Tool point frequency response function prediction using RCSA based on Timoshenko beam model

In advanced manufacturing, tool point frequency response function (FRF) is the most extensive requirement in avoiding the unstable condition of a machine tool, especially in generating a stability lobe diagram which is widely used in predicting the milling stability for chatter avoidance. However, compared with the analytical method that uses a Euler-Bernoulli beam model for calculating the tool point FRF, the analysis based on a Timoshenko beam model mathematically or analytically is seldom provided. Experimental validation is also not sufficient. In this paper, an approach of tool point frequency response prediction based on Timoshenko beam model is presented, using receptance coupling substructure analysis. This approach employs the combination of experimental result and numerical beam analysis. The proposed receptance calculate theory allows to better estimate the matrix of receptance related to rotation. Based on this theory, an unknown tool point FRF can be predicted by an already known tool point FRF. In the meantime, no additional experiment is required after a single experiment to compute tool holder frequency response. Prediction method has been verified by experiments. The results show the effectiveness and reliability of the proposed method in tool point frequency prediction and effective manufacturing.