طراحی شکل خالی بهینه توسط تجزیه و تحلیل حساسیت

A method of blank shape design based on sensitivity analysis for the non-circular deep drawing process has been proposed. By assuming the final deformation shape to be a drawn cup with a uniform trimming allowance at the flange, the corresponding initial blank which gives the final shape after deformation has been found. With the aid of a well-known dynamic explicit analysis code PAM-STAMP, shape sensitivity has been obtained. To obtain the shape sensitivity numerically, a couple of deformation processes have been analyzed. In order to validate this method, deep drawings of a square cup, a clover shaped cup and an L-shaped cup have been chosen as the examples. In every case converged results have been obtained only after a few times of modification. With the predicted optimal blank, both computer simulation and experiment are performed. Excellent agreement is noted between simulation and experiment in every case. Through the investigation, the proposed systematic method of optimal blank design is found to be very effective in the design of a deep drawing process.

In order to optimize sheet metal forming processes, the effects of a considerable number of process parameters are evaluated experimentally or analytically. Basically the optimization processes are based on the trial-and-error method owing to the inherent characteristics of metal forming processes. Because of the nature of the trial-and-error method, however, a significant number of iterations are usually required to optimize the processes. In general, sheet metal forming products in modern industries have a complicated shape and the forming process consists of several successive operations until the final shape is formed. Because of the complexity, the use of 3D CAD systems is increasing in the design of sheet metal product. With 3D CAD data, the die surface can be machined by CAM and the deformation process can be analyzed by a CAE technique. In the deep drawing processes, the use of an optimal blank not only saves the material but also it may reduce the occurrence of defects e.g. wrinkling, tearing. However, it is not easy to find the optimal blank because of the complexity of material behaviour. Several methods have been developed to design the optimal blank and there are many different approaches to find the optimal blank. Among the methods, the slip line field method [1], [2], [3], [4] and [5], the geometric mapping method [6] and [7], the trial-and-error method based on the FE method [8], [9] and [10], the inverse method [11], [12] and [13], ideal forming [14], backward tracing [15], the volume addition/subtraction method [16], and the analogy method [17] and [18] are notable. In this study, a systematic method based on sensitivity analysis has been proposed to find the optimal blank for the deep drawing of arbitrary shape cups described by a 3D CAD system.

A systematic method of optimal blank design based on sensitivity analysis for the non-circular deep drawing process has been proposed. From the results of deformation process, the shape sensitivity has been obtained numerically. With the shape sensitivity and the shape error, initial blank has been modified in order to obtain the final drawn cup shape. The numerical and experimental results of the three kinds of cup drawing demonstrate that the present method provides excellent prediction of the blank shape and the blank shape gives the target shape almost exactly. Through the investigation, the proposed systematic method of optimal blank design is found to be very effective.