Abstract
In the present paper, the amplitude-frequency characteristics of torsional vibration are discussed theoretically and experimentally for automotive powertrain. A bending-torsional-lateral-rocking coupled dynamic model with time-dependent mesh stiffness, backlash, transmission error etc. is proposed by the lumped-mass method to analysis the amplitude-frequency characteristic of torsional vibration for practical purposes, and equations of motive are derived. The Runge–Kutta method is employed to conduct a sweep frequency response analysis numerically. Furthermore, a torsional experiment is performed and validates the feasibility of the theoretical model. As a result, some torsional characteristics of automotive powertrain are obtained. The first three-order nature torsional frequencies are predicted. Torsional behaviors only affect the vibration characteristics of a complete vehicle at low-speed condition and will be reinforced expectedly while increasing torque fluctuation. Gear mesh excitations have little effects on torsional responses for such components located before mesh point but a lot for ones behind it. In particular, it is noted that the torsional system has a stiffness-softening characteristic with respect to torque fluctuation.
Highlights
universal joint (U-joint) Main drive sha Intermediate support driveshaft on a complete vehicle by experimental and finite element method. ey reached a conclusion that fluctuation of nonlinear contact force in sliding mechanism accounts for the complete vehicle vibration
Xu et al [11] and Zhang et al [12] analyzed dynamics of transmission shaftrear driving axle based on ADAMS and experimental demonstration, and the coupling effects between transmission shaft and rear axle were discussed
It is noted that the key of analytical solution for the main reducer is the development of the dynamic model of hypoid gear, with timevarying meshing stiffness, damping, clearance, bear, and other line or nonlinear factors, which inherits the research studies on spur and helical gear pair conduct by Kahraman and Singh [15,16,17], Cai and Hayashi [18], and Velex et al [19,20,21], and remarkable achievements can be found within documents of Lim’s team [22,23,24,25,26] and other researchers
Summary
The equivalent moments of inertia for the chained system are calculated by. Where ζ is the damping ratio, generally set as a range of 0.03 to 0.17 [25]; mp and mg are equivalent mass of pinion and gear, respectively. In order to eliminate the difference in magnitude between parameters, which will reduce the solvability and even lead to no convergence for solving equations of motion mentioned above, b is defined as the characteristic length and a new time parameter τ is introduced as follows:. Equivalent damping coefficients can be obtained. e parameters of the main reducer can be calculated by substituting system parameters listed in Table 2 into equations (17)–(31). e solution procedures for dimensionless parameter are carried out by using preceding calculated parameters and the relationships proposed in previous parts
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