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A multi-point hypoid gear mesh model based on 3-dimensional loaded tooth contact analysis is incorporated into a coupled multi-body dynamic and vibration hypoid gear model to predict more detailed dynamic behavior of each tooth pair. To validate the accuracy of the proposed model, the time-averaged mesh parameters are applied to linear time-invariant (LTI) analysis and the dynamic responses, such as dynamic mesh force, dynamic transmission error, are computed, which demonstrates good agreement with that predicted by single-point mesh model. Furthermore, a nonlinear time-varying (NLTV) dynamic analysis is performed considering the effect of backlash nonlinearity and time-varying mesh parameters, such as mesh stiffness, transmission error, mesh point and line-of-action. Simulation results show that the time history of the mesh parameters and dynamic mesh force for each pair of teeth within a full engagement cycle can be simulated.

High speed, precision geared rotor systems are often plagued by excessive vibration and noise problems. The response that is primarily excited by gear transmission error is actually coupled to the large displacement rotational motion of the driveline system. Classical pure vibration model assumes that the system oscillates about its mean position without coupling to the large displacement motion. To improve on this approach and understanding of the influences of the dynamic coupling, a coupled multi-body dynamic and vibration simulation model is proposed. Even though the focus is on hypoid geared rotor system, the model is more general since hypoid and bevel gears have more complicated geometry and time and spatial-varying characteristics compared to parallel axis gears.

This paper discusses an enhanced active vibration control concept to suppress the dynamic response associated with gear mesh frequencies. In active control application, the control of dynamic gear mesh tonal response is essentially the rejection or suppression of periodical disturbance. Our active control experimental work shows that the existence of un-controlled harmonic result in the increase at these harmonics when applying direct control to the target mesh frequencies. To address this problem, the effect of the existence of un-correlated harmonic components in error signal when applying active control to suppress the target gear mesh harmonics is examined. The proposed adaptive controller that is designed specifically for tackling gear mesh frequency vibrations is based on an enhanced filtered-x least mean square algorithm (FXLMS) with frequency estimation to synthesize the required reference signal.

In the present study, several welded beam and plate specimens are fabricated using an electrical resistance type spot welder and studied experimentally applying the frequency response function approach. The experimental data is used to guide the dynamic finite element modeling effort, and to determine the weld joint representation that most accurately characterizes the measured dynamic response. The results reveal the compliant nature of the spot welds at higher frequencies and in applications consisting of more complex geometrical structures and boundary conditions. This finding shows the inadequacy in the classical rigid element representation that is widely used in current dynamic modeling practices.

Vehicle NVH performance is significantly affected by the dynamics of various primary systems. In the automotive industry, different design activities or vendors are responsible for designing various different systems simultaneously. Therefore, it is highly desirable to gain a better understanding of the individual system characteristics and the interaction between the primary systems to achieve a desirable overall NVH performance. Unfortunately, it is usually quite difficult to construct a proper fixture to accurately measure and quantify the actual uncoupled system characteristics. This paper examines an alternate approach of applying the FRF-based substructuring method to back-calculate the system response characteristics from the full vehicle system measurements. The results are then used to forward-compute the dynamic response of the vehicle, which are also validated by comparison to the direct response function measurements.

The feasibility of applying a dynamic sub-structuring approach to model and analyze the vibration response of critical automotive components in its coupled vehicle state is examined using an idealized beam-flange-plate system. The beam-flange component is regarded as the primary component of interest while the plate is assumed to be the base structure. Both modal and spectral-based formulations are considered, which account for the true dynamic coupling/interaction between the component of interest and base structure. For the modal-based sub-structuring approach, a unique modeling scheme that utilizes a set of multi-point constraint equations for representing the transformation matrix between the modal coordinates of the base structure and the physical coordinates of the primary component is applied. On the other hand, the spectral-based approach relies on the frequency response functions of the base structure directly to predict the overall system response spectra.

The vibratory energy from the ring gear resulting due to planet/ring gear dynamic forces is typically transmitted via structure-borne paths and is most evident in the range of 1-6000 Hz for automotive transmissions. In this paper, a comprehensive parametric force response analysis to study the vibration transmissibility characteristics of typical automotive planetary ring gears is performed. Effects of various geometrical parameters and number of planets on vibration transmissibility characteristics of ring gear structure are also studied. The planet/ring gear mesh forces are explicitly defined as externally applied force. Vibration transmissibility is defined by the spatial average acceleration response of the outer surface of the ring gear. The root mean square (RMS) value of these average responses is also predicted.

This paper is intended to describe some of the advances in automotive NVH research and applications based on recent developments in the Structural Dynamics Research Laboratory (SDRL) at the University of Cincinnati. State-of-the-art vibro-acoustic research capabilities and infrastructure ranging from advanced vibration modal analysis and spectral techniques for linear and nonlinear automotive systems to computational tools for structure-borne acoustic noise generation, transmission and synthesis problems are discussed. These systems have been devised with the intent of integrating a versatile set of experimental, computational and analytical approaches in order to be able to investigate a variety of crucial automotive NVH concerns. The materials will be grouped into three separate but closely related sets of applications consisting of (i) powertrain noise and vibration control, (ii) analysis and control vehicle system dynamics, and (iii) NVH and sound quality.

A multi-coordinate FRF-based inverse substructuring approach is proposed to partition a vehicle system into two or more substructures, which are coupled at discrete interface points. The joint and free substructure dynamic characteristics are then extracted from the coupled system response spectra. Depending on the actual form of the structural coupling terms, three forms of the coupling matrix are assumed here. The most general one constitutes the non-diagonal form, and the other two simpler cases are the block-diagonal and purely diagonal representations that can be used to simplify testing process and overcome computational problems. The paper is focused on the investigation of the durability of these three formulations when the input FRFs are noise contaminated. A finite element model of a simplified vehicle system is used as the case study.

A spectral-based substructuring approach applying linear frequency response functions (FRF) is proposed for improving the accuracy of simulating the dynamics of coupled systems. The method also applies a least square singular value decomposition (SVD) scheme to overcome the inherent computational deficiency in the basic substructuring formulation. The computational problem is caused by the magnification of measurement errors during any one of the matrix inversion calculations required for this method. The primary objective of applying this approach is to examine the possibility of analyzing higher frequency response that is normally not possible using conventional modeling technique such as the direct finite and boundary element, and lumped parameter techniques. In this study, additional concepts are also evaluated to quantify the limitations and range of applicability of the proposed substructuring approach for simulating the vibration response of complex powertrain structures.

The design of automotive components for low structure-borne interior noise and vibration requires the ability to reliably simulate total vehicle system response over a wide operating frequency range. This implies that the car body, its interior acoustic cavity, and critical structural components must be included in this overall dynamic model. Unfortunately, most noise and vibration problems occur in the 200-1000 Hz frequency range where existing finite element and experimental modal methods have limited applicability. This is due to the high modal density, high damping levels, and sensitivity to fine geometric detail. Moreover, it is highly doubtful that these methods will ever be practical tools for the study of the total body dynamics over the frequency range of 200-1000Hz. In this paper, a practical hybrid experimental-analytical approach is proposed in response to the need to simulate high frequencies structure-borne noise and vibration in automotive systems.

The design of automotive components for low structure-borne interior noise and vibration is facilitated by the ability to reliably simulate total vehicle system response over a wide operating frequency range. This requires that the car body, its interior acoustic cavity, and critical chassis components must be included in the overall dynamic model. Unfortunately, most noise and vibration problems occur in the 200-1000 Hz frequency range where finite element and experimental modal methods have limited applicability. This is due to the high modal density, high damping levels, and sensitivity to fine geometric detail. A simulation method has been proposed earlier which uses component finite element models and component experimental transfer functions to predict combined system response [1]. This method has allowed for a practical approach to automotive system noise and vibration simulation.

A proposed multi-coordinate spectral-based inverse substructuring approach is applied experimentally to examine the vibration transmissibility through chassis mounts. In this formulation, the vehicle system is partitioned into two substructures. One substructure comprises of the chassis and suspension, while the second one is the body structure and other attached components. The approach yields the free substructure dynamic characteristics that are extracted from the measured coupled system response spectra. The resultant free substructure transfer functions are verified by comparison of the re-synthesized results to the actual vehicle system measurements. A real life vehicle setup is utilized to demonstrate the salient features and capabilities of this approach, which includes the ability to compute the main structure-borne paths, dynamic interactions between the chassis and body, and interior noise and vibration response.

A new multi-level substructuring approach is proposed to predict the NVH response of driveline systems for the purpose of analyzing rear axle gear whine concern. The fundamental approach is rooted in the spectral-based compliance coupling theory for combining the dynamics of two adjacent subsystems. This proposed scheme employs test-based frequency response functions of individual subsystems, including gear pairs, propshaft, control arms and axle tube, in free-free state as sequential building blocks to synthesize the complete system NVH response. Using an existing driveline design, the salient features of this substructuring approach is demonstrated. Specifically, the synthesized results for the pinion-propshaft assembly and complete vehicle system are presented. The predictions are seen to be in excellent agreement with the experimental data from direct vehicle measurements.

The vehicle axle gear whine noise and vibration are key issues for the automotive industry to design a quiet, reliable driveline system. The main source of excitation for this vibration energy comes from hypoid gear transmission error (TE). The vibration transmits through the flexible axle components, then radiates off from the surface of the housing structure. Thus, the design of hypoid gear pair with minimization of TE is one way to control the dynamic behavior of the vehicle axle system. In this paper, an approach to obtain minimum TE and improved dynamic response with optimal tooth profile modification parameters is discussed. A neural network algorithm, named Back Propagation (BP) algorithm, with improved Particle Swarm Optimization (PSO) is used to predict the TE if some tooth profile modification parameters are given to train the model.

The component response synthesis approach utilizing frequency response function (FRF) has been used to analyze the dynamic interaction of two or more vehicle components coupled at discrete interface points. This method is somewhat suitable for computing higher frequency response because experimental component FRFs can be incorporated into the formulation directly. However its calculations are quite sensitive to measurement errors in the FRFs due to the several matrix inversion steps involved. In the past, researchers have essentially used a combined direct inverse and truncated singular valued decomposition (TSVD) technique to ensure a stable calculation, which is typically applied semi-empirically due to the lack of understanding of the influence of measurement error.

A series of system level experiments were conducted using 2 vehicles of identical design to measure, analyze and quantify crank rumble noise from the viewpoint of source strength and path dynamic response. One of the vehicles was known to produce relatively severe crank rumble response (noisy), while the second vehicle was almost free of the annoying response (quiet). Two specific operating conditions most susceptible to crank rumble noise were of interest: (1) no load snaps in neutral and (2) hard acceleration in second gear. For each condition, the vibration and sound pressure responses throughout the vehicle were obtained. The measured data was analyzed critically to determine frequency content and strength of rumble noise at each location. Calculations were also performed from the measured data to determine the modes of transmission and the relative contributions from air-borne and structure-borne paths.

In this paper, we discuss methods used to investigate a clearly audible gear whine problem in a modern automobile. Currently available PC-based computer software, coupled with more traditional engineering tools, such as spectrum analyzers, are employed to efficiently observe noise and vibration phenomena. Jury evaluations are conducted, using in-vehicle noise data, to rank actual gear whine levels. Additional jury studies using synthesized gear whine help us further understand listener preferences. Unloaded gear transmission error testing is explored as a means of predicting gear whine levels under light loads, such as those seen during highway cruising. We finally correlate many results to better understand the source and paths of the gear noise, and make recommendations for further exploration of this type of problem.

This paper describes the procedures used to reduce the tonal noise of a class eight truck engine timing gear train that was initially found to be objectionable under idle operating conditions. Initial measurements showed that the objectionable sounds were related to the fundamental gear mesh frequency, and its second and third harmonics. Experimental and computational procedures used to study and trouble-shoot the problem include vibration and sound measurements, transmission error analysis of the gears under light load condition, and a dynamic analysis of the drive system. Detail applications of these techniques are described in this paper.

Active noise control (ANC) technique with the filtered-x least mean square (FXLMS) algorithm has proven its efficiency and drawn increasingly interests in vehicle noise control applications. However, many vehicle interior and/or exterior noises are exhibiting non-Gaussian type with impulsive characteristic, such as diesel knocking noise, injector ticking, impulsive crank-train noise, gear rattle, and road bumps, etc. Therefore, the conventional FXLMS algorithm that is based on the assumption of deterministic and/or Gaussian signal may not be appropriate for tackling this type of impulsive noise. In this paper, an ANC system configured with modified FXLMS (MFXLMS) algorithm by adding thresholds on reference and error signal paths is proposed for impulsive noise control. To demonstrate the effectiveness of the proposed algorithm, an experimental study is conducted in the laboratory.