Ph.D. Proposal Presentation by Bo Li
Wednesday, January 20, 1999

(Dr. Shreyes N. Melkote, advisor)

"Analysis and Synthesis of Machining Fixture-Workpiece Systems with Multiple Frictional Contacts"


A fixture is a critical component of the machining system. At present, the design and development of machining fixtures is largely experience-based and relies on significant trial-and-error. With growing demands on improved product quality and shorter time-to-market, there is need for rigorous but practical analytical tools to support the fixture design and analysis process. Previous work has focused mainly on quasi-static analysis and synthesis, with inadequate or no experimental verification. Since machining is often characterized by periodic forces and vibration, consideration of dynamic effects in fixture design is crucial. Therefore, the primary objectives of this thesis are: 1) to develop and experimentally validate models for quasi-static and dynamic analysis of fixture-workpiece systems, and 2) to develop a fixture design synthesis method that considers the fixture- workpiece system dynamics in determining the optimum fixture layout and clamping forces.

In quasi-static model, the frictional contact between a fixture element and the workpiece surface is modeled as an elastic half-space subjected to distributed normal and tangential loads. The principle of total complementary potential energy is used to formulate the multiple, frictional contact elasticity problem as a constrained quadratic program. The model is experimentally verified and found to yield accurate predictions of the normal and tangential contact forces for different clamping forces. A dynamic fixture-workpiece model is also developed to simulate the instantaneous workpiece motion in the fixture during machining and its impact on workpiece location accuracy.  The model is capable of simulating stick, slip, and loss of contact conditions at a fixture-workpiece contact. Also, the model includes the effect of interfacial slip damping arising from micro-slip at the fixture-workpiece contacts. Its influence on workpiece motion is studied in detail through experiments and model simulations. For the range of conditions investigated, its effect on workpiece motion is found to be significant, with the tangential force amplitude being the most significant factor.

Finally, fixture layout and clamping force optimal synthesis techniques are developed.  The quasi-static and dynamic layout optimization algorithms are shown to significantly reduce the workpiece location error induced by the contact region deformation. The quasi-static clamping force optimization problem is formulated as a multi-objective problem, and the theoretical minimum clamping force obtained from the algorithm compares favorably with the measured values. In the dynamic synthesis case, an iterative fixture layout and clamping force optimization procedure that yields the "best" improvement in the objective function value is presented.