Least-Square Formulation of the Object Function, applied on Hydro Mechanical Tube Forming

摘要

There has been an increasing interest in the area of optimization combined with sheet metal forming in recent years due to the increased robustness of the simulations tools and the increasing computer power, however, the CPU cost and response time are still considerable. The high CPU cost raises the demands for efficient and robust optimization algorithms. The method used in this paper will take advantage of the structure of object function, i.e. formulate the optimization problem as a least square problem, furthermore, Broydens "good approximation" is used to approximate the Jacobian matrix. The performance of the optimization strategy is illustrated by a hydro tube forming example. In order to solve the tube-problem, a method for describing the geometric derivation is needed. The layout for such an algorithm is given in which the ideal geometry is defined as StL-model exported from a CAD-program. The example illustrates the effectiveness of the chosen optimization strategy. For a problem with no less than 6 design parameters, a solution is reached within 31 simulations.