1、 第 1 页 共 7 页 Dynamic Modeling of Vehicle Gearbox for Early Detection of Localized Tooth Defect Nagwa Abd-elhalim, Nabil Hammed, Magdy Abdel-hady, Shawki Abouel-Seoud and Eid S. Mohamed Helwan University ABSTRACT Dynamic modeling of the gear vibration is a useful tool to study the vibration response
2、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 inc
3、luding 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 mo
4、difications. 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 simil
5、ar 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, gear NOMENCLATURE DJ ， 1J ， 2J ， LJ Drive motor, pinion, gear, and load mass moment of inertia replacement decisi
6、on in a suitable time. 1m ， 1m Masses of pinion and gear. DT Driving motor torque. LT Load torque. 第 2 页 共 7 页 1FT ， 2FT Friction torque. 1C ， 2C Viscous damping coefficient of pinion and gear bearing. mC Gear mesh damping. mK Gear mesh stiffness. 1K ， 2K Pinion and gear shaft stiffness. 4 The varia
7、nce square. N The number of samples. f The defect width in face direction. hK Unit width Hertzian stiffness. D ， 1 ， 2 ， L Angular displacement of drive motor, pinion, gear and load. D ， 1 ， 2 ， L Angular velocity of drive motor, pinion, gear and load. D ， 1 ， 2 ， L Angular acceleration of drive mot
8、or, pinion, gear and load. INTRODUCTION Much 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 t
9、o 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 gea
10、r 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 d
11、ue o the complexity of the power train system, which 第 3 页 共 7 页 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) 1-3. A comprehensive review of mathematical models u
12、sed in gear dynamics, published before 1986, has been presented by 4. 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 singl
13、e-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 cal
14、culated the optimum profile modification has been proposed in order to obtain a zero vibration of the gear pair 5-7. They also proposed a linear approximate equation to mode the gear pair by using a single-degree-of freedom model Gear rattle vibration is a undesirable vibration for passenger cars an
15、d 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 vi
16、bration 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 lev
17、el 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 8. The gear pair dynamic models including defects have been done by 9. The study
