Abstract
“Orowan's ω-function" in the theory of rolling is defined by a definite integral, and the general method of computing it is a time-consuming numerical integration. An alternative method is “zero-degree approximation" in the gradient of the roll surface, because, according to Orowan, the error in the ω-function is less than 0.01. However, this is inconsistent with the aim of his theory to “avoid all mathematical approximations," and the resulting error in overall rolling analysis has not yet been examined. In the present paper, we elaborate on the effects of the approximation by comparing it with numerical integration and second-degree approximation. The error of the latter in the ω-function is 0.0002 at the largest. Since errors in the roll force, torque, and forward slip are much smaller than the error in the ω-function itself, the error could be regarded as negligible even with zero-degree approximation in practical situations. The two equations of second-degree approximation provide reference values in place of numerical integration from the viewpoint of accuracy, and the computing time is sufficiently short for online use.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Japan Society for Technology of Plasticity
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
