This study analytically examines the effects of non-proportional damping and spectrally varying mount properties on the dynamics of a six-degree of freedom automotive powertrain (engine-gearbox) system. The effect of coupling between powertrain motions is of particular interest and an emphasis is placed on the torque roll axis decoupling. One shortcoming of the existing theories and design methods is that they ignore non-proportional viscous damping in their formulations. To overcome this deficiency, the analytical problem for a non-proportionally damped linear system is first formulated while recognizing that significant damping may be possible with passive (such as hydraulic) or adaptive (or smart) mounts. Complex mode method is employed and the torque roll axis decoupling paradigm is re-examined given mount rate ratios, mount locations and orientation angles as key design parameters. A necessary axiom for a mode in the torque roll axis direction is derived provided two eigenvalue problems, in terms of stiffness and damping matrices, are concurrently satisfied.
Second, the influence of spectrally varying mount properties (including stiffness and damping) on the dynamics of powertrain motions is analytically examined. To overcome the deficiencies (limited to only the frequency domain analysis) in direct inversion method, two methods are developed by employing transfer function (in Laplace domain) and analogous mechanical formulations, respectively. Those analytical models are verified by comparing the frequency responses with numerical results obtained by the direct inversion method based on Voigt type mount model. Eigensolutions and transient responses of a spectrally varying mounting system are also predicted based on these models. Based on complex eigenstructure, new coupling indices, including spectral modal kinetic energy fractions, are defined for each method. Given spectral variance in the mount properties, a simple roll mode decoupling scheme is suggested. An axiom for torque roll axis decoupling is also provided by employing direct and adjoint eigenvalue problems.
Third, dynamics of the powertrain with active and passive mounts is analyzed from the system perspective. An analytical model for actuator displacement type active mounts is first developed in the form of transfer function that relates the transmitted force through the active mount of interest to both driving point motion and active displacement terms. It is incorporated into a mounting system to develop 6-degree of freedom rigid body active mounting system model in time and frequency domain. Eigenstructure and multi-dimensional dynamics (especially motion coupling) from those mounting systems adopting active mounts are studied.