Research on Vibration Reliability and Vibration Damping Strategy with Modification of Gears
|Course||Mechanical Design and Theory|
|Keywords||Gear Vibration Reliability Profile modification Stochastic process|
Gear system plays an indispensable role in the era of industry process changing rapidly, it is widely used in many field such as electric power, energy, transport, national defense and aviation. As the key transmission component in motor, gears always work in the condition of high speed and overload. Besides, it must meet the need of low noise, light weight, high reliability as well as long life span. Therefore, it is significant and meaningful to develop the study of vibration reliability and explore the method of modification to decreases the vibration for gears. Recently, the researches of gear concerning the vibration mainly focus on the aspects of natural characteristics and dynamic responses. However, the stochastic factors of gear parameters such as error, whose stochastic property is accurate to express with probability, are rare to taken into consideration. Therefore, it is possible to adopt reliability theory to design gears in accessory gearbox. Basing on vibration analysis, reliability research can be developed in high speed and overload gears. Still, optimization methods can be use into the analysis of modification and vibration damping. The research is important to enhance the working performance and reliability of gears in accessory gearbox.The research regards spur gears as the object from the engineering application perspective, and transmission error reliability, nonlinear vibration reliability, structural frequency reliability and profile modification for vibration damping are systematically studied based on integrating some advanced theories and techniques such as the Genetic Algorithm (GA), modification theory, stochastic parameter vibration, nonlinear vibration and dynamic reliability. The main researches are shown as follows:(1) Basing on nonlinear vibration model of gear sysytem, the probability characteristics of random parameters are reflected in the stochastic response by numerical integration scheme, with the stochastic process introduced into vibration reliability. A method of calculate reliability is formed with failure criteria that random amplitude exceeds the prescribed value in a vibration cycle. For the complexity of gear nonlinear vibration, this method assesses the probability distribution of the vibration response directly by numerical solution, and avoids the error of approximation algorithms. It can be directly used in engineering design. (2) To determine the parameters of gear profile modification accurately, the meshing process of a pair of gears was simulated via Finite Element Method (FEM). With GA introduced into the process to reduce the fluctuation of transmission error, the profile modification parameters of spur gears were designed optimally and accurately. Obviously, the method is accurate and efficient to decrease the torsion vibration greatly by analyzing the vibration damping effect.(3) In order to discovery the nature of nonlinear behavior of gear system and avoid the chaotic vibration, nonlinear dynamic model of both single backlash and multiple backlash gear systems are built concerning the transmission error, time-varying mesh stiffness. The model is solved with numerical method, and the nonlinear dynamic characteristic is analyzed. The chaotic character is shown from the phase map and Poincare map, and the bifurcation diagram and largest Lyapunov exponent diagram are plotted while the frequency ratio varies. Lyapunov exponent is applied to identify the chaotic vibration numerically, and to fix the region of chaotic vibration. It provides a basis of nonlinear vibration reliability for gears.(4) For studying the modification parameters effect on transmission error reliability, the limit state function for the transmission error of gear stochastic parameters is established with Response Surface Method (RSM). And method of Monte-Carlo reliability and reliability sensitivity is applied to acquire the reliability and reliability sensitivity when the transmission error amplitude is not crossing.(5) Basing on ANSYS Parametric Design Language (APDL) ANSYS, parameter FEM models of involute tooth profile, linear modification profile and parabolic modification profile are established respectively. The model is accurate to simulate the meshing process of gears with stochastic parameters. The time-varying mesh stiffness and transmission error of gear are calculated as well.(6) The reliability of gear structures with stochastic parameter vibration is defined on the basis of the relation criterion of the difference not beyond special value of the natural frequency and driving frequency. The frequency reliability analysis methods for spur gear and spiral bevel gear are carried out to avoid the resonant. The effect of statistical characteristic change of stochastic parameter is evaluated for frequency reliability of gear structure. The result provides a theoretical basis for improving the gear structure and ensuring the gear system working safely.