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Weight reduction is very important in automotive design because of stringent demand on fuel economy. Structural optimization of dynamic systems using finite element (FE) analysis plays an important role in reducing weight while simultaneously delivering a product that meets all functional requirements for durability, crash and NVH. With advancing computer technology, the demand for solving large FE models has grown. Optimization is however costly due to repeated full-order analyses. Reanalysis methods can be used in structural vibrations to reduce the analysis cost from repeated eigenvalue analyses for both deterministic and probabilistic problems. Several reanalysis techniques have been introduced over the years including Parametric Reduced Order Modeling (PROM), Combined Approximations (CA) and the Epsilon algorithm, among others.

To improve fuel economy, there is a trend in automotive industry to use light weight, high strength materials. Automotive body structures are composed of several panels which must be downsized to reduce weight. Because this affects NVH (Noise, Vibration and Harshness) performance, engineers are challenged to recover the lost panel stiffness from down-gaging in order to improve the structure borne noise transmitted through the lightweight panels in the frequency range of 100-300 Hz where most of the booming and low medium frequency noise occurs. The loss in performance can be recovered by optimized panel geometry using beading or damping treatment. Topography optimization is a special class of shape optimization for changing sheet metal shapes by introducing beads. A large number of design variables can be handled and the process is easy to setup in commercial codes. However, optimization methods are computationally intensive because of repeated full-order analyses.

A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.

An approach for Probabilistic Reanalysis (PRA) of a system is presented. PRA calculates very efficiently the system reliability or the average value of an attribute of a design for many probability distributions of the input variables, by performing a single Monte Carlo simulation. In addition, PRA calculates the sensitivity derivatives of the reliability to the parameters of the probability distributions. The approach is useful for analysis problems where reliability bounds need to be calculated because the probability distribution of the input variables is uncertain or for design problems where the design variables are random. The accuracy and efficiency of PRA is demonstrated on vibration analysis of a car and on system reliability-based optimization (RBDO) of an internal combustion engine.

In this paper, the development of random vibration testing schedules for durability design verification of engine mounted products is presented, based on the equivalent fatigue damage concept and the 95th-percentile customer engine usage data for 150,000 miles. Development of the 95th-percentile customer usage profile is first discussed. Following that, the field engine excitation and engine duty cycle definition is introduced. By using a simplified transfer function of a single degree-of-freedom (SDOF) system subjected to a base excitation, the response acceleration and stress PSDs are related to the input excitation in PSD, which is the equivalent fatigue damage concept. Also, the narrow-band fatigue damage spectrum (FDS) is calculated in terms of the input excitation PSD based on the Miner linear damage rule, the Rayleigh statistical distribution for stress amplitude, a material's S-N curve, and the Miles approximate solution.

The advantages of having higher stiffness to weight ratio and strength to weigh ratio that composite materials have resulted in an increased interest in them. In automotive engineering, the weight savings has positive impacts on other attributes like fuel economy and possible noise, vibration and harshness (NVH). The driveline of an automotive system can be a target for possible use of composite materials. The design of the driveshaft of an automotive system is primarily driven by its natural frequency. This paper presents an exact solution for the vibration of a composite driveshaft with intermediate joints. The joint is modeled as a frictionless internal hinge. The Euler-Bernoulli beam theory is used. Lumped masses are placed on each side of the joint to represent the joint mass. Equations of motion are developed using the appropriate boundary conditions and then solved exactly.

In a CAS system, the distance and relative velocity between front and host vehicles are estimated to calculate time-to-collision (TTC). The distance estimates by different methods will certainly include noise which should be removed to ensure the accuracy of TTC calculations. Kalman filter is a good tool to filter such type of noise. Nevertheless, Kalman filter is a model based filter, which means a correct model is important to get the good filtering results. Usually, a vehicle is either moving with a constant velocity (CV) or constant acceleration (CA) maneuvers. This means the distance data between front and host vehicles can be described by either constant velocity or constant acceleration model. In this paper, first, CV and CA models are used to design two Kalman filters and an interacting multiple model (IMM) is used to dynamically combine the outputs from two filters.

A comprehensive formulation is presented for the dynamics of a rotating flexible crankshaft coupled with the dynamics of an engine block through a finite difference elastohydrodynamic main bearing lubrication algorithm. The coupling is based on detailed equilibrium conditions at the bearings. The component mode synthesis is employed for modeling the crankshaft and block dynamic behavior. A specialized algorithm for coupling the rigid and flexible body dynamics of the crankshaft within the framework of the component mode synthesis has been developed. A finite difference lubrication algorithm is used for computing the oil film elastohydrodynamic characteristics. A computationally accurate and efficient mapping algorithm has been developed for transferring information between a high - density computational grid for the elastohydrodynamic bearing solver and a low - density structural grid utilized in computing the crankshaft and block structural dynamic response.

An application of variation simulation for predicting vehicle interior driveline vibration is presented. The model, based on a “Monte Carlo”-style approach, predicts the noise, vibration and harshness (NVH) response of the vehicle driveline based on distributions of imbalance and runout derived from manufacturing production variation (the forcing function) and the vehicle's sensitivity to the forcing function. The model is used to illustrate the change in vehicle interior vibration that results when changes are made to production variation for runout and imbalance of driveline components, and how those same changes result in different responses based on vehicle sensitivity.

The second part of a detailed examination of multivariate correlation of several axle assembly and component parameters to the assembly NVH performance (vibration) measured at the end of the assembly process is presented focusing on the multivariate linear regression analysis. The study is based on test results and measurements acquired from multiple axle assemblies built with the same hypoid gearset, thus effectively eliminating the affect of gearset variation on the test result. Several major components within the axle are considered including the differential housing (that controls wheel differentiation during turns), the axle housing, and several assembly parameters. Details of the multivariate regression include formulation of the linear regression model, model refinements through analysis of subsets of the variables, tests of significance and residual analysis.

The first part of a detailed examination of multivariate correlation of several axle assembly and component parameters to the assembly NVH performance (vibration) measured at the end of the assembly process is presented focusing on preparing the data for multivariate regression analysis. The study is based on test results and measurements acquired from multiple axle assemblies built with the same hypoid gearset, thus effectively eliminating the affect of gearset variation on the test result. Several major components within the axle are considered including the differential housing (that controls wheel differentiation during turns), the axle housing, and several assembly parameters.

A nonlinear finite element passenger car radial-ply tire model was developed to investigate a tire's three-dimensional transmissibility in the X, Y, and Z directions. The reaction forces of the tire axle in longitudinal (X axis), lateral (Y axis), and vertical (Z axis) directions were recorded when the tire encountered a cleat, and then the FFT (Fast Fourier Transform) algorithm was applied to extract tire's transient response information in the frequency domain. The result showed that this passenger car tire has clear peaks at 47-51 and 91-92 Hz longitudinal, 41-45 Hz lateral, and 80-83Hz vertical. An analytical rigid ring model was also formulated, based on the dynamic equations of the rigid ring tire model. The characteristic equations were obtained and solved for eigenvalues and eigenvectors, which represent tire's free vibration natural frequencies and mode shapes.

The system response of many engineering systems depends on time. A random process approach is therefore, needed to quantify variation or uncertainty. The system input may consist of a combination of random variables and random processes. In this case, a time-dependent reliability analysis must be performed to calculate the probability of failure within a specified time interval. This is known as cumulative probability of failure which is in general, different from the instantaneous probability of failure. Failure occurs if the limit state function becomes negative at least at one instance within a specified time interval. Time-dependent reliability problems appear if for example, the material properties deteriorate in time or if random loading is involved which is modeled by a random process. Existing methods to calculate the cumulative probability of failure provide an upper bound which may grossly overestimate the true value.

Fretting is an important phenomenon that happens in many mechanical parts. It is the main reason in deadly failures in automobiles, airliners, and turbine engines. The damage is noticed between two surfaces clamped together by bolts or rivets that are nominally at rest, but have a small amplitude oscillation because of vibration or local cyclic loading. Fretting damage can be divided into two types. The first type is the fretting fatigue damage where a crack would initiate and propagate at specific location at the interface of the mating surfaces. Cracks usually initiate in the material with lower strength because of the local cyclic loading conditions which eventually lead to full failure. The second type is the fretting wear damage because of external vibration. Researchers have investigated this phenomenon by theoretical modeling and experimental approaches. Although a lot of research has been done on fretting damage, some of the parameters have not been well studied.

This research proposes an automatic computer-aided design, analysis, and optimization process of a twist beam rear suspension system. The process combines CAD (Computer-Aided Design), CAE (Computer-Aided Engineering), and optimization technologies into an automation procedure, which includes: structural design, dynamic analysis, vibration analysis, durability analysis, and multidisciplinary optimization. The automation results shown the twist beam rear suspension weight reduced, the durability fatigue life increased, and the K&C (kinematics & compliance) characteristics are improved significantly.

This work analyzes a cantilevered piezoelectric beam device for harvesting energy from the simultaneous rotation and translational vibration of vehicle wheels. The device attaches to the wheel rim so that it displaces tangentially during operation. A lumped-parameter analytical model for the coupled electromechanical system is derived. The device has one natural frequency that is speed-dependent because of centripetal acceleration affecting the total stiffness of the device. Even though the device has one natural frequency, it experiences three resonances as the rotation speed varies. One resonance occurs when the rotation speed coincides with the speed-dependent natural frequency of the device. The other two resonances are associated with excitations from the vibration of the vehicle wheel. The device’s parameters are chosen so that these three resonances occur when the wheel travels near 30 mph, 55 mph, and 70 mph.

A finite element/contact mechanics formulation is used to analyze the dynamic tooth forces that arise from damage-induced vibrations in spur gear pairs. Tooth root crack damage of varying sizes are analyzed for a wide range of speeds that include resonant gear speeds. The added localized compliance from tooth root crack damage leads to a re-distribution of the forces on the individual gear teeth in mesh. At speeds away from resonance, smaller dynamic forces occur on the damaged tooth and larger dynamic forces occur on the tooth that engages immediately after it. These dynamic tooth contact forces cause additional transient dynamic response in the gear pair. For certain speeds and sufficiently large tooth root cracks, the damage-induced dynamic response causes large enough vibration that tooth contact loss nonlinearity occurs. For some speeds near resonance, the damage-induced vibrations cause teeth that normally lose contact to remain in contact due to vibration.

Passengers' frequent requests are for less Noise, Vibration and Harshness (NVH) in the vehicle compartment. This and the reduction of noise and vibration levels from major sources like the engine necessitate better performance of other sources of noise and vibrations in a vehicle. Some of these sources are the hydraulic circuits including the power steering system. Fluid pulses or pressure ripples, generated typically by a pump, become excitation forces to the structure of a vehicle or the steering gear and represent a considerable source of discomfort to the vehicle passengers. Current power steering technology attenuates this ripple along the pressure line connecting the pump to the steering gear. Finding the optimum design configuration for the components (hose, tuner, tube, and others) has been a matter of experience-based trial and error. This paper is a part of a program to simulate and optimize fluid borne noise in hydraulic circuits.

Adhesively bonded joints have been applied in the automotive industry for the past few decades due to their advantages such as higher fatigue resistance, light weight, capability of joining dissimilar materials, good energy absorption, and high torsional stiffness for overall body structure. They also provide an effective seal against noise and vibration at a low cost. There exists the challenge of defining the fatigue characteristics of adhesive joints under cyclic loading conditions, and conventional methods have limitations in detecting the crack initiation of a bonded joint. This study introduces a method of detecting crack initiation by using the frequency method. It is found that stiffness change in the system is highly correlated to change in natural frequencies. By monitoring the change in natural frequencies, the crack initiation can be detected.