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Mathematical Problems in Engineering
Volume 2017, Article ID 2425645, 21 pages
Research Article

A Model of Surface Residual Stress Distribution of Cold Rolling Spline

1School of Mechatronics Engineering, Henan University of Science and Technology, Henan, China
2Collaborative Innovation Center of Machinery Equipment Advanced Manufacturing of Henan Province, Luoyang 471003, China
3School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China

Correspondence should be addressed to Z. H. Ding; moc.qq@021373946

Received 17 April 2017; Revised 19 June 2017; Accepted 11 July 2017; Published 5 September 2017

Academic Editor: Edoardo Artioli

Copyright © 2017 Z. H. Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Residual stress is an important parameter in the evaluation of the performance of a cold rolling spline surface. However, research on cold rolling spline is rare. To improve the surface property of a spline, an involute spline is selected as the object of this study. The contour method for determining cold roll-beating residual stress involves measuring the force spatial distribution, performing a statistical analysis of the experimental results, establishing the parameters for the tooth profile for different positions (dedendum, pitch, and addendum) of residual stress, and determining the effect of pressure on the relationship between stress and the depth of the cold roll-beating. A response surface method is used to establish the spline tooth profile of the dedendum, pitch, and addendum of the residual stress and different depths of the stress layer to obtain the parameters of a multiple regression model and perform a comparative analysis of the experimental and prediction results. Research indicates that the prediction results have high reliability. The establishment of this model has important guiding significance to control the residual stress in the cold roll-beating forming process, optimize the cold roll-beating processing parameters, and improve the surface properties of cold rolling spline.