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The vibration isolation effectiveness of powertrain mount configurations is examined for electric vehicle application by considering the effect introduced by internal mount resonances. Unlike internal combustion engines where mounts are typically designed only for static support and low frequency dynamics, electric motors have higher excitation frequencies in a range where mount resonances often occur. The problem is first analytically formulated by considering a simple 3-dimensional powertrain system, and the vibration isolation effectiveness significantly deteriorates at the mount resonance(s). It is shown that by modifying the mount shape, the mount resonance(s) can be shifted while maintaining the same static rate, tuning the frequency away from any engine excitation or natural frequencies. Further, internal mount resonances are utilized to improve vibration isolation over a narrow frequency range, using non-identical mounts to split mount resonance peaks.

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.

Elastomeric joints are utilized in many automotive applications, and exhibit frequency and excitation amplitude dependent properties. Current methods commonly identify only the cross-point joint property using displacement excitation at stepped single frequencies. This process is often time consuming and is limited to measuring a single dynamic stiffness term of the joint stiffness matrix. This study focuses on developing tractable laboratory inverse experiments to identify frequency dependent stiffness matrices up to 1000 Hz. Direct measurements are performed on a commercial elastomer test system and an inverse experiment consisting of an elastic beam (with a square cross section) attached to a cylindrical elastomeric joint. Sources of error in the inverse methodology are thoroughly examined and explained through simulation which include ill-conditioning of matrices and the sensitivity to modeling error.

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.

Damping material for automotive structures is often quantified in terms of composite loss factor or damping ratio by using ASTM/SAE beam or modal tests. Simplified expressions have also been used to estimate certain material properties. However, none of these tests provide any information on the properties of viscoelastic core material such as rubber or adhesive in practical structures. To overcome this deficiency, a refined estimation procedure is proposed. A new sandwich beam model has been developed which describes all layers of an arbitrarily applied damping patch. By using both analytical predictions and modal experiments on a cantilever beam, spectrally-varying loss factor and shear modulus of the unknown core are determined.

This study examines clutch-damper subsystem dynamics under transient excitation and validates predictions using a new laboratory experiment (which is the subject of a companion paper). The proposed models include multi-staged stiffness and hysteresis elements as well as spline nonlinearities. Several example cases such as two high (or low) hysteresis clutches in series with a pre-damper are considered. First, detailed multi-degree of freedom nonlinear models are constructed, and their time domain predictions are validated by analogous measurements. Second, key damping sources that affect transient events are identified and appropriate models or parameters are selected or justified. Finally, torque impulses are evaluated using metrics, and their effects on driveline dynamics are quantified. Dynamic interactions between clutch-damper and spline backlash nonlinearities are briefly discussed.

A reduced model is developed for transient analysis of gear rattle in an automatic transmission (AT) powertrain. Linear modal analysis for the reduced order model compares well with a detailed model that includes planetary gear dynamics. Clearance type lash functions are used for the reduced geared coordinates of the automatic transmission and final drive. Impacts within the gear pairs are affected by the engine surging, shaft stiffness, component inertias, engine harmonics, drag torques, braking, viscous damping and vehicle load. The occurrence of these impacts, or clunk, from shuffle and axle oscillations is demonstrated under typical driving conditions.

Many powertrain structural sub-systems are often tested under steady state conditions on a dynamometer or in a full vehicle. This process (while necessary) is costly and time intensive, especially when evaluating the effect of component properties on transient phenomena, such as driveline clunk. This paper proposes a laboratory experiment that provides the following: 1) a bench experiment that demonstrates transient behavior of a non-linear clutch damper under non-rotating conditions, 2) a process to efficiently evaluate multiple non-linear clutch dampers, and 3) generates benchmark time domain data for validation of non-linear driveline simulation codes. The design of this experiment is based on a previous experimental work on clunk. A commercially available non-linear clutch damper is selected and the experiment is sized accordingly. The stiffness and hysteresis properties of the clutch damper are assumed from the measured quasi-static torque curve provided by the manufacturer.

Hydraulic bushings with amplitude sensitive and spectrally varying properties are commonly used in automotive suspension. However, scientific investigation of their dynamic properties has been mostly limited to linear system based theory, which cannot capture the significant amplitude dependence exhibited by the devices. This paper extends prior literature by introducing a nonlinear fluid compliance term for reduced-order bushing models. Quasi-linear models developed from step sine tests on an elastomeric test machine can predict amplitude dependence trends, but offer limited insight into the physics of the system. A bench experiment focusing on the compliance parameter isolated from other system properties yields additional understanding and a more precise characterization.

Fluid filled bushings are commonly used in vehicle suspension and sub-frame systems due to their spectrally-varying and amplitude-dependent properties. Since the literature on this topic is sparse, a controlled laboratory prototype bushing is first designed, constructed, and instrumented. This device provides different internal combination of long and short flow passages and flow restriction elements. Experiments with sinusoidal displacement excitations are conducted on the prototype, and dynamic stiffness spectra along with fluid chamber pressure responses are measured. The frequency-dependent properties of several commonly seen hydraulic bushing designs are experimentally studied and compared under two excitation amplitudes. Further, new linear time-invariant models with one long and one short flow passages (in parallel or series) are proposed along with the limiting cases.

The brake torque variation (BTV) generated due to geometric irregularities in the disc surface is generally accepted as the fundamental source of brake judder; geometric imperfections or waviness in a disc brake caliper system is often quantified as the disc thickness variation (DTV). Prior research has mainly focused on the vibration path(s) and receiver(s), though such approaches grossly simplify the source (frictional contact) dynamics and often ignore caliper dynamics. Reduction of the effective interfacial contact stiffness could theoretically reduce the friction-induced torque given a specific DTV, although this method would severely increase static compliance and fluid volume displacement. An experiment is designed to quantify the effect of disc-pad contact modifications within a floating caliper design on BTV as well as on static compliance.

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 non-proportionally 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.

The elastomeric joints (bushings or mounts) in vehicle structural frames are usually described as uncoupled springs (only with diagonal terms) in large scale system models. The off-diagonal terms of an elastomeric joint have been previously ignored as they are often unknown since their properties cannot be measured in a uniaxial elastomer test system. This paper overcomes this deficiency via a scientific study of a laboratory frame that is designed to maintain a high fidelity with real-world vehicle body subframes in terms of natural modes under free boundaries. The steel beam construction of the laboratory frame, with four elastomeric mounts at the corners, permits the development of a highly accurate, yet simple, beam finite element model. This allows for a correlation study between the experiment and model that helps shed light upon the underlying physical phenomenon.

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.

This paper examines the natural frequencies, mode shapes and modal damping ratios of a specially designed laboratory fixture with integral, welded or glued joints. The influence of these alternate joints on the dynamic properties of an assembly is demonstrated, using experimental, computational and analytical methods. Dimensions of a typical welded joint configuration are varied to study their effects on the modal properties of an assembly. Predictions are successfully compared with experimental modal data. This study should help in selecting the welded joint configuration to meet strength, durability or dynamic design criteria.

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.

Performance characteristics of passive, active, and broadband adaptive engine mounts are compared over a wide frequency range up to 250 Hz in the context of a quarter-vehicle heave model. The optimal damping coefficient of a rubber-metal mount is determined using random vibration theory. The small-scale active mount employs proportional-plus-integral control based on linear optimal control theory. The new adaptive hydraulic mount system implements an on-off damping control mode by using engine intake-manifold vacuum and a microprocessor-based solenoid valve controller. Through analytical methods, it is observed that this adaptive mount provides most desirable dynamic performance with regard to the engine-bounce control, shock absorption and vibration isolation performance requirements. Although technical prospects of the proposed adaptive system appear promising, in-situ performance needs to be evaluated.

Previously we had found significant errors in the interfacial force results for a source-path-receiver system where only translational motions were measured. This paper examines the sources of those errors by using computational finite and boundary element models. The example case consists of a source structure (with few modes), a receiver (with many modes) and three steel rod paths. We first formulate indirect, yet exact, methods for estimating interfacial forces, by assuming that six-dimensional motions at any location are available though we focus on only the driving points. One- and three-dimensional sub-sets of the proposed formulation are compared with the six-dimensional theory in terms of interfacial force and partial sound pressure spectra.

Accurate quantification of welded or adhesive joints in automotive chassis structures is necessary before reliable models can be developed. Such joints undergo shear and rotational deformations, which must be characterized via diagonal stiffness elements and cross-stiffness terms in order to describe static and dynamic problems. In this paper, a frequency domain decomposition technique is employed to extract static stiffness and viscous damping matrices of dimension 2 via analytical, computational or experimental models. Methods are applied to a laboratory fixture and alternate joints are compared.

Many discrete tonal type noise and vibration problems in automotive systems and other physical structures require passive multi-layer visco-elastic damping treatments in mid to high frequency regimes. To address such issues, experimental modal analysis and dynamic finite element methods are suggested as suitable tools. Results are presented in terms of several test structures (four thin elastic beams, a thick elastic plate and an automotive brake pad) with free-free boundary conditions. Composite modal loss factors are measured and predicted for two different damping insulators consisting of adhesive, steel and coating combinations. Special attention is paid to the elastic deformation modes of test structures and spectral scaling of material properties for the finite element models.