Simplified Grinding Temperature Model Study

Author(s): Lishchenko N. V.1*, Larshin V. P.2, Krachunov H.3

1 Odessa National Academy of Food Technologies, 112 Kanatna St., 65039 Odessa, Ukraine; 
2 Odessa National Polytechnic University, 1 Shevchenko Ave., 65044 Odessa, Ukraine;
University of Varna, Studentska Str., Varna, 9010, Bulgaria

*Corresponding Author’s Address: [email protected]

Issue: Volume 6; Issue 2 (2019)

Paper received: June 12, 2019
The final version of the paper received: September 3, 2019
Paper accepted online: September 8, 2019

Lishchenko N. V., Larshin V. P., Krachunov H. (2019). Simplified grinding temperature model study. Journal of Engineering Sciences, Vol. 6(2), pp. A1-A7, doi: 10.21272/jes.2019.6(2).a1/

DOI: 10.21272/jes.2019.6(2).a1/

Research Area:  MANUFACTURING ENGINEERING: Machines and Tools

Abstract. A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth.

Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.


  1. King, R. I., Hahn, R. S. (1986). Handbook of Modern Grinding Technology. Chapman and Hall, New York, London.
  2. DeVries, W. R. (1991). Analysis of Material Removal. Springer-Verlag, New York.
  3. Isii, T., Simoyama, I., Inoue, H., et al. (1988). Mechatronics. The Piece, Moscow.
  4. Lima, P. U., Saridis, G. N. (1996). Design of Intelligent Control Systems Based on Hierarchical Stochastic Automata. World Scientific Publishing Co Pre Ltd., Singapore.
  5. Ross, A. (2016). The Industries of the Future. New York, Simon & Schuster Inc.
  6. Carslaw, H. S., Jaeger, J. C. (1959). Conduction of Heat in Solids. 2nd edition. Oxford University Press, Oxford.
  7. Jaeger, J. C. (1942). Moving sources of heat and temperature at sliding contacts. Proceedings of the Royal Society, Vol. 76, рр.203–224.
  8. Malkin, S., Guo, C. (2008). Grinding Technology: Theory and Application of Machining with Abrasives. Industrial Press Inc., New York.
  9. Akbari, M., Sinton, D., Bahrami, M. (2011). Geometrical effects on the temperature distribution in a half-space due to a moving heat source. Journal of Heat Transfer, Vol. 133(6), pp. 064502-1–064502-10.
  10. Sipaylov, V. A. (1978). Thermal Processes during Grinding and Surface Quality Control. Mashinostroenie, Moscow.
  11. Lishchenko, N., Larshin, V. (2020). Temperature field analysis in grinding. Advances in Design, Simulation and Manufacturing II, DSMIE 2019, Lecture Notes in Mechanical Engineering, Springer, рр. 199–208. Springer, Cham.
  12. Larshin, V., Lishchenko, N. (2019). Adaptive profile gear grinding boosts productivity of this operation on the CNC machine tools. Advances in Design, Simulation and Manufacturing, DSMIE 2018, Lecture Notes in Mechanical Engineering, Springer, pp. 79–88.
  13. Larshin, V. P., Kovalchuk, E. N., Yakimov, A. V. (1986). Application of solutions of thermophysical problems to the calculation of the temperature and depth of the defective layer during grinding. Interuniversity Collection of Scientific Works, pp. 9–16.
  14. Lishchenko, N. (2018). Profile Grinding Productivity Increasing on CNC Machines on the Basis of Grinding System Elements Adaptation. DSc. thesis, 05.02.08 – Manufacturing Engineering. National Technical University “Kharkiv Polytechnic Institute”, Kharkiv.

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