Abstract
A standard analytical presentation for the minimal-zone-based tolerancing is proposed. For this purpose, the form-invariant vector (FIV) of elementary errors is formulated; small deviations of the FIV components leave the predetermined form of the toleranced feature unaltered. Then, the toleranced features are presented in terms of the FIV components, and a set of constraints is presented in terms of the transfer factors for these components. The set of the constraints and the results of the measurements of the real feature enable us to obtain a standard presentation of the linear-programming problem, which is solved with respect to the FIV. A comparison of this solution with the least-mean-square-based assessment is given. Both well-studied cases (accuracy of a plane and a cylinder) and more complicated cases, such as the tolerancing of the helical surfaces, element-by-element analysis of the form accuracy, etc., are considered in order to illustrate the applications of the theoretical results.
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Portman, V.T., Weill, R.D., Shuster, V.G. (1998). Variational Method for Assessment of Toleranced Features. In: ElMaraghy, H.A. (eds) Geometric Design Tolerancing: Theories, Standards and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5797-5_10
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DOI: https://doi.org/10.1007/978-1-4615-5797-5_10
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