Intersecting chord method for minimum zone evaluation of roundness deviation using Cartesian coordinate data

Fei, Liu; Xu, Guizhi; Li, Lin; Zhang, Qing; Liu, Dan

doi:10.1016/j.precisioneng.2015.05.006

Cited by 16 publications

(9 citation statements)

References 15 publications

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“…In recent years, Kim et al [7] proposed a two-step circle detection algorithm using pairs of chords which revealed how a pair of two intersecting chords locates the center of the circle. Liu et al [8] used the crossing relationship of chords to construct the intersecting structure and the minimum zone model of the roundness deviation. These are both effective explorations into intersecting chord methods.…”

Section: Formulation Of the Intersecting Chordsmentioning

confidence: 99%

“…I is the farthest point to V 1 in dataset P i . The virtual centre V 2 of intersecting chords is determined by the coordinates of G, H and I using equation (8). The purpose of this step is to determine two chords, GH and GI.…”

Section: The Evaluation Model Of the Mcsp Based On The Intersecting C...mentioning

confidence: 99%

“…The point M is the nearest point to V 1 in dataset P k . The virtual centre V 2 of the intersecting chords is determined with the coordinates of points Q, L, M using equation (8).…”

Section: The Models Of the Misp Based On The Intersecting Chordsmentioning

confidence: 99%

“…Samuel et al [6] developed algorithms based on computational geometric techniques, which are characterized by the use of the limacoids as assessment features to be considered for evaluating the sphericity error using form data. In addition, other scholars have acquired a lot of valuable research in this field [7][8][9][10][11][12][13][14]. The above-described research studies have established different models of spherical error and proposed different evaluation methods.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

Liu¹,

Xu²,

Zhang³

et al. 2015

Meas. Sci. Technol.

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As one of the Geometrical Product Specifications that are widely applied in industrial manufacturing and measurement, sphericity error can synthetically scale a 3D structure and reflects the machining quality of a spherical workpiece. Following increasing demands in the high motion performance of spherical parts, sphericity error is becoming an indispensable component in the evaluation of form error. However, the evaluation of sphericity error is still considered to be a complex mathematical issue, and the related research studies on the development of available models are lacking. In this paper, an intersecting chord method is first proposed to solve the minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error. This new modelling method leverages chord relationships to replace the characteristic points, thereby significantly reducing the computational complexity and improving the computational efficiency. Using the intersecting chords to generate a virtual centre, the reference sphere in two concentric spheres is simplified as a space intersecting structure. The position of the virtual centre on the space intersecting structure is determined by characteristic chords, which may reduce the deviation between the virtual centre and the centre of the reference sphere. In addition,two experiments are used to verify the effectiveness of the proposed method with real datasets from the Cartesian coordinates. The results indicate that the estimated errors are in perfect agreement with those of the published methods. Meanwhile, the computational efficiency is improved. For the evaluation of the sphericity error, the use of high performance computing is a remarkable change.

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Section: Formulation Of the Intersecting Chordsmentioning

confidence: 99%

Section: The Evaluation Model Of the Mcsp Based On The Intersecting C...mentioning

confidence: 99%

“…The point M is the nearest point to V 1 in dataset P k . The virtual centre V 2 of the intersecting chords is determined with the coordinates of points Q, L, M using equation (8).…”

Section: The Models Of the Misp Based On The Intersecting Chordsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

Liu¹,

Xu²,

Zhang³

et al. 2015

Meas. Sci. Technol.

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show abstract

“…Cui et al proposed an iterative neighborhood search approach for roundness evaluation [12], with a quickly converging algorithm. Based on the feature points model, Fei et al [13] and Liu et al [14] studied an intersecting chord method for the minimum zone evaluation of roundness. This method uses the crossing relationship of the chords to construct the intersecting structure and evaluation model of the minimum zone roundness (MZR) deviation.…”

Section: Introductionmentioning

confidence: 99%

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

Huang¹,

Chao²,

Jiang³

et al. 2019

Meas. Sci. Technol.

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This paper reports an improved method that integrates a bidirectional search of unequal probability and an offset movement mechanism (BSOM) to evaluate the minimum zone roundness (MZR) with high speed and accuracy. The centre and roundness of a least-squares circle are first solved to construct an original search zone, and the initial candidate points of the minimum zone circle centre are configured. A bidirectional search of unequal probability that considers the subsequent points either toward or away from the current best candidate point is designed to enhance the global search ability. Considering the candidate points at different located positions have different effects on convergence characteristics, the search area is divided into two sections based on the average distance between the current best candidate point and the other candidate points, and different forward and backward search probabilities are configured. An adaptive offset movement mechanism is integrated to generate new candidate points for the next generation. The effectiveness of the proposed method is experimentally verified using datasets from previous studies. The configurations of BSOM parameters and influence of the distribution and number of data points on evaluation accuracy and efficiency are analyzed. The experimental examples and comparison results demonstrate the excellent convergence performance of the proposed method, which reaches the global optimum faster than previous methods. Across six different datasets, only 0.0095 s–0.0282 s is required when the average distance D ⩽ 1.0 × 10−7 mm as the iteration convergence condition, and the standard deviation of the MZR is less than 5.3777 × 10−9 mm, while the search parameters are set as P1 = 0.6, P2 = 0.95, and b = 0.6. The proposed approach is expected to be suitable for on-line evaluation of roundness error.

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A study on machining error prediction model of precision vertical grinding machine based on the tolerance of key components

Li,

Fan,

Pan

et al. 2024

Int J Adv Manuf Technol

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Intersecting chord method for minimum zone evaluation of roundness deviation using Cartesian coordinate data

Cited by 16 publications

References 15 publications

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

An intersecting chord method for minimum circumscribed sphere and maximum inscribed sphere evaluations of sphericity error

Improved evaluation of minimum zone roundness by integrating bidirectional search of unequal probability and offset mechanisms

A study on machining error prediction model of precision vertical grinding machine based on the tolerance of key components

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