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Surface derivative method for inverse thermal analysis in dry grinding. (English) Zbl 1420.35407
Summary: Starting from Jaeger’s classical formula for the field of temperature rise during dry surface grinding, an analytical expression for the profile of the heat flux going to the workpiece is derived. This analytical approach, termed the surface derivative method, can be applied very easily to inverse thermal analysis in surface grinding, and is compared herein with other inverse analysis methods reported in literature, viz. the temperature matching method and the Gauss-Newton method. In contrast to these methods, the surface derivative method is much less computationally expensive and does not collapse for high Péclet number.
35Q79 PDEs in connection with classical thermodynamics and heat transfer
46N20 Applications of functional analysis to differential and integral equations
80A23 Inverse problems in thermodynamics and heat transfer
Full Text: DOI
[1] Malkin, S., Current trends in CBN grinding technology, CIRP Ann Manuf Technol, 34, 557-563, (1985)
[2] Guo, C.; Malkin, S., Inverse heat transfer analysis of grinding. Part 1: methods, J Eng Ind, 118, 137-142, (1996)
[3] Knothe, K.; Liebelt, S., Determination of temperatures for sliding contact with applications for wheel-rail systems, Wear, 189, 91-99, (1995)
[4] Lavisse B, Sinot O, Lefebvre A, Weiss B, Henrion E, Tidu A (2016) Heat flux distribution model in grinding from an inverse heat transfer analysis and foil/workpiece thermocouple measurements. In: Proceedings of the Thirteenth International Conference on High Speed Machining, Metz
[5] Carvalho, RN; Orlande, HRB; Özisik, MN, Estimation of the boundary heat flux in grinding via the conjugate gradient method, Heat Transf Eng, 21, 71-82, (2000)
[6] Brosse, A.; Naisson, P.; Hamdi, H.; Bergheau, JM, Temperature measurement and heat flux characterization in grinding using thermography, J Mater Process Technol, 201, 590-595, (2008)
[7] Björck A (1996) Numerical methods for least squares problems. SIAM, Amsterdam · Zbl 0847.65023
[8] Skuratov, D.; Ratis, Y.; Selezneva, I.; Pérez, J.; Fernández de Córdoba, P.; Urchueguía, J., Mathematical modelling and analytical solution for workpiece temperature in grinding, Appl Math Model, 31, 1039-1047, (2007) · Zbl 1153.80002
[9] González-Santander, JL; Pérez, J.; Fern ández de Córdoba, P.; Isidro, JM, An analysis of the temperature field of the workpiece in dry continuous grinding, J Eng Math, 67, 165-174, (2010) · Zbl 1194.74053
[10] Jaeger, JC, Moving sources of heat and the temperature at sliding contacts, Proc R Soc N S W, 76, 204-224, (1942)
[11] Oldham KB, Myland J, Spanier J (2010) An atlas of functions: with equator, the atlas function calculator. Springer, New York · Zbl 1167.65001
[12] Marinescu ID, Rowe WB, Dimitrov B, Inaski I (2004) Tribology of abrasive machining processes. William Andrew Inc., New York
[13] Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Clarendon Press, Oxford · Zbl 0029.37801
[14] González-Santander JL, Valdés Placeres JM, Isidro JM (2011) Exact solution for the time-dependent temperature field in dry grinding: application to segmental wheels. Math Probl Eng. ID 927876
[15] Lebedev NN (1965) Special functions and their applications. Prentice-Hall, New Jersey · Zbl 0131.07002
[16] Zarudi, I.; Zhang, LC, A revisit to some wheel-workpiece interaction problems in surface grinding, Int J Mach Tool Manuf, 42, 905-913, (2002)
[17] Murav’ev, VI; Yakimov, AV; Chernysev, AV, Effect of deformation, welding, and electrocontact heating on the properties of titanium alloy VT20 in pressed and welded structures, Met Sci Heat Treat, 45, 419-422, (2003)
[18] Lavine, AS, A simple model for convective cooling during the grinding process, J Eng Ind, 110, 1-6, (1988)
[19] Lavine, AS; Malkin, S.; Jen, TC, Thermal aspects of grinding with CBN wheels, CIRP Ann Manuf Technol, 38, 557-560, (1989)
[20] Guo, C.; Malkin, S., Analysis of energy partitions in grinding, J Eng Ind, 117, 55-61, (1995)
[21] Sauer WJ (1971) Thermal aspects of grinding. Ph.D. dissertation, Carnegie-Mellon University
[22] Guo, C.; Wu, Y.; Varghese, V.; Malkin, S., Temperatures and energy partition for grinding with vitrified CBN wheels, CIRP Ann Manuf Technol, 42, 247-250, (1999)
[23] Mahdi, M.; Zhang, L., Applied mechanics in grinding-VI. Residual stresses and surface hardening by coupled thermo-plasticity and phase transformation, Int J Mach Tool Manuf, 38, 1289-1304, (1998)
[24] Rowe, WB; Black, SC; Mills, B.; Qi, HC; Morgan, MN, Experimental investigation of heat transfer in grinding, CIRP Ann Manuf Technol, 44, 29-332, (1995)
[25] Guo, C.; Malkin, S., Inverse heat transfer analysis of grinding, part 2: applications, J Eng Ind, 118, 143-149, (1996)
[26] Keys, R., Cubic convolution interpolation for digital image processing, IEEE Trans Acoust Speech, 29, 1153-1160, (1981) · Zbl 0524.65006
[27] González-Santander, JL; Martín, G., Relative distance between two scalar fields. Application to mathematical modelling approximation, Math Methods Appl Sci, 37, 2906-2922, (2014) · Zbl 1310.35018
[28] Li, YT; Wong, R., Integral and series representations of the Dirac delta function, Commun Pure Appl Anal, 7, 229-247, (2008) · Zbl 1151.46030
[29] Gradsthteyn IS, Ryzhik IM (2007) Table of integrals, series and products, 7th edn. Academic Press Inc., New York
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