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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.

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.

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.

An enhanced, frequency domain filtered-x least mean square (LMS) algorithm is proposed as the basis for an active control system for treating powertrain noise. There are primarily three advantages of this approach: (i) saving of computing time especially for long controller’s filter length; (ii) more accurate estimation of the gradient due to the sample averaging of the whole data block; and (iii) capacity for rapid convergence when the adaptation parameter is correctly adjusted for each frequency bin. Unlike traditional active noise control techniques for suppressing response, the proposed frequency domain FXLMS algorithm is targeted at tuning vehicle interior response in order to achieve a desirable sound quality. The proposed control algorithm is studied numerically by applying the analysis to treat vehicle interior noise represented by either measured or predicted cavity acoustic transfer functions.

The noise and vibration response of hypoid or bevel geared rotor system, primarily excited by transmission error (TE), and mesh vector and stiffness variations, can be affected significantly by the coupling between the driveline rotor dynamics and gear vibratory response. This is because of the inherent design comprising of non-parallel rotational axes and time-varying as well as spatial-varying gear mesh characteristics. One of the important factors of the driveline system dynamics is the rotor gyroscopic effect that has not been studied extensively in traditional gear dynamics. To address this gap in the literature, this paper attempts to examine the influence of incorporating gyroscopic terms in the hypoid gear dynamic simulation. A multi-degrees-of-freedom, multi-body dynamic model is used as a generalized representation of a hypoid geared rotor system.

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.

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.

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 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.

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.

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.

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.

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.