CN102645200B - Method for measuring gear pitch variation based on double-face engagement - Google Patents

Abstract

A method for measuring gear pitch variation based on double-face engagement belongs to the technical field of precision testing technology, precision testing instruments and mechanical transmission. A rack measuring head is used for measuring the pitch variation of a measured gear based on double-face engagement, the rack measuring head is provided with only one tooth with a straight tooth profile, the rack measuring head sequentially enters all measured toothed grooves and closely contacts with a left tooth surface and a right tooth surface of the measured gear, the deviation value of the rack measuring head is measured, and finally, the pitch variation of the measured gear can be obtained. According to the requirements of on-site gear measurement, the method is used for measuring the gear pitch variation based on double-face engagement by means of engaging the rack measuring head with the measured gear, the pitch variation of the left tooth surface and the right tooth surface of the measured gear can be simultaneously obtained by means of one-step measurement, and measuring efficiency is greatly improved.

Description

Based on two-sided meshed gears tooth pitch bias measurement method

Technical field

The present invention relates to one based on two-sided meshed gears tooth pitch bias measurement method, belong to Precision Inspection and instrument, mechanical transmissioning technology field.

Background technology

At present the annual value of production of China Gear industry is nearly 1,400 hundred million, world rankings the second, and wherein gear of vehicle accounts for 2/3rds, needs the gear Quick Measurement that solves production scene badly, realizes 100% measurement, to meet the requirement to its quality.And China's research and application is in this respect almost blank.

Gear measurement has: analytical measurement, composite measurement, entirety are measured.Analytical measurement comprises flank profil deviation, spiral deviation, tooth pitch deviation of prototype gear etc.Composite measurement mainly contains one side engagement measurement and two-sided engagement is measured two kinds.

The quick Site Detection instrument of gear that is applied in the world at present production scene all adopts the two-sided measuring principle engaging of tested gear and prototype gear conventionally.It is tight without the two-sided gear motion of sideshake to be that tested gear and prototype gear do, and by the rotate a circle variation of centre distance of sensor record, exports continuous radial composite error curve.Then analyze and can draw radially the radially comprehensive total departure of comprehensive total departure and a tooth, individual event deviation (flank profil deviation, spiral deviation, tooth pitch deviation) that can not prototype gear.

Beijing University of Technology and Harbin measuring and cutting tool group company combine the 3501 gear fast on-line measurement machines of having released.This measuring machine has adopted gear two-sided engaging multidimensional measuring principle, it is in keeping traditional double to nibble measurement advantage, the tooth alignment error information that can obtain fast gear, its measure the item comprises: the radially comprehensive total departure of radially comprehensive total departure, a tooth, teeth directional are beated, radially comprehensive teeth directional dip deviation, comprehensive teeth directional taper tolerance etc. radially.

Traditional measuring method of tooth pitch deviation has: direct method (absolute method) and relative method.Direct method is that the physical location of the each gear teeth of direct prototype gear is with respect to the correctness of theoretical position.The namely deviation of the actual angular pitch of the direct each gear teeth of prototype gear to theoretical angular pitch, then obtain as calculated tooth pitch deviation.Relative method is taking any one tooth pitch of gear as benchmark, instrument indicating gauge is adjusted to a certain indicating value (being generally zero), then in turn measure the deviate of other tooth pitch with respect to datum tooth distance along the whole gear ring of same shaft section, draw tooth pitch deviation through data processing.The instrument that tooth pitch is measured has: tooth pitch measuring instrument, universal gear tester etc. automatically.

Eighties of last century the nineties, domestic once someone had proposed imagination, adopted tooth bar gauge head and tested gear to do two-sided engagement, measured the tooth pitch deviation of the left and right flank of tooth simultaneously.Up to the present the method has also just been carried out to Primary Study, lacked further investigation and practice, and do not developed the rapid measurement device that can be applied to production scene based on this principle.Abroad there are no by the pertinent literature of two-sided engagement prototype gear tooth pitch deviation.

Summary of the invention

The present invention is directed to the demand of on-the-spot gear measurement, proposed a kind of tooth bar gauge head based on two-sided engagement and engage with tested gear the method for prototype gear tooth pitch deviation, can realize one-shot measurement and obtain simultaneously the tooth pitch deviation of the tested gear left and right flank of tooth.And provide feasible measuring process.

Basic thought of the present invention is as follows:

From the theory of engagement of involute gear, the track of two involute profile contact points in the fixed coordinate system of space is straight line, and this straight line is called action line.It is the active line that involute gear transmits force and motion.The error of transmission is transmitted by active line, and action line is also to transmit the active line of gear error.Gear drive is to carry out along the action line direction of a pair of gear teeth, and gear error reflects in action line.

For analysis and calculation gear error need to be set up gear error computing system.When tooth bar gauge head and tested gear two-sided gear motion, by the contact point of tooth bar gauge head and tested the two flank profil of gear, can make two action line in left and right, the error on tested gear teeth face is all transformed in these two action line.Error in this action line can be regarded meshing point as and instantaneously move more or moved less an additional distance along action line direction at this, is called action line increment.In tooth pitch is measured, tooth bar gauge head successively enters in the teeth groove of tested gear successively, contacts with the two-sided engagement of left and right flank profil of tested gear.Because tested gear teeth face has error, contact point will produce displacement increment along action line direction.Displacement increment in action line is decomposed on horizontal direction and vertical direction and analyzed, solve by setting up Related Mathematical Models the tooth pitch deviation that obtains tested gear.

Concrete technical scheme of the present invention is as follows:

Based on two-sided meshed gears tooth pitch bias measurement method, it adopts a kind of tooth bar gauge head, based on the tooth pitch deviation of the tested gear of two-sided engagement contact measurement, this tooth bar gauge head only has a tooth, its flank profil is straight line, the angle of tooth bar gauge head center line and flank profil straight line is the profile angle note α s of tooth bar gauge head

${\mathrm{\α}}_s=\mathrm{\α}+\frac{\mathrm{\π}}{2z}---\left(1\right)$

Wherein:

α is tested gear compound graduation circle pressure angle;

Z is the tested gear number of teeth.

Described measuring method is specific as follows:

S1: tested gear can initiatively rotate around axle center, tooth bar gauge head can move along level and vertical both direction; Certain teeth groove of optional tested gear is as the teeth groove of the 1st measurement, rotate tested gear and make the center line of teeth groove of the 1st measurement of tested gear and the centerline of tooth bar gauge head on the vertical straight line of same, tooth bar gauge head up, tested gear below; Tooth bar gauge head enters the teeth groove of tested gear, contacts with the two-sided engagement of the tested gear left and right flank of tooth.

S2: make two the action line n in left and right with the contact point of tooth bar gauge head and tested the two flank profil of gear ₁, n ₂, set up fixing rectangular coordinate system, with two action line n ₁, n ₂intersection point be initial point O, move horizontally direction as X-direction taking tested gear, level is to the right positive dirction, with tested gear centre point O ₁with the line of initial point O be Y direction, depart from tested gear centre point O ₁for forward;

S3: on the basis of above-mentioned fixing rectangular coordinate system, in the teeth groove of the 1st measurement of record, tooth bar gauge head is along the deviate on X-axis and Y-axis both direction; When setting tooth bar gauge head contacts with the 1st teeth groove of tested gear, it is Δ x that tooth bar gauge head produces deviate in X-direction ₁, in Y direction, producing deviate is Δ y ₁, obtain like this 1st teeth groove deviate group (Δ x ₁, Δ y ₁); Then exit tested gear tooth slot; Complete the measurement of the 1st teeth groove.

S4: be rotated counterclockwise tested gear

angle, the measurement that enters the 2nd teeth groove, after measurement, exits the 2nd teeth groove, and then is rotated counterclockwise tested gear, successively measures successively all teeth groove of tested gear; If while measuring i teeth groove, producing deviate in tooth bar gauge head X-direction is Δ x _i, in tooth bar gauge head Y direction, producing deviate is Δ y _i, can obtain i teeth groove deviate group (Δ x _i, Δ y _i); While measuring j teeth groove, in tooth bar gauge head X-direction, producing deviate is Δ x _j, in tooth bar gauge head Y direction, producing deviate is Δ y _j, can obtain j teeth groove deviate group (Δ x _j, Δ y _j), wherein i, j=1,2 ..., z, i ≠ j, z is the tested gear number of teeth; The tooth pitch deviation that has completed so tested gear is measured.

S5: by the z group deviate measuring, every two groups of (Δ x _i, Δ y _i), (Δ x _j, Δ y _j), i, j=1,2 ..., z, in the following mathematical model formula of substitution, can solve the tooth pitch deviation that obtains the tested gear left and right flank of tooth respectively.

$\left\{\begin{array}{c}{F}_{\mathrm{PL}}=\max |\frac{{\mathrm{\Δx}}_i\sin {\mathrm{\α}}_s+{\mathrm{\Δy}}_i\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}-\frac{{\mathrm{\Δx}}_j\sin {\mathrm{\α}}_s+{\mathrm{\Δy}}_j\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}|\\ F_{\mathrm{PR}}=\max |\frac{-({\mathrm{\Δx}}_i\sin {\mathrm{\α}}_s-{\mathrm{\Δy}}_i\cos {\mathrm{\α}}_s)}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}+\frac{{\mathrm{\Δx}}_j\sin {\mathrm{\α}}_s-{\mathrm{\Δy}}_j\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}|\end{array}\right.---\left(3\right)$

Wherein:

i＝1，2…z；j＝1，2…z；i≠j；

Z is the tested gear number of teeth, and i is i teeth groove number of tested gear, and j is j teeth groove number of tested gear;

Δ x _iduring for tooth bar gauge head and i teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in X-direction;

Δ y _iduring for tooth bar gauge head and i teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in Y direction;

Δ x _jduring for tooth bar gauge head and j teeth groove double contact of tested gear, tooth bar gauge head is along X-axis

In direction, produce deviate;

Δ y _jduring for tooth bar gauge head and j teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in Y direction;

α _sfor the profile angle of tooth bar gauge head;

F _pLfor left transverse pitch deviation;

F _pRfor right transverse pitch deviation.

The method of this invention can obtain following beneficial effect:

1) the present invention can realize two-sided engagement and measure the tooth pitch deviation of tested gear, and radially comprehensive total departure and the radially comprehensive deviation of a tooth that can only draw tested gear are measured in traditional two-sided engagement, can not obtain tooth pitch deviation;

2) the present invention can improve measurement efficiency: the present invention proposes a kind of tooth bar gauge head based on two-sided engagement and engage with tested gear the method for prototype gear tooth pitch deviation, can realize one-shot measurement and obtain simultaneously the tooth pitch deviation of the tested gear left and right flank of tooth.

3) the present invention can meet the measurement demand of on-the-spot gear: the present invention adopts two-sided engagement to measure, and principle is simple, without strict demand, can adapt to relatively severe production on-site environment to measurement environment.

Brief description of the drawings

Fig. 1 is the outside drawing that tooth pitch is measured middle rack gauge head

Fig. 2 is the foundation that tooth pitch is measured coordinate system

Fig. 3 is tooth pitch measuring principle

Fig. 4 is tooth pitch measurement procedure

Embodiment

1 enforcement is taking a concrete gear z=18 as example, and the present invention is described further by reference to the accompanying drawings:

1) basic parameter of known tested gear is as follows: number of teeth z=18, modulus m=2, pressure angle α=20 °;

2) profile angle of tooth bar gauge head is calculated

Measure the profile angle computing formula (1) of middle rack gauge head according to tooth pitch

${\mathrm{\α}}_s=\mathrm{\α}+\frac{\mathrm{\π}}{2z},$ Can obtain:

α _s＝25°。Flank profil is measured the outside drawing of middle rack gauge head, as shown in Figure 1.

3) set up coordinate system

As shown in Figure 2, set up rectangular coordinate system.With two of left and right action line n ₁, n ₂intersection point be initial point O, move horizontally direction as X-direction taking tested gear, level is to the right forward, with tested gear centre point O ₁with the line of initial point O be Y direction, depart from tested gear centre point O ₁it is upwards forward.As shown in Figure 3, tested gear teeth face has error to tooth pitch deviation measuring principle, and contact point will produce displacement increment along action line direction.Displacement increment in action line is decomposed on X-axis and Y-axis both direction and analyzed, obtain tooth bar gauge head in X-axis and Y-axis deviate by measurement, set up mathematical model and also finally solve and obtain tooth pitch deviation.

4) tooth pitch deviation data gathers

Use profile angle α _sthe tooth bar gauge head of=25 ° is measured tested gear.

An optional teeth groove, as the teeth groove of the 1st measurement, guarantees that the center line of teeth groove and the centerline of tooth bar gauge head are on the vertical straight line of same.Allow tooth bar gauge head enter in the teeth groove of tested gear, with the tight double contact of the left and right flank of tooth of tested gear.The deviate of tooth bar gauge head on X-axis and Y-axis both direction obtained in measurement.Then allow tooth bar gauge head exit tested teeth groove, the 1st teeth groove measured complete.Be rotated counterclockwise tested gear, successively measure successively all teeth groove of tested gear, altogether measure z=18 time, obtained 18 groups of deviate groups.While measuring i teeth groove, the deviate group of acquisition is designated as (Δ x _i, Δ y _i), while measuring j teeth groove, the deviate group of acquisition is designated as (Δ x _j, Δ y _j), wherein i, j=1,2 ..., 18, i ≠ j.The measurement of whole like this gear is just through with.

4) calculate tooth pitch deviation

By the deviate group of above-mentioned acquisition, in the mathematical model formula (3) of every two groups of difference substitution tooth pitch deviations, can calculate tested gear left and right transverse pitch deviation.

2 measuring processs

The method is undertaken by step shown in Fig. 4.

1) determine the basic parameter (number of teeth z, modulus m, pressure angle α) of tested gear;

2) be chosen as the tooth bar gauge head of measuring tested gears tooth pitch deviation and design;

3) select arbitrarily certain teeth groove of tested gear as the teeth groove of the 1st measurement, adjust the position of tested gear and tooth bar gauge head, allow tooth bar gauge head enter in tested gear tooth slot, and with the tight double contact of the tested gear left and right flank of tooth, record the deviate of tooth bar gauge head on X, Y both direction;

4) tooth bar gauge head exits the 1st teeth groove of tested gear, completes the measurement of the 1st teeth groove;

5) tested gear turns clockwise

degree, this hour rack gauge head faces the 2nd teeth groove of tested gear, tooth bar gauge head enters in the 2nd teeth groove of tested gear, and with the tight double contact of the tested gear left and right flank of tooth, record the deviate of tooth bar gauge head on X, Y both direction;

6) tooth bar gauge head exits the 2nd teeth groove of tested gear;

7) repeat 3)～6), repeat to measure z time altogether successively;

8) tooth pitch that has completed tested gear is measured;

9) calculate tested gears tooth pitch error.

Claims (1)

1. based on two-sided meshed gears tooth pitch bias measurement method, it is characterized in that: adopt a kind of tooth bar gauge head, based on the tooth pitch deviation of the tested gear of two-sided engagement contact measurement, this tooth bar gauge head only has a tooth, its flank profil is straight line, and the angle of tooth bar gauge head center line and flank profil straight line is the profile angle note α of tooth bar gauge head _s,

${\mathrm{\α}}_s=\mathrm{\α}+\frac{\mathrm{\π}}{2z}---\left(1\right)$

Wherein:

α is tested gear compound graduation circle pressure angle;

Z is the tested gear number of teeth;

Described measuring method is specific as follows:

S1: tested gear can initiatively rotate around axle center, tooth bar gauge head can move along level and vertical both direction; Certain teeth groove of optional tested gear is as the teeth groove of the 1st measurement, rotate tested gear and make the center line of teeth groove of the 1st measurement of tested gear and the centerline of tooth bar gauge head on the vertical straight line of same, tooth bar gauge head up, tested gear below; Tooth bar gauge head enters the teeth groove of tested gear, contacts with the two-sided engagement of the tested gear left and right flank of tooth;

S2: make two the action line n in left and right with the contact point of tooth bar gauge head and tested the two flank profil of gear ₁, n ₂, set up fixing rectangular coordinate system, with two action line n ₁, n ₂intersection point be initial point O, move horizontally direction as X-direction taking tested gear, level is to the right positive dirction, with tested gear centre point O ₁with the line of initial point O be Y direction, depart from tested gear centre point O ₁for forward;

S3: on the basis of above-mentioned fixing rectangular coordinate system, in the teeth groove of the 1st measurement of record, tooth bar gauge head is along the deviate on X-axis and Y-axis both direction; When setting tooth bar gauge head contacts with the 1st teeth groove of tested gear, it is Δ x that tooth bar gauge head produces deviate in X-direction ₁, in Y direction, producing deviate is Δ y ₁, obtain like this 1st teeth groove deviate group (Δ x ₁, Δ y ₁); Then exit tested gear tooth slot; Complete the measurement of the 1st teeth groove;

S4: be rotated counterclockwise tested gear

angle, the measurement that enters the 2nd teeth groove, after measurement, exits the 2nd teeth groove, and then is rotated counterclockwise tested gear, successively measures successively all teeth groove of tested gear; If while measuring i teeth groove, producing deviate in tooth bar gauge head X-direction is Δ x _i, in tooth bar gauge head Y direction, producing deviate is Δ y _i, can obtain i teeth groove deviate group (Δ x _i, Δ y _i); While measuring j teeth groove, in tooth bar gauge head X-direction, producing deviate is Δ x _j, in tooth bar gauge head Y direction, producing deviate is Δ y _j, can obtain j teeth groove deviate group (Δ x _j, Δ y _j), wherein i, j=1,2 ..., z, i ≠ j, z is the tested gear number of teeth; The tooth pitch deviation that has completed so tested gear is measured;

S5: by the z group deviate measuring, every two groups of (Δ x _i, Δ y _i), (Δ x _j, Δ y _j), i, j=1,2 ..., z, in the following mathematical model formula of substitution, can solve the tooth pitch deviation that obtains the tested gear left and right flank of tooth respectively;

$\left\{\begin{array}{c}{F}_{\mathrm{PL}}=\max |\frac{\mathrm{\Δ}{x}_i\sin {\mathrm{\α}}_s+\mathrm{\Δ}{y}_i\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}-\frac{\mathrm{\Δ}{x}_j\sin {\mathrm{\α}}_2+\mathrm{\Δ}{y}_j\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}|\\ F_{\mathrm{PR}}=\max |\frac{-(\mathrm{\Δ}{x}_i\sin {\mathrm{\α}}_s-\mathrm{\Δ}{y}_i\cos {\mathrm{\α}}_s)}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_2}+\frac{\mathrm{\Δ}{x}_j\sin {\mathrm{\α}}_s-\mathrm{\Δ}{y}_j\cos {\mathrm{\α}}_s}{2\sin {\mathrm{\α}}_s{\cos }^2{\mathrm{\α}}_s}|\end{array}\right.---\left(3\right)$

Wherein:

i=1,2"z；j=1,2"z；i≠j；

Z is the tested gear number of teeth, and i is i teeth groove number of tested gear, and j is j teeth groove number of tested gear;

Δ x _iduring for tooth bar gauge head and i teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in X-direction;

Δ y _iduring for tooth bar gauge head and i teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in Y direction;

Δ x _jduring for tooth bar gauge head and j teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in X-direction;

Δ y _jduring for tooth bar gauge head and j teeth groove double contact of tested gear, tooth bar gauge head is along producing deviate in Y direction;

α _sfor the profile angle of tooth bar gauge head;

F _pLfor left transverse pitch deviation;

F _pRfor right transverse pitch deviation.

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