M.S. Thesis Presentation by Krishnakumar Kulankara
Monday, March 15, 1999

(Dr. Shreyes Melkote, advisor)

"Machining Fixture Layout synthesis using the Genetic Algorithm"


Machining fixtures are used to locate, support, and constrain workpieces during machining. The elastic deformation of the workpiece under the influence of machining and fixturing forces gives rise to geometric errors. Thus, fixture design, which involves determining optimum locating and clamping points and the optimum clamping forces, plays an important role in controlling the accuracy and surface finish of the machined part.

Previous work in this area have used a combination of either rigid body analysis, contact elasticity modeling, or finite element modeling to represent the fixture-workpiece system. Non-linear programming methods are used with one of these modeling methods to search for the fixture layout and clamping force that minimizes the machining error. Since this problem lacks a direct analytical relationship between the optimization variables and the objective function and possibly has multiple local minima, non-linear programming methods fail to yield the "true" optimum solution. Also, the optimization approaches reported earlier do not consider the entire cutting tool path/operation.

In this thesis, a Genetic Algorithm (GA) based approach to synthesize the optimum fixture layout and clamping forces for an entire machining operation was developed. Compared to standard non-linear programming methods, the GA is suited for problems that lack a direct relationship between the design variables and the objective function. It also is known to possess superior properties with regard to searching for the global optimum. The finite element method was used to model the fixture-workpiece system. Machining process models were used to predict the machining forces. Static finite element analysis was carried out to determine the elastic deformation under the influence of machining and clamping forces for a given fixture. Since it is computationally expensive to solve the full finite element model at each step of the machining simulation, a more efficient method has to be used. Model order reduction was carried out using the Guyan method and improvements in the computational efficiency of the solution were investigated. Experimental verification of the proposed method was also conducted.

The GA was found to be very effective in optimizing the fixture layout and clamping forces for a given cutting tool path. It converged for all the simulations and significant reduction in the maximum elastic deformation of the workpiece was obtained. The overall trends predicted by the optimization procedure were verified using actual machining experiments. The primary contribution of this thesis is the development of an efficient tool for automating the design of optimum fixtures for an entire machining operation.