Abstract: Based on the finite element method， we created a parametric three-dimension finite element model for spindle system and simplified the bearing as elastic support. Taken pulley and chuck into consideration， modal analysis of the entire system was conducted， thus the natural frequencies of the first eight vibrations and the corresponding spindle vibration modes were acquired. Critical speed of rotation was analyzed. We compared the working speed with rotation speed of the lowest non-zero set of frequency， hereby the rationality of design was verified. The ISIGHT integrated with ANSYS was used in designing orthogonal experiment and in calculating the lowest non-zero set of frequency. Diameters and length with tolerance requirements， and basic physical parameters considered as random variables， the BP neural network fitting method was used to get the relationship between the lowest non-zero set of frequency and random variables. The first order second moment (FOSM) method was used to calculate the spindle system reliability with specific rotation speed and reliability sensitivity of random variables.

Key words: spindle system, finite element method, neural network, reliability, reliability sensitivity