A unified process damping model considering the varying stiffness of the milling system

Existing process damping models only consider the effect of a single factor, i.e. either the velocity variation or the ploughing indentation, and thus cannot be used to reveal the dynamic behaviour of the milling process with varying stiffness. This article presents a unified process damping model by comprehensively considering multi-factors such as the cutting velocity, the ploughing indentation and the stiffness of the milling system. First, the actual cutting velocity is used to theoretically detect the effects of both shearing and ploughing mechanisms on process damping. Second, different from the previous relevant works that only used the boundaries of the nominal indented zone to calculate the indented volume, this model includes the deflections of the tool and workpiece to calculate the actual indented volume, and thus realizes characterizing the influence of the milling system's stiffness on the ploughing force for the first time. Third, the weighting of the ploughing indentation and velocity change on process damping is analysed by introducing a concept of proportion factor, which is subsequently determined by theoretically formulating a calibration algorithm. Besides, an efficient approach to predict the vibration displacements and velocities of the tool-workpiece system, which are needed in solving the established process damping model, is developed. Finally, a series of milling tests with different stiffness proves the correctness of the proposed unified process damping model together with the embedded calibration and prediction algorithms.