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A model for heat transfer in grinding. (English) Zbl 0947.74040
From the introduction: We present a mathematical model which deals with the thermal aspects of a grinding process. In this model we are concerned only with thermal effects, leaving the mechanical effects for other studies. In effect, then, the part or workpiece and the grinding wheel are assumed to be perfectly rigid. The mathematical problem is formulated in abstract terms, so that the existence of a weak solution can be established. The proof is based on a theorem for degenerate evolution systems. Under additional assumptions on the data, we establish uniqueness and existence of a weak solution to the steady-state thermal problem. Interest in this problem is heightened by experimental evidence that an almost steady state is reached very quickly after grinding is initiated.
MSC:
74M15Contact (solid mechanics)
74F05Thermal effects in solid mechanics
74H20Existence of solutions for dynamical problems in solid mechanics
74H25Uniqueness of solutions for dynamical problems in solid mechanics
74G20Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics