Study of the temperature field formed in the process of milling with the use of ultrasonic vibrations under various processing modes

Study of the temperature field of the milling process with the imposition of ultrasonic vibrations (USV), under various ratios of the vibration amplitude to the depth of tooth penetration into the blank, will allow predicting the efficiency of the milling process with USV under various processing modes. The purpose of this study is to develop physical and mathematical models of the milling process with the imposition of USV, allowing identifying the influence of ultrasonic vibrations on the efficiency of the milling process under various ratios of the vibration amplitude to the depth of tooth penetration. Three sources of heat generation are considered: in the deformation (chip formation) area and in the zones of contact of the chip with the cutting plate (cutter tooth) and the plate with the blank. The authors have developed heat transfer models that take into account, in particular, the change in boundary conditions on the surfaces of the cutting plate and the blank under the USV imposition. When the plate is in contact with the blank, heat flows are directed to the blank, chips and cutter tooth, and the conditions of thermal interaction within the zones of contact of the plate with the chips and the blank are described by boundary conditions of the 2nd type. When the plate leaves the contact with the blank during the ultrasonic imposition and the chip formation process stops, then on all surfaces of the tooth (plate) and the blank that are in contact with the environment (cutting fluid or air), the convective heat transfer is described by the Newton–Richmann law (boundary conditions of the 3rd type). The results of numerical modelling are presented, confirming the assumption that the effect of using ultrasonic vibrations is higher at high values of the ratio of the ultrasonic vibration amplitude to the depth of tooth penetration into the blank.