A method to predict position-dependent structural natural frequencies of machine tool

• Mathematical models for predicting natural frequency change rate both in the case of mass change and structural change are proposed.
• Both the two mathematical models are validated with simulation method.
• Mathematical model in the case of structural change is validated on a machine tool.
• The natural frequencies of different machine tool structures were predicted with the mathematical model.
• The predicted results indicate that position change of different moving components have different influence on the structural natural frequencies.

Machine tool structure has a strong influence on the dynamic properties of the tool. The change of a machine tool's structure will cause variations in the dynamic parameters of the entire tool, such as its natural frequency, which will result in changes to the stability of the tool and poor machining quality. Thus, a study on the variations of machine tool dynamics is essential for high performance cutting. In this paper, using the mass change method, a basic mathematical model for predicting the natural frequency change resulting from structural change was presented followed by an experimental validation of the model. The mathematical model indicates that structural change will lead to the outward variation of the natural frequency, which is essentially related to the change of the squared mode shape values between the original position and the modified position of the moving component. With this natural frequency change rate prediction model, the natural frequency in the case of structural change can be easily predicted. The predicted results indicate that the positional change of different moving components has differing influences on the natural frequency of the machine tool.