A unified approach to form error evaluation

Weber, Timothy G.; Motavalli, Saeid; Fallahi, Behrooz; Cheraghi, S. Hossein

doi:10.1016/s0141-6359(02)00105-8

Cited by 74 publications

(43 citation statements)

References 9 publications

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“…The programming condition is the minimum condition of the evaluation, which is the basic principle of the geometric error evaluation, and it plays a very important role in the theory comprehension, equation resolution and result judgment. The minimum condition can not only taken as the principle and the criterion for geometric error evaluation, but also verify the correctness of the theory evaluation model [8,9].…”

Section: The Minimum Condition Of Geometric Error Evaluationmentioning

confidence: 72%

Optimization Evaluation of Geometric Error Based on Correctional Simplex Method

Zheng

Zhang

Zheng

et al. 2006

J. Phys.: Conf. Ser.

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Abstract. This paper researches the theory of geometric error evaluation and its application. On the basis of the geometric model of error evaluation, the features of the geometric error enclosure evaluation are analyzed, and the paper has founded the linear programming model of minimum zone association, maximum inscribed association and minimum circumscribed association. By taking the minimum conditions criterion and the theory on minimizing the extremal difference function as rules of geometric error evaluation, a correctional simplex method for direct solution of the programming model is proposed, and also the process is given. Furthermore, the method is verified by giving an example of the cylindricity error evaluation and comparing the experiment results with the ones obtained from other common methods. In addition, this designed method is also used to other geometric error evaluation in practice. The theoretical analysis and experimental results indicate that, the proposed correctional simplex method does provide well accuracy on geometric error evaluation. The outstanding advantages conclude not only high efficiency and stability but also good universality and practicality.

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Section: The Minimum Condition Of Geometric Error Evaluationmentioning

confidence: 72%

Optimization Evaluation of Geometric Error Based on Correctional Simplex Method

Zheng

Zhang

Zheng

et al. 2006

J. Phys.: Conf. Ser.

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“…This will further help in minimizing the economic loss occurring in manufacturing of the part. The result shows that MPSO algorithm has higher computational accuracy and its optimization result surpassed those from the other methods [3], [8], [29] and from LSM. The iterative curve for PSO and MPSO is shown in Fig.4.a), Fig.4.b) confirming better performance and efficiency of the proposed MPSO algorithm.…”

Section: Practical Examples (Straightness)mentioning

confidence: 95%

“…Table 2 shows the results presented in literature [30] along with the solution provided by the proposed MPSO algorithm. For example 1, it is observed that minimum zone straightness error obtained by LSM is 0.0017, Optimization Technique Zone (OTZ) [8] is 0.0017, Linear Approximation Technique (LAT) [8] is 0.0017, GA [3] is 0.001672, and PSO [29] is 0.001711, while the minimum zone straightness error obtained by the proposed MPSO is 0.00160. If the allowable straightness tolerance is 0.00165 inch, all the algorithms except the MPSO algorithm overestimate the tolerances and hence result in rejection of good parts.…”

Section: Practical Examples (Straightness)mentioning

confidence: 99%

“…Seun and Chang [13] developed an interval bias linear neural based approach with least mean squares learning algorithm for straightness and flatness evaluation and analysis. Weber et al [8] propounded a unified linear approximation technique for use in evaluating the form errors. The non-linear equation for individual form was linearized implementing Journal homepage: http://www.degruyter.com/view/j/msr Taylor expansion and it was solved using a linear program.…”

Section: Introductionmentioning

confidence: 99%

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Evaluating Geometric Characteristics of Planar Surfaces using Improved Particle Swarm Optimization

Pathak¹,

Kumar²,

Nayak³

et al. 2017

Measurement Science Review

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This paper presents a modified particle swarm optimization (MPSO) algorithm for the evaluation of geometric characteristics defining form and function of planar surfaces. The geometric features of planar surfaces are decomposed into four components; namely straightness, flatness, perpendicularity, and parallelism. A non-linear minimum zone objective function is formulated mathematically for each planar surface geometric characteristic. Finally, the result of the proposed method is compared with previous work on the same problem and with other nature inspired algorithms. The results demonstrate that the proposed MPSO algorithm is more efficient and accurate in comparison to other algorithms and is well suited for effective and accurate evaluation of planar surface characteristics.

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“…Many researchers have cast the roundness evaluation as the solution of a general optimization problem (Choi and Kurfess, 1999;Gou et al, 1999;Sharma et al, 2000;Weber et al, 2002;Yau and Menq, 1996). To get a value that is close to the global minimum, some researchers addressed the initial conditions and adopted coordinate transformation techniques (Endrias and Feng, 2003;Lai and Chen, 1996) or suggested approximating orthogonal residuals by functions that are linear in the feature parameters (Shunmugam, 1991).…”

Section: Introductionmentioning

confidence: 99%