Investigation of tool and workpiece clamping effect on stability lobes in milling process

Chatter is undesirable self-exciting vibration that occurs during machining process and could cause damage to the tool and the machine and surface finish of the workpiece. This phenomenon is generated from interaction of the tool and workpiece during cutting process and is one of the limiting factors for achieving a high cutting rate. In this paper, the effect of clamping of tool and workpiece on stability lobes of the milling process is investigated by employing a four degrees of freedom model of tool and workpiece. For this reason, the dynamic of cutting process is modeled through a set of coupled delay differential equations by considering regenerative chatter and loss of contact effect. Structural parameters of this model are measured by using the modal test in different clamping torques of the tool and the workpiece. Simulated stability lobes diagram is constructed based on full-discretization method. To validate the presented model, half immersion up-milling cuts were performed, and the limit values of axial depth of cut in different tool and workpiece clamping are determined experimentally for two different spindle speeds. The results indicated a good agreement between the stability lobes diagram obtained by FDM method and the experimental limit values. In addition, the results showed that the torque of clamping tool and workpiece have effect on the boundary of the stability lobes, that is, the increase of torque clamping lead to increment of the minimum critical cutting depth and reduces amplitude of vibration in stable and unstable cases over determined time interval.