The application of meta functions to the quasi-static analysis of workpiece displacement within a machining fixture

Spherical-tipped locators and clamps are often used for the restraint of workpieces during machining. For structurally rigid fixtures and workpieces, contact region deformation, slip, and lift-off are the predominant modes of workpiece displacement during clamp actuation and machining. This paper presents a general model for the quasi-static analysis of workpiece displacement. It also shows how meta functions can be applied to simplify the modeling of contact forces. Through the use of meta functions, the general model can be formulated and solved quickly. This paper concludes with a description of an experimental study used to validate this model.