Solution of rectangular bar forging with bulging of
sides by strain rate vector inner-product
sides by strain rate vector inner-product
(1. School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China;
2. Shanghai Shenhua Acoustics Equipment Co. Ltd., Shanghai 201709, China;
3. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, China)
2. Shanghai Shenhua Acoustics Equipment Co. Ltd., Shanghai 201709, China;
3. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110004, China)
Abstract: A new linear integration solution was constructed for determining the total pressure developed during forging of a rectangular bar with flat tools. The effective strain rate for rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The inner-product of the vector was termwise integrated and summed. The integral mean value theorem was applied to determining the ratio of the strain rate components and the values of direction cosine of the vector and then an analytical solution of stress effective factor was obtained. The compression experiments of pure lead bar were performed to test the accuracy of the solution. The optimized results of total pressure by golden section search were compared with those of the indicator readings of the testing machine. It indicates that the optimized total pressures are 2.60%−10.14% higher than those measured. The solution is available and still an upper-bound solution.
Key words: rectangular bar forging; bulging; strain rate vector; inner-product; golden section search