In order to study on the vehicle’s dynamic behavior, this study presents a new dynamic modeling of the vehicle by considering the engine dynamics. The coordinate systems are considered separately for the sprung mass and unsprung masses. By using Newton’s equations of motion, the force-torque equations of the sprung mass and unsprung masses are derived in the vehicle coordinate system. In general, the sprung mass in modeling of the vehicle is considered as a rigid body. However, in this study the components rotation of the sprung mass such as the engine crankshaft is considered and its gyroscopic effects are exerted in the governing equations. The lateral and longitudinal forces of the tire are evaluated by Pacejka model. In fishhook maneuver, the vehicle's dynamic behavior is studied by the numerical simulation method under the supervision of the National Highway Traffic Safety Administration (NHTSA). The numerical simulation results are also validated by ADAMS/Car software. According to the results, the 15-DOF model in this research simulates the vehicle’s dynamic behavior with a good accuracy and the maximum roll rate of the vehicle reaches about 37 degrees per second. پرونده مقاله

In dynamic model of planetary gears, one of the key design parameters and one of the main sources of vibration is time–varying mesh stiffness of meshing gears. According to previous researches, the finite element method and analytical method are two techniques to estimate the mesh stiffness of meshing gears. In this work, in an innovation the periodically time–varying mesh stiffness of meshing gears is examined by both of finite element and analytical methods. The planetary gear set is modeled as a set of lumped masses and springs. Each element such as sun gear, carrier, ring gear and planets possesses three degrees of freedom and is considered as rigid body. The influence of effective parameters on the mesh stiffness of meshing gears and also numerical results of natural frequencies and vibration modes of the system are obtained. Based on the results, the influence of the higher pressure angles on the mesh stiffness of meshing gears is perceptible. By using the proposed mesh stiffness of meshing gears, for the system with numbers of odd and even equally and unequally spaced planets, natural frequencies and vibration modes are validated with a high accuracy. پرونده مقاله

This work studies on analytical model of the single–stage spur planetary gear in form of lumped–parameter model. It includes key nonlinear factors of planetary gear vibration such as mesh stiffness and backlash of meshing gears. The planetary gear set is modeled as a set of lumped masses and springs and dynamic model of the planetary gear set is presented. Nonlinear equations of motion are presented for each component and each component has three degrees of freedom in planar motion. We have numerically evaluated a set of linear and nonlinear equations to obtain natural frequencies and analysis of vibration behavior of the system under nonlinear factors and fixed output. In previous researches, natural frequencies of planetary gears were evaluated from two points of view: the first one considered fixed output for planetary gears and the second one consists of free rotational output. In this research, the influence of the output flexibility is evaluated on natural frequencies of the planetary gear. Meanwhile, by considering the fixed output, vibration behavior of the nonlinear system is investigated. Results show that the most important effect of the output flexibility is on the principal natural frequency. Because of chaotic phenomenon, vibration behavior of components in translational directions is different. پرونده مقاله

In industry applications, planetary gear systems are widely used in power transmission systems. In planetary gears, dynamic loads, noise and reduction the structural life are produced by system vibrations. For gear transmission systems, the parametric excitation which introduced by the periodically time–varying mesh stiffness of each gear oscillation is the main source of vibration. Generally, there are two methods to evaluate the gear mesh stiffnesses, the finite element method and the analytical method. In this wok, the periodically time–varying mesh stiffness of planetary gears is investigated. The influence of pressure angles on mesh stiffness of meshing gears is shown and the dynamic model of planetary gear sets is studied. When planets of the single–stage spur planetary gear system are meshed by new planets, the system is converted to special type of system with meshed planets. Vibration for geometrical structures (symmetric and anti–symmetric) of planetary system with meshed planets is investigated. Mesh stiffness of meshing gears by estimation function is obtained and numerical results of natural frequencies and vibration modes are derived. پرونده مقاله