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Spiral bevel gears are commonly used in heavy-duty trucks and buses. An integrated dynamic model of the spiral bevel gears with mixed elastohydrodynamic lubrication is proposed in this study. First, loaded tooth contact analysis was performed to evaluate the kinematic parameters and calculate the mesh force variation for one mesh cycle. These kinematic quantities are used in the mixed elastohydrodynamic lubrication (EHL) calculation to determine the EHL parameters such as pressure, film thickness, and shear distribution considering the surface roughness profile of the spiral bevel gears. Then, the EHL pressure and film thickness are used in the calculation of the coefficient of friction, damping, and oil film elastohydrodynamic lubrication stiffness. Last, these tribological parameters are used in the dynamic calculation of the spiral bevel gears.

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.

A general time-varying nonlinear dynamic model of a hypoid gear pair for rear axle applications is proposed. The dynamic model considers time-varying mesh position, line of action, mesh stiffness, mesh damping and backlash nonlinearity. Based on the model, dynamic analysis is conducted to study the effect of mean load, mesh damping and mesh parameter variations on dynamic mesh force response and the interaction between them and backlash nonlinearity. Numerous nonlinear phenomena such as tooth impacts and jump discontinuities are revealed by computational results.

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.

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 changes of dynamic frequency response, commonly used to determine the dynamic characteristic of built-up structures, were studied over the entire fatigue failure process for tensile-shear spot-welded joints. The results of an experimental study showed that the natural frequency varies non-linearly with the fatigue damage fraction. This behavior was modeled using finite element analysis of a progressively growing crack, initiating at the joining surface, then progressing to the outside surface of the specimen, and finally extending from the spot weld nugget. The relationship between dynamic frequency response and crack propagation may be applied to study effect of aging (high mileage) in NVH quality.

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 natural modes of the ring gear structure commonly used in automotive transmissions are predicted using the finite element approach, and the sensitivities of these modes to boundary conditions between the housing and ring gear are analyzed. The specific boundary conditions of interest include free-free, simply-supports at equally spaced angular points, and discrete and distributed spring elements. For the free-free boundary condition, clear well-defined modes are observed that can be classified into four fundamental groups corresponding to radial inextensional, extensional, out-of-plane bending and pure torsional. However, when other boundary conditions are applied the mode shapes become more complex. For instance, in the simply-supported case the radial inextensional and torsional modes are seen to appear highly distorted. Also, the natural frequencies of these modes are higher than the free-free ones.

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.