CN107167105A - 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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- G—PHYSICS
- 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
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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 X-axis and Y-axis deflection angle 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 in measurement process by using a kind of method based on Coordinate Conversion and greatly improves measurement accuracy after the measurement error caused by clamping, compensation indirectly.
Description
Technical field
The present invention relates to cycloid gear detection, it is related to as the detection error compensation scheme caused by installation deviation, specifically relates to
And a kind of error compensating method of cycloid gear detection.
Background technology
Cycloid gear reductor because its have gearratio big, compact conformation, efficiency high, operate steadily it is excellent with long lifespan
Characteristic, is widely used in the industrial circles such as machinery, mine, metallurgy, chemical industry, weaving, national defense industry.Cycloid gear is used as reductor
In a core component, its accuracy of manufacture directly affects overall performance.Therefore, to the quality of the cycloid gear part after processing
Detection, has become an important step of whole production process, any one trickle measurement error factor all can directly be led
The erroneous judgement to product quality is caused, therefore, needing a kind of error compensating method badly can be to as the measurement error caused by Rig up error
It is modified, so as to obtain that the true measurement of part crudy can be reflected.
At present, the detection of conventional cycloid gear flank profil is carried out on three-coordinates measuring machine, due to the clamping of cycloid gear
Error, the axial line of cycloid gear and the Z axis of three-coordinates measuring machine it cannot be guaranteed that completely it is misaligned, so alignment error can be produced
So as to influence the measurement accuracy to tooth corridor face, but this error is inevitable again.
When measuring cycloid gear total profile deviation, such as Fig. 1, due to flank profil face to be measured, first fixes probe bracket in Z axis side
To position, then along Y direction mobile probe, and cycloid gear is turned about the Z axis, until probe contacts to cycloid gear
Tooth corridor face, read measurement point coordinate value, record result, then cycloid gear is angularly rotated about the z axis again, one is often rotated
It is secondary, the coordinate value of one-shot measurement point is recorded, until cycloid gear rotates a circle, measurement is completed.In the teeth directional of measurement cycloid gear
During deviation, fixed probe turns about the Z axis cycloid gear in the position of Y direction, until probe contacts to cycloid gear, reads
The coordinate value of measurement point, records result, then will pop one's head in along Z-direction, equidistantly moves a certain distance, often movement once, is recorded
The coordinate value of one-shot measurement point, is removed until popping one's head in along cycloid gear teeth directional, completes measurement.But, measured in above-mentioned reality
Cheng Zhong, clamping cycloid gear always has more or less deviation, for example, bias and the inclination of cycloid gear axial line, this kind of inclined
Difference is again inevitable, but thus caused measurement error can directly affect the standard of measurement result again in actual measurement process
True property.
The content of the invention
It is an object of the invention to provide a kind of method compensated to the error that cycloid gear is detected, to solve existing skill
The problem of measured deviation is big in art.In consideration of it, the present invention proposes a kind of error compensation amendment scheme：Because in three-coordinates measuring machine
Under the cycloid gear coordinate that measures, be the position of cycloid gear relative measurement instrument coordinate system, so cycloid gear axial line is inclined
The heart is exactly its skew relative to measuring instrument coordinate origin in fact, similarly, and the inclination of cycloid gear axial line can regard axle as
What heart line was produced after the rotation of each reference axis.Thinking based on this coordinate transform, it is possible to initial to cycloid gear to install
Error is compensated, i.e., obtain offset and the anglec of rotation of the cycloid gear axial line relative to origin first, then by coordinate system
It is corresponding to move a certain distance and rotate a certain angle, it is possible to eliminate this error.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention is：
A kind of error compensating method of cycloid gear detection, is measured using three-coordinates measuring machine measurement cycloid gear,
It is characterised in that it includes following steps：
Step 1: X, Y and Z axis for defining three-coordinates measuring machine are original coordinates, cycloid is measured using three-coordinates measuring machine
P (the x in different height direction on gear axis line1,y1,z1) and Q (x2,y2,z2) two point coordinates, pendulum can be drawn using formula (5)
Deflection angle θ of the line gear axial line relative to X-axis and Y-axis1And θ2,
Wherein, θ1It is cycloid gear axial line relative to X-axis deflection angle, θ2It is inclined relative to Y-axis for cycloid gear axial line
Gyration；
Step 2: passing through P (x1,y1,z1) and Q (x2,y2,z2) two point coordinates determine cycloid gear axial line equation, it is
Formula (6), as z=0, formula (6) is changed into formula (7), you can obtain cycloid gear axial line and XOY plane intersecting point coordinate S
(xs,ys), wherein,
Step 3: being measured by three-coordinates measuring machine to the tooth corridor face of cycloid gear, measured value (x is obtainedm,ym,
zm), the data of measurement carry out changing to obtain revised measured value (x, y, z) by formula (3)；
Step 4: then will be by former coordinate system around X, Y-axis rotates corresponding angle and moves corresponding distance relative to the center of circle,
Revised measured value (x, y, z) by formula (8) by changing, the coordinate value (x after being compensatedα,yα,zα), that is, complete pendulum
The compensation of line gear tooth corridor planar survey.
Preferably, in step 3, it is considered to which probe radius influences on the tooth corridor planar survey of cycloid gear, will pass through formula
(3) correction value (x, y, z) obtained is converted to the correction-compensation value (x for considering probe radius size by formula (4)p,yp,
zp),
Then by (xp,yp,zp) changed by formula (4), the coordinate value (x after being compensatedα,yα,zα), that is, complete cycloid
The compensation of gear teeth corridor planar survey.
Further, above-mentioned measuring three-coordinates measuring machine and measurement compensation method can be applied to product design, mould
Has the accurate measurement of the mechanical manufacture of equipment, gear measurement, Blade measuring, frock clamp, vapour mould accessory and electronic apparatus.
The beneficial effects of the invention are as follows：
The present invention by way of error compensation, is eliminated indirectly by using a kind of method based on Coordinate Conversion
Measurement error in measurement process caused by clamping, so as to meet the requirement to tooth corridor face high-acruracy survey, it is ensured that pendulum
The quality of production of line gear.
Brief description of the drawings
Fig. 1 coordinate system transfer principle schematic diagrames.
Fig. 2 is using three-coordinates measuring machine to cycloid gear flank profil instrumentation plan.
Fig. 3 cycloid tooth gear teeth corridors face equation generating structure schematic diagram.
Cycloid gear axial line relative position schematic diagrames of the Fig. 4 in the case of tilting and be eccentric.
1- pedestals, 2- turntables, 3- cycloid gears, 4- probes, 5- probe brackets, 6- thimbles, 7- slides, 8- axial lines.
Embodiment
Two-dimensional assemblage example
As shown in figure 1, coordinate system is with respect to origin rotate counterclockwise θ angles, certain coordinate of point under non-rotating coordinate system is A
Coordinate is B (x ', y ') under (x, y), postrotational coordinate system, and same point has different coordinate values under different coordinates,
Obviously the relation between them, is the key for connecting two coordinate systems, by calculating, and can obtain this o'clock in two seats
Relational expression under mark system is as follows：
Conversion of the same point under different coordinates is so achieved that, point can be derived so under two-dimensional coordinate system
Relation, can similarly derive three-dimensional system of coordinate also has similar relation.
As shown in Fig. 2 the structure includes：Pedestal 1, turntable 2, cycloid gear 3, probe 4, probe bracket 5, thimble 6, slide
7 and axial line 8.
Pedestal 1 is played a supporting role, and one end of cycloid gear 3 is placed on turntable 2, and other end thimble 6 is fixed, and is visited
First 4 are arranged on probe bracket 5, and probe bracket 5 is in turn mounted on slide 7, as shown in Figure 2：Probe 4 can be caused in X, Y, Z
Side is moved up, to realize the measurement to the tooth corridor face of cycloid gear 3.The present invention is proposed when measuring 3 tooth corridor face of cycloid gear,
Based on coordinate system conversion, a kind of compensation scheme for 4 alignment errors of popping one's head in pops one's head in 4 when measuring 3 tooth corridor face of cycloid gear, due to
The relative origin of the meeting of axial line 8 of cycloid gear 3 is offset, and moreover, the axial line 8 is it also occur that tilt, this is in measurement
When be inevitable, for this high-precision travelling gear of cycloid gear 3, small error can all influence it
Measurement accuracy, so being made up in measurement this because during measurement, the inclination of the axial line 8 of cycloid gear 3 and eccentric brings
Error is just particularly important.In order to preferably explain compensation scheme, first simply introducing the tooth corridor face equation of cycloid gear 3 is
How to generate, as shown in figure 3, round as a ball center of circle O1It is a with basic circle center of circle O distances, it is round as a ball by O1Along basic circle O outside, do circumscribed
PURE ROLLING is to O2Position, correspondingly, round as a ball upper point M1Move to point M, wherein M1The movement locus of point is exactly epicycloidal tooth
Wide curve, then generating point M can be represented by (2) formula：
In (2) formula, r1, r2Basic circle and round as a ball radius are represented respectively,It is round as a ball rotational angle, l is to generate point along Z
The height of axle.When the axial line 8 in view of cycloid gear 3 is eccentric and tilts, the tooth corridor surface model of cycloid gear 3 can be by formula 3
Represent：
θ in formula (3)1, θ2Represent respectively, the axial line 8 of cycloid gear 3 is relative to X, the deflection angle of Y-axis,For pendulum
The measured value in the tooth corridor face of line gear 3,For rotation gear axis line 8 and XOY plane point of intersection S (xs,ys, 0) and coordinate,For
Consider the axial line of cycloid gear 3 bias and tilt, the tooth corridor face of cycloid gear 3 it is corrected after measured value, if it is considered that
To the radius size of probe, formula (3) can be changed into formula (4),
In (4) formula, rμRepresent the size of probe radius, n (nx,ny,nz) be the axial line 8 of cycloid gear 3 eccentric and
Normal line vector under inclination conditions, (xp,yp,zp) it is to consider the measured value after probe radius size post-equalization.So by (3) formula
It can draw, as long as having drawn the axial line 8 of cycloid gear 3 relative to X, the deflection angle and axial line of Y-axis are inclined with respect to the center of circle
Shifting amount can be carried out the compensation of alignment error, and coordinate system conversion is carried out by formula (8) again after being compensated by formula (4).
The program is, as shown in Figure 4：Coordinate P (the x in axle center above cycloid gear 3 are measured with three-coordinates measuring machine1,y1,
z1) and following axle center coordinate Q (x2,y2,z2), then axial line is relative to X-axis and the tilt angle theta of Y-axis1, θ2Can be by formula (5)
Draw：
This 2 points coordinate of P and Q is measured, then the space line equation of the axial line 8 of cycloid gear 3 just may establish that, i.e.,
Formula (6), then in XOY plane, z=0, (6) formula can be rewritten as：
The axial line 8 and XOY plane point of intersection S (x of cycloid gear 3 can be obtaineds,ys, 0) and coordinate,
Wherein,And then the axle center of cycloid gear 3 can be drawn
Offset of the line 8 relative to origin.
Then the tooth corridor face of cycloid gear 3 is measured using three-coordinates measuring machine and obtains (xm,ym,zm), the seat of measurement
Scale value is modified compensation according to formula (3), obtains (x, y, z), then will be by former coordinate system around X, and Y-axis rotates corresponding angle
Corresponding distance is moved with relative to the center of circle.Coordinate Conversion is carried out by formula (8), obtains surveying on tooth corridor face after coordinate system conversion amendment
Measure the coordinate (x of pointm,ym,zm)。
In formula, RxAnd RyIt is around X, the spin matrix of Y-axis, T (Δs respectivelye) represent translation matrix；
In (xm,ym,zm) be measurement point on the tooth corridor face of cycloid gear 3 of actual measurement coordinate, last is several
Word 1；
In (xα,yα,zα) it is the coordinate that coordinate system changes measurement point on tooth corridor face after amendment, last is also to be
Numeral 1, because the transformation matrix of description space three-dimensional conversion is 4 × 4 form, adds 1 in last column of matrix, constitutes one
Individual 4 × 4 matrix.Each measurement point will obtain revised measured value by Coordinate Conversion, so as to reach elimination inclination angle
Degree and the error amount of skew.Because the skew and inclination of the axial line 8 of cycloid gear 3 are micro and inevitable, original
Coordinate system in, these errors can be revealed in measurement, in order to compensate these deviations, can be carried out coordinate system certain
Reverse " inclination " and " bias " processing, be corresponding rotation and offset, come the inclination of the axial line 8 of offsetting cycloid gear 3
And bias.This thinking is a kind of conversion of object in fact, and it is feasible and is convenient operation.Make its measured value
Reach ideal value.
Claims (3)
1. a kind of error compensating method of cycloid gear detection, is measured using three-coordinates measuring machine measurement cycloid gear, its
It is characterised by, comprises the following steps：
Step 1: X, Y and Z axis for defining three-coordinates measuring machine are original coordinates, cycloid gear is measured using three-coordinates measuring machine
P (the x in different height direction on axial line1,y1,z1) and Q (x2,y2,z2) two point coordinates, cycloid tooth can be drawn using formula (5)
Take turns deflection angle θ of the axial line relative to X-axis and Y-axis1And θ2,
Wherein, θ1It is cycloid gear axial line relative to X-axis deflection angle, θ2It is cycloid gear axial line relative to Y-axis deflection angle
Degree；
Step 2: passing through P (x1,y1,z1) and Q (x2,y2,z2) two point coordinates determine cycloid gear axial line equation, as formula
(6), as z=0, formula (6) is changed into formula (7), you can obtain cycloid gear axial line and XOY plane intersecting point coordinate S (xs,
ys), wherein,
Step 3: being measured by three-coordinates measuring machine to the tooth corridor face of cycloid gear, measured value (x is obtainedm,ym,zm), survey
The data of amount carry out changing to obtain revised measured value (x, y, z) by formula (3)；
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Step 4: then will be by former coordinate system around X, Y-axis rotates corresponding angle and moves corresponding distance, amendment relative to the center of circle
Measured value (x, y, z) afterwards obtains the coordinate value (x after coordinate system correction-compensation by being changed by formula (8)α,yα,zα), i.e.,
Complete the compensation of cycloid tooth gear teeth corridor planar survey.
2. the error compensating method that a kind of cycloid gear is detected according to claim 1, it is characterised in that：In step 3,
Consider that probe radius influences on the tooth corridor planar survey of cycloid gear, the correction value (x, y, z) that will be obtained by formula (3) is by public affairs
Formula (4) is converted to the correction-compensation value (x for considering probe radius sizep,yp,zp),
Then by (xp,yp,zp) changed by formula (8), obtain the coordinate value (x after coordinate system correction-compensationα,yα,zα), i.e., it is complete
Into the compensation of cycloid tooth gear teeth corridor planar survey.
3. a kind of error compensating method of cycloid gear detection according to claim 1 or claim 2, it is characterised in that：Above-mentioned measurement
Three-coordinates measuring machine and measurement compensation method can be applied to product design, mould equipment, gear measurement, blade measuring machine
Tool manufacture, frock clamp, the accurate measurement of vapour mould accessory and electronic apparatus.
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| CN108645322A (en) * | 2018-06-21 | 2018-10-12 | 北京工业大学 | Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error |
| CN108645323A (en) * | 2018-06-21 | 2018-10-12 | 北京工业大学 | Involute spur gear wheel total profile deviation assessment method under the influence of installation error |
| CN109631812A (en) * | 2018-12-29 | 2019-04-16 | 哈工精测(岳阳)智能装备有限公司 | A kind of method of automatic measurement gear size |
| CN111609777A (en) * | 2019-02-26 | 2020-09-01 | 利勃海尔齿轮技术股份有限公司 | Method for calibrating a measuring probe in a gear cutting machine |
| CN112414341A (en) * | 2020-09-29 | 2021-02-26 | 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 |
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| CN113899335A (en) * | 2021-08-27 | 2022-01-07 | 北京工业大学 | Method for correcting installation error of gear measured by using contourgraph |
| CN115647932A (en) * | 2022-11-02 | 2023-01-31 | 湖北工业大学 | Method for controlling mounting precision of detachable milling head |
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| CN108645322A (en) * | 2018-06-21 | 2018-10-12 | 北京工业大学 | Involute spur gear wheel circular pitch deviation assessment method under the influence of installation error |
| CN108645323A (en) * | 2018-06-21 | 2018-10-12 | 北京工业大学 | Involute spur gear wheel total profile deviation assessment method under the influence of installation error |
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| 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 |
| CN111609777A (en) * | 2019-02-26 | 2020-09-01 | 利勃海尔齿轮技术股份有限公司 | Method for calibrating a measuring probe in a gear cutting machine |
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| CN112414341A (en) * | 2020-09-29 | 2021-02-26 | 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 |
| CN113739703A (en) * | 2021-08-27 | 2021-12-03 | 浙江大学台州研究院 | Revolving body scanning measurement method and data compensation calibration method thereof |
| CN113899335A (en) * | 2021-08-27 | 2022-01-07 | 北京工业大学 | Method for correcting installation error of gear measured by using contourgraph |
| CN115647932A (en) * | 2022-11-02 | 2023-01-31 | 湖北工业大学 | Method for controlling mounting precision of detachable milling head |
| 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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