Inner-product of strain rate vector through direction cosine in coordinates for disk forging
(State Key Laboratory of Rolling and Automation, Northeastern University,
Shenyang 110004, China)
Shenyang 110004, China)
Abstract: A new linear integration for plastic power was proposed. The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector, and then its direction cosines were determined by the ratio of coordinate increments. Furthermore, inner-product of the vector for plastic power was term integrated by term and summed. Thereafter, through a formula for determination of bulge an analytical solution of stress effective factor was obtained. Finally, through compression tests, the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine. It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%. However, when the reduction gets up to 25.34% and 33.12%, the corresponding errors between the calculated and measured results also get up to 6% and 13.5%, respectively.
Key words: disk forging; bulge; strain rate vector; direction cosine; inner-product; analytical solution