Form error evaluation using L1-approximation

Namboothiri, V. N. N.; Shunmugam, M.S.

doi:10.1016/s0045-7825(97)00338-1

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…The (5) is equivalent to the following: (8) Moreover, let and denote the matrices constructed by the remaining rows of and which are not included in and , respectively. The complete system in (7) [or (6)] can be written as follows: (9) Suppose that a few samples have been taken. We introduce a wavelet-based interpolating scheme which interpolates the sampled points and adopts the minimum energy principle.…”

Section: Wavelet-based Random Curve Interpolating Algorithmmentioning

confidence: 99%

“…The OLS method fits an ideal feature to CMM data by minimizing the sum of squared orthogonal residuals and uses the range of the resulting orthogonal residuals to estimate the form error. Some variants of the OLS method have been also proposed for more robust estimation of the form error in the presence of measurement outliers [7]- [9]. The MZ method finds the maximum inscribing and minimum circumscribing features that bound all the CMM data and uses the orthogonal width to estimate the form error.…”

Section: Introductionmentioning

confidence: 99%

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A Lipschitz Regularity-Based Statistical Model With Applications in Coordinate Metrology

Kim

Huo

Shilling

et al. 2014

IEEE Trans. Automat. Sci. Eng.

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In dimensional inspection using coordinate measuring machines (CMMs), the following issues are critical to achieve accurate inspection while minimizing the cost and time: 1) How can we select the sampling positions of the measurements so that we can get as much information from a limited number of samples as possible and 2) given the limited number of measurements, how can we assess the form error so that one can reliably decide whether the product is acceptable? To address these problems, we propose a wavelet-based model that takes advantage of the fact that the Lipschitz regularity holds for the CMM data. Under the framework of the proposed model, we derive the optimal sampling positions and propose a systematic procedure to estimate the form error given the limited number of sampled points. The proposed method is validated using both synthetic and real CMM data sets for straightness measurements. The comparison with other existing methods demonstrates the effectiveness of our method.Note to Practitioners-This paper was motivated by the problem of measuring a machined part and assessing the part compliance with tolerance specifications in dimensional inspection using CMMs. In coordinate measurements, there is an important tradeoff between the number of inspected points and inspection time. Therefore, it is important to determine optimal locations on the part to be inspected in order to gain maximum part information out of limited number of points. Given these limited number of measurement points, it is also important and challenging to decide the part acceptance reliably. This paper proposes a wavelet-based model for CMM measurements. The proposed model provides practitioners with the optimal sampling positions and the estimated form error given the sampled measurement points. While traditional methods often suffer from the underestimation of the form error, the proposed method estimates the form error unbiasedly with even a small number of measurements. The proposed method can be easily implemented using existing wavelet software packages. Even though this paper was motivated by issues that arise with CMM measurements, the methodology can be easily adapted to a wide range of industrial applications where taking measurements is expensive.

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Section: Wavelet-based Random Curve Interpolating Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Lipschitz Regularity-Based Statistical Model With Applications in Coordinate Metrology

Kim

Huo

Shilling

et al. 2014

IEEE Trans. Automat. Sci. Eng.

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show abstract

“…Most papers surveyed in Dowling et al (1997) provided algorithms to realize the two ideas for various kinds of geometric features. Dowling et al (1997) also discussed some variants of the OLS method, which use a different objective function, e.g., the least average deviation used in Shunmugam (1987Shunmugam ( , 1991 and Namboothiri and Shunmugam (1998), which is supposed to be more robust in the presence of measurement outliers.…”

Section: Introductionmentioning

confidence: 99%

Gaussian process method for form error assessment using coordinate measurements

2008

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A Gaussian process method for modeling and assessing form errors is presented. The Gaussian process method decomposes a geometric feature into three components: designed geometric form, systematic manufacturing errors and random manufacturing errors. It models the systematic manufacturing errors as a spatial model using a Gaussian correlation function and models the random manufacturing errors as independent identically distributed noises. Based on a handful of coordinate measurements, the Gaussian process model reconstructs the part surface and assesses the form error better than traditional methods. The Gaussian process method also provides an empirical distribution of the form error, allowing engineers to quantify the decision risk on part acceptance. This method works for generic geometric features. The method is implemented on two common features: a straight and a round feature. Simulated datasets as well as actual coordinate measuring machine data are used to demonstrate the improvement achieved by the proposed method over the traditional approaches.

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Qualification and validation the metrology module located on CN machine tool -EMCO PC Mill 155 –

Merghache

Ghernaout

2014

J. Phys.: Conf. Ser.

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Form error evaluation using L1-approximation

Cited by 3 publications

References 11 publications

A Lipschitz Regularity-Based Statistical Model With Applications in Coordinate Metrology

A Lipschitz Regularity-Based Statistical Model With Applications in Coordinate Metrology

Gaussian process method for form error assessment using coordinate measurements

Qualification and validation the metrology module located on CN machine tool -EMCO PC Mill 155 –

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