents
On-machine detection method for face gear Download PDFInfo
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- CN113639682A CN113639682A CN202111123776.9A CN202111123776A CN113639682A CN 113639682 A CN113639682 A CN 113639682A CN 202111123776 A CN202111123776 A CN 202111123776A CN 113639682 A CN113639682 A CN 113639682A
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- 238000001514 detection method Methods 0.000 title claims abstract description 25
- 238000005259 measurement Methods 0.000 claims abstract description 54
- 238000000227 grinding Methods 0.000 claims abstract description 27
- 238000012545 processing Methods 0.000 claims abstract description 12
- 238000010862 gear shaping Methods 0.000 claims abstract description 7
- 238000000034 method Methods 0.000 claims description 17
- 239000013598 vector Substances 0.000 claims description 14
- 239000000523 sample Substances 0.000 claims description 10
- 239000004576 sand Substances 0.000 claims description 7
- 238000004364 calculation method Methods 0.000 claims description 6
- 210000003781 tooth socket Anatomy 0.000 claims description 3
- 230000009466 transformation Effects 0.000 claims description 3
- 238000007689 inspection Methods 0.000 claims 4
- 238000003754 machining Methods 0.000 abstract description 5
- 238000000691 measurement method Methods 0.000 abstract description 3
- 238000009966 trimming Methods 0.000 abstract description 3
- 230000005540 biological transmission Effects 0.000 description 6
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The invention discloses an on-machine detection method for a face gear, and belongs to the field of gear measurement. And a novel distribution grid is adopted to carry out on-machine detection on the gear tooth surface precision of the surface gear. The grid is composed of a contact line of a transverse face gear and a gear shaping cutter and a contact trace of a vertical face gear and a worm grinding wheel. And after the measuring head passes through the groove aligning of the measuring head and the tooth surface during measurement, measuring the geometric errors of the grid points, completing the error measurement of all the grid points on a single tooth surface according to a planned track, and processing the measured data. The measurement method has guiding significance for analyzing error generation reasons and reversely trimming and adjusting the measurement grids planned from a machining angle.
Description
Technical Field
The invention belongs to the field of gear detection, particularly relates to measurement of face gears, and particularly relates to an on-machine detection method for the face precision of the face gears.
Technical Field
The face gear transmission pair has the advantages of large transmission ratio, compact structure, good interchangeability, high contact ratio, insensitivity to installation error and the like compared with a bevel gear pair when the transmission direction is vertically changed, and the face gear transmission pair is mainly applied to the field of speed reducers of helicopter propellers and the like. The high-speed and heavy-load working conditions of the device put high requirements on transmission performance. The face gear processing technology in China is not mature, and the processing precision of the tooth face is not high. In the face gear machining, error detection of a machined tooth surface is required to correct machining errors and improve final machining precision of the tooth surface.
The face gear is often more in tooth number, the size is great, and the optimal detection mode during processing is machine detection, can avoid off-line detection to introduce positioning error, saves the time of installing and removing the work piece simultaneously. In the aspect of gear detection, a measuring head type and a scanning type on-machine detection method are researched in the temple of the university of north and middle province for application in hypoid gear measurement; the Wangliang of northwest university of industry has studied the online detection method of the helical gear and carried on the error analysis; the Beijing university of aerospace Ding Zhi Zhan researches a method for planning a detection path of a face gear tooth face; the Tang dynasty of the university of China and south researched a method for measuring a face gear on a three-coordinate measuring machine; the tooth surface error of the face gear is analyzed by using a difference plane by the square eosin of the Hunan industry university; the forest ultrasonic reference of Chongqing university other gear on-machine detection mode provides a specific measurement mode of face gear on-machine detection and a measuring head adjusting method. At present, most of the measurement methods adopt a traditional point distribution mode, namely 5 multiplied by 9 grid point distribution crossed in the horizontal and vertical directions, the mode can only carry out approximate point distribution planning on the tooth surface of the face gear, but the detected data cannot directly guide reverse trimming of the tooth surface machining error. Therefore, the development of an on-machine detection technology which better accords with the tooth surface characteristics and the processing method of the face gear has important significance for improving the processing precision of the face gear and developing and perfecting the processing equipment of the face gear made in China.
Disclosure of Invention
According to the defects of the existing on-machine detection method, the invention provides a novel on-machine detection method for a face gear, which takes a spherical point measurement type measuring head as a measuring tool, uses a novel point distribution grid to measure the face gear tooth surface, and can be applied to the detection of the face gear tooth surface precision after worm grinding and gear shaping. The new point distribution grid is still a 5 multiplied by 9 measurement grid on the tooth surface of the face gear to be measured, but the horizontal line of the grid is a contact line of the face gear and the virtual gear shaper cutter, and the vertical line is a contact trace of the face gear and the worm grinding wheel. The integral characteristic of the point coordinate geometric error extracted by the grid can obtain whether the pressure angle of a processing cutter (namely, a worm grinding wheel or a pinion cutter) meets the processing requirement or not, and simultaneously can obtain whether the grinding quantity of the worm grinding wheel meets the requirement or not in the processing process. The contact position of the worm grinding wheel and the pinion cutter during processing can be quickly determined according to the points on the grid, so that whether obvious defects exist on the cutter or not can be judged.
The tooth slot centering method before measurement is as follows: starting the measuring shaft to reach above the face gear body (x)0,0,z0) Position such that | x0|＝Dmax2-10, i.e. approximately near the inner side of the face gear outer circle, slowly down until the measuring shaft contacts the face gear. Recording the position z of the z-axis at that time1The recorded data is compared with the addendum height. If z is1Z-axis position below peak of tooth crest2Then, the measuring shaft collides with the tooth surface or the tooth bottom, and the measuring shaft z is lifted to a certain height to reach z3So that the position z of the axis center of the sphere is measured at this time3Ratio z2Low specific collision position z1High. Slowly rotating the workpiece shaft to record the angle theta of collision0Then, the workpiece shaft is rotated in the reverse direction until it collides again with the workpiece and the rotation angle θ 'is recorded'0. Raising the measuring shaft above the face gear body z0Position, the workpiece axis rotates again to (θ)0+θ′0) The/2 position, whereby centering of the face gear groove is accomplished. If z is1Higher than the crest height z2This indicates that the gear collides with the upper end surface or a very close position of the gear. When in measurement, the measuring tool rotates by half tooth angle, namely 180 degrees/n2The operation of the first case is repeated.
And measuring a certain pair of points on the grid, namely measuring the collision points of the measuring shaft and the left and right tooth surfaces in the same tooth socket when the gear rotates clockwise and anticlockwise. In order to form the grid, the key is to specifically determine the equations for the contact traces on the grid. The gear tooth surface of the envelope molding surface can be solved by a gear shaper cutter and a worm grinding wheel respectively.
Firstly, a face gear equation for the enveloping forming of the slotting cutter is given, the equation is also an important basis for subsequently determining the coordinate position of a point on a tooth face, and the specific equation and the parameter meanings are as follows:
wherein r isbsIs the base radius of the pinion cutter, m2sIs the gear ratio of the slotting cutter to the face gear, thetaosIs the half angle of the tooth socket, phisAngle of rotation of the slotting cutter, [ theta ]sThe tooth surface parameter angle of the gear shaping cutter. Determine a phisAnd thetasCan uniquely determine a point on a tooth surface, and when given a thetasGiving a series of phisThe tooth flank contact trace of one slotting cutter can be uniquely determined.
The contact trace of the worm grinding wheel and the face gear is solved more complicated, the worm grinding wheel needs to be enveloped by the pinion cutter firstly, and the tooth surface parameter angle of the pinion cutter is also arranged in the worm grinding wheel equation. The worm wheel equation for envelope formation (single face) is:
wherein m isswIs the transmission ratio of the pinion cutter to the worm grinding wheel, lambda0Is the helix angle of the drum-shaped worm grinding wheel, and E is the axial height difference phi 'between the worm grinding wheel and the gear shaper cutter when the worm grinding wheel is meshed with the face gear'sIs the gear shaping cutter angle phi in the equation of the face gearsAt the same thetasThe following is not the same. Likewise determine a phi'sAnd thetasA point on the grinding worm can be uniquely determined.
Then, a contact trace between the worm grinding wheel and the face gear is obtained by removing the envelope face gear by using the worm grinding wheel, and the following coordinate changes are required to be firstly carried out:
phi 'is eliminated according to an engagement equation'sPhi and phiwTo obtain
The meshing equation is as follows:
M(φwl) is a coordinate transformation matrix, where L is the distance of the central plane of the worm from the axis of the face gear, phiwFor the rotation angle of the worm, a series of theta is obtained by solvingsAnd L, obtaining the coordinates of each point on the grid.
The upper and lower boundaries of the grid can be determined by referring to the original mode, namely determining the approximate coordinates of the grid points at the lower left corner and the upper right corner of the grid according to the principle that 5% is left at the upper and lower parts and 10% is left at the left and right parts. The coordinates are substituted into a face gear equation to calculate thetasThe three middle values are averaged according to the tangent function of the difference between the upper and lower values. The range of L is increased or decreased by 10% according to the inner diameter and the outer diameter of the face gear, the intermediate value is divided equally according to the difference between the inner diameter and the outer diameter, and theta corresponding to 45 grid points is obtainedsAnd L. Substituting the obtained product into an engagement equation to obtain all phi'sAnd phiwPrepared from phi'sAnd phiwAnd substituting the coordinates into an equation after the worm coordinate transformation to obtain the coordinates of all the points. And verifying the correctness of the grid according to whether the determined grid points are on the surface gear tooth surface formed by the gear shaper cutter in an enveloping way.
The method also needs to reversely deduce the sphere center coordinate O when in theoretical contact according to the coordinate of the measuring point2From O2Deducing a rotation starting point O1. When the spherical probe just collides with the measured point, the line connecting the sphere center and the measured point is the normal vector of the measured point. O is2The coordinates are normal unit vector multiplied by measuring head radius plus measuring point coordinates, and the specific formula is as follows:
wherein D is the diameter of the measuring head, and O can be used for measuring1The symmetry plane is taken as xoz plane of the machine coordinate system. Coordinates of its rotation start point O1And actual measurement point O 'in the machine tool coordinate system'2The coordinates are:
the measuring contact points and the starting points of all measuring points are obtained by adopting the method, and the next point is measured after the single-point measurement is finished. In order to save time, the multiple points should move along the shortest path as much as possible, and the single-point measurement movement is repeated and recorded every time when passing through one point. After completing the geometric error measurement of all points, the measurement axis is raised again to z0Location. The workpiece axis is then rotated by a tooth angle of 360 DEG/n2And repeating the above method to complete all the tooth surface measurements.
The measured tooth surface shape error data needs to be preprocessed as follows: namely, the actual symmetry plane is determined, and the rotation starting plane and the actual symmetry plane are not completely overlapped due to the error in the initial tooth space centering and the subsequent indexing. The measurement angle for a certain point pair is set to thetai> 0 and theta'i< 0, if the error does not exist, then theta'i+θi0. But actually theta'i+θi＝θaFirst, determine θ from 45 pointsaThe actual value of (c). The formula determined by the statistical theory is as follows:
corrected measurement angle thetai-θa2 and theta'i-θa/2, from
The solving method of (1) obtains the actual measurement coordinate and makes a difference with the theoretical coordinate vector to obtain the error vector
Its normal vector to the theoretical measuring point
And performing dot product to obtain the measurement error of the point.
Drawings
FIG. 1 is a schematic view of a face gear measurement point grid;
FIG. 2 is a schematic diagram of probe movement;
FIG. 3 is a schematic diagram of the coordinates of the sphere center before and after the probe moves;
FIG. 4 is a schematic diagram of probe path planning;
detailed description of the invention
The invention is described in further detail below with reference to the figures and the detailed description.
The on-machine detection method of the face gear takes the face gear formed by gear shaping or worm grinding wheel grinding as a detection object and takes a spherical point measurement type measuring head as a measuring tool to carry out on-machine detection, and the measuring mode has a direct guiding function on subsequent reverse trimming.
This measurement method is to plan the measurement points on the tooth surface into a grid as shown in fig. 1, and the coordinate calculation of the points on the grid is as described in the above summary. The horizontal curve is the contact trace of the gear shaper cutter and the face gear, and the vertical curve is the contact trace of the worm grinding wheel and the face gear. Specific coordinate calculation the following table of design parameters exemplify specific coordinate calculations.
In actual measurement, after the loading workpiece is machined, firstly, an oil nozzle of a machine tool is turned off, the machine tool rotates for a plurality of circles at a high speed, and oil stains and the like on the surface of a gear are dried to avoid influencing measurement precision; subsequently, a cogging centering of the measuring shaft is performed, i.e. the measuring ball runs to the symmetry plane of the cogging.
Starting the measuring shaft to reach above the face gear body (x)0,0,z0) Position such that | x0175, i.e., near the inside of the face gear outer circle, then slowly descends until the measuring shaft contacts the face gear. Recording the position z of the z-axis at this time1The recorded data is compared with the addendum height. If z is1Position z lower than z-axis of highest point of tooth crest2Then, the measuring shaft collides with the tooth surface or the tooth bottom at the moment, and the measuring shaft at the momentz rises to a certain height to reach z3So that the position z of the axis center of the sphere is measured at this time3Ratio z2Low specific collision position z1High. Then slowly rotating the workpiece shaft to record the angle theta when collision occurs0Rotating the workpiece shaft in the reverse direction until it collides again with the workpiece and recording the rotation angle theta'0. Raising the measuring shaft above the face gear body z0Position, the workpiece axis rotates again to (θ)0+θ′0) The/2 position, whereby centering of the face gear groove is accomplished. If z is1Higher than the crest height z2It means that the collision occurs with the upper end face or a position close to the upper end face of the gear. Should be rotated by half a tooth angle first, i.e. 180 DEG/n2After 2.1 °, the operation of the first case was repeated.
For a certain pair of points on the grid for measurement, namely the measurement points with the same positions on the left tooth surface and the right tooth surface in the same tooth space, the specific movement of the spherical probe is firstly moved to a specified position O with reference to fig. 21The machine tool workpiece shaft is then slowly rotated until the probe impacts the face gear tooth surface, and the angle θ of rotation of the workpiece shaft at the time of impact is recorded1When the center of the sphere is at the position O2. The workpiece spindle then returns to home position and continues to rotate in the opposite direction until it encounters the other flank surface, again recording the angle θ'1When the center of the sphere is at the position O3. After the recording is finished, the workpiece shaft returns to the original position to finish the complete measurement of one point and moves to the next measurement point O'1. The coordinates of the sphere center at theoretical contact without error are reversely deduced from the coordinates of the measuring points2Then reversely deducing the rotation starting point O1. When the spherical probe just collides with the measured point, the line connecting the sphere center and the measured point is the normal vector of the measured point, so the coordinate is the normal unit vector multiplied by the radius of the measuring head and the coordinate of the measured point. At the time of measurement, O1The symmetry plane is taken as xoz plane of the machine coordinate system. The coordinates of the rotation starting point and the coordinates of the actual measurement point (part) in the machine tool coordinate system are as follows:
TABLE 1.1 contact point center of sphere coordinates
TABLE 1.2 rotation start point center of sphere coordinates
The distribution of the measuring contact points and the starting points of all the measuring points is shown in figure 3. After the single-point measurement is completed, the measurement of the next point can be performed. In order to save time, when moving at multiple points, the movement should be made along the shortest path as much as possible, and according to calculation, the shortest path is planned as shown in fig. 4, and the single-point measurement movement is repeated and recorded every time when reaching one point. After all measurements have been made, the measuring shaft is raised again to z0Location. The workpiece axis is then rotated by a tooth angle of 360 DEG/n2The above method is repeated again at 4.186 deg., and all tooth surface measurements are made.
The measured data were preprocessed as follows: and determining the actual symmetry plane, wherein the rotation starting plane and the actual symmetry plane are not completely overlapped due to partial errors caused by the centering of the tooth grooves at the beginning and the subsequent indexing. The measurement angle for a certain point pair is set to thetai> 0 and theta'i< 0, if the error does not exist, then theta'i+θi0. But actually theta'i+θi＝θaFirst, determine θ from 45 pointsaThe actual value of (c). The formula determined by the statistical theory is as follows:
corrected measurement angle thetai-θa2 and theta'i-θa/2, from
The solving method of (1) obtains the actual measurement coordinate and makes a difference with the theoretical coordinate vector to obtain the error vector
Its normal vector to the theoretical measuring point
And performing dot product to obtain the measurement error of the point. The theoretical arc of rotation is given here. To prevent the measuring shaft from colliding with the machine tool, a maximum rotation angle should be set. When the rotation angle exceeds the maximum rotation angle, the error is reported and the rotation is stopped, and the maximum angle is about the radian plus D/Dmin＝0.0016。
Table 1.3 theoretical rotation angles (radians) of the probes for each point.
Claims (7)
1. A face gear on-machine detection method is characterized in that a point distribution grid for measuring a tooth surface is formed by intersecting a contact trace of a face gear and a worm grinding wheel and a contact line of the face gear and a gear shaping cutter, the grid can be applied to face gear error measurement of worm grinding wheel grinding or gear shaping, and measurement of the full tooth surface is completed by tooth space centering, grid point coordinate calculation, single-point measurement movement, multi-point track planning and measurement data processing before gear measurement.
2. The on-machine detection method of a face gear according to claim 1, characterized in that the novel measurement grid plans the gear face of the face gear to be detected to be 45 points, 5 horizontal lines are composed of contact lines of a slotting cutter and the face gear, 9 vertical lines are composed of contact tracks of a worm grinding wheel and the face gear, the positions of the highest point and the lowest point are 5% of the whole height from the highest position and the lowest position of the face gear, and the positions of the leftmost end and the rightmost end are about 10% of the whole length from the leftmost position and the rightmost position of the face gear.
3. The method for on-machine testing a face gear as recited in claim 2, wherein the grid points are calculated by enveloping the face gear tooth surface with a pinion cutter to obtain a pinion cutter trace, and the worm grinding wheel trace is obtained by enveloping the worm grinding wheel tooth surface with the pinion cutter, and then performing coordinate transformation and two-parameter enveloping, wherein the two track focuses are the grid points.
Wherein r isbsIs the base radius of the pinion cutter, m2sIs the gear ratio of the slotting cutter to the face gear, thetaosIs the half angle of the tooth socket, phisAngle of rotation of the slotting cutter, [ theta ]sDetermining a tooth surface parameter angle phi of the gear shaper cuttersAnd thetasA point on one tooth surface can be uniquely determined.
4. A face gear on-machine inspection method as claimed in claim 1, characterised in that the measuring shaft is activated to reach physically above the face gear (x)0,0,z0) Position such that | x0|＝Dmax/2-10，DmaxTo face gear outside diameter, then slowly lowered until the measuring shaft contacts the face gear and the z-axis position z at that time is recorded1If z is1Position z lower than the highest point of tooth crest2The measuring axis z is raised to a certain height to reach z3So that the position z of the axis center of the sphere is measured at this time3Ratio z2Low ratio z1High, then slowly rotating the workpiece axis and recording the angle θ at which the collision occurred0And then the workpiece shaft is rotated in the reverse direction and the collision rotation angle theta 'is recorded'0The workpiece axis is again rotated in the reverse direction to (θ)0+θ′0) Position/2 if z1Higher than z2Firstly, the gear should be rotated by half a tooth angle, i.e. 180 DEG/n2＝2.1°，n2The face gear teeth count is then operated as in the first case to complete the centering of the face gear tooth slots.
5. An on-machine inspection of a face gear according to claim 1The method is characterized in that for single-point measurement, the spherical probe is firstly moved to a specified position O1The workpiece shaft of the machine tool is then slowly rotated until the probe impacts the face gear tooth surface, the angle θ at which the workpiece shaft rotates upon impact1The theoretical center of sphere is O2Then the workpiece shaft returns to home position and continues to rotate in the opposite direction until it encounters the other side tooth surface, again recording the angle θ'1Finally go back to completion O1All measurements, O1The coordinate calculation method is as follows
Wherein
Coordinate vector representing measured point, D is measuring sphere diameter, thetas、φsTo determine the two parameters of the coordinates of the tooth flank points,
and
each represents O1、O2The coordinate position of (a).
6. The on-machine inspection method for face gears of claim 1 wherein the multi-point measurement of the tooth face uses a serpentine path to minimize the total path of the entire grid to save measurement time.
7. The on-machine inspection method for face gears according to claim 1, wherein the measurement angle of a certain point is set as θ in the data processingi> 0 and theta'i＜0，θ′i+θi＝θaDetermining theta from 45 pointsaTo make the point symmetry the bestThe formula determined by the statistical theory is as follows:
corrected measurement angle thetai-θa2 and theta'i-θaAnd/2, obtaining actual measurement coordinates by a solving method of actual points and obtaining error vectors by making difference with theoretical coordinate vectors
Normal vector to theoretical measurement point
And performing dot product to obtain the measurement error of the point.
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| CN114754698A (en) * | 2022-04-11 | 2022-07-15 | 重庆大学 | Surface gear tooth surface measuring point planning and on-machine measuring method |
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| CN114754698B (en) * | 2022-04-11 | 2023-08-04 | 重庆大学 | Face gear tooth surface measuring point planning and on-machine measuring method |
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