CN105277165B - A kind of method that flank of tooth equal interval sampling improves gear measurement precision - Google Patents
A kind of method that flank of tooth equal interval sampling improves gear measurement precision Download PDFInfo
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- CN105277165B CN105277165B CN201510703588.1A CN201510703588A CN105277165B CN 105277165 B CN105277165 B CN 105277165B CN 201510703588 A CN201510703588 A CN 201510703588A CN 105277165 B CN105277165 B CN 105277165B
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Abstract
A kind of method that flank of tooth equal interval sampling improves gear measurement precision, can be during gear measurement, the measurement accuracy problem of gear measuring instrument flank profil is influenceed on the deficiency in current data acquisition technology, and cutter, gear reconditioning are difficult to the problems such as accurate reference corresponding error curve diagram and solved, tooth top sampled point is compensate for dredge compared with tooth root sampled point, the problem of being unable to the reaction flank of tooth microcosmos geometric shape of integrated facticity, is advantageous to the raising of gear measurement precision；Error curve can the analysis of one-to-one with practical tooth each point intuitive, be more beneficial for the error analysis of gear, preferably provide reference for the reconditioning of cutter for gear wheel.
Description
Technical field
The invention belongs to gear measuring instrument detection field, is related to a kind of from flank of tooth equal interval sampling raising gear measurement essence
The method of degree.
Background technology
It is well known that in gear measurement, the measurement of flank profile form error is the main project of gear measurement.At present
The gear measuring instrument that the country uses is all based on greatly electronics and transformed into or mechanical generating principle, and flank of tooth data acquisition modes are also mostly
Using involute flank equal interval sampling mode.Profile error measures detailed process：When tooth form involute deploys, C axles drive
Gear Rotating with Uniform, tangential balladeur train drive gauge head system at the uniform velocity to be moved forward and backward along X-axis.According to electronics generating principle, in theory
The gauge head system scanning flank of tooth under TRAJECTORY CONTROL, now the mode of gauge head gathered data is involute equal interval sampling, gauge head
The data of system acquisition are profile error data.Due to photoelectric technology, computer technology, precise grating sensor and software
The continuous development and application of technology, gear measuring instrument disclosure satisfy that the measurement accuracy of various gears at present, but involute etc.
Sampled point non-uniform phenomenon be present in interval sampling mode.Because involute each point curvature is different, main shaft turns over same angleΔ φWhen, gauge head the sampled point of tip portion two distance than the sampled point of root portions two distance, as shown in figure 1, reflection arrive
On sampling number, i.e. tip portion is fewer than the sampling number of root portions, and it is close that this just results in tooth root sampled point, tooth top sampled point
Thin sampling non-uniform phenomenon.Flank of tooth sampling is uneven to detect flank profil microcosmos geometric shape error with being unable to complete and accurate, draws
Play the irrationality of data processing.Profile error influences the stationarity of transmission in Meshing Process of Spur Gear, and tip portion is also shadow
The key factor of profile error result is rung, it is few if as sampled point at tooth top, and taking for indivedual overproof points is omitted, will certainly
Profile error result is influenceed, influences the scientific evaluation of the steady sexual factor of gear joggleword.In addition, repairing in hobcutter and gear
In mill, it is sometimes desirable to reference to the curve that can truly reflect profile error shape, the gear measuring instrument sampled using the above method,
The point on profile error curve map provided does not correspond with the point in actual tooth form, and cause to show on error curve surpasses
Corresponding point can not be almost found on the flank of tooth, so as to reduce the reference value of cutter and gear reconditioning.
The content of the invention
, can be in tooth it is an object of the invention to provide a kind of method that gear measurement precision is improved from flank of tooth equal interval sampling
During wheel measurement, the measurement accuracy problem of gear measuring instrument flank profil is influenceed on the deficiency in current data acquisition technology, with
And cutter, gear reconditioning are difficult to the problem of accurate reference corresponding error curve diagram and solved.
The present invention, which adopts the following technical scheme that, realizes above-mentioned purpose：It is of the present invention to be improved from flank of tooth equal interval sampling
The method of gear measurement precision is as follows:
（1）According to tooth-face roughness and sampling thheorem selection flank of tooth interval, 10 that gear measuring instrument is related to are given
The gear sampling interval of grade；
（2）The sampling interval of the flank of tooth is resolved into two variables of length of run and the angle of spread, calculate the flank of tooth respectively sampling between
EveryΔS i Corresponding expansion angular spacingΔφ i With length of run intervalΔL i ；
ByS=1/2r b φ 2 ：φ=(2S/r b )1/2--- --- --- --- --- --- --- (formula 1),
ByΔS=ΔS i -ΔS i-1 ;I=1,2 ... n:
ΔS=1/2r b (φ i-1 Δφ i +Δφ i 2 );I=1,2 ... n------------（Formula 2）,
Formula 2 is deformed into：ΔS=1/2r b Δφ i (φ i +φ i-1)；I=1,2 ... n--（Formula 3）,
The interval in the angle of spread and length of run must be corresponded to by formula 1 and formula 3：
Δφ i =(i 1/2 –(i-1) 1/2 ) (2ΔS/r b )1/2 I=1,2 ... n----- （Formula 4）,ΔL i =(i 1/2 –(i- 1) 1/2 ) (2ΔSr b )1/2 I=1,2 ... n------（Formula 5）,
In formula:r b ———— Involute base radius；
Δφ i --- theiIndividual expansion angular spacing；
ΔL i --- theiIndividual length of run interval.
（3）The sampled point of Circular gratings is handled, each sampling is specifically calculated by software according to sampling interval formula
The position of point, these sampled points are compared with all sampling point positions of Circular gratings, select each sampled point with calculating
Position point the most similar, reformulate one group of sampled point.
（4）The new sampled data obtained with gear measuring instrument to processing carries out follow-up traditional processing, draws measurement
Profile error curve and error result.
It is of the invention to be using the beneficial effect obtained after above-mentioned technical proposal：Solve current most of gear measuring instruments
Uneven the problem of bringing is sampled, tooth top sampled point is compensate for and is dredged compared with tooth root sampled point, it is impossible to which the reaction flank of tooth of integrated facticity is micro-
The problem of seeing geometry, is advantageous to the raising of gear measurement precision；Error curve can be one-to-one with practical tooth each point
Intuitive is analyzed, and is more beneficial for the error analysis of gear, preferably provides reference for the reconditioning of cutter for gear wheel.
Brief description of the drawings
Fig. 1 is the present invention between involute employed in the method for flank of tooth equal interval sampling raising gear measurement precision etc.
Every sampling schematic diagram.
Fig. 2 be the present invention from flank of tooth equal interval sampling improve gear measurement precision method employed in the flank of tooth at equal intervals
Sample schematic diagram.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.The present invention operating principle be：Flank of tooth equal interval sampling is said
It is bright, as shown in Fig. 2.Flank of tooth equal interval sampling is to determine a series of uniform sampling points on flank of tooth involute section in advance, when
These backsteppings are to length of run（Or the angle of spread）When upper, it can be seen that the now interval in length of run (or angle of spread)ΔL(or expansion angular spacingΔφ) it is unequal, length of run interval is maximum at tooth root, closer to gear tip clearance every smaller,
Interval reaches minimum at tooth top, but flank of tooth up-sampling intervalΔSIt is equal.
The specific method of gear measurement precision is improved from flank of tooth equal interval sampling is：
（1）According to the sampling interval of tooth-face roughness and sampling thheorem selection flank of tooth equal interval samplingΔS, the present embodiment knot
The sampling interval that practice gives the gear for 10 grades that gear measuring instrument is related to is closed, see the table below.
（2）As shown in Fig. 2 the sampling interval of the flank of tooth is resolved into two variables of length of run and the angle of spread, tooth is calculated
Face each sampling intervalΔS i （ΔS i =Δ S, i=1,2 ... n）, corresponding expansion angular spacingΔφ i With length of run intervalΔL i ；
ByS=1/2r b φ 2 ：φ=(2S/r b )1/2--- --- --- --- --- --- --- (formula 1),
ByΔS=ΔS i -ΔS i-1 ;I=1,2 ... n
ΔS=1/2r b (φ i-1 Δφ i +Δφ i 2 );I=1,2 ... n------------（Formula 2）,
Formula 2 is deformed into：ΔS=1/2r b Δφ i (φ i +φ i-1)；I=1,2 ... n--（Formula 3）, by formula 1 and public affairs
Formula 3 must correspond to the interval in the angle of spread and length of run：
Δφ i =(i 1/2 –(i-1) 1/2 ) (2ΔS/r b )1/2 I=1,2 ... n---（Formula 4）,
ΔL i =(i 1/2 –(i-1) 1/2 )(2ΔSr b )1/2 I=1,2 ... n------（Formula 5）,
In formula:r b --- involute base radius；
Δφ i --- theiIndividual expansion angular spacing；
ΔL i ——iIndividual length of run interval；
In practical application, gear measuring instrument can be with sampling on the basis of long grating, can also be with the basis of Circular gratings
Sampling.Sample mode on the basis of Circular gratings, it is workable, it is more beneficial for sampling, so it is proposed that using Circular gratings
On the basis of sample mode.（3）The sampled point of Circular gratings is handled.Specifically calculated often by software according to sampling interval formula
The position of one sampled point, these points are compared with all sampling point positions of Circular gratings, selects and is adopted with each of calculating
Sampling point position point the most similar, reformulate one group of sampled point.
（4）Gear measuring instrument carries out follow-up traditional processing to the new sampled data that processing obtains, and is measured
Profile error curve and error result.
Claims (1)
1. a kind of method that flank of tooth equal interval sampling improves gear measurement precision, its feature and specific method are as follows：
（1）The sampling interval of flank of tooth equal interval sampling is selected according to accuracy of gear grade, roughness and sampling thheoremΔS, with reference to
Practice gives the sampling interval of the gear for 10 grades that gear measuring instrument is related to, so as to reasonable selection；
（2）According to tested gear health, sampling interval when setting flank of tooth equal interval sampling asΔSi, due to being uniform sampling site etc.
Interval,ΔSi =ΔS,I=1,2 ... n, you can a series of uniform sampling points are determined on flank of tooth involute section in advance；By this
It is corresponding to obtain each length of run interval when putting backsteppings to involute length of run a bitΔL i Computational methods, so as to maintain
The flank of tooth samples at equal intervalsΔS；Each angle of spread corresponding to determination can also be passed through by these backsteppings to the involute angle of spread
IntervalΔφ i Computational methods, and then realize flank of tooth equal interval sampling；（3）By the sampling interval of the flank of toothΔS i Resolve into expansion
LengthΔL i And the angle of spreadΔφ i Two variables, because of flank of tooth equal interval samplingΔS i =ΔS, so as to calculate the flank of tooth respectively sampling between
Every when corresponding expansion angular spacingΔφ i With length of run intervalΔL i ：
Δφ i =(i 1/2 –(i-1) 1/2 ) (2ΔS/r b )1/2 ；I=1,2 ... n
ΔL i =(i 1/2 –(i-1) 1/2 ) (2ΔSr b )1/2；I=1,2 ... n
In formula:r b ———— Involute base radius；
Δφ i --- theiIndividual expansion angular spacing；
ΔL i --- theiIndividual length of run interval；（4）The sampled point of Circular gratings is handled, turned according to sampling interval formula
Analysis is changed, the position of each sampled point is specifically calculated by software, by these sampled points and all sampling point positions of Circular gratings
Compare, select each sampling point position point the most similar with calculating, reformulate one group of sampled point；Surveyed with gear
Measuring appratus carries out follow-up processing to the new sampled data that processing obtains, and draws the profile error curve and error knot of measurement
Fruit.
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| CN107255562A (en) * | 2017-06-09 | 2017-10-17 | 江苏大学 | The establishing method of Circular gratings sample frequency in gear train assembly torsional vibration measurement experiment |
| CN110608879B (en) * | 2018-05-29 | 2021-05-25 | 江苏毅合捷汽车科技股份有限公司 | Measuring method of gear parts |
| CN110285751B (en) * | 2019-05-28 | 2021-04-20 | 中国北方车辆研究所 | Automatic annular multi-tooth component tooth bottom axial surface roughness measuring instrument |
| CN111288936B (en) * | 2020-03-03 | 2021-02-09 | 深圳市海翔铭实业有限公司 | Measurement and evaluation method for roughness of meshing contact surface of cylindrical gear |
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| CN2273847Y (en) * | 1996-02-12 | 1998-02-04 | 浙江大学 | Arrangement for measuring the error of modified involute gear teeth shape |
| EP1504838A1 (en) * | 2003-08-04 | 2005-02-09 | Harmonic Drive Systems Inc. | Resharpenable pinion type cutter with arbitrary tooth shape |
| CN103606156A (en) * | 2013-11-29 | 2014-02-26 | 长春理工大学 | One-dimensional non-uniform gear morphology point cloud precise registration method |
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