Data for evaluating circularity error can be obtained from coordinate measuring machines or form measuring instruments. In this article, appropriate methods based on computational geometric techniques have been developed to deal with coordinate measurement data and form data. The computational geometric concepts of convex hulls are used, and a new heuristic algorithm is suggested to arrive at the inner hull. Equi-Distant (Voronoi) and newly proposed Equi-Angular diagrams are employed for establishing the assessment features under different conditions. The algorithms developed in this article are implemented and validated with the simulated data and the data available in the literature.

Shunmugam M S

Department of Mechanical Engineering

G. L. Samuel

Algorithms

Computational geometry

Heuristic methods

CIRCULARITY EVALUATION

COORDINATE MEASURING MACHINES

Computer aided manufacturing

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Evaluation of circularity from coordinate and form data using computational geometric techniques

Precision Engineering

Engineering parts usually deviate from their intended shapes during their manufacturing due to the inaccuracies of machine tools, deformation of various elements of machine tool, cutting tools and workpiece. Resulting geometric errors affect the functionality and assembly of the parts significantly. This demands a reliable strategy to accurately assess the errors during the final part quality inspection. Among all the geometric features, circular feature is very common on the majority of the engineering parts. Hence, the measurement and evaluation of circularity with a high degree of accuracy are of utmost importance. In the present work, a hybrid approach is proposed to accurately evaluate the circularity error. This approach comprises a least squares method (LSM) and a novel probabilistic global search Lausanne (PGSL) technique. The LSM is used to reduce the search space initially. Within the reduced search space, the PGSL performs efficient, fine and global search. In the process of establishing minimum zone circles to the measured data of the circular features, the proposed approach dynamically updates the probability distribution function of the circularity parameters continuously. The update procedure ensures that the probability of moving towards the potential optimal solutions is increased. The algorithm has been tested using several benchmark datasets for its generalization capability and robustness. The proposed strategy is found to be efficient in yielding accurate results. Therefore, the algorithm can be implemented in computer-aided circularity measuring instruments in order to minimize acceptance of bad parts and rejection of good parts. © 2017, Springer-Verlag London.

International Journal of Advanced Manufacturing Technology

Minimum zone evaluation of roundness using hybrid global search approach

Manufactured components are verified using Coordinate Measuring Machine (CMM) and form-measuring instruments or setups. Standards define form error based on a Minimum Zone (MZ) principle which establishes an ideal reference feature. This principle is extended in the present work to arrive at the relationship errors. Additionally, idealisation of relationship has been attempted for the first time. Support Vector Regression (SVR) technique is used to evaluate form and relationship errors from CMM and form data. For new data sets and data taken from literature, the results show that SVR method can produce unique parameters for MZ. © 2008, Inderscience Publishers.

International Journal of Manufacturing Research

Application of Support Vector Regression in assessment of geometric errors

The present work deals with evaluation of form error from the measured profiles obtained using a form tester, namely roundness/cylindricity measuring instrument. In Part I, details of circularity evaluation are presented. Due to eccentricity in component setting and radius-suppression inherent in the measurement, circularity error has to be evaluated with reference to a limacon. A computational geometry-based algorithm is proposed for establishing minimum circumscribed, maximum inscribed and minimum zone limacons. A new type of control hull for directly constructing equi-angular diagrams and a new procedure for updating are introduced. Validation has been done with bench-mark data set and corresponding results available in the literature. Being geometry-based algorithm, it is simple to follow and each iteration can be visualized and interpreted geometrically. On comparison with simplex search method, the proposed algorithm is found to be computationally efficient in terms of accuracy and time taken. The proposed methods can be easily implemented in computer-aided roundness measuring instruments. Extension of this work for evaluation of cylindricity error has been dealt in Part II. © 2006 Elsevier Ltd. All rights reserved.

International Journal of Machine Tools and Manufacture

Evaluation of form data using computational geometric techniques-Part I: Circularity error

The form tester having a straight datum in addition to rotational axis provides the cylindricity data. Due to misalignment between axis of the component and instrument axis, and size-suppression inherent in such measurements, a limacon-cylinder has to be used for cylindricity evaluation. For the first time, an attempt has been made in the present work to establish the limacon-cylinder using computational geometric techniques. Concepts involved in the construction of limacon from 2D control hull as brought out in Part I are further extended in this Part II to establish the limacon-cylinder. The algorithms developed in this paper have been applied for minimum circumscribed, maximum inscribed and minimum zone evaluations of the data available in the literature. The proposed algorithms are fast and yield accurate results, and can be implemented in computer-aided form measuring instruments. © 2006 Elsevier Ltd. All rights reserved.

Evaluation of form data using computational geometric techniques-Part II: Cylindricity error

The coordinate measuring machines (CMMs) have proven to be reliable, flexible and very much suitable for determining the acceptability of manufactured parts. In this paper, techniques for evaluating circularity and sphericity error from CMM data are presented. The form error can be evaluated directly from CMM data by employing circle/sphere as assessment features and using normal deviations. The CMM data can also be transformed by applying appropriate methods that not only suppress the size but also introduce distortion. The form error is evaluated from the transformed data by employing limacon/limacoid as assessment features and using linear deviations. The methods for handling CMM and transformed data are given in this paper. The proposed methods are validated using the data available in literature. © 2003 Elsevier Science B.V. All rights reserved.

Journal of Materials Processing Technology

Evaluation of circularity and sphericity from coordinate measurement data

ISO defines form error based on the concept of minimum zone, but does not describe the methods to obtain the same. In this paper, drawbacks of the available methods are discussed and a new algorithm is presented. This algorithm is guaranteed to give the minimum value of form error. The algorithm is well-suited for implementation on a computer which may be interfaced with a Coordinate Measuring Machine. © 1991.

Journal	Data powered by TypesetPrecision Engineering
Publisher	Data powered by TypesetElsevier Science Inc, New York
ISSN	01416359
Open Access	No