翻译部分英文原文Parametric study of dynamics of worm and worm-gear set undersuddenly applied rotating angleM.Y. Chung, D. ShawDepartment of Power Mechanical Engineering, National Tsing-Hua University, No. 101 Kung Fu Road Section II, Hsin Chu, Taiwan, ROCReceived 13 September 2006; received in revised form 23 January 2007; accepted 25 February 2007Available online 17 April 2007AbstractThe dynamics of a worm-gear set under instantly applied rotating angle are affected by several factors (including thefriction force and elastic deformation of the surface between gear teeth). It is found that those factors cause a nonnegligible rotational positioning error. The goals of this study are to (1) set up a mathematic model, (2) carry out anumerical simulation, and (3) carry out an experiment and compare it with the numerical results. The experiments and numerical results have very good agreement. In this research, themoment-inertia of fly wheel, friction, rigidity of shaft andrigidity of gear tooth are also studied. The results can be used as error estimations of relevant angles, angular speed andangular acceleration under a suddenly applied rotational angle, and are useful for establishing the error compensationrequired for position control.1. IntroductionWhen radar tracks an aircraft which turns at a sharp angle; the radar may not be able to lock onto the target due to the small oscillation of the antenna. Sometimes, the oscillation even causes a failure of the radar system . Accurate positioning is a crucial subject in a tracking system. However, due to the design of the trackingtransmission mechanism is restricted by both space and weight, the volume and the weight of the transmissionmechanism must be limited. The worm-gear set is a good choice due to its small volume and high reduction ratio. Owing to the oscillation of the antenna is an important dynamics behavior for high precision positioningof radar system, the dynamics of a worm-gear set under instantly applied large torque is very important tounderstand this behavior. This behavior is affected by several factors including the friction force and elasticdeformation of the surface between gear teeth. To understand the effect of those factors, a lot of research hasbeen conducted. Yuksel and Kahraman 1 studied the in.uence of surface wear on the dynamic behavior of a typical planetary gear set. The wear model employed a quasi-static gear contact model to compute contact pressures and Archards wear model to determine the wear depth distributions. Parker et al. 2 analyzed the dynamic response of a spur pair of a wide range of operating speeds and torques. Comparisons were made to other researchers published experiments that reveal complex nonlinear phenomena. The dynamic response of a spur pair was investigated using a .nite element/contact mechanics model that offers signi.cant advantages for dynamic gear analyses. Maliha 3 created a nonlinear dynamic model of a spur gear pair, which was coupled with linear .nite element models of the shafts carrying them, and with discrete models of bearings and disks. The excitations considered in the model were external static torque and internal excitation caused by mesh stiffness variation, gear errors and gear tooth pro.le modi.cation. Britton 4 produced a super .nished gear teeth (with a approximately 0.05 mm Ra Film) and the friction traction in the experiments were simulated theoretically using a thin .lm non-Newtonian micro-elastohydrodynamic lubrication solver and encouraging agreement between friction measurements and theoretical predictions was obtained. Kong 5 predicted elastic contact and elastohydrodynamic .lm thickness in worm gears. Using the undeformed geometry of the gap between gear teeth in contact a three-dimensional elastic contact simulation technique had been developed for calculation of the true area of elastic contact under load relative the wheel and worm surfaces. Tuttle 6 studied the harmonic drives, which exhibited very nonlinear dynamic behavior, in his model not only dynamic models include accurate representation of transmission friction, compliance and kinematical error were understand, but also important features of harmonic-drive gear-tooth geometry and interaction. Experimental observations were used to guide the development of a model to describe harmonic-drive operation.It is important to be aware that worm-gear performance is in.uenced by the lubricant applied and maintained. Helouvry 7 discussed the issue of the servo-orientation control being affected by a surge of both maximum static friction force and dynamic friction force. They reported the occurrence of a stable positioning error, as well as the stopping (or stoking) during tracking at the turning point of a limiting loop of the tracking system. When the system was in a one directional low-speed tracking, it was possible for the stickslip