Timoshenko beam-based stability and natural frequency analysis for heavy load mechanical spindles

The heavy load mechanical spindle is an important functional component in a 5-axis computer numerical control (CNC) machine tool, which is used to process large and complex free-form surfaces. It is necessary to obtain the natural frequency and analyze the spindle stability for improving the machining precision. In this paper, Timoshenko beam theory is introduced to model the mechanical spindle shaft, where the centrifugal force and gyroscopic effects are considered. Stability of the heavy load mechanical spindle shaft is analyzed, and the buckling load of the spindle shaft is obtained under different rotational speeds. The natural frequency of spindle is investigated in a freedom and restraint state, respectively. Comparing the proposed method with the simplified hollow cylinder and shaft prototype in the freedom state, the results show that they are highly correlated with experimental results. For the restraint state, the axial load, rotational speed, gyroscopic effect, and centrifugal force are discussed, and all of these parameters affect the natural frequency. The proposed modeling approach can be used for spindle design and optimization in a given machining process and can be easily extended to other spindle design.