A Computer Aided Design (CAD) program has been developed in which both simulation and optimization techniques are utilized. A nonlinear representation of the shock absorber damping characteristics has been considered. The output of this CAD program is the optimum shape of this nonlinear characteristics. This is obtained by minimization of a performance index consisting of a weighted sum of the root mean square (rms) of both tire terrain normal force (as a measure of controllability) and the sprung masses acceleration (as a measure of ride comfort). The time response can also be obtained graphically as an output option. Two different mathematical models are considered: A simple one with two degrees of freedom (Bounce of the sprung and unsprung mass) and a more sophisticated one with four degrees of freedom (Bounce and pitch of the sprung mass and vertical motion of the unsprung rear and front masses). The two models are checked and validated by comparing their results with other published works. The program results obtained for a typical vehicle show a good improvement of the performance of the optimum nonlinear system compared to the optimum linear one.

An extensive survey is presented for the analysis of both in-plane and out-of-plane pneumatic tyre models. The single plane tyre model[2,9] is developed to represent the influence of tyre width by using many conical shell shapes built from spokes with different head angles. The general form of the new tyre model is based on the well-known single plane steady state version of the tyre model. The mathematical analysis and geometrical form of the developed model is given. A computer program is designed for desk top P.C. without costly running times which makes it useful for representing the pneumatic tyre/road contact forces. Model assumptions and parameters were chosen to give qualitative and quantitative agreements between theoretical and experimental results. The paper also presents an experimental study for investigating the influence of working conditions on tyre/road contact forces. The experimental results were carried out using the steady state tyre testing machine constructed in the Automotive Engineering Department, Helwan University [3,10]. Experimental findings for 145 SR 13 tyres are compared with the new model theoretical results. Experiments on real tyres show good agreement with the predicted theoretical results of the new generally applicable model.

The frequencies and mode shapes of rolling rings with radial and circumferential displacement constraints are investigated. The displacement constraints practically come from the point contact, e.g. , rolling tire on the road, or other applications. The proposed approach to analysis is calculating the natural frequencies and modes of a non-contacted spinning ring, then employing the receptance method for displacement constraints. The frequency equation for the constrained system is hence obtained, and it can be solved numerically or graphically. The receptance matrix developed for the spinning ring is surprisingly found not symmetric as usual. Moreover, the cross receptances are discovered to form complex conjugate pairs. That is a feature that has never been described in literature. The results show that the natural frequencies for the spinning ring in contact, as expected, higher than those for the non-contacted ring. The variance of frequencies to rotational speeds are then illustrated. The analytic forms of mode shapes are also derived and sketched. The traveling modes are then shown for cases.

A seven-DOF vehicle model comprising a full car body and four wheel-axle assemblies is used to investigate the influence of active and semiactive suspensions on ride performance. The active control of car body roll, pitch and bounce is based on an optimal control strategy assuming the tire deflection measurements are not available. The frequency analysis shows a significant attenuation in car body modes but a potential increase in wheel motions. Dissipative dampers with solenoid valves are used as the semiactive control mechanism. Simulation results in the time domain indicate that suboptimal values exist in the damping “on” state and an on-off damping control scheme can effectively reduce the car body motions and suspension travels.

Many studies have shown that active suspensions using full state feedback can significantly improve the ride performance of ground vehicles. Using a seven degree of freedom vehicle model and a Kalman filter, this paper investigates the effects of reduced state feedback on active and semi-active suspension systems. Particular attention is given to control of pitch motion, which is usually considered to be the most uncomfortable of rigid body motions. The effects of phase differences between the tires is presented using frequency response surfaces. The Kalman filter, which reconstructs the state variables from a reduced set of observed variables, yields improvements in ride which compare well with the ideal active suspension without the need to measure all states. The Kalman filter system with active dampers instead of ideal actuators also yields ride improvements approaching the ideal systems.

During the early stages of project initiation, the information available to a designer may be uncertain (imprecise or stochastic). In response to this need, two extensions of the crisp compromise Decision Support Problem using fuzzy set theory and Bayesian statistics are developed to model uncertainty in design problems. The fuzzy compromise DSP is used to model imprecise information and the Bayesian compromise DSP is used to model stochastic information. The design of an aircraft tire is used as an illustrative example.

As a first approximation, a steel-belted radial tire can be modeled as a one dimensional rotating ring connected elastically to a moving hub. This ring can be modeled mathematically using a set of three nonlinear partial differential equations, where the three degrees of freedom are a radial displacement, a tangential displacement and a section rotation. In this study, only quadratic geometric nonlinearities are considered. The system is excited by a temporally harmonic point load f ^ ( t ) and a temporally harmonic hub motion z ^ ( t ) that have the same harmonic frequency. The point load f ^ ( t ) appears in the equations of motion as a single in-homogeneous term, while the hub motion z ^ ( t ) appears in inhomogeneous and parametric excitation terms. To simplifying the ensuing analysis, the rotation rate of the hub is assumed to be constant. The partial differential equations of motion are reduced to a set of four second-order ordinary differential equations by using two linear normal modes to approximate the spatial distribution of the displacements. A region of the parameter space, as defined by ranges of values of the excitation amplitude z and the excitation frequency ω (or detuning parameter σ), is identified, from a Strutt diagram, where the parametric excitation is expected to be dominant. In this region σ is varied to locate a secondary Hopf bifurcation that leads to a set of complex steady-state quasi-periodic solutions. These solutions contain two families of frequency components where the fundamental frequencies of these families are non-commensurate, and they are characterized by Poincaré sections with closed or nearly closed “orbits” as opposed to the distinct points displayed by periodic responses and the strange attractor sections displayed by chaotic solutions.

A new fully mobile omnidirectional vehicle with improved kinematic, dynamic and dead reckoning performance is presented. The vehicle has a unique ball wheel mechanism which has no kinematic singularity and, moreover, possesses configuration-invariant kinematics and dynamics. Uniform kinematic and dynamic characteristics allow smooth motion and precise motion control. First, the ball wheel mechanism, with a unique ring bearing to hold a spherical tire, is presented. Second, we generalize upon this particular design and look for solutions within a wider class of mechanisms. Analysis reveals essential kinematic requirements and we show theoretically why spherical tires are difficult to hold. The ring bearing arrangement is developed as a solution to this problem. Third, incorporation of the ball wheels into vehicles is analyzed and optimized with respect to traction and anti-slip control. A prototype vehicle is designed, built and tested, and smooth motion and precision dead reckoning are accomplished.

A method for designing ball wheel mechanisms for vehicles with omnidirectional motion capability is presented in this paper. A ball wheel mechanism holds a spherical tire while allowing it to rotate with two degrees of freedom such that it may roll in an arbitrary direction on the floor. This paper concerns a particular class of ball wheel mechanisms which hold a spherical tire in a special arrangement of rollers. Due to point contacts between these rollers and the tire, and between the tire and the ground, specific considerations are required to achieve large payload capacity and traction as well as high position control accuracy. First, we review the kinematic conditions for theoretical functionality of the class of ball wheels and describe a proof-of-concept prototype vehicle. Starting from the generalized ball wheel mechanism, we then identify a subset of designs that contains the optimal ball wheel mechanisms for most applications. Within this subset, the design is optimized by parameterizing the design space. By analyzing the phenomena relating the design parameters to three performance indices — payload capacity, acceleration and repeatability — a surface can found in the performance space that represents the maximum ball wheel performance for all permutations of the design parameters. This surface will be used by vehicle designers to evaluate ball wheel performance in comparison with other omnidirectional drive mechanisms. A simple lookup table can then be used to find the design parameter values which provide desired performance.

An important part of the design of airplane brakes is the laboratory verification of their capability to absorb the kinetic energy of the airplane under various operating conditions ranging from normal service energy levels to the very high energy of a rejected takeoff (RTO). These “stops”, as dynamometer brake applications are called, must demonstrate acceptable temperature levels for the wheel and tire, the ability of the brake to carry out numerous taxi and service type stops without any servicing, and acceptable wear rates for the friction material so as to make the brake economically feasible for use by the airlines. These laboratory tests are typically carried out on an adjustable inertia roadwheel dynamometer. The wheel and tire are “landed” against the flywheel of the dynamometer until the correct radial load is developed on the tire. The brakes are then applied to decelerate the dynamometer to a low taxi speed or stop it completely. With such a system various spectrums of landing and multiple taxi stops can be programmed to yield a simulation of actual airplane operation. An attempt has been made to extend this type of dynamometer testing to examine the vibrational characteristics of the brake as part of the total landing gear system, in addition to its performance as an energy absorber. Since these total-system vibrations can be destructive to both the brake and the landing gear structure, this type of vibrational evaluation is as important as the energy evaluation of the brake. For many transport aircraft, particularly those with four or more wheels per landing gear, it is impossible to incorporate the entire landing gear into the dynamometer testing. The nature of the testing extension has therefore been to simulate the behavior of the gear with simpler devices called simulators. In order to duplicate as nearly as possible the vibrational characteristics that will be experienced on the airplane, various types of landing gear simulators have been used in conjunction with dynamometer testing. This paper discusses the pros and cons of landing gear simulators and a proposed approach that would utilize the simulator in a program to more accurately predict actual airplane landing gear vibrational characteristics.

The objective of this paper is to address finite element modeling for dynamics and its applications to aircraft landing and braking systems. The components of the system in the example model include the entire landing gear, wheels, brakes, and tires. The use of finite element modeling techniques in dynamics as a design tool for landing and braking systems is discussed. Vibration mode shapes from the finite element analysis, including both whirl and squeal, are shown. Correlation between the finite element models and the experimental modal analyses of various system components are presented. Correlation between the performance of the complete landing and braking system model and the actual system during aircraft operation is also presented.

An electric powered Hot Metal Ladle Car was designed to safely transport a ladle filled with 160 metric tons of molten steel. The ladle geometry and space constraints within the use environment were specified. A final design was prepared and documented which met the design requirements and could be efficiently manufactured. An initial design was developed using past designs of a similar nature as a basis. By hand stress calculations were performed and the design modified to get stress values to acceptable levels. Preliminary design drawings were developed. At this stage of the design, some engineering personnel felt that the “by hand” stress analysis was sufBciently accurate to go ahead with fabrication. After much discussion it was decided to perform a Finite Element Analysis (FEA) to verify the design stresses calculated “by hand”. The FEA analysis predicted stresses that were significantly higher than indicated “by hand” in some critical change of section regions. These stress levels were much higher than the allowable stresses for this design. The difference between the FEA stresses and “by hand” stresses were evaluated. After much discussion and thought an insight to the actual load flow was developed which was consistent with the FEA results. With this insight, modifications were made to the design and incorporated into the FEA model. These changes needed to be practical from a manufacturing and end use viewpoint. After a few iterations on the design tire FEA stresses were reduced to an acceptable level. These changes were incorporated into the design. The final design of the ladle car was fabricated. The design was significantly improved due to the ability to accurately calculate stresses in transition regions of the frame where “by hand” methods were not really applicable. The combination of “by hand” methods to ballpark a design and FEA methods to reftne a design proved to be a powerful method to get a truly good design.

Due to the continual diminishment of engine, power train and tire noise levels, squeak and rattle as become a primary source of undesired noise in automobiles. This article presents a finite-element-based methodology for the improvement of rattle performance of vehicle components. This approach attacks complicated nonlinear impact problems involving rigid and flexible structures by a rather indirect method that allows for the generation of design sensitivity information related to impact frequency and severity from large-scale computer models. This is done by adjusting the system parameters of a related linear problem in such a manner that the nonlinear system response is improved. For implementation purposes, it has been applied to study the rattle of the latch and corner rubber snubbers of a glove compartment. Results from the glove compartment study are summarized herein. Extensions to other rattle problems are also highlighted.

In this work, the main object was to perform simulations using a realistic model of a truck and trailer passing over a flexible bridge structure. Two driving cases were considered: straight forward driving with and without braking. In the latter case control logic was used to distribute the braking torques to the wheel axles. A general multibody dynamics computer program, DADS, and its tire subroutines were interfaced with our FEM routines in order to create a vehicle/structure interaction computer program. A part of this process was to integrate different time stepping algorithms from the multibody dynamics and FEM disciplines into a “common” time integration procedure. Another part was to write code to search for finite elements where tire/structure interaction takes place.

In recent years technology development for the design of electric and hybrid-electric vehicle systems has reached a peak, due to ever increasing restrictions on fuel economy and reduced vehicle emissions. An international race among car manufacturers to bring production hybrid-electric vehicles to market has generated a great deal of interest in the scientific community. The design of these systems requires development of new simulation and optimization tools. In this paper, a description of a real-time numerical environment for Virtual Proving Grounds studies for hybrid-electric vehicles is presented. Within this environment, vehicle models are developed using a recursive multibody dynamics formulation that results in a set of Differential-Algebraic Equations (DAE), and vehicle subsystem models are created using Ordinary Differential Equations (ODE). Based on engineering knowledge of vehicle systems, two time scales are identified. The first time scale, referred to as slow time scale, contains generalized coordinates describing the mechanical vehicle system that includs the chassis, steering rack, and suspension assemblies. The second time scale, referred to as fast time scale, contains the hybrid-electric powertrain components and vehicle tires. Multirate techniques to integrate the combined set of DAE and ODE in two time scales are used to obtain computational gains that will allow solution of the system’s governing equations for state derivatives, and efficient numerical integration in real time.

Anti-squat is a transient vehicle suspension parameter which can dramatically affect tractive effort available at motorcycle drive tire. In the drag racing environment, maximizing tractive effort is essential to competitive performance. Tuning a four-link rear suspension to provide anti-squat increases rear tire traction at the starting line, which increases tractive effort and vehicle acceleration performance. Minimization of the time required to initiate and maintain forward acceleration, often considered the most important part of a drag race, enables peak overall race performance to be realized. Utilizing PC based CAD, finite element analysis, and dynamic system analysis software, a motorcycle rear suspension system was designed, built and tested under actual racing conditions. Parametric studies using dynamic theoretical models were conducted for both unsuspended and four-link equipped versions of the same vehicle. Results and conclusions are presented. Based on the results, it is shown the four-link suspension, when applied to a drag racing motorcycle, does provide opportunity for improving tractive effort at the beginning of a race which will improve overall drag racing performance.

An improved moving deformable barrier (MDB) model was developed for simulation of fuel system performance tests. This MDB model was designed to replace a bullet vehicle model for the vehicle-to-vehicle impact simulations where a bullet vehicle impacts a target vehicle at 50mph. This study included three crash modes, rear-inline, rear-50% offset, and side impact-centerline of fuel filler, required in the fuel system integrity test. The MDB model is composed of a barrier facial, same as the FMVSS (Federal Motor Vehicle Safety Standards) 214 [1] side impact barrier facial, and a movable cart on which the barrier facial is mounted. The main block and bumper block in the barrier facial are modeled by using solid elements while aluminum plates are represented by using shell elements. The movable cart is modeled by using beam elements with four air-bag tires. Two dynamic component tests were adopted to calibrate the barrier facial properties. To assure the model is applicable to all vehicle lines and different test modes, extensive validation was conducted. The full system validation contained a car, a mini-van, a van, and a pick-up truck. Three different test modes were all included in this study. Both accuracy and numerical stability of the model were examined carefully in each simulation. For accuracy, the deformation modes and responses of the MDB were compared to those of the tests. Time steps were monitored in each simulation to investigate the degradation of numerical stability. Through calibration and validation, the MDB model was found to be robust and numerically stable.

This study presents the effect of steering/suspension compliance and hysteresis on the time lag in handling responses of automobiles. A multi-body modeling approach is used to construct the tire, steering, and combined subsystem models. The tire subsystem model focuses on the tire lateral compliance induced time lag. The steering subsystem model focuses on steering/suspension compliance and hysteresis effect on the time lag. The combined model, which is an integration of the tire and steering subsystem models, is to show the combined effect of the subsystems. The simulation results show that the compliance and hysteresis in the steering and/or suspension subsystems are the sources of time lag in responses and that the hysteresis significantly increases the initial time lag.

This paper proposes a simple relation of the lateral guidance mechanism for automatic, guided vehicles and Dual Mode Trucks, and named it SSM (Sensor Steering Mechanism). SSM consists of a guide bar and deceleration gear which reduces the bar angle to one-second. In order to demonstrate the effectiveness of this relation, this paper examines the stability of the dynamic behavior of the front wheel steering of the vehicle. These results show that there is no limitation of the moving speed unless without a slip of the tire. For the test, a self-standing mobile robot, reduced to a scale of one-twentieth of the real car, is developed. Experimental results show that high-speed automatic moving is realized by using this relation.

The most time taking processes in a dynamic analysis of multibody vehicle models are generation and LU-decomposition of various matrices. This research proposes a vector oriented implementation algorithm for explicit numerical integration methods so that relatively low cost computers can be used for the realtime simulation of the multibody vehicle dynamics models consisting of many bodies and joints, a powertrain model, antiroll bars, and tires. Newton chord method is employed to solve the equations of motion and constraints. The equations of motion and constraints are formulated such that the Jacobian matrix for Newton chord method is needed to be generated and LU-decomposed only once for a dynamic analysis. As a result, only computations which need to be carried out in runtime are residual vectors of the governing equations. Convergence analysis of Newton chord method with the proposed Jacobian generation method is carried out. The proposed algorithm yielded close solutions to exact solutions for a prototype vehicle multibody model in realtime on a 400 Mhz PC compatible.