考虑摩擦和间隙的柔性滚珠丝杠进给系统建模与分析

Modeling and Analysis of Flexible Ball Screw Driven Servomechanisms with Friction and Backlash

摘要:

为了研究高速滚珠丝杠进给伺服系统的动态特性，提出了一种建立进给系统机械子系统振动模型的混合建模方法，采用带有轴向和扭转自由度的欧拉-伯努利梁单元描述丝杠的轴向、扭转和弯曲振动，采用集中参数方法描述交流伺服驱动子系统和进给系统的其余部件，建立了包含摩擦、间隙非线性因素及外切削力干扰的柔性进给系统模型。实验证明了混合模型能够较准确反映机械系统的振动特性。在此基础上，数值仿真分析表明，低速运动中摩擦和间隙非线性会导致进给系统产生较大的速度波动，在高速运动中机械系统的轴向和扭转振动会导致进给系统不稳定。

Abstract:

In order to get the structural dynamic of the high speed ball screw driven servomechanism, a hybrid modeling method was proposed. The proposed model took the axial, torsional and bending vibrations of the screw into consideration by the Euler-Bernoulli beam elements with axial and torsional theories. The servo subsystems and the other more rigid components were modeled by the lumped parameter method. The flexible ball screw feed drive servomechanism was proposed, including the friction, backlash and the cutting disturbance. Compared with the experimental results, the hybrid model could accurately capture the structural dynamics of ball screw drives. Numerical simulation indicated that the nonlinearities of friction and backlash could cause velocity fluctuations at the low speed. The torsional and axial vibrations made the servo system unstable, especially in the high speed application.