A finite difference method is presented to predict tool and chip temperature fields in continuous machining and time varying milling processes. Continuous machining operations like orthogonal cutting are studied by modeling the heat transfer between the tool and chip at the contact zone. The shear energy created in the primary zone, the friction energy produced at the rake face - chip contact zone and the heat balance between the moving chip and stationary tool are considered. The temperature distribution is solved using finite difference method. Later, the model is extended to milling where the cutting is interrupted and the chip thickness varies with time. The time varying chip is digitized into small elements with differential cutter rotation angles. The temperature field in each differential element is modeled as a first order dynamic system, whose time constant is identified based on the thermal properties of the tool and work material, and the initial temperature at the previous chip segment. The transient temperature variation is evaluated by recursively solving the first order heat transfer problem at successive chip elements. The proposed model combines the steady-state temperature prediction in continuous machining with transient temperature evaluation in interrupted cutting operations where the chip and the process change in a discontinuous manner. The mathematical models and simulation results are in satisfactory agreement with experimental temperature measurements reported in the literature.

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