A New Algorithm to Assess Revolute Surfaces through Theory of Surface Continuous Symmetry

This paper presents a new approach to the evaluation of revolute surfaces based on surface invariance with regard to the rigid motions. The approach transforms the measurement data through an opportune homogeneous transformation matrix in order to minimize the distance between the cloud of measured points and the reference element of the class of revolution surfaces from which the sampling comes. The best transformation parameters are searched minimizing the distance between the cloud of measured points and a geometric element having the same geometric nature of the reference element of the class of the revolution surface. Afterwards the individuation of the best-fit set of transformation parameters, the form tolerance of the inspected feature can be assessed following the tolerance definition supplied by the GD&T Y 14.5 standard. Numerical simulations were performed in order to validate the effectiveness and the robustness of the approach. The great advantage of this new algorithm is that its formulation may be applied to assess any kind of surfaces without any adaptation effort.

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

[2]  Thomas R. Kurfess,et al.  Dimensional Measurement Data Analysis, Part 1: A Zone Fitting Algorithm , 1999 .

[3]  Quirico Semeraro,et al.  The harmonic fitting method for the assessment of the substitute geometry estimate error. Part I : 2D and 3D theory , 2001 .

[4]  Eros Gian Alessandro Pasero,et al.  Detection of continuous symmetries in 3D objects from sparse measurements through probabilistic neural networks , 2001, VIMS 2001. 2001 IEEE International Workshop on Virtual and Intelligent Measurement Systems (IEEE Cat. No.01EX447).

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

[6]  M. S. Shunmugam,et al.  New approach for evaluating form errors of engineering surfaces , 1987 .

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

[8]  Vijay Srinivasan.  A geometrical product specification language based on a classification of symmetry groups , 1999, Comput. Aided Des..

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

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

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

[12]  Chia-Hsiang Menq,et al.  A unified least-squares approach to the evaluation of geometric errors using discrete measurement data , 1996 .