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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.

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.

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 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.

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.

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 standard approach often used to reduce gear noise in automotive system is to minimize the transmission error. This is done by using stringent quality control measures in the gear manufacture, selecting desirable gear parameters, and applying profile modifications. This approach may be effective in many instances. However, there are numerous examples where the gear quality is the best that can be achieved within the manufacturing constraints, and the noise levels still exceed acceptable limits. In many cases, the system dynamics cause the gear train design to be highly sensitive to manufacturing induced transmission error. Therefore, it is advantageous to perform dynamic analysis to examine the influence of gear train dynamics and design parameters on gear noise. Proper design modifications may then be identified and applied to reduce gear noise levels.

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.

In this paper, we will present parametric results of performing dynamic analysis of layshaft gear trains typically used in automotive transmissions with emphasis on the vibratory response due to transmission error excitation. A three-dimensional multiple degrees of freedom lumped parameter dynamic model of a generic layshaft type geared rotor system (with three parallel rotating shafts coupled by two sets of gear pairs) has been formulated analytically. The model includes the effects of both rotational and translational displacements of each gears, and bounce and pitch motions of the counter-shaft. The natural frequencies and mode shapes are computed numerically by solving an eigenvalue problem derived from applying harmonic solutions to the equations of motion. The complete set of mode shapes are then used in forced response calculations based on the modal expansion method to predict gear accelerations, dynamic transmission errors, mesh force and bearing loads.

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.

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.

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.