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

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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.