Solution of rectangular bar forging with bulging of sides by strain rate vector inner-product

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 t...

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Bibliographic Details
Published in:Transactions of Nonferrous Metals Society of China 2011-06, Vol.21 (6), p.1367-1372
Main Authors: WANG, Lei, JIN, Wen-zhong, ZHAO, De-wen, LIU, Xiang-hua
Format: Article
Language:English
Subjects:
Bulging
China
Compression tests
Construction equipment
Forging
golden section search
inner-product
Mathematical analysis
rectangular bar forging
Strain rate
strain rate vector
Vectors (mathematics)
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Summary: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.
ISSN:1003-6326
DOI:10.1016/S1003-6326(11)60867-4