Minimum-zone form tolerance evaluation using particle swarm optimisation

Robust and accurate evaluation of form tolerances is of paramount importance in today's world of precision engineering. Present-day Coordinate Measuring Machines (CMMs) and other optical scanning machines operate at high speed and have a high degree of accuracy and repeatability which are capable of meeting the stringent measurement requirements. However, the evaluation algorithms used in conjunction with them are not robust and accurate enough, because of the highly non-linear nature of the minimum-zone form tolerance formulation. Evolutionary Algorithms (EAs) have proved effective in solving non-linear optimisation problems. In this paper, Particle Swarm Optimisation (PSO) is employed to evaluate various minimum-zone form tolerances. An unconstrained formulation of the minimum-zone form tolerance is used for the optimisation. The methodology is validated by testing on several datasets from published literature and yields equal or better results than other existing minimum-zone algorithms. It is also extremely robust and the quality of the results is not affected by the number of points in the dataset.

[1]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[2]  M. S. Shunmugam,et al.  Evaluation of sphericity error from form data using computational geometric techniques , 2002 .

[3]  Kirsten Marie Carr,et al.  Verification of form tolerances part II: Cylindricity and straightness of a median line , 1995 .

[4]  Tohru Kanada.  Estimation of sphericity by means of statistical processing for roundness of spherical parts , 1997 .

[5]  Utpal Roy,et al.  Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error , 1992, Comput. Aided Des..

[6]  Han Ding,et al.  A steepest descent algorithm for circularity evaluation , 2003, Comput. Aided Des..

[7]  THOM J. Hodgson,et al.  Evaluation of cylindricity using combinatorics , 1999 .

[8]  Jiing-Yih Lai,et al.  Minimum zone evaluation of circles and cylinders , 1996 .

[9]  M. S. Shunmugam,et al.  Evaluation of straightness and flatness error using computational geometric techniques , 1999, Comput. Aided Des..

[10]  Saeid Motavalli,et al.  A unified approach to form error evaluation , 2002 .

[11]  Konstantinos E. Parsopoulos,et al.  Initializing the Particle Swarm Optimizer Using the Nonlinear Simplex Method , 2002 .

[12]  Jyunping Huang,et al.  An exact solution for the roundness evaluation problems , 1999 .

[13]  Wen-Yuh Jywe,et al.  Precision modeling of form errors for cylindricity evaluation using genetic algorithms , 2000 .

[14]  M. A. Abido,et al.  Optimal power flow using particle swarm optimization , 2002 .

[15]  Jyunping Huang.  An exact minimum zone solution for sphericity evaluation , 1999, Comput. Aided Des..

[16]  P. M. Griffin,et al.  Parametric-Based Determination of Cylindrical Variations in Geometric Tolerancing , 2000 .

[17]  J W Zhao,et al.  Roundness error assessment based on particle swarm optimization , 2005 .

[18]  Michael N. Vrahatis,et al.  Modification of the Particle Swarm Optimizer for Locating All the Global Minima , 2001 .

[19]  T.S.R. Murthy,et al.  Minimum zone evaluation of surfaces , 1980 .

[20]  Liu Chien-Hong,et al.  A study on analyzing the problem of the spherical form error , 2000 .

[21]  Sam Anand,et al.  ASSESSMENT OF CIRCULARITY ERROR USING A SELECTIVE DATA PARTITION APPROACH , 1999 .

[22]  Wen-Yuh Jywe,et al.  The min–max problem for evaluating the form error of a circle , 1999 .

[23]  Albert A. Groenwold,et al.  Sizing design of truss structures using particle swarms , 2003 .

[24]  Han Ding,et al.  Application of kinematic geometry to computational metrology: distance function based hierarchical algorithms for cylindricity evaluation , 2003 .

[25]  Sam Anand,et al.  Minimum-Zone Circularity Evaluation Using Particle Swarm Optimization , 2005 .

[26]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[27]  M. S. Shunmugam,et al.  Evaluation of circularity and sphericity from coordinate measurement data , 2003 .

[28]  Andries P. Engelbrecht,et al.  Effects of swarm size on Cooperative Particle Swarm Optimisers , 2001 .

[29]  Sam Anand,et al.  A genetic algorithm based approach for robust evaluation of form tolerances , 2000 .

[30]  M. S. Shunmugam,et al.  On assessment of geometric errors , 1986 .

[31]  Russell C. Eberhart,et al.  Parameter Selection in Particle Swarm Optimization , 1998, Evolutionary Programming.

[32]  Placid Mathew Ferreira,et al.  Verification of form tolerances part I: Basic issues, flatness, and straightness , 1995 .

[33]  L. Jeff Hong,et al.  Robust evaluation of flatness and straightness tolerance using simulated annealing , 2001 .

[34]  R. Saravanan,et al.  Optimization of cutting conditions during continuous finished profile machining using non-traditional techniques , 2005 .

[35]  M. S. Shunmugam,et al.  An algorithm for form error evaluation: using the theory of discrete and linear Chebyshev approximation , 1991 .

[36]  S. H. Cheraghi,et al.  Straightness and flatness tolerance evaluation: an optimization approach , 1996 .