A Variational Method of Robust Fixture Configuration Design for 3-D Workpieces

Abstract

Fixtures are used to locate and hold workpieces during manufacturing. Because workpiece surface errors and fixture set-up errors (called source errors) always exist, the fixtured workpiece will consequently have position and/or orientation errors (called resultant errors). In this paper, we develop a variational method for robust fixture configuration design to minimize workpiece resultant errors due to source errors. We utilize both first-order and second-order workpiece geometry information to deal with two types of source errors, i.e., infinitesimal errors and small errors. Using the proposed variational approach, other fundamental fixture design issues, such as deterministic locating and total fixturing, can be regarded as integral parts of the robust design. Closed-form analytical solutions are derived and numerical examples are shown. By employing the nonlinear programming technique, simulation software called RFixDesign is developed. This paper presents a new procedure for robust fixture configuration design that contributes especially to fixture designs where deformation is not influential.