附 录A1Dynamic Modeling of Vehicle Gearbox for EarlyDetection of Localized Tooth DefectABSTRACTDynamic modeling of the gear vibration is a useful tool to study the vibration response of a geared system under various gear parameters and operating conditions. An improved understanding of vibration signal is required for early detection of incipient gear failure to achieve high reliability. However, the aim of this work is to make use of a 6-degree-of-freedom gear dynamic model including localized tooth defect for early detection of gear failure. The model consists of a gear pair, two shafts, two inertias representing load and prime mover and bearings. The model incorporates the effects of time-varying mesh stiffness and damping, backlash, excitation due to gear errors and modifications. The results indicate that the simulated signal shows that as the defect size increases the amplitude of the acceleration signal increases. The crest factor and kurtosis values of the simulated signal increase as the fault increases. Though the crest factor and kurtosis values give similar trends, kurtosis is a better indicator as compared to crest factor.KEYWORDS：Vibration acceleration, system modeling, Crest Factor, Kurtosis value, defect size, gear meshing, pinion, gearINTRODUCTIONMuch of the past research in the dynamic modeling area has concluded that an essential solution to the problem is to use a comprehensive computer modeling and simulation tool to aid the transmission design and experiments. These have been two major obstacles to such an approach: (1) Progress in understanding of the basic gear rattle phenomenon has been limited and slow. This is because the engine-clutch-transmission system involves some strong nonlinearities including gear backlash, multi-valued springs, dry friction, hysteresis, and the like. (2)The gear rattle is a system problem and not only problem of gear teeth. Even through the research and industrial community has discussed the difficulties in varies stages of the problem, yet no thorough frame work covering the entire investigation process of such problem currently exists. This is largely due o the complexity of the power train system, which may make a computer analysis tool inefficient, in particularly when many different elements and clearances are encountered (e.g., gears, bearings, splines, synchronizers, and clutch).A comprehensive review of mathematical models used in gear dynamics, published before 1986, has been presented by. In this review, gear dynamic models without defects have been discussed. In the past few years, researchers have been working on the gear dynamic models which include defects like pitting, spalling, crack and broken tooth.A single-degree-of-freedom model is used which include the e4ffects of variable mesh stiffness, damping, gear errors, profile modifications and backlash. The effect of time-varying meshing damping is also included in this case, The solution is obtained by using the harmonic balance methods. A method of calculated the optimum profile modification has been proposed in order to obtain a zero vibration of the gear pair. They also proposed a linear approximate equation to mode the gear pair by using a single-degree-of freedom modelGear rattle vibration is a undesirable vibration for passenger cars and light trucks equipped with manual transmissions. Unlike automatic transmissions, manual transmission do not have the high viscous damping inherent to a hydrodynamic torque converter to suppress the impacting of gear teeth oscillating through their gear backlash. Therefore a significant level of vibration an be produced by the gear rattle and transmitted both inside the passenger compartment and outside the vehicle. Gear rattle, idle shake, and other vibration generated in the automobile driveline have become an important concern to automobile manufactures in their pursuit of an increased level of perception of high vibration quality. The torsional vibration o driveline is a major source of gear rattle vibration. The manual transmission produces gear rattle by the impacting of gear oscillating through their gear backlash. The impact collisions are transmitted to the transmission housing via shafts and bearings.The gear pair dynamic models including defects have been done by. The study suggests that little work has been done on modeling of gear vibration with defect and an accurate analytical procedure to predict gear vibrations in the presence of local tooth fault has yet to be developed.However, the purpose of this paper is to develop a multidegree-of-freedom nonlinear model for a gear pair that can be used to study the effect of lateral-torsional vibration coupling on vibration response in the presence of localized tooth defect. A typical fault signal is assumed to be impulsive in nature because of the way it is generated. The simulation artificially introduced pitting in gears in multi-stage automotive transmission gearbox