Chatter modeling and stability lobes predicting for non-uniform helix tools

Regenerative chatter is self-excited vibration which may occur during the machining process. Chatter will inhibit the improvement of productivity, produce poor surface finish, even damage the tool or machine and so on. Simultaneously, cutters with variable pitch angle or non-uniform helix angle are helpful for avoiding the regenerative chatter. So, the stability prediction for the cutter, especially for the cutter with non-uniform pitch and helix angle has become more and more important for current high performance machining process. In this paper, in order to combine the effect of the cutter's variable-helix angle's effect, the mathematical model with multi-delays of the dynamic machining process is firstly constructed. In this model, the cutter is divided into a series of cutting elements along the cutter axis. Then the model of the chatter for non-uniform helix tools can be deduced after all cutting elements' dynamic equations are obtained. Subsequently, every period of the rotational spindle is divided by a series of knots which are not equally distributed for the sake of computing this model. After that, a method is proposed to predict the stability boundaries. Finally, four groups of examples are conducted to verify the validity of the proposed method. And the first group of the example is 1-dof dynamic system, the radial cutting depth is very small and two types of cutters with uniform and non-uniform pitch angles are chosen. The second section is made up of 2-dof dynamic systems utilizing three types of cutters, they are the cutter with uniform pitch and zero helix angle, the cutter with variable pitch and zero helix angle as well as the cutter with variable pitch and non-zero helix angle. Another group concludes two cutters with non-uniform helix angle for 1-dof dynamic machining system. The last group is composed by an experiment with thin-wall part. The comparing results show that the curves computed using the presented model agree closely to that in literatures and experiment, which proves that the model is correct and the stability lobes can be predicted with high accuracy whatever the dynamic system with the radial cutting depth is small or large, the dynamic system is 1-dof or 2-dof and the cutter's pitch angle of the dynamic system is variable or uniform.