Microscopic Behavior of Leadscrew Used in Ultra-precision Positioning and Its Dynamic Model

本研究探讨了丝杠在1 μ m范围内的一些微观行为，旨在阐明在任何条件下的微观行为，并提出了一个动态模型的行为。设计并建造了一套新的实验装置。螺杆轴水平固定，螺母绕螺杆轴旋转。旋转扭矩通过无触点的电励磁施加到螺母上，而旋转角度和轴向位移通过非接触式电容间隙传感器测量。对恒压型和定位型两种预紧滚珠丝杠进行了实验研究，当螺母准静态地施加小阶跃扭矩时，扭矩输入与螺母位移之间存在非线性弹性特性。实验初步阐明，在微观范围内，旋转角与螺母位移之间的关系与宏观范围内一样也受螺旋导程的影响。正弦扭矩输入下的实验表明，随着预紧力的增加，弹性特性变得更加刚性和线性。扭矩变化速度对滞回效应的影响不大，因此粘性对细观特性的影响较小.根据实验结果，认为非线性弹性特性存在刚度不同的两个区域.提出了一种由两个弹性元件和摩擦元件组成的力学模型，并根据该模型确定了被测滚珠丝杠副的弹簧常数。利用该模型对滚珠丝杠固有频率的估计与动态响应试验结果吻合较好，从而验证了该模型的有效性。

This study deals with some microscopic behavior of leadscrews within the range of 1 mum, aiming at clarifying the microscopic behavior under any conditions and proposing a dynamic model of the behavior. A new experimental apparatus is designed and constructed. The screw shaft is fixed horizontally and the nut rotates around the screw shaft. The rotational torque is applied to the nut by electrical solenoids without any contacts, while the rotational angle and the axial displacement are measured by non-contacting capacitive gap sensors. The experiments are performed on two types of preloaded ball screws ; a constant pressure type and a fixed position type.When the small stepping torque is applied quasi-statically to the nut, the nonlinear elastic characteristics are observed between the torque input and the nut displacement. It is clarified originally by the experiments that, in this microscopic range, the relation between the rotational angle and the nut displacement is also subject to the lead of screw as it is in the macroscopic range. The experiments with the sinusoidal torque input shows that the elastic characteristics becomes stiffer and more linear according to the increase of the preload. The hysteretic effect is not greatly influenced by the speed of toque change, so that the viscosity has less effect on the microscopic behavior.On the basis of the experimental results, it is considered that the nonlinear elastic characteristics have two regions differing in the stiffness. A mechanical model is proposed, which consists of two elastic elements and frictional elements, and the spring constants of the tested ball screws are identified corresponds to the model. The estimation of the natural frequency with the model of the ball screw agreed to the results of dynamical response test, so that the availability of the model is verified.