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Journal Article

Multi-Point Mesh Modeling and Nonlinear Multi-Body Dynamics of Hypoid Geared System

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.
Technical Paper

Active Vibration Control to Suppress Gear Mesh Response

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.
Journal Article

Influence of Gyroscopic Effect on Hypoid and Bevel Geared System Dynamics

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.
Technical Paper

Driveline NVH Modeling Applying a Multi-subsystem Spectral-based Substructuring Approach

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.
Technical Paper

Coupled Multi-Body Dynamic and Vibration Analysis of High-Speed 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.
Technical Paper

Time-Varying Non-Linear Dynamics of a Hypoid Gear Pair for Rear Axle Applications

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.
Technical Paper

A Parametric Study on the Vibration Transmissibility Characteristics of Transmission Ring Gear Structure

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.
Technical Paper

Case History: Engine Timing Gear Noise Reduction

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.
Technical Paper

Effects of Boundary Conditions on the Natural Modes of Transmission Ring Gear Structure

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.
Technical Paper

Methods for Researching Gear Whine in Automotive Transaxles

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.
Technical Paper

Crankshaft Rumble Noise Phenomenon: Experimental Characterization of Source Strength and Path Response

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.
Technical Paper

Dynamic Analysis of Automotive Gearing Systems

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.
Technical Paper

Dynamic Analysis of Layshaft Gears in Automotive Transmission

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.
Technical Paper

Optimization of Hypoid Gear Tooth Profile Modifications on Vehicle Axle System Dynamics

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.