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Computation of the thermal field in tools during machining processes. (English) Zbl 0824.65139
Summary: This paper deals with the modelling and computation of the thermal field inside turning tools during machining processes. The analysis is developed for the parabolic heat equation both in the transient and steady case as well as for inverse-type problems where some information on the solution is obtained from experimental data. Some numerical simulations are performed and a discussion on some research perspectives is proposed.

65Z05 Applications to the sciences
65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R30 Inverse problems for PDEs
80A23 Inverse problems in thermodynamics and heat transfer
Full Text: DOI
[1] Chan, C.L.; Chandra, A., A boundary element method analysis of the thermal aspects of metal cutting processes, ASME J. engng. ind., 114, 311-319, (1991)
[2] Stephenson, D.A.; Ali, A., Tool temperature in interrupted metal cutting, ASME J. eng. ind., 114, 127-137, (1992)
[3] Stevenson, D.A.; Wright, P.K.; Chow, J.P., Further development in applying the finite element method to the calculation of temperature distribution in machining and comparisons with experiments, ASME J. eng. ind., 105, 149-154, (1983)
[4] Yen, D.W.; Wright, P.K., A remote temperature sensing technique for estimating the cutting interface temperature distribution, ASME J. engng. ind., 108, 252-263, (1986)
[5] Stephenson, D.A., An inverse method for investigating deformation zone temperatures in metal cutting, ASME J. eng. ind., 113, 129-136, (1991)
[6] Subramani, G.; Withmore, M.C.; Kapoor, S.C., Temperature distribution in a hollow cylindrical workplace during machining: theoretical model and experimental results, ASME J. eng. ind., 113, 373-380, (1991)
[7] Kottenstette, J.P., Measuring tool-chip interface temperatures, ASME J. eng. ind., 108, 101-104, (1986)
[8] Lezanski, P.; Shaw, M.C., Tool face temperatures in high speed milling, ASME trans. J. eng. ind., 112, 132-135, (1990)
[9] Stephenson, D.A., Assessment of steady-state metal cutting temperature models based on simultaneous infrared and thermocouple data, ASME J. eng. ind., 113, 121-128, (1991)
[10] Chow, J.; Wright, P., On-line estimation of tool/chip interface temperatures for a turning operation, ASME trans. J. eng. ind., 110, 56-64, (1988)
[11] Dutt, R.P.; Brewer, R.C., On the theoretical determination of the temperature field in orthogonal machining, ASME J. of engng. ind., 4, 91-114, (1965)
[12] Dawson, P.T.; Malkin, S., Inclined moving heat source model for calculating metal cutting temperatures, ASME J. eng. ind., 106, 179-184, (1984)
[13] Strenkwski, J.S.; Moon, K.J., Finite element prediction of chip geometry and tool/workpiece temperature distributions in orthogonal metal cutting, ASME J. eng. ind., 112, 313-318, (1990)
[14] Back, J.; Blackwell, B.; Clair, C.St., Inverse heat conduction, (1985), Wiley London
[15] Bellomo, N.; Preziosi, L., Modelling mathematical methods and scientific computation, (1994), CRC Press Boca Raton
[16] Preziosi, L.; Teppati, G.; Bellomo, N., Modelling and solution of stochastic inverse problems in mathematical physics, Comp. math. modelling, 16, 37-51, (1993) · Zbl 0755.60102
[17] Adomian, G., Nonlinear stochastic operator equations, (1986), Academic Press New York · Zbl 0614.35013
[18] Cherruault, Y., Convergence of Adomian’s method, Cybernetics, 18, 31-38, (1989) · Zbl 0697.65051
[19] Bellomo, N.; Brzezniak, Z.; De Socio, L.M., Nonlinear stochastic evolution problems in applied sciences, (1992), Kluwer Amsterdam · Zbl 0770.60061
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