CN107167105B - A kind of error compensating method of cycloid gear detection - Google Patents
A kind of error compensating method of cycloid gear detection Download PDFInfo
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/20—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring contours or curvatures, e.g. determining profile
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Abstract
The invention discloses a kind of error compensating method of cycloid gear detection, measured using three-coordinates measuring machine measurement cycloid gear, define the X of three-coordinates measuring machine, Y and Z axis are original coordinates, the point coordinates of P and Q two of different height on cycloid gear axial line is measured using three-coordinates measuring machine, can draw cycloid gear axial line relative to the deflection angle of X-axis and Y-axis and, then cycloid gear axial line equation is determined by P and the point coordinates of Q two, the tooth corridor face of cycloid gear is measured by three-coordinates measuring machine again, obtain measured value, the data of measurement are by formula around X, the spin matrix and translation matrix of Y-axis carry out being converted to the revised measured value of coordinate system, complete the compensation of cycloid tooth gear teeth corridor planar survey.The present invention by way of error compensation, eliminates the measurement error caused by clamping in measurement process, measurement accuracy is greatly improved after compensation indirectly by using a kind of method based on Coordinate Conversion.
Description
Technical Field
The invention relates to cycloidal gear detection, relates to a detection error compensation scheme caused by installation deviation, and particularly relates to an error compensation method for cycloidal gear detection.
Background
The cycloidal gear speed reducer has the excellent characteristics of large transmission ratio, compact structure, high efficiency, stable operation and long service life, and is widely applied to the industrial fields of machinery, mines, metallurgy, chemical industry, textile, national defense industry and the like. The cycloid gear is used as a core component in the speed reducer, and the manufacturing precision of the cycloid gear directly influences the performance of the whole machine. Therefore, the quality detection of the machined cycloid gear part becomes an important link of the whole production process, and any slight measurement error factor directly causes misjudgment on the product quality, so that an error compensation method is urgently needed to correct the measurement error caused by improper installation, and a real measurement result capable of reflecting the machining quality of the part is obtained.
At present, the tooth profile detection of a cycloidal gear is commonly carried out on a three-coordinate measuring instrument, and due to the clamping error of the cycloidal gear, the axial lead of the cycloidal gear cannot be completely misaligned with the Z axis of the three-coordinate measuring instrument, so that an alignment error is generated to influence the measurement accuracy of a tooth flank surface, but the error is inevitable.
When measuring the tooth profile deviation of the cycloid gear, as shown in fig. 1, as the tooth profile surface is to be measured, the position of the probe bracket in the Z-axis direction is fixed, then the probe is moved along the Y-axis direction, and the cycloid gear is rotated around the Z-axis until the probe contacts the tooth profile surface of the cycloid gear, the coordinate value of the measuring point is read, the result is recorded, then the cycloid gear is rotated around the Z-axis at an equal angle, and the coordinate value of the measuring point is recorded once every rotation until the cycloid gear rotates for a circle, so that the measurement is completed. When the tooth direction deviation of the cycloid gear is measured, the position of the probe in the Y-axis direction is fixed, the cycloid gear is rotated around the Z-axis until the probe contacts the cycloid gear, the coordinate value of a measuring point is read, the result is recorded, the probe is moved for a certain distance at equal intervals along the Z-axis direction, the coordinate value of the measuring point is recorded once every time the probe is moved, and the measurement is completed until the probe is moved out along the tooth direction of the cycloid gear. However, in the actual measurement process, the clamping cycloid gear always has more or less deviations, such as eccentricity and inclination of the axis of the cycloid gear, which are inevitable in the actual measurement process, but the measurement error caused by the deviation directly influences the accuracy of the measurement result.
Disclosure of Invention
The invention aims to provide a method for compensating errors detected by a cycloid gear so as to solve the problem of large measurement deviation in the prior art. In view of this, the present invention provides an error compensation and correction scheme: because the coordinates of the cycloid gear measured by the three-coordinate measuring instrument are the positions of the cycloid gear relative to the coordinate system of the measuring instrument, the eccentricity of the axis of the cycloid gear is actually the deviation of the axis of the cycloid gear relative to the origin of the coordinate system of the measuring instrument, and similarly, the inclination of the axis of the cycloid gear can be generated after the axis rotates around each coordinate axis. Based on the thought of coordinate transformation, the initial installation error of the cycloid gear can be compensated, namely, the offset and the rotation angle of the axis of the cycloid gear relative to the origin are firstly obtained, and then the coordinate system is correspondingly moved for a certain distance and rotated for a certain angle, so that the error can be eliminated.
In order to solve the technical problems, the invention adopts the technical scheme that:
an error compensation method for cycloidal gear detection is used for measuring a cycloidal gear by using a three-coordinate measuring instrument, and is characterized by comprising the following steps of:
step one, defining X, Y and Z axis of a three-coordinate measuring instrument as original coordinates, and measuring P (x) in different height directions on the axis of the cycloid gear by using the three-coordinate measuring instrument1,y1,z1) And Q (x)2,y2,z2) Two-point coordinates, and the deflection angle theta of the axis of the cycloid gear relative to the X axis and the Y axis can be obtained by using the formula (5)1And theta2，
Wherein, theta1Is the angle of deflection of the axis of the cycloid gear with respect to the X-axis, theta2The deflection angle of the axis of the cycloid gear relative to the Y axis is adopted;
step two, passing P (x)1,y1,z1) And Q (x)2,y2,z2) Determining the axis line equation of the cycloid gear by two-point coordinates, namely equation (6), when z is 0, equation (6) is changed into equation (7), and then the intersection point coordinate S (x) of the axis line of the cycloid gear and the XOY plane can be obtaineds,ys) Wherein
step three, measuring the tooth profile surface of the cycloid gear through a three-coordinate measuring instrument to obtain a measured value (x)m,ym,zm) The measured data is converted by formula (3) to obtain corrected measured values (x, y, z);
step four, rotating the original coordinate system by corresponding angles around the X and Y axes and moving the original coordinate system by corresponding distances relative to the circle center, and enabling the corrected measured values (X, Y, z) to pass through the publicThe coordinate value (x) after compensation is obtained by the conversion of the formula (8)α,yα,zα) And then the compensation of the cycloidal gear tooth profile surface measurement is completed.
Preferably, in step three, the corrected compensation value (x) considering the size of the radius of the probe is obtained by converting the corrected value (x, y, z) obtained by the formula (3) into the formula (4) in consideration of the influence of the radius of the probe on the measurement of the tooth profile surface of the cycloid gearp,yp,zp)，
Then (x)p,yp,zp) The coordinate value (x) after compensation is obtained through the conversion of the formula (4)α,yα,zα) And then the compensation of the cycloidal gear tooth profile surface measurement is completed.
Furthermore, the three-coordinate measuring instrument and the measurement compensation method for measurement can be applied to product design, die equipment, gear measurement, blade measurement machine manufacturing, tool fixtures, steam die fittings and precision measurement of electronic and electric appliances.
The invention has the beneficial effects that:
according to the invention, a coordinate conversion-based method is adopted, and a measurement error caused by clamping in the measurement process is indirectly eliminated in an error compensation mode, so that the requirement on high-precision measurement of the tooth profile surface is met, and the production quality of the cycloid gear is ensured.
Drawings
Fig. 1 is a schematic diagram of a coordinate system conversion principle.
Fig. 2 is a schematic diagram of a cycloidal gear tooth profile measurement using a three-coordinate measuring machine.
FIG. 3 is a schematic diagram of a cycloidal gear tooth profile surface equation generation structure.
FIG. 4 is a schematic view of the relative positions of the axes of a cycloid gear with pitch and eccentricity.
The device comprises a base 1, a turntable 2, a cycloid gear 3, a probe 4, a probe bracket 5, a thimble 6, a slide seat 7 and an axial lead 8.
Detailed Description
Example of planar coordinate conversion
As shown in fig. 1, the coordinate system is rotated counterclockwise by an angle θ with respect to the origin, the coordinate of a certain point in the non-rotated coordinate system is a (x, y), the coordinate of the rotated coordinate system is B (x ', y'), the same point has different coordinate values in different coordinates, and obviously, the relationship between them is a key for connecting the two coordinate systems, and the following relation of the point in the two coordinate systems can be obtained by calculation:
therefore, the conversion of the same point in different coordinate systems is realized, the relation can be deduced from the point in a two-dimensional coordinate system, and the similar relation can also be deduced from a three-dimensional coordinate system in the same way.
As shown in fig. 2, the structure includes: the device comprises a base 1, a rotary table 2, a cycloid gear 3, a probe 4, a probe support 5, a thimble 6, a sliding seat 7 and an axial lead 8.
The base 1 plays a supporting role, one end of the cycloid gear 3 is placed on the rotary table 2, the other end of the cycloid gear is fixed by the ejector pin 6, the probe 4 is installed on the probe support 5, and the probe support 5 is installed on the sliding seat 7, as shown in fig. 2: the probe 4 can be moved in the X, Y, Z directions to realize the measurement of the tooth profile of the cycloid gear 3. The invention provides a compensation scheme for measuring the alignment error of a probe 4 based on coordinate system conversion when a gear profile surface of a cycloid gear 3 is measured, and the probe 4 is used for measuring the cycloid gearIn the case of a 3-tooth profile, since the axis 8 of the cycloid gear 3 is offset from the origin, and in addition, the axis 8 is inclined, which is inevitable in measurement, for a high-precision transmission gear such as the cycloid gear 3, a small error affects the measurement precision, and it is important to compensate for the error caused by the inclination and eccentricity of the axis 8 of the cycloid gear 3 in measurement. To better explain the compensation scheme, it is first briefly described how the tooth surface equation of the cycloid gear 3 is generated, as shown in FIG. 3, with the center O of the rolling circle1A distance of a from the center O of the base circle, and a rolling circle consisting of1Performing externally tangent pure rolling motion to the base circle O along the outer side of the base circle O2Position, correspondingly, a point M on the round1Move to point M, where M1The motion trajectory of the point is an epicycloid tooth profile curve, and the generation point M can be represented by the formula (2):
in the formula (2), r1，r2Respectively representing the radii of the base circle and the rolling circle,is the rounding rotation angle and l is the height of the generation point along the Z-axis. When the eccentricity and inclination of the axis line 8 of the cycloid gear 3 are taken into consideration, the tooth profile model of the cycloid gear 3 can be represented by equation 3:
theta in the formula (3)1，θ2Respectively, the angles of deflection of the axis 8 of the cycloid gear 3 with respect to the X, Y axes,as measured by the profile of the cycloid gear 3,is the intersection point S (x) of the axis 8 of the swing gear and the XOY planes,ys0) the coordinates of the object to be inspected,in order to take account of the eccentricity and inclination of the axis of the cycloid gear 3, the corrected measured value of the tooth profile of the cycloid gear 3, if the radius of the probe is taken into consideration, the formula (3) can be changed into the formula (4),
in the formula (4), rμDenotes the size of the radius of the probe, n (n)x,ny,nz) Is the normal vector of the shaft axis 8 of the cycloid gear 3 under eccentric and inclined conditions, (x)p,yp,zp) To take into account the corrected measurement after the size of the probe radius. Therefore, the compensation of the alignment error can be performed by only obtaining the deflection angle of the axis 8 of the cycloid gear 3 relative to the X and Y axes and the offset of the axis relative to the center of a circle according to the formula (3), and the coordinate system conversion is performed through the formula (8) after the compensation through the formula (4).
The scheme is as shown in figure 4: measuring the coordinate P (x) of the upper axis of the cycloid gear 3 by a three-coordinate measuring instrument1,y1,z1) And the coordinate Q (x) of the lower axis2,y2,z2) The inclination angle theta of the axis line with respect to the X-axis and the Y-axis1，θ2This can be derived from equation (5):
when the coordinates of two points P and Q are measured, the equation (6) for the space straight line of the axis 8 of the cycloid gear 3 can be established, and in the XOY plane, z is 0, and the equation (6) can be rewritten as:
the intersection S (x) of the axis 8 of the cycloid gear 3 and the XOY plane can be obtaineds,ys0) the coordinates of the object to be inspected,
wherein,further, the offset amount of the shaft axis 8 of the cycloid gear 3 with respect to the origin can be obtained.
Then the three-coordinate measuring instrument is used for measuring the tooth profile surface of the cycloid gear 3 to obtain (x)m,ym,zm) And (3) correcting and compensating the measured coordinate values according to a formula (3) to obtain (X, Y, z), and then rotating the original coordinate system by corresponding angles around X and Y axes and moving the original coordinate system by corresponding distances relative to the circle center. Coordinate conversion is carried out according to a formula (8) to obtain coordinates (x) of a measuring point on the tooth profile surface after coordinate system conversion and correctionm,ym,zm)。
In the formula, RxAnd RyAre rotation matrices about the X, Y axes, T (Δ)e) Representing a translation matrix;
in (x)m,ym,zm) Is the coordinate of the measuring point on the tooth profile surface of the cycloid gear 3 which is actually measured, and the last one is the number 1;
in (x)α,yα,zα) The coordinates of the measurement points on the tooth profile surface after the coordinate system conversion and correction, and the last one is also the number 1, because the transformation matrix describing the three-dimensional transformation of the space is in the form of 4 × 4, and 1 is added to the last row of the matrix to form a 4 × 4 matrix. Each measuring point is subjected to coordinate conversion to obtain a corrected measuring value, so that the error values of the inclination angle and the offset are eliminated. Since the offset and inclination of the axis 8 of the cycloid gear 3 are slight and unavoidable, these errors are displayed during measurement in the original coordinate system, and in order to compensate for these deviations, the coordinate system can be subjected to certain inverse "tilting" and "eccentricity" processes, i.e. corresponding rotations and offsets, to counteract the inclination and eccentricity of the axis 8 of the cycloid gear 3. This idea is really an object transformation and it is feasible and easy to operate. Bringing its measured value to the desired value.
Claims (3)
1. An error compensation method for cycloidal gear detection is used for measuring a cycloidal gear by using a three-coordinate measuring instrument, and is characterized by comprising the following steps of:
step one, defining X, Y and Z axis of a three-coordinate measuring instrument as original coordinates, and measuring P (x) in different height directions on the axis of the cycloid gear by using the three-coordinate measuring instrument1,y1,z1) And Q (x)2,y2,z2) Two-point coordinates, and the deflection angle theta of the axis of the cycloid gear relative to the X axis and the Y axis can be obtained by using the formula (5)1And theta2，
Wherein, theta1Is the angle of deflection of the axis of the cycloid gear with respect to the X-axis, theta2The deflection angle of the axis of the cycloid gear relative to the Y axis is adopted;
step two, passing P (x)1,y1,z1) And Q (x)2,y2,z2) Determining the axis line equation of the cycloid gear by two-point coordinates, namely equation (6), when z is 0, equation (6) is changed into equation (7), and then the intersection point coordinate S (x) of the axis line of the cycloid gear and the XOY plane can be obtaineds,ys) Wherein
step three, measuring the tooth profile surface of the cycloid gear through a three-coordinate measuring instrument to obtain a measured value (x)m,ym,zm) The measured data is converted by formula (3) to obtain corrected measured values (x, y, z);
in the formula (8), RxAnd RyAre a rotation matrix about the X, Y axes, T (△), respectivelye) Representing a translation matrix;
fourthly, rotating the original coordinate system around the X and Y axes by corresponding angles and phasesMoving the circle center by a corresponding distance, and converting the corrected measured value (x, y, z) through a formula (8) to obtain a coordinate value (x) of the coordinate system after correction and compensationα,yα,zα) And then the compensation of the cycloidal gear tooth profile surface measurement is completed.
2. The error compensation method for cycloid gear detection of claim 1, wherein: in the third step, the influence of the radius of the probe on the measurement of the tooth profile surface of the cycloid gear is considered, and the corrected value (x, y, z) obtained by the formula (3) is converted by the formula (4) to obtain the corrected compensation value (x) considering the radius of the probep,yp,zp)，
Then (x)p,yp,zp) The coordinate value (x) after the coordinate system is corrected and compensated is obtained through the conversion of the formula (8)α,yα,zα) And then the compensation of the cycloidal gear tooth profile surface measurement is completed.
3. The error compensation method for cycloid gear detection as recited in claim 1 or 2, wherein: the three-coordinate measuring instrument and the measurement compensation method for measurement can be applied to product design, die equipment, gear measurement, blade measurement machine manufacturing, tool fixtures, steam die fittings and precision measurement of electronic and electric appliances.
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| CN108645322B (en) * | 2018-06-21 | 2019-06-14 | 北京工业大学 | Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error |
| CN108645323B (en) * | 2018-06-21 | 2019-06-14 | 北京工业大学 | Involute spur gear wheel total profile deviation assessment method under the influence of installation error |
| CN109631812B (en) * | 2018-12-29 | 2020-12-18 | 哈工精测(岳阳)智能装备有限公司 | Method for automatically measuring size of gear |
| DE102019104891B3 (en) * | 2019-02-26 | 2020-03-12 | Liebherr-Verzahntechnik Gmbh | Method for calibrating a probe in a gear cutting machine |
| CN112414341B (en) * | 2020-09-29 | 2022-07-01 | 天津旗领机电科技有限公司 | Detection device and detection method for cycloid wheel of planetary cycloid pin gear reducer |
| CN113739703B (en) * | 2021-08-27 | 2024-09-10 | 浙江大学台州研究院 | Revolving body scanning measurement method and data compensation calibration method thereof |
| CN113899335B (en) * | 2021-08-27 | 2022-12-16 | 北京工业大学 | Method for correcting installation error of gear measured by using contourgraph |
| CN115647932B (en) * | 2022-11-02 | 2023-07-18 | 湖北工业大学 | Detachable milling head installation precision control method |
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| JP2001330428A (en) * | 2000-05-23 | 2001-11-30 | Natl Inst Of Advanced Industrial Science & Technology Meti | Evaluation method for measuring error of three- dimensional measuring machine and gage for three- dimensional measuring machine |
| CN102147331B (en) * | 2010-11-25 | 2012-09-05 | 哈尔滨工业大学 | Mounting eccentric error compensating method based on CNC (Computerized Numerical Control) gear measuring center |
| CN103206515A (en) * | 2013-04-19 | 2013-07-17 | 北京工业大学 | Loaded tooth surface contact analysis method direct at epicycloid bevel gear errors |
| CN103353270B (en) * | 2013-07-24 | 2015-10-28 | 东南大学 | A kind of flank of tooth is from benchmark large-scale straight spur gear circular pitch deviation measurement mechanism |
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