This paper presents an optimization approach for the accurate evaluation of minimum-zone form tolerances from discrete coordinate measurement data. The approach minimizes the minimum-deviation objective function defined as the difference between the maximum and minimum distances of the measured coordinate data from the reference feature. The objective function is formulated as a function of rigid-body coordinate transformation parameters and involves fewer independent parameters than the existing tolerance evaluation algorithms. As a result, improved convergence efficiency and numerical stability are achieved. A standard direct search algorithm, the downhill simplex search algorithm, is employed to minimize the objective function. The least-squares estimates are employed as good initial conditions to facilitate convergence to the global solutions. A new method, named as the Median Technique, is implemented to well center the circularity measured data and well align the cylindricity measured data in order to provide valid least-squares estimates based on the Limacon approximation. Results from simulation and comparative studies have shown that the proposed method evaluates minimum-zone form tolerances with reliable accuracy.
Minimum-Zone Form Tolerance Evaluation Using Rigid-Body Coordinate Transformation
Contributed by the Computer Aided Product Development (CAPD) Committee for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 2002; revised February 2003. Guest Editor: C. H. Menq.
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Endrias, D. H., and Feng, H. (May 15, 2003). "Minimum-Zone Form Tolerance Evaluation Using Rigid-Body Coordinate Transformation ." ASME. J. Comput. Inf. Sci. Eng. March 2003; 3(1): 31–38. https://doi.org/10.1115/1.1565075
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