Analytical modeling of temperature distribution in lead-screw whirling milling considering the transient un-deformed chip geometry

High temperature often occurs at the local cutting area during lead-screw whirling milling, which significantly affects workpiece surface integrity as well as tool life. The cutting process of lead-screw whirling milling comprises several recurrent characteristics, such as the un-deformed chip thickness and un-deformed chip width. The combined effects of un-deformed chip thickness and width cause time-varying variation in the size of the heat source, thus further affect the temperature distribution in the cutting area. This paper proposes a transient thermal analytical model to analyze the temperature distribution in the cutting area for lead-screw whirling milling. According to the complex trajectory of the tool relative to the rotation workpiece, the un-deformed chip geometry has been studied in detail at the two cutting stages. The time-varying tool-chip contact area and boundary equations of frictional heat source are firstly formulated to describe the size of the time-varying heat source. Secondly, the transient thermal analytical model is constructed taking into account the heat liberation intensity of the time-varying heat source. A series of experiments of whirling milling for lead-screw shaft are carried out, and the theoretical results evaluated by the proposed analytical model agree well with the experimental results. Furthermore, the effects of cutting conditions and un-deformed chip geometry on the temperature distribution have been analyzed, which can be used for process designers to make decisions in choosing the cutting parameters with optimized surface integrity and tool life.