Reduced error separating method for pitch calibration on gears

Keller, Frank; Stein, Martin; Kniel, Karin

doi:10.1142/9789813274303_0020

Cited by 3 publications

(7 citation statements)

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“…Since for the (complete) three-rosette method, the measurement effort increases with the square N 2 of the number of teeth, this method becomes very time-consuming for large N. Therefore, some approaches have been presented in the literature for a reduced method that requires less measurement effort [6,[11][12][13][14]. The method introduced in [11] for interferometric angle graduation measurements is briefly explained in the following subsection in the context of pitch deviation measurement of gears.…”

Section: Reduced Three-rosette Methodsmentioning

confidence: 99%

“…Since this is a linear least-squares problem with linear constraints, the solution is straightforward, see [11,14] for details. The pitch errors of the divided circles A and C are separated by performing measurements in different positions rotated to each other.…”

Section: Reduction Of the Relative Positionsmentioning

confidence: 99%

“…For linear least-squares problems, the calculation of the standard deviations for the fitted parameters is straightforward. Reference [14] is referred to for the calculations in the present case. In the following, the results achieved therein are used.…”

Section: Choice Of Relative Positionsmentioning

confidence: 99%

“…From the covariance matrix for the centred cumulative pitch deviations A, the variances for the cumulative pitch deviations F p,k = A k − A N−1 and for the single pitch deviations f p,k = A k − A k−1 can be easily calculated. Using the results from [14], this leads to…”

Section: Contributions From the Least-squares Fitmentioning

confidence: 99%

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Validation and uncertainty analysis of a reduced self-calibrating method for pitch measurements of cylindrical gears

Keller¹,

Stein²,

Kniel³

2021

Meas. Sci. Technol.

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The three-rosette method is a well-established self-calibrating error-separation method used for highly accurate pitch calibrations of cylindrical gears on coordinate measuring machines or gear measuring machines. It is based on the principle of circle closure and uses multiple measurements in different relative positions of the gear with respect to the measuring device. However, since its measurement effort is proportional to the square of the number of teeth, the method is of limited usability for gears with a large number of teeth. In this paper, a reduced method which requires much fewer measurements is described. This method is based on the same error model and is still self-calibrating. The measurement uncertainties for this method are only slightly higher than for the complete method. After an introduction to the three-rosette method, this paper describes the impact of the number and choice of the measured relative positions on the measurement uncertainty. Moreover, the problem of an erroneously determined gear axis is addressed. Finally, the effectiveness of the reduced three-rosette method is shown in intercomparison measurements with four participants. The obtained E n scores show that the reduced three-rosette method allows pitch calibrations with nearly the same accuracy as can be achieved with the complete method. The reduced three-rosette method is part of the TraCIM online service (https://tracim.ptb.de) of the Physikalisch-Technische Bundesanstalt (PTB) allowing software manufacturers or calibration laboratories to obtain a certificate for their algorithms of the reduced three-rosette method after a successfully performed software test. Moreover, calibration laboratories can receive accreditation by the German national accreditation body (DAkkS) for pitch calibrations performed by using the reduced three-rosette method.

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Section: Reduced Three-rosette Methodsmentioning

confidence: 99%

Section: Reduction Of the Relative Positionsmentioning

confidence: 99%

Section: Choice Of Relative Positionsmentioning

confidence: 99%

Section: Contributions From the Least-squares Fitmentioning

confidence: 99%

See 2 more Smart Citations

Validation and uncertainty analysis of a reduced self-calibrating method for pitch measurements of cylindrical gears

Keller¹,

Stein²,

Kniel³

2021

Meas. Sci. Technol.

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“…For appropriate choices of R and S, equation ( 14) together with the constraints gives unique solutions for all parameters. Reference is made to [10,11] for some necessary conditions for choices of the ball and CMM positions. However, in this setting, appropriate choices may be defined by the requirement that the matrix formed by the constrained linear system given by equation ( 14) together with the above constraints must have full rank.…”

Section: Constraintsmentioning

confidence: 99%

A reduced self-calibrating method for rotary table error motions

Keller

Stein²

2023

Meas. Sci. Technol.

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A novel method for the determination of rotary table errors in six degrees of freedom on coordinate measuring machines or machine tools is introduced. The method is based on the measurement of an uncalibrated circular ball plate in different rotational positions on the rotary table, also referred to as the three-rosette method. The novel procedure allows to reduce the number of measurement positions significantly compared to the complete three-rosette method whereas the measurement uncertainty still remains sufficiently small. The method relies on error separation and is self-calibrating which means that no external reference is required. The sophisticated design of a new ball plate allows to determine the rotary table errors in angular steps of only 5°.

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