Analysis of minimum zone sphericity error using minimum potential energy theory

Fan, Kuang‐Chao; Lee, Ji-Chun

doi:10.1016/s0141-6359(98)00024-5

Cited by 55 publications

(45 citation statements)

References 7 publications

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“…So the unnecessary failed products can be avoided without the expense of losing product function, and �nally, it will save the manufacturing cost. LSM [6,10] 0.008486 MZS [6] 0.00766 GA [10] 0 F 2: e uncertainty of sphericity error veri�cation.…”

Section: Uncertainty Applicationmentioning

confidence: 99%

“…According to the above paragraph the example in [6] is quoted to evaluate the sphericity error and calculate the uncertainty. e data points are generated randomly so that they are all located between two concentric spherical surfaces of radii equal to 0.995 mm and 1.005 mm, respectively.…”

Section: Case Studymentioning

confidence: 99%

“…Some attempts were made to develop methods for evaluating the sphericity error. e existing approaches are mainly based on the least squares sphere, minimum zone sphere, minimum circumscribed sphere, and maximum inscribed sphere, among which the technique of least squares sphere is quite mature and widely accepted [5][6][7][8][9][10]. Huang [5] developed a mathematical model based on the 3D Voronoi diagrams to get the exact minimum zone solution.…”

Section: Introductionmentioning

confidence: 99%

“…is method also indicated that the minimum sphericity was determined by a small number of critical measured points that gave an efficient way to save the computation time. Fan and Lee [6] proposed an approach with minimum potential energy analogy to the minimum zone solution of spherical error, which assumed an imaginary spring was located between the concentric spheres containing all measured points. is method can also be extended to solve other minimum zone form error problems.…”

Section: Introductionmentioning

confidence: 99%

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An Approach for the Evaluation of Sphericity Error and Its Uncertainty

Mao

Zhao

2013

Advances in Mechanical Engineering

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e veri�cation uncertainty theory in new generation geometrical product speci�cation (GPS) has been applied in the whole process of geometrical product speci�cation and veri�cation. According to the uncertainty theory, a novel method for the uncertainty evaluation of sphericity errors was proposed. e association operator in new generation GPS was applied. e mathematical model of the sphericity error and the optimal objective function were developed under the condition of minimum zone. Particle swarm optimization (PSO) algorithm was used to search for the optimal solution of sphericity error. e coefficients of the correlation element and propagation of uncertainty were calculated so that the sphericity error and the uncertainty of the result can be obtained. e evaluation results are accurate and consistent with requirements of a new generation GPS standard. It also indicates that this method can improve the integrity and veracity of veri�cation.

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Section: Uncertainty Applicationmentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Approach for the Evaluation of Sphericity Error and Its Uncertainty

Mao

Zhao

2013

Advances in Mechanical Engineering

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“…Datasets 9 and 10 for cylindricity assessment, Table 3, correspond to the datasets 1 and 2 reported in [17] (generated datasets), while datasets 11-15 correspond to the examples 1-5 in [28] (CMM-cylindricity datasets). Dataset 10 for sphericity assessment, Table 4, corresponds to the dataset presented in [29] (generated) and datasets 11-12 are the datasets 2-3 in [30] (measurements). The other datasets were generated for each class of symmetry.…”

Section: Applicationsmentioning

confidence: 99%

Flatness, Cylindricity and Sphericity Assessment Based on the Seven Classes of Symmetry of the Surfaces

Prisco

Polini

2010

Advances in Mechanical Engineering

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Dimensional inspection of a manufactured surface by means of a coordinate measuring machine (CMM) produces a set of Cartesian coordinates. The coordinates are processed to yield the geometric tolerance of the surface. This paper presents a new approach to the evaluation of flatness, cylindricity and sphericity tolerance based on surface invariance with regard to the rigid motions. The proposed algorithm transforms, through homogeneous transformation matrices, the coordinates measured to best fit the reference element of the surface class from which the actual measurements were sampled. The transformation matrix is simplified taking into account the invariance of the sum of the squared normal distances of the measured points from the nominal surface as regards some rigid motions. This invariance is a consequence of the invariance as regards some displacements of the nominal surface from which the data points were sampled. In this way, the number of parameters to be optimised is reduced in comparison with the six parameters characterizing the general homogeneous transform matrix. The methodology was computer implemented and numerical simulations were performed for planes, cylinders, and spheres in order to validate the effectiveness of the approach. The results indicate that the proposed algorithm provides accurate and quick assessments.

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Evaluation of Form Errors to Large Measurement Data Sets Using Scatter Search

Chen¹,

Chen²

2004

New Optimization Techniques in Engineering

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The automatic acquisition and interpretation of the information of product features is an important procedure in modern manufacturing systems. Roundness and sphericity are the basic geometric forms expected from part features. There is a requirement to develop an automatic inspection method that will cater the needs of assessing roundness and sphericity. To produce better quality parts, manufacturers can adequately control the production process and accurately evaluate the form errors. The assessment algorithms for form errors are typically applied to meet the intent of the ASME Y14.5M standard (1994). This standard identifies that a substitute feature (geometric form that best fits the measured points) must be established from the sampled data to minimize the maximum deviation between the substitute (reference) feature and the actual feature concerned.For evaluating the roundness error from the actual measurement, a reference circle must be established from the measurement data to minimize the maximum deviation between the reference circle and the actual one. The roundness error is then defined as the maximum peak-to-valley distance from the reference circle. Sphericity is a type of form error, which is broadly used in industry for the geometrical measurement of precision balls. The sphericity is defined as the minimum shell width (minimum zone) between the concentric circumscribed and inscribed spheres enclosing all the measurement data. The roundness and sphericity assessments involve the optimization step to find the center coordinates and radii of the reference features. The evaluation of roundness and sphericity based on the minimum zone condition is a non-linear and non-convex problem that is difficult to solve mathematically. Therefore, the efficient and accurate assessment of roundness and sphericity is an important issue.The data sampled from measuring instruments are treated by an evaluation algorithm to accurately estimate the form errors. There exists no precise mathematical definition of the constraints implied by tolerance specifications in the ASME G. C.

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Analysis of minimum zone sphericity error using minimum potential energy theory

Cited by 55 publications

References 7 publications

An Approach for the Evaluation of Sphericity Error and Its Uncertainty

An Approach for the Evaluation of Sphericity Error and Its Uncertainty

Flatness, Cylindricity and Sphericity Assessment Based on the Seven Classes of Symmetry of the Surfaces

Evaluation of Form Errors to Large Measurement Data Sets Using Scatter Search

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