Implementing meta-functions into a quasi-static model to analyze workpiece displacement within a machining fixture

Workpiece displacement within a fixture is a major source of geometric error during clamp actuation and machining. Despite this fact, fixture designers have few tools to analyze the impact of design parameters on workpiece displacement. The major barrier to this analysis is the modeling of the fixture-workpiece contact, which requires the formulation of conditional boundary constraints. Traditionally, predictor-corrector methods are applied to solve this type of problem. Unfortunately predictor-corrector methods are impractical for most industrial applications.;This research solves this problem through the development and application of meta-functions. Meta-functions can be applied to formulate unconditional boundary constraints at the fixture-workpiece contact regions. The meta-functions are continuous functions used to predict the behavior at the fixture-workpiece contact regions. In fixture analysis the contact regions could exhibit elastic-plastic deformation, stick, slip and lift-off.;This work presents a quasi-static analysis model to predict workpiece displacement during clamp actuation and machining. The model can be formulated and solved quickly because it utilizes meta-functions. Meta-functions also can be implemented into a dynamics formulation to eliminate a predictor-corrector technique.;The quasi-static model can be used with other developed models to predict the geometric errors of various workpiece features based on a minimum zone. Also the quasi-static model can be used in combination with a tool path compensation model to reduce the magnitude of geometric workpiece error.;The theoretical models developed were validated using several experiments. This includes the validation of the quasi-static model to test its capability of accurately predicting workpiece displacement. Also the predicted minimum zones were validated against the actual measured geometric errors. Finally the tool path compensation model was validated using measured geometric errors from both uncompensated and compensated results.