CN108645322B - Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error - Google Patents

Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error Download PDF

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CN108645322B
CN108645322B CN201810646713.3A CN201810646713A CN108645322B CN 108645322 B CN108645322 B CN 108645322B CN 201810646713 A CN201810646713 A CN 201810646713A CN 108645322 B CN108645322 B CN 108645322B
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coordinate system
gear
axis
installation error
measurement point
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CN108645322A (en
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汤洁
魏建杰
石照耀
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Beijing University of Technology
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Beijing University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B5/00Measuring arrangements characterised by the use of mechanical means
    • G01B5/14Measuring arrangements characterised by the use of mechanical means for measuring distance or clearance between spaced objects or spaced apertures
    • G01B5/16Measuring arrangements characterised by the use of mechanical means for measuring distance or clearance between spaced objects or spaced apertures between a succession of regularly spaced objects or regularly spaced apertures
    • G01B5/166Measuring arrangements characterised by the use of mechanical means for measuring distance or clearance between spaced objects or spaced apertures between a succession of regularly spaced objects or regularly spaced apertures of gear teeth

Abstract

The invention discloses the involute spur gear wheel circular pitch deviation assessment methods under the influence of installation error, initially set up coordinate system of machine O0‑X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position includes two Section Points up and down, gear upper end millet cake, any one right flank profil point and the tooth pitch measurement point of tested gear mandrel, obtains the tooth pitch measurement point under the influence of installation error;Revolution paraxial equation is calculated, coordinate system O is established1‑X1Y1Z1, tooth pitch measurement point is reverted into initial position, error of rotary axle of the corrected tooth away from measurement point;It is Z with tested gear upper surface normal vector direction2Axis direction establishes coordinate system O2‑X2Y2Z2, tooth pitch measurement point position is modified;The basic circle center of circle that tested gear is solved by Newton iteration method, establishes workpiece coordinate system Ow‑XwYwZw, geometric eccentricity error of the corrected tooth away from measurement point;Circular pitch deviation numerical value is obtained relative to the rotation angle in the basic circle center of circle by the involute of tooth pitch measurement point by calculating, to correct the influence that installation error evaluates circular pitch deviation.

Description

Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error
Technical field
The present invention relates to Precision Inspection and instrument field, the gears tooth pitch under the influence of specifically a kind of installation error is inclined The assessment method of difference.
Background technique
Gear is most important and most widely used transmission mechanism in machine driving.Gear is widely used in automobile The fields such as manufacture, aerospace, wind power equipment and equipment manufacturing.The accuracy of gear, quality directly affect the efficiency of equipment, make an uproar Sound, kinematic accuracy and service life.With the development of science and technology gear is as key components and parts, above-mentioned every profession and trade is to design of gears The accuracy of manufacture proposes requirements at the higher level.Since gear testing technology complements each other with gear machining technology, the inspection to gear Survey is just particularly important.
It is known as the measurement of gear individual event deviation by the measurement of measurement item of circular pitch deviation, spiral deviation and circular pitch deviation.Tooth Wheel individual event deflection measurements reflect the difference of machine tooling ability and institute's workpieces processing and design size.
Circular pitch deviation is mainly since each tooth of gear circumferentially unevenly causes, when circular pitch deviation engages gear Vibration noise and service life have a significant impact, therefore be of great significance to the detection of gears tooth pitch deviation.Standard Circular pitch deviation is defined as by tooth individual circular pitch error, individual circular pitch error, tooth pitch cumulative departure and tooth by ISO1328-1:2013 Away from accumulation total deviation.
The inclined measurement method of gears tooth pitch is usually the direct method of measurement and relative measurement method.Gears tooth pitch deviation is surveyed The instrument of amount has very much, including gear measuring center, three coordinate measuring machine, laser gear measurement machine, gear meshingtester, ten thousand It can gear tester and tooth pitch instrument etc..Wherein gear measuring center is most widely used.
When being measured using gear measuring center to gears tooth pitch deviation, due to gear measuring center it is upper and lower it is top not To just and measurement when the centre of gyration be not overlapped with gear geometric center, to introduce installation error.
The presence of installation error makes the actual measurement location deviation theory measurement position of gear, if not to actual measurement Data are modified, and will reduce the measurement accuracy of gear measuring center, or even cause gear rating mistake.In order to reduce peace Influence of the error to gear measurement is filled, the value of installation error should be adjusted to as small as possible, but this requires a great deal of time simultaneously And installation error cannot completely eliminate.Therefore, quantifier elimination is surveyed with important to the gears tooth pitch deviation under the influence of installation error Meaning.
Installation error is divided into three parts by the present invention: 1) gear error of rotary axle is since gear measuring center pushes up up and down Point is not to the location error between just caused practical rotating shaft and theoretical rotating shaft;2) Gear tipping error is in gear geometry Error of tilt between mandrel and practical rotating shaft;3) gear geometric eccentricity error is the geometric center of gear measured section and returns Turn the location error between center.Traditional installation error treating method often only considers one of installation error, processing Process is usually the influence for analyzing installation error to circular pitch deviation evaluation result, and the compensation of installation error is carried out at result.
The present invention is directed to measure to the gear with installation error, the gear measurement number under the influence of installation error is obtained According to by the assessment method of invention by gear measurement data correction to ideal mounting position and according to standard ISO1328-1:2013 Gears tooth pitch deviation is evaluated, the gears tooth pitch amount of deflection and rating under ideal position are obtained.
Summary of the invention
To solve the problems, such as to propose in background technique, the invention proposes the gear teeth under the influence of a kind of new installation error Assessment method away from deviation.It is inclined that installation error is divided into gear error of rotary axle, Gear tipping error and gear geometry by this method Heart error is established machine by determination, the determination of gear upper surface law vector and the reverse in the basic circle center of circle to rotating shaft and is sat Transformation relation between mark system and workpiece coordinate system, so that the tooth pitch measurement point under the influence of installation error is adapted to ideal installation Circular pitch deviation is evaluated according to standard ISO1328-1:2013 in position, and the circular pitch deviation obtained under ideal mounting position is commented Determine result and rating.
The technical solution adopted by the present invention is the involute spur gear wheel circular pitch deviation evaluation side under the influence of installation error The realization process of method, this method is as follows:
1) coordinate system of machine O is established0-X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position packet Include two Section Points up and down, tested gear upper end millet cake, any one group of right flank profil point and the tooth pitch measurement point of tested gear mandrel;
2) according to two Section Points for being tested gear mandrel under coordinate system of machine, make Least Square Circle fitting, obtain two The central coordinate of circle in section is Z with two sections circle center line connecting direction1Axis direction is positive direction in orientation, by coordinate system O0- X0Y0Z0Successively around X0Axis and Y0Axis rotation makes Z0Axis and Z1Axis is parallel, in plane X0O0Y0It is interior that Z is made by the translation of coordinate system0Axis with Z1Overlapping of axles obtain coordinate system O1-X1Y1Z1.Establish coordinate system O0-X0Y0Z0With coordinate system O1-X1Y1Z1Between transformation relation, Obtain coordinate system O1-X1Y1Z1Under gear measurement point, and the measurement point of tested gear is reverted into initial position;
3) according to O1-X1Y1Z1It is tested gear upper surface measurement point under coordinate system and makees plane fitting, obtains tested gear upper end Facial plane equation and its normal vector are Z with the normal vector direction2Axis direction is positive in orientation, with Z1The friendship of axis and measured section Point O2For origin.By coordinate system O1-X1Y1Z1Successively around X1Axis and Y1Axis rotation makes Z1Axis and Z2Axis is parallel, passes through the flat of coordinate system Shifting makes O1Point and O2Point is overlapped, and obtains coordinate system O2-X2Y2Z2
4) coordinate system O is established1-X1Y1Z1With coordinate system O2-X2Y2Z2Between transformation relation.Obtain coordinate system O2-X2Y2Z2 Under tested gears tooth pitch measurement point, due to the presence of installation error, so that tooth pitch actual measurement location deviates measured section Reference circle, therefore in coordinate system O2-X2Y2Z2Under tested gears tooth pitch measurement point position is modified;
5) according to coordinate system O2-X2Y2Z2Under revised flank profil measurement point establish least square target equation, pass through newton Solution by iterative method is tested the basic circle center of circle of gear, in X2O2Y2Translational coordination system O in plane2-X2Y2Z2, make Z2Axis passes through basic circle circle The heart establishes workpiece coordinate system Ow-XwYwZw, obtain coordinate system O2-X2Y2Z2With coordinate system Ow-XwYwZwBetween transformation relation, obtain Tooth pitch measurement point under to workpiece coordinate system;
6) in workpiece coordinate system Ow-XwYwZwIt is lower according to standard ISO1328-1:2013 to the circular pitch deviation of tested gear into Row evaluation obtains circular pitch deviation relative to the rotation angle in the basic circle center of circle by involute where calculating tested gears tooth pitch measurement point Numerical value, to correct the influence that installation error evaluates circular pitch deviation.
The ideal mounting position of gear is the workpiece coordinate system position corrected after installation error.Above and below tested gear mandrel Two Section Points or two Section Points for top circle.
Present invention has an advantage that
Gear with installation error is measured, the tooth pitch measurement data under the influence of installation error is obtained, passes through hair Bright assessment method by measurement data be adapted to ideal mounting position and according to standard ISO1328-1:2013 it is inclined to gears tooth pitch Difference is evaluated, and the gears tooth pitch amount of deflection and rating under ideal position is obtained, to have modified installation error to tooth Influence away from deviation evaluation.
Detailed description of the invention
Fig. 1 coordinate system of machine establishes schematic diagram.
Fig. 2 number of gear teeth number schematic diagram.
The amendment schematic diagram of Fig. 3 tooth pitch measurement point.
Fig. 4 workpiece coordinate system establishes schematic diagram.
Fig. 5 involute cylindrical gear circular pitch deviation Evaluation model schematic diagram.
Fig. 6 is the implementation flow chart of the method for the present invention.
Specific embodiment
To be more clear derivation process of the invention, the present invention is done furtherly below in conjunction with attached drawing and derivation formula It is bright.
Establish coordinate system of machine O as shown in Figure 10-X0Y0Z0, with the rotating shaft of gear measuring center and rotating platform Intersection point is origin, and X, Y, the tri- axis rail direction Z is change in coordinate axis direction.In coordinate system of machine O0-X0Y0Z0Under gear is surveyed Amount, measurement position include two Section Points up and down of tested gear mandrel, tested gear upper end millet cake, any one group of right flank profil point With tooth pitch measurement point.
Mandrel section and gear upper surface are measured when gear measuring center rotating shaft registration is zero, by this position Initial position when as gear measurement guarantees that gear measuring center rotating shaft is motionless, only operates X at this time0、Y0And Z0Axis variation. Mandrel Section Point is denoted as { P0 Aj_k(X0 Aj_k, Y0 Aj_k, Z0 Aj_k)};Gear upper end millet cake is denoted as { P0 Uj(X0 Uj, Y0 Uj, Z0 Uj)};
The measurement of flank profil and tooth pitch point needs rotating shaft and X0、Y0And Z0Axis is four-axle linked to be measured, and right flank profil point is remembered ForLeft and right tooth is denoted as away from measurement pointWith
Wherein, L and R respectively indicates the left and right flank of tooth, and i indicates that i-th of tooth, j indicate at j-th point, and k represents k-th of section, U Gear upper surface is represented, A represents mandrel surface.
Number of teeth sequence is as shown in Fig. 2, in the case where measuring initial position, with X0The right flank of tooth in lower section first (including with X0Axis phase Hand over) where tooth be the 1st tooth, be incremented by a clockwise direction.
Least Square Circle fitting is carried out to two groups of mandrel surface points, obtains mandrel two sections central coordinate of circle (A1 0,B1 0,Z1 0) (A2 0,B2 0,Z2 0) and revolution paraxial equation.
As shown in Figure 1, being Z with rotating shaft direction1Axis direction, with Z1Axis and plane X0O0Y0Intersection point O1For origin, By by coordinate system O0-X0Y0Z0Translation makes O0Point and O1Point is overlapped, by successively around X0Axis and Y0Axis rotates so that Z0Axis and Z1Axis It is overlapped, to obtain coordinate system O1-X1Y1Z1
Establish coordinate system O0-X0Y0Z0And O1-X1Y1Z1Between transformational relation are as follows:
For rotating shaft and plane X0O0Y0Intersecting point coordinate, γ0 xAnd γ0 yFor around X0Axis and Y0Axis rotation Angle.
Above-mentioned transformation is to correct error of rotary axle.At this point, in coordinate system O1-X1Y1Z1It is lower to revert to tooth pitch measurement point Initial position obtains { P1 Li(X1 Li, Y1 Li, Z1 Li) and { P1 Ri(X1 Ri, Y1 Ri, Z1 Ri)}。
Least square plane fitting is carried out to gear upper surface point, gear upper surface law vector is obtained and is denoted as
As shown in Figure 1, being with the intersection point of rotating shaft and measured sectionFor origin, law vector direction is Z2Axis Coordinate system O is established in direction2-X2Y2Z2.Obtain coordinate system O1-X1Y1Z1And O2-X2Y2Z2Between transformational relation are as follows:
γ1 xAnd γ1 yFor around X1Axis and Y1The angle of axis rotation
Above-mentioned transformation is corrected gear heeling error.At this point, in coordinate system O2-X2Y2Z2It is lower to correct tooth pitch measurement point To measured section X2O2Y2On, as shown in Figure 3.Revised tooth pitch point is denoted as { P2 Li(X2 Li, Y2 Li, 0) } and { P2 Ri(X2 Ri, Y2 Ri, 0)}。
Least square target equation is established according to flank profil measurement point, solution obtains basic circle central coordinate of circle and is denoted as Ow 0(aw 0, bw 0)
Translational coordination system O2-X2Y2Z2, makeWith the obtained center of circle(aw 0,bw 0) be overlapped, establish workpiece shown in Fig. 4 Coordinate system Ow-XwYwZw.Coordinate system O2-X2Y2Z2With workpiece coordinate system Ow-XwYwZwBetween transformation relation are as follows:
Above-mentioned transformation is corrected gear geometric eccentricity error.At this point, obtaining tooth pitch measurement point under workpiece coordinate system and being {Pw Li(Xw Li, Yw Li, 0) } and { Pw Ri(Xw Ri, Yw Ri, 0) }.
Gears tooth pitch deviation is evaluated under workpiece coordinate system, establishes design involute equation as shown in Figure 5:
ξ is the exhibition angle of involute.α is pressure angle.θ is the angle of spread.
Left tooth Profile Design involute is with YwThe intersection point of axis and basic circle is starting point, equation are as follows:
Calculate the corresponding involute angle of spread ξ of each tooth pitch measurement pointRi
According to angle of spread ξRi, the coordinate value for calculating design involute is (xw D_Ri,yw D_Ri)。
I indicates i-th of tooth.
Design involute is rotated around workpiece coordinate system origin, makes to design each survey that involute passes through practical involute Point is measured, rotation angle γ is calculatedRi
γ at this timeRiThe deviation of involute where as each tooth pitch measurement point will deviate from the tooth pitch measurement of reference circle with this Point is adapted on reference circle, obtains circular pitch deviation value.
On the basis of the right flank of tooth of the first tooth, it is believed that the right flank of tooth position of the first tooth is design involute position, according to mark Quasi- ISO1328-1:2013 is to the available tooth pitch cumulative departure relative to the flank of tooth 1 of the definition of gears tooth pitch deviation are as follows:
Wherein:For reference radius, m is modulus, and z is the number of teeth,.
Total cumulative pitch error are as follows:
Fp=max (Fpi)-min(Fpi)
By tooth individual circular pitch error:
fpi=Fpk-Fpk-1
Individual circular pitch error:
fp=max | fpi|=max (Fpk-Fpk-1)
Algorithm is evaluated to the circular pitch deviation under the influence of above-mentioned installation error by Matlab to emulate.It is 5mm with modulus, The number of teeth 18, for reference diameter is the involute cylindrical gear of 90mm, according in international standards for gears ISO1328-1:2013 Provide that 2 class precisions choose emulation data-oriented are as follows:
The given every error value of the installation error studied according to the present invention is respectively as follows:
The tooth pitch measurement point under the coordinate system of machine with installation error is generated by MATLAB are as follows:
Algorithm according to the present invention carries out circular pitch deviation evaluation to above-mentioned tooth pitch measurement data, obtains simulation figure and tooth pitch The amount of deflection:
If directly carrying out circular pitch deviation evaluation without the amendment of installation error to above-mentioned tooth pitch measurement data, being imitated True figure and circular pitch deviation numerical value.
Obtain given circular pitch deviation numerical value and the simulation result table of comparisons.
It can be seen that for modulus be 5mm, the number of teeth 18,2 grades of involutes of reference diameter angle 90mm by the above-mentioned table of comparisons Spur gear wheel, the circular pitch deviation assessment method under the influence of installation error measures the tooth pitch with installation error through the invention The evaluation result that data are evaluated and given value are almost the same, and gear rating is identical;Without installation error Amendment directly is evaluated to obtain evaluation result to the tooth pitch measurement data with installation error differs larger with given value, gear Rating is 7 grades, is far longer than given grade.Prove the circular pitch deviation assessment method amendment under the influence of installation error of the present invention The influence of installation error, algorithm are correctly feasible.

Claims (6)

1. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error, it is characterised in that: the reality of this method Existing process is as follows, and 1) establish coordinate system of machine O0-X0Y0Z0, tested gear is measured under coordinate system of machine, measurement position Two Section Points up and down, tested gear upper end millet cake, any one group of right flank profil point and tooth pitch measurement including being tested gear mandrel Point;Mandrel two sections central coordinate of circleWithLeft and right tooth is denoted as away from measurement pointWith
2) according to two Section Points for being tested gear mandrel under coordinate system of machine, make Least Square Circle fitting, obtain two sections Central coordinate of circle, the circle center line connecting direction with two sections is Z1Axis direction is positive direction in orientation, by coordinate system O0-X0Y0Z0 Successively around X0Axis and Y0Axis rotation makes Z0Axis and Z1Axis is parallel, in plane X0O0Y0It is interior that Z is made by the translation of coordinate system0Axis and Z1Axis It is overlapped, obtains coordinate system O1-X1Y1Z1;By coordinate system O0-X0Y0Z0With coordinate system O1-X1Y1Z1Between converted, obtain coordinate It is O1-X1Y1Z1Under tested gear measurement data, and the measurement point of tested gear measurement data is reverted into initial position;
3) according to O1-X1Y1Z1It is tested gear upper surface measurement point under coordinate system and makees plane fitting, it is flat to obtain tested gear upper surface Face equation and its normal vector are Z with the normal vector direction2Axis direction is positive in orientation, with Z1The intersection point O of axis and measured section2 For origin;By coordinate system O1-X1Y1Z1Successively around X1Axis and Y1Axis rotation makes Z1Axis and Z2Axis is parallel, is made by the translation of coordinate system O1Point and O2Point is overlapped, and obtains coordinate system O2-X2Y2Z2
4) coordinate system O is established1-X1Y1Z1With coordinate system O2-X2Y2Z2Between transformation relation;Obtain coordinate system O2-X2Y2Z2Under Tested gears tooth pitch measurement point, due to the presence of installation error, so that tooth pitch actual measurement location deviates the indexing of measured section Circle, therefore in coordinate system O2-X2Y2Z2Under tested gears tooth pitch measurement point position is modified;
5) according to coordinate system O2-X2Y2Z2Under revised flank profil measurement point establish least square target equation, pass through Newton iteration Method solves the basic circle center of circle of tested gear, in X2O2Y2Translational coordination system O in plane2-X2Y2Z2, make Z2Axis is built by the basic circle center of circle Vertical workpiece coordinate system Ow-XwYwZw, obtain coordinate system O2-X2Y2Z2With coordinate system Ow-XwYwZwBetween transformation relation, obtain workpiece Tooth pitch measurement point under coordinate system;
6) in workpiece coordinate system Ow-XwYwZwUnder the circular pitch deviation of tested gear is evaluated, pass through the tooth for calculating tested gear Involute away from measurement point obtains circular pitch deviation numerical value relative to the rotation angle in the basic circle center of circle, to correct installation error to tooth pitch The influence of deviation evaluation.
2. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error according to claim 1, Be characterized in that: the ideal mounting position of gear is the workpiece coordinate system position corrected after installation error.
3. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error according to claim 1, It is characterized in that: two Section Points up and down or two Section Points for top circle of tested gear mandrel.
4. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error according to claim 1, It is characterized in that: installation error is divided into gear error of rotary axle, Gear tipping error and gear geometric eccentricity error.
5. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error according to claim 1, It is characterized in that: gears tooth pitch deviation being evaluated according to standard ISO1328-1:2013.
6. the involute spur gear wheel circular pitch deviation assessment method under the influence of installation error according to claim 1, Be characterized in that: the eccentricity of tested gear is by solving in coordinate system O2-X2Y2Z2The least square target equation of lower foundation obtains It arrives.
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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
CN112222538A (en) * 2020-09-28 2021-01-15 南京工业大学 Tooth pitch accumulated error compensation method for forming and milling tooth machining
CN112414352B (en) * 2020-11-10 2022-04-01 重庆市计量质量检测研究院 Method for correcting sampling pose and measuring profile shape of measured object on camshaft
CN112577454B (en) * 2020-11-25 2022-05-06 华北水利水电大学 Method for measuring key machining error of pin gear shell of cycloidal pin gear speed reducer for robot
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

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