Roundness deviation evaluation method based on statistical analysis of local least square circles

Cao, Zhimin; Yun, Wu; Han, Jian

doi:10.1088/1361-6501/aa770f

Cited by 13 publications

(4 citation statements)

References 17 publications

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“…The Least Squares Circle (LSC) [14][15] [16] method is widely used in a variety of occasions of data processing including roundness error evaluation. The results of least square data processing are affected by all the data involved in the calculation, so its processing effect is easily affected by data distribution.…”

Section: Circle Fitting Methodsmentioning

confidence: 99%

Research on coaxiality measurement system of inner spline-bevel gear composite gears shaft

Lü¹,

Fang²,

Xu³

et al. 2023

Preprint

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Aiming at the inner spline-bevel gear composite gears shaft’s coaxiality error measurement, this paper presents a non-contact optical measurement method based on a laser displacement sensor (LDS) and spectral confocal sensor. According to the least square circle (LSC) to calculate the center coordinates of the section, and the space least square fitting to get the reference axis. A standard part is used to calibrate the sensors’ installation errors, and use CMM to verify the system’s accuracy. Ten sets of measurements are made for the same internal spline-bevel gear part, in conclusion, the measurement uncertainty is 0.028 mm, the repeated measurement error is not more than 0.015 mm, the accuracy of the measurement system is 0.055 mm, can meet the needs of industrial production which required accuracy is 0.1mm.

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Section: Circle Fitting Methodsmentioning

confidence: 99%

Research on coaxiality measurement system of inner spline-bevel gear composite gears shaft

Lü¹,

Fang²,

Xu³

et al. 2023

Preprint

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show abstract

“…In the following, the possibilities of the Bayesian approach for geometry element fitting are illustrated by using a real data example. This is done exemplarily by performing circular fits, since this task frequently occurs in practice [1,4,32] and may highly benefit from including prior knowledge into the fitting process. The potential of the Bayesian approach is demonstrated here by the example of a profile roughness measurement using an optical sensor on a cylindrical surface.…”

Section: Application On Measured Datamentioning

confidence: 99%

“…Fitting standard geometric elements such as circles, straight-lines or ellipses (as well as the three-dimensional pendants sphere, plane and ellipsoid) into a set of measured points is a frequently occurring task in many technical applications, e.g. to quantify form deviations between measured data and its underlying nominal geometry [1][2][3][4].…”

Section: Introductionmentioning

confidence: 99%

Bayesian analysis of uncertainties in circle, straight-line and ellipse fitting considering a-priori knowledge − comparative analysis with total-least-squares approaches

Keksel,

Eli,

Eifler

et al. 2024

Surf. Topogr.: Metrol. Prop.

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Fitting standard geometric elements into measurement data using Least-Squares techniques is a common task in signal processing across various technical applications. However, the application of these well-established but purely data-based methods does not consider potentially available prior knowledge about the measurand of interest or the measuring device. Thus, up to this day, additional information is usually left unused beyond a few academic applications. By applying a Bayesian approach, this prior knowledge can be incorporated into the fitting task, potentially leading to a reduction in overall uncertainty and fragility of the evaluation result. In this study, Bayesian models are proposed for incorporating prior knowledge into circular, linear, and ellipse fitting tasks. The general approaches as well as specific results are compared to the established Total-Least-Squares method within the example of the application of the F-operator in surface texture measurement illustrating the practical benefits of the approach.

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“…Currently, there are no generally accepted recommendations for filtering the signal when measuring CMM. Only a few papers [1][2][3][4][5] on this problem are known. Therefore, it is advisable to follow the ISO 16610-1:2015 standard and the analogy with the problems of measuring roundness and roughness, considered in [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the applicability of filtration methods for coordinate measurements

2018

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At present, surface metrology solves such important tasks as monitoring the production process and optimizing the exploitation of parts. A significant part of the measurements is performed by a contact method using Coordinate Measuring Machines. One of the important steps in the processing of measurement information is the filtration of the received signal. The existing standards regulate only the processes of measuring roundness and roughness. Therefore, researches on the applicability of filtration methods in the general case for coordinate measurements are relevant. Based on the review presented in the article, the filters that have received the greatest application in other fields of technology are defined by the strategy of their application for coordinate measurements. It is recommended to use the following sequence: elimination of gross errors based on the Grubbs’ test, discrete Fourier transform for revealing systematic errors, elimination of systematic errors from the signal, minimization of the random error with the bilateral Gaussian filter, surface reconstruction after filtering based on inverse Fourier transform. The above example of signal filtering for flatness confirmed the effectiveness of the proposed approach.

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Roundness deviation evaluation method based on statistical analysis of local least square circles

Cited by 13 publications

References 17 publications

Research on coaxiality measurement system of inner spline-bevel gear composite gears shaft

Research on coaxiality measurement system of inner spline-bevel gear composite gears shaft

Bayesian analysis of uncertainties in circle, straight-line and ellipse fitting considering a-priori knowledge − comparative analysis with total-least-squares approaches

Analysis of the applicability of filtration methods for coordinate measurements

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