Mathematical Modelling of Residual Stresses in End Milling

  • S.J. Ojolo Department of Mechanical Engineering, University of Lagos, Lagos, Nigeria
  • A.A. Ogundare
  • O. Kofoworola
Keywords: End milling, Residual Stresses, Simulation, Stainless Steel


During end milling, the residual stresses is developed from two sources which includes, stresses due to plastic
deformation of material and then stresses due to thermal energy generated. This work looks into the two sources
combined into one and then predicts how to best combine the machining parameters in order to minimize the
residual stresses in the components. The aim of this work is to develop a mathematical model that can be used to
predict the residual stresses in milling. Analytical method was used in developing this model; the model captured the
mechanical stress and the thermal stress. The simulation was done with MATLAB and from the results obtained; it
was observed that mill cutter with nose radius of 0.4mm and a constant cutting speed of 3m/min while the depth of
cut varies from 0.1mm to 0.4mm, the resulting residual stress varied from 50MPa to 150MPa respectively. From the
graphs it was also observed that the value of the residual stress at a particular depth of cut is the same in both the
x-x and z-z directions and that the stress reduces exponentially as it approaches zero.


Kline, W. A., Devor, R. E., and Lindberg, J. R., (1982). The prediction of cutting forces in end milling with application
to cornering cuts. International Journal of Machine Tool Design and Research, 22(1): 7-22.
Liu, M., Takagi, J. I. and Tsukuda, A. (2004). Effect of Tool Nose Radius and Tool Wear on Residual Stress
Distribution in Hard Turning of Bearing Steel. Journal of Materials Processing Technology, 150(3): 234-
Mansilla, C., Martinez-Martinez, D., Ocelik, V., and De Hosson, J. T. M. (2015). On the determination of local
residual stress gradients by the slit milling method. Journal of Materials Science, 50(10): 3646-3655.
Okushima, K., and Kakino, Y. (1972). Study of the residual stress produced by metal cutting, Mem. Fac. Eng. Kyoto
Univ., April, 34(2): 234-248.
Su, J.C., (2006). Residual stress modeling in machining processes, Georgia Institute of Technology: Atlanta.
Sutherland, J. W., and Devor, R., (1986). An improved method for cutting force and surface error prediction in
flexible end milling systems. Journal of engineering for industry, 108(4): 269-279.
Ulutan, D., Alaca, B. E., and Lazoglu, I. (2007). Analytical modeling of residual stresses in machining. Journal of
Materials Processing Technology, 183(1):77-87.
Wang, J., Zhanga, D., Wua, B., Luo, M. (2017). Residual Stresses Analysis in Ball end Milling of Nickel-Based
Superalloy Inconel 718, Materials Research. 20(6): 1681-1689
Wu, D.W. and Matsumoto, Y. (1990). Effect of hardness on residual stresses in orthogonal machining of ANSI
4340 steel. Journal of Engineering for Industry, 112(3): 245-252.
How to Cite
Ojolo, S., Ogundare, A., & Kofoworola, O. (2020). Mathematical Modelling of Residual Stresses in End Milling. Journal of Engineering Research, 23(2), 35-44. Retrieved from