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Shaped elastomeric joints such as engine mounts or suspension bushings undergo broadband, multi-axis loading; however, in practice, the elastomeric joint properties are often measured at stepped single frequencies (non-resonant test method). This article helps provide insight into multi-axis properties with new benchmark experiments that are designed to permit direct comparison between system resonant and non-resonant identification methods of the dynamic stiffness matrices of elastomeric joints, including multi-axis (non-diagonal) terms. The joints are constructed with combinations of inclined elastomeric cylinders to control non-diagonal terms in the stiffness matrix. The resonant experiment consists of an elastic metal beam end-supported by elastomeric joints coupling the in-plane transverse and longitudinal beam motion.

The engine start-up process introduces speed-dependent transient vibration problems in ground vehicle drivelines as the torsional system passes through the critical speeds during the acceleration process. Accordingly, a numerical study is proposed to gain more insights about this transient vibration issue, and the focus is on nonlinear analysis. First, a new nonlinear model of a multi-staged clutch damper is developed and validated by a transient experiment. Second, a simplified nonlinear torsional oscillator model with the multi-staged clutch damper, representing the low frequency dynamics of a typical vehicle driveline, is developed. The flywheel velocity measured during the typical engine start-up process is utilized as an excitation. The envelope function of the speed-dependent response amplification is estimated via the Hilbert transform technique. Finally, the envelope function is effectively utilized to examine the effect of multi-staged clutch damper properties.

A laboratory experiment is designed to examine the clunk phenomenon. A static torque is applied to a driveline system via the mass of an overhanging torsion bar and electromagnet. Then an applied load may be varied via attached mass and released to simulate the step down (tip-out) response of the system. Shaft torques and torsional and translational accelerations are recorded at pre-defined locations. The static torque closes up the driveline clearances in the pinion/ring (crown wheel) mesh. With release of the applied load the driveline undergoes transient vibration. Further, the ratio of preload to static load is adjusted to lead to either no-impact or impact events. Test A provides a ‘linear’ result where the contact stiffness does not pass into clearance. This test is used for confirming transient response and studying friction and damping. Test B is for mass release with sufficient applied torque to pass into clearance, allowing the study of the clunk.

Many automotive components and sub-systems require viscoelastic damping treatments to control noise and vibration characteristics. To aid the dynamic design process, new approaches are needed for modeling of partial damping treatments and characterization of the overall dynamic behavior. The analytical component of the design process is illustrated via the transmission casing cover, along with supporting experiments. First, the vibration response of production casing plates is examined, with and without the constrained layer treatment. A modified flat plate is employed along with a generic housing that provides the realistic boundary conditions for subsequent work. A simplified analytical damping model for constrained viscoelastic layer damping is suggested based on assumed modal functions. Using the analytical model, design guidelines in terms of optimal patch shapes and locations are suggested.

In many vibration isolation problems, translational motion has been regarded as a major contributor to the energy transmitted from a source to a receiver. However, the rotational components of isolation paths must be incorporated as the frequency range of interest increases. This article focuses on the flexural motion of an elastomeric isolator but the longitudinal motion is also considered. In this study, the isolator is modeled using the Timoshenko beam theory (flexural motion) and the wave equation (longitudinal motion), and linear, time-invariant system assumption is made throughout this study. Two different frequency response characteristics of an elastomeric isolator are predicted by the Timoshenko beam theory and are compared with its subsets. A rigid body is employed for the source and the receiver is modeled using two alternate formulations: an infinite beam and then a finite beam. Power transmission efficiency concept is employed to quantify the isolation achieved.

The knowledge of frequency-dependent dynamic stiffnesses of mounts, in axial and flexural motions, is needed to determine the behavior of many automotive sub-systems. Consequently, characterization and modeling of vibration isolators is increasingly becoming more important in mid and high frequency regimes where very few methods are known to exist. This paper critically examines some of the approximate identification methods that have been proposed in the literature. Then we present a new experimental identification method that yields frequency-dependent multi-dimensional dynamic stiffnesses of an isolator. The scope is however limited to a linear time-invariant system and our analysis is restricted to the frequency domain. The new characterization method uses two inertial elements at both ends of an isolator and free boundary conditions are maintained during testing.

A vibration isolator or mount is often modeled by the Voigt model describing uni-axial (longitudinal) motion with frequency-invariant parameters. However, wave effects due to the mass distribution within the isolator are observed as the frequency is increased. Further, flexural stiffness components play an important role, leading to off-axis and coupling effects. Thus, the simplified mount models could lead to erroneous predictions of the dynamic behavior of an overall system such as automotive powertrain or chassis mounting systems. This article compares various approximate isolator models using a multi-dimensional mobility model that is based on the continuous system theory. Harmonic force and moment excitations are separately applied to a rigid body source to investigate the multi-dimensional vibratory behavior. Analysis is however limited to a linear time-invariant system and the mobility synthesis method is utilized to predict the frequency domain behavior.

Structure-borne noise within vehicle structures is often transmitted in a multi-dimensional manner and thus the vibro-acoustic model(s) of automotive powertrain or chassis must incorporate longitudinal and transverse (flexural) motions as well as their couplings. In this article, we employ the continuous system theory to model a typical vibration isolator (say the engine mounting system) and a compliant receiver that could simulate the body structure. The powertrain source is however assumed to be rigid, and both harmonic force and moment excitations are considered. Our analysis is limited to a linear time-invariant system, and the frequency domain based mobility method is utilized to synthesize the overall system. Contributions of both in-plane and flexural motions to structure-borne and radiated noise are incorporated. Two examples are considered to illustrate the methodology.

This article studies the effects of tooth surface waviness and sliding friction on the dynamics and radiated structure-borne noise of a spur gear pair. This study is conducted using an improved gear dynamics model while taking into account the sliding frictional contact between meshing teeth. An analytical six-degree-of-freedom (6DOF) linear time varying (LTV) model is developed to predict system responses and bearing forces. The time varying mesh stiffness is calculated using a gear contact mechanics code. A Coulomb friction model is used to calculate the sliding frictional forces. Experimental measurements of partial pressure to acceleration transfer functions are used to calculate the radiated structure-borne noise level. The roles of various time-varying parameters on gear dynamics are analyzed (for a specific example case), and the predictions from the analytical model are compared with prior literature.

Most of the prior work on active mounting systems has been conducted in the context of a single degree-of-freedom even though the vehicle powertrain is a six degree-of-freedom isolation system. We seek to overcome this deficiency by proposing a new six degree-of-freedom analytical model of the powertrain system with a combination of active and passive mounts. All stiffness and damping elements contain spectrally-varying properties and we examine powertrain motions when excited by an oscillating torque. Two methods are developed that describe the mount elements via a transfer function (in Laplace domain). New analytical formulations are verified by comparing the frequency responses with numerical results obtained by the direct inversion method (based on Voigt type mount model). Eigensolutions of a spectrally varying mounting system are also predicted by new models.