Effect of Engine Mount Damping on the Torque Roll Axis Decoupling

Several mounting system design concepts have been conceptually used to decouple the engine roll mode though limited success is observed in practice. One shortcoming of the existing theories is that they ignore damping in their formulations. To overcome this deficiency, we re-formulate the problem for a nonproportionally damped, linear system while recognizing that significant damping may be possible with passive (such as hydraulic), adaptive or active mounts. Only rigid body modes of power train are considered and chassis is assumed to be rigid. Complex mode method is employed and the torque roll axis (TRA) paradigms are re-examined in terms of mount rate ratios, mount locations and orientation angles. We will show that true TRA decoupling is not possible with non-proportional damping though it is theoretically achieved for a proportionally damped system. Results for both steady state (in the form of frequency response functions) and transient (given impulsive excitations) responses will be illustrated. The natural modes obtained using complex eigensolution method are coupled for the nonproportional damping case, even though they are completely decoupled for the proportional damping case. It is also seen that a higher value of non-proportionality induces more coupling between the rigid body motions of a powertrain. Our method and results are expected to lead to a better design of the mounting systems. INTRODUCTION The torque roll axis (TRA) decoupling concept was investigated by Jeong and Singh [1]. Their analysis assumed a proportionally damped mounting system (from zero to moderate viscous damping ratios) when excited by the oscillating torque. Unlike other decoupling methods, their TRA decoupling method provided complete decoupling between roll and other motions. However, in reality the damping matrix is often non-proportional (assuming it is a linear system of course). For instance, consider the case when one or two hydraulic mounts are combined with rubber mounts; the resulting damping matrix would be non-proportional since the effective viscous damping coefficient of a hydraulic mount is much higher than of a rubber mount [2]. In this paper, we consider the non-proportional damped mounting system and then extend the previous TRA study. This will allow us to comparatively evaluate undamped, proportionally damped, and nonproportionally damped systems. The degree of TRA decoupling will be quantified first in terms of the frequency response functions given unit harmonic torque. Then transient responses to an impulse torque input will be examined. Figure 1 illustrates a typical powertrain isolation system that is composed of an inertial body, 3 or 4 mounts and a rigid foundation. The powertrain is assumed to be a rigid mass element of dimension 6 with time-invariant inertial properties. The resilient mounts are described by three tri-axial stiffness elements and they are assumed to be linear (insensitive to excitation amplitude). Each stiffness element is associated with viscous (or structural) damping characteristics. Further, it is assumed that the orientation of any mount can be arbitrarily adjustable to the desired direction. External or internal excitation forces are applied to the rigid inertial body. By assuming a rigid chassis, a 6-DOF linear timeinvariant model is obtained. As a result of the assumptions made above, our model is limited to the lower frequency range. Over middle and higher frequency regimes, the powertain body and chassis are expected to be compliant and the mounts could even exhibit the standing wave effect [3]. ANALYTICAL FORMULATION The following three coordinate systems are used in our work: Inertial coordinates ( )g XYZ , TRA coordinates , and mount (local) coordinates ( ) ( )TRA XYZ mi XYZ .