Solution and Application for Vibration Characteristics of Combined Stepped Beam

In the process of machining, vibration characteristics of the machine tool spindle tool system can be improved by structure optimization of machine tool spindle and appropriate selection of tool and toolholder, reaching a higher machining quality and efficiency with good vibration characteristics. To study the vibration characteristics of the machine tool spindle, this paper proposed a method based on combined stepped beam model. The method for solving bending vibration natural frequency and mode of stepped cantilever beam was developed with the use of Euler-Bernoulli beam theory. Based on the tool-toolholder coupled system from the practical condition, this paper refined the stepped beam model to the combined stepped beam and gave the equivalent bending rigidity and density of the combined part. This method was applied to calculate the vibration characteristics of the tool-toolholder coupled system and it was verified though the finite element method (FEM) and experiment. Results show that compared with the Timoshenko beam theory, this method doubles the computational efficiency whereas calculation error keeps small in condition of large ratio of length to diameter and low order of modal is considered like the machine tool spindle tool system.