A comparison of different algorithms for cylindricity evaluation

Murthy, T.S.R.

doi:10.1016/0020-7357(82)90006-3

Cited by 40 publications

(13 citation statements)

References 2 publications

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“…Each data set consists of three evenly spaced horizontal sections, each in turn comprising 4096 evenly spaced points. 3 Specimen brXYZ is a rather coarse specimen, whereas dkXYZ is extremely fine. Each data set has been subjected to the same sequence of steps as the published Carr-Ferreira sets.…”

Section: Resultsmentioning

confidence: 99%

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Accurate cylindricity evaluation with axis-estimation preprocessing

Lao

Leong

Preparata

et al. 2003

Precision Engineering

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Evaluating cylindricity is a very important application in metrology. In this paper, we focus on cylindricity evaluation based on radial form measurements. The standard characterization of cylindricity is the notion of zone cylinder, i.e. the cylindrical crown contained between two coaxial cylinders with minimum radial separation and containing all the data points. Unfortunately, the construction of the zone cylinder is a very complex geometric problem, which can be formulated as a nonlinear optimization. Recently a new method (referred to here as the hyperboloid method) has been discussed, which avoids the direct construction of the zone cylinder of a point set, but approximates it with guaranteed accuracy through a computationally very efficient iterative process based on a linearization of the underlying problem. The iterations can be viewed as the construction of a sequence of "zone hyperboloids" tending to the desired "zone cylinder." An important requirement of the method, however, is that the initial position of the cylindrical specimen axis be nearly vertical, since significant deviations from this condition essentially invalidate the process. It is the purpose of this paper to remove this shortcoming of the hyperboloid technique by providing a simple procedure for appropriately initializing the data (axis estimation). Axis estimation and the hyperboloid technique constitute an integrated methodology for cylindricity evaluation, which is currently the most effective. The theoretical foundations of the method are reviewed from a viewpoint that highlights its essential features and intuitively explains its effectiveness. The analytical discussion is complemented by experimental data concerning a few significant samples.

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Section: Resultsmentioning

confidence: 99%

“…[1][2][3]5,6]. In addition, various data acquisition (measurement) protocols have been suggested, concerning the geometric configuration of the data points: on radial sections, on generatrices, on a bird-cage (a combination of radial sections and generatrices).…”

Section: Introductionmentioning

confidence: 99%

Accurate cylindricity evaluation with axis-estimation preprocessing

Lao

Leong

Preparata

et al. 2003

Precision Engineering

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“…In some attempts (Murthy 1982) normal deviations are considered to obtain the ideal geometrical feature and the form errors are computed on this basis. To demonstrate the effectiveness of the method, these values are compared with the errors obtained using the linearized deviations.…”

Section: S Shunmugammentioning

confidence: 99%

“…Recently, the evaluation of form errors has gained importance and many techniques have been tried. The least squares techniques are based on sound mathematical techniques (Murthy 1982 andKakino andKitazawa 1978) but the values obtained are not always the minimum. Attempts have, therefore, been made to derive the minimum value (Gota and Lizuka 1977, Murthy and Abdin 1980and Fukuda and Shimokohbe 1984.…”

Section: Introductionmentioning

confidence: 99%

On assessment of geometric errors

Shunmugam

1986

International Journal of Production Research

109

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“…Whitehouse [8] employed the least-squares fitting method for a partial arc. Murthy [9,10] proposed several techniques such as an orthogonal polynomial technique, the surface development method, the Monte Carlo technique and the simplex method to evaluate circularity, sphericity, and cylindricity. Chetwynd [11] employed the linear programming method to model circularity, Correspondence and offprint requests to: Professor C.-K. Chen, Department of Mechanical Engineering, National Cheng-Kung University, Tainan, 701 Taiwan.…”

Section: Introductionmentioning

confidence: 99%

Study on the Form Error Evaluation Model of a Conical-Shank Ball-End Milling Cutter

Chen

2001

Int J Adv Manuf Technol

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This paper presents a complete form error evaluation model of a conical-shank ball-end cutter. The complete conical-shank ball-end cutter comprises three major revolving portions including the conical shank, cylindrical section, and spherical head. By using the central line of the minimum circumscribed conical shank as a datum axis and employing profile data measured directly from cutter surfaces, the proposed evaluation method systematically computes the exact revolving envelopes of the conical shank, cylindrical part, and spherical part separately, and then combines them. One application example is presented to illustrate the effectiveness of the proposed modelling method. This paper provides a simple, logical, and precise method for the quality evaluation of a special rotating cutter and can be further extended for use in the quality assessment of various complicated cutters.

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A comparison of different algorithms for cylindricity evaluation

Cited by 40 publications

References 2 publications

Accurate cylindricity evaluation with axis-estimation preprocessing

Accurate cylindricity evaluation with axis-estimation preprocessing

On assessment of geometric errors

Study on the Form Error Evaluation Model of a Conical-Shank Ball-End Milling Cutter

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