A method for integrating form errors into tolerance analysis

The purpose of this research is to investigate a computer-aided approach to tolerance analysis for assemblies and mechanisms. This new tolerance analysis method is based on the "generate-and-test" approach. In this approach, a series of "as manufactured" component variant models are generated within a solid modeling environment. These models reflect errors in component geometry that are characteristic of the manufacturing processes used to manufacture the components. The effects of different manufacturing process errors on product function is tested by simulating the assembly of these imperfect-form component models and measuring geometric attributes of the assembly that are measures of functionality. A tolerance analysis model is constructed by generating-and-testing a sequence of component variants that represent manufacturing process capabilities.;A solid-modeling engine that can generate non-uniform, rational, b-spline (NURBS) surfaces is used to produce the imperfect-form component models. Suitability of this NURBS surface representation as a tool for tolerance analysis is tested by modeling a series of as-manufactured surfaces produced by milling operations. Close correlation is found between measurements of actual machined surfaces and their corresponding NURBS surface representation.;Assembly of imperfect-form components is simulated by formulating surface mating relationships as a sequence of nonlinear mathematical programming problems. The characteristics of this imperfect-surface mating problem are investigated, and a problem formulation based on the penalty-function method is proposed. Three different solution methods for this penalty-function formulation are investigated. A solution algorithm based on a quasi-Newton method is found to be effective in solving the mating simulation problem.;The generate-and-test approach to tolerance analysis is demonstrated using a case study that is based on a high-speed stapling mechanism. This mechanism consists of a compound prismatic joint with multiple sliding components. For each component, as-manufactured models that correspond to two different levels of manufacturing precision are generated. Assembly between groups of components with different precision levels is simulated. Misalignment angles that correspond to functionality of the stapling mechanism are measured at the end of each simulation. The results of these simulations are used to build a tolerance analysis model and select a set of geometric form and orientation tolerances for the mechanism components.