Framework for Cone Feature Measurement Using Coordinate Measuring Machines

Abstract

Complex forms such as conicity have been largely ignored in the coordinate form literature, in spite of the sufficient need to inspect them in parts such as tapered rollers in bearings. This paper attempts to develop guidelines for inspection of cones and conical frustums using probe-type coordinate measuring machines. The sampling problem, the path determination, and fitting of form zones are each addressed in detail. Moreover, an integrative approach is taken for form verification and detailed experimental analysis is conducted as a pilot study for demonstrating the need for the same. Three separate sampling methods are applied: Hammersley, Halton-Zaremba, and Aligned Systematic; at various sample sizes using sampling theory and prior work in two-dimensional sampling. Linear and nonlinear deviations are formulated using optimization and least-squared methods and solved to yield competitive solutions. Comprehensive experimental analysis investigated issues of model adequacy, nesting, interactions, and individual effects, while studying conicity as a response variable in the light of sampling strategies, sizes, cone surface areas, and fitting methods. In summary, an orderly framework for sampling and fitting cones is developed which can lead to the development of comprehensive standards and solutions for industry.