The optimization of the variable binder force in U-shaped forming with uncertain friction coefficient

In this paper, an uncertain optimization method is suggested to obtain the optimal variable binder force in U-shaped forming. The friction coefficient is regarded as the uncertain coefficient, and the stepped variable binder force model is used. The finite element method is employed to simulate the forming process, and an uncertain objective function which represents the springback magnitude is created. The uncertain friction coefficient is treated as an interval, no need to know its probabilistic distribution. Through a nonlinear interval number programming method, the uncertain optimization problem is converted into a deterministic two-objective optimization problem. A hybrid optimization algorithm based on the intergeneration projection genetic algorithm and neural network is used to obtain the optimum. The presented method is applied to optimize the variable binder force parameters of the model from NUMISHEET'93. The forming quality based on the optimal variable binder force from the presented method is compared with constant binder force. The results indicate that the presented method can find the fair variable binder force to obtain both of the small springback and strain under the uncertain friction coefficient. (c) 2006 Elsevier B.V. All rights reserved.