Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 5387612, 14 pages
http://dx.doi.org/10.1155/2016/5387612
Research Article

Maximum Temperature and Relaxation Time in Wet Surface Grinding for a General Heat Flux Profile

Universidad Católica de Valencia “San Vicente mártir”, C/ Guillem de Castro 94, 46001 Valencia, Spain

Received 26 November 2015; Accepted 24 February 2016

Academic Editor: John D. Clayton

Copyright © 2016 J. L. González-Santander. 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.

Linked References

  1. S. Malkin and C. Guo, Grinding Technology: Theory and Application of Machining with Abrasives, Industrial Press, New York, NY, USA, 2008.
  2. J. B. J. W. Hegeman, J. T. M. De Hosson, and G. De With, “Grinding of WC—Co hardmetals,” Wear, vol. 248, no. 1-2, pp. 187–196, 2001. View at Publisher · View at Google Scholar · View at Scopus
  3. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Science Publications, Oxford, UK, 1986. View at MathSciNet
  4. N. R. DesRuisseaux and R. D. Zerkle, “Temperature in semi-infinite and cylindrical bodies subjected to moving heat surfaces and surface cooling,” Journal of Heat Transfer, vol. 92, pp. 456–464, 1970. View at Google Scholar
  5. J. C. Jaeger, “Moving sources of heat and the temperature at sliding contracts,” Proceedings of the Royal Society of New South Wales, vol. 76, pp. 204–224, 1942. View at Google Scholar
  6. J. L. González-Santander, “Calculation of an integral arising in dry flat grinding for a general heat flux profile. Application to maximum temperature evaluation,” Journal of Engineering Mathematics, vol. 88, pp. 137–160, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. W. J. Sauer, Thermal aspects of grinding [PhD dissertation], Carnegie Mellon University, Pittsburgh, Pa, USA, 1971.
  8. M. C. Shaw, “Temperatures in cutting and grinding,” American Society of Mechanical Engineering, vol. 146, pp. 17–24, 1990. View at Google Scholar
  9. A. S. Lavine, S. Malkin, and T. C. Jen, “Thermal aspects of grinding with CBN wheels,” CIRP Annals—Manufacturing Technology, vol. 38, no. 1, pp. 557–560, 1989. View at Publisher · View at Google Scholar · View at Scopus
  10. C. Guo and S. Malkin, “Analysis of energy partition in grinding,” Journal of Engineering for Industry, vol. 117, no. 1, pp. 55–61, 1995. View at Publisher · View at Google Scholar
  11. L. C. Zhang, T. Suto, T. H. Noguchi, and T. Waida, “An overview of applied mechanics in grinding,” Manufacturing Review, vol. 4, pp. 261–273, 1992. View at Google Scholar
  12. M. Mahdi and L. Zhang, “Applied mechanics in grinding—VI. Residual stresses and surface hardening by coupled thermo-plasticity and phase transformation,” International Journal of Machine Tools and Manufacture, vol. 38, no. 10-11, pp. 1289–1304, 1998. View at Publisher · View at Google Scholar · View at Scopus
  13. L. C. Zhang, T. Suto, H. Noguchi, and T. Waida, “Applied mechanics in grinding. Part II: modelling of elastic modulus of wheels and interface forces,” International Journal of Machine Tools and Manufacture, vol. 33, no. 2, pp. 245–255, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. C. Guo, Y. Wu, V. Varghese, and S. Malkin, “Temperatures and energy partition for grinding with vitrified CBN wheels,” CIRP Annals, vol. 48, no. 1, pp. 247–250, 1999. View at Publisher · View at Google Scholar · View at Scopus
  15. I. Zarudi and L. C. Zhang, “A revisit to some wheel—workpiece interaction problems in surface grinding,” International Journal of Machine Tools and Manufacture, vol. 42, no. 8, pp. 905–913, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. W. B. Rowe, S. C. E. Black, B. Mills, H. S. Qi, and M. N. Morgan, “Experimental investigation of heat transfer in grinding,” CIRP Annals—Manufacturing Technology, vol. 44, no. 1, pp. 329–332, 1995. View at Publisher · View at Google Scholar · View at Scopus
  17. J. González-Santander, “Analytic solution for maximum temperature during cut in and cut out in surface dry grinding,” Applied Mathematical Modelling, vol. 40, no. 3, pp. 2356–2367, 2016. View at Publisher · View at Google Scholar
  18. J. L. González-Santander, J. M. Isidro, and G. Martín, “An analysis of the transient regime temperature field in wet grinding,” Journal of Engineering Mathematics, vol. 90, pp. 141–171, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. K. Oldham, J. Myland, and J. Spanier, An Atlas of Functions, Springer, New York, NY, USA, 2nd edition, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  20. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Washington, DC, USA, 1972.
  21. J. L. González-Santander and G. Martín González, “Closed form expression for the surface temperature in wet grinding. Application to maximum temperature evaluation,” Journal of Engineering Mathematics, vol. 90, pp. 173–193, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. J. L. González-Santander and G. Martín, “A theorem for finding maximum temperature in wet grinding,” Mathematical Problems in Engineering, vol. 2015, Article ID 150493, 13 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  23. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Advances in Computational Mathematics, vol. 5, no. 4, pp. 329–359, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. V. I. Murav'ev, A. V. Yakimov, and A. V. Chernyshev, “Effect of deformation, welding, and electrocontact heating on the properties of titanium alloy VT20 in pressed and welded structures,” Metal Science and Heat Treatment, vol. 45, no. 11-12, pp. 419–422, 2003. View at Publisher · View at Google Scholar · View at Scopus
  25. D. L. Skuratov, Y. L. Ratis, I. A. Selezneva, J. Pérez, P. Fernández de Córdoba, and J. F. Urchueguía, “Mathematical modelling and analytical solution for workpiece temperature in grinding,” Applied Mathematical Modelling, vol. 31, no. 6, pp. 1039–1047, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. A. S. Lavine, “A simple model for convective cooling during the grinding process,” Journal of Engineering for Industry, vol. 110, no. 1, pp. 1–6, 1988. View at Publisher · View at Google Scholar · View at Scopus
  27. R. P. Brent, “An algorithm with guaranteed convergence for finding a zero of a function,” in Algorithms for Minimization without Derivatives, chapter 4, Prentice-Hall, Englewood Cliffs, NJ, USA, 1973. View at Google Scholar
  28. H. Takahasi and M. Mori, “Double exponential formulas for numerical integration,” Publications of the Research Institute for Mathematical Sciences, vol. 9, pp. 721–741, 1973. View at Google Scholar