基于分数布朗运动的转轴径向回转误差分析

Analyzing Rotor Rotating Error Using Fractional Brownian Motion

通过分析某精密转轴轴心径向回转误差运动轨迹的方差变化规律,证明该轴的回转运动具备了分数布朗运动的基本特征.继而文章采用无量纲的分形盒维数描述了该轴径向回转误差运动,并以其作为评价轴心运动轨迹复杂度的参数.最后根据赫斯特指数对该轴回转运动的稳定性进行了描述.

According to variance changing laws of a precise rotor radial rotating error motion, it can be proved that the rotor's motion track is characterized by fractional Brownian motion. Then non-dimension fractal box counting dimension has been adopted to describe the rotor's radial rotating error motion, and it also be taken as a parameter to estimate the complexity of axes motion track. At last, Hurst exponent was adopted to describe the stability of axes rotating motion.