A class of slipline field solutions for metal machining with Coulomb friction at the chip–tool interface

The present investigation is concerned with a class of slipline field solutions for metal machining involving chip-curl assuming Coulomb friction at the chip–tool interface. An elastic contact zone is assumed beyond the plastically stressed region to satisfy the statical requirements of the fields. The non-linearity arising due to Coulomb friction at the interfaces is analysed by the method proposed in the literature. At low coefficient of friction, the chip–tool contact is governed by slipping friction only and the frictional shear stress nowhere equals the yield stress in shear. As coefficient of friction increases, sticking of the chip begins at the tool tip and spreads to the plastic contact region. At high coefficient of friction, the plastic contact is therefore governed by sticking as well as slipping friction followed by slipping contact in the elastic contact zone. Results are presented for variation in natural contact length, sticking contact length, cutting forces and pressure distribution at the chip–tool interface with variation in rake angle and interface friction condition both for power law and exponential pressure distribution in the elastic contact zone.