Suspension Elements Research Articles

Nonstationary Response of Bridge Due to Eccentrically Moving Vehicles at Variable Velocity

The non-stationary response of a simply supported girder bridge induced by the vehicle travelling at variable speed has been studied. The deck unevenness has been considered as the realization of homogeneous random process described by power spectral density (PSD) function. The vehicle has been idealized as rigid beam connected by front and rear suspension elements moving at an eccentricity with the centre line. The bridge has been idealized as a continuous system with distributed mass, stiffness and damping properties having flexural and torsional degrees of freedom. Monte Carlo simulation technique has been used to simulate deck profile for generation of input samples in numerical integration of the system equations. A detailed parametric study has been conducted to examine the effect of variable speed, suspension characteristics, vehicle mass, eccentricity of vehicle path, torsional rigidity of the bridge and deck unevenness on the dynamic amplification factors of the response.

Robust vibration control of dynamical systems based on the derivative of the state

Vibrations may be undesirable in dynamical systems for several reasons. They may affect the security, such as vibrations in primary cycle parts of (nuclear) power plants. They may decrease the quality and functionality of products, such as those manufactured by machine tools. And they may lower the comfort, such as vibrations in car wheel suspension systems or in power trains of cars. One possibility to attenuate these vibrations is by employing active suspension elements. Mounted at appropriate places inside the systems or with respect to their environment, they are able to interchange or dissipate kinetic and potential energy in an effective way with moderate control effort. Their effectiveness depends greatly on the control scheme applied to change damping and stiffness characteristics of the suspension elements. The control schemes, however, very often need information on the state variables involved in the mathematical modeling. On the other hand, it is mostly the acceleration or speed of certain parts that can be sensed reasonably and measured with sufficient accuracy. We propose here a control scheme which is solely based on the derivative of the state variables, provided that active suspension elements or actuators with the above-mentioned properties may be employed within the system. Furthermore, we only use control actions within a discrete set of possible values, which aids the real-time implementation of the designed control algorithms. And, last but not least, the number of control inputs (actuators) may be arbitrary, that is, the system may be mismatched. The scheme is based on the Lyapunov stability theory, which involves discontinuities of the Lyapunov function candidates along trajectories of the state derivative. The effectiveness and behavior of the control scheme is demonstrated on a two-DOF model of an active car seat suspension in order to enhance the driving comfort.

Modeling and Dynamics of Friction Wedge Dampers in Railroad Freight Trucks

A mechanical model for the vertical response of the bolster and friction-wedge suspension elements in a railroad freight truck is developed. The model incorporates linear stiffnesses and dry friction contact between rigid elements. Numerical bifurcation diagrams for sticking events, obtained for parameterizations of the amplitude and frequency of a harmonic track excitation, and for various friction laws, reveal distinct parameter-dependent dynamic responses: strongly nonlinear stick-slip oscillations, observed away from period-1 resonance; and weakly nonlinear, nearly harmonic responses, observed near the period-one resonance. The analytical method of harmonic balance is applied to develop a first order approximation for the period-1 response, and, as should be expected, is found to correspond well with the numerical results in the large amplitude limit and near the resonance location. Given that such weakly nonlinear, large amplitude, period-1 responses are not common for the speeds and system parameters of most freight vehicles, we conclude that friction-wedge models based on some form of equivalent linearization may be inadequate for simulating freight car dynamics in many cases of practical importance.

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Computer simulation is essential to design the suspension elements of railway vehicle. By computer simulation, engineers can assess the feasibility of the given design factors and change them to get a better design. But if one wishes to perform complex analysis on the simulation, such as railway vehicle dynamic, the computational time can become overwhelming. Therefore, many researchers have used a surrogate model that has a regression model performed on a data sampling of the simulation. In general, metamodels(surrogate model) take the form y(<TEX>$\chi$</TEX>)＝f(<TEX>$\chi$</TEX>)＋<TEX>$\varepsilon$</TEX>, where y(<TEX>$\chi$</TEX>) is the true output, f(<TEX>$\chi$</TEX>) is the metamodel output, and is the error. In this paper, a second order polynomial equation is used as the RSM(response surface model) for high speed train that have twenty-nine design variables and forty-six responses. After the RSM is constructed, multi-objective optimal solutions are achieved by using a nonlinear programming method called VMM(variable matric method) This paper shows that the RSM is a very efficient model to solve the complex optimization problem.

Effect of suspension spring stiffness on vehicle dynamics

Vehicle suspension systems and suspension working space are of great interest to designers and researchers of road vehicles. This paper deals with an investigation into the influence of suspension spring stiffness on vehicle dynamics. A mathematical model of a quarter vehicle for twin spring, passive and active suspension systems is developed. These systems are compared in terms of their relative performance capabilities. The vehicle itself is treated as a rigid body undergoing vertical motions. Also, a longitudinal half vehicle model for passive suspension is used to investigate the effect of front and rear spring stiffness on the vehicle dynamics. A chassis dynamometer was used to perform the experimental work. The predicted results were compared with experimental measurements. The experimental and theoretical results obtained indicate that the mathematical model produces optimistic results for the vertical direction of body acceleration and suspension working space. The effect of using active suspension elements to obtain improved ride is discussed. The results obtained give a solution to the vehicle dynamics problem and show optimum values of spring stiffness and damping coefficient.

Intelligent Feedback Linearization for Active Vehicle Suspension Control

Effective control of ride quality and handling performance are challenges for active vehicle suspension systems, particularly for off-road applications. Off-road vehicles experience large suspension displacements, where the nonlinear kinematics and damping characteristics of suspension elements are significant. These nonlinearities tend to degrade the performance of active suspension systems, introducing harshness to the ride quality and reducing off-road mobility. Typical control strategies rely on linear, time-invariant models of the suspension dynamics. While these models are convenient, nominally accurate, and tractable due to the abundance of linear control techniques, they neglect the nonlinearities and time-varying dynamics present in real suspension systems. One approach to improving the effectiveness of active vehicle suspension systems, while preserving the benefits of linear control techniques, is to identify and cancel these nonlinearities using Feedback Linearization. In this paper the authors demonstrate an intelligent parameter estimation approach using structured artificial neural networks that continually “learns” the nonlinear parameter variations of a quarter-car suspension model. This estimation algorithm becomes the foundation for an Intelligent Feedback Linearization (IFL) controller for active vehicle suspensions. Results are presented for computer simulations, real-time experimental tests, and field evaluations using an off-road vehicle (a military HMMWV). Experimental results for a quarter-car test rig demonstrate 60% improvements in ride quality relative to baseline (non-adapting) control algorithms. Field trial results reveal 95% reductions in absorbed power and 65% reductions in peak sprung mass acceleration using this IFL approach versus conventional passive suspensions.

On freight wagon dynamics and track deterioration

To increase understanding of the running behaviour of freight wagons a research project was started at the Royal Institute of Technology (KTH) in 1996. The background to the project included plans to increase axle load, loading gauge and speed of freight trains in Sweden to make freight traffic more competitive. Simulation models for three different types of UIC freight wagon running gear were developed. The present paper focuses on track deterioration of freight wagons caused by high vertical wheel-rail forces. First the characteristics and modelling of some suspension elements are described, followed by a description of the deterioration model. Then the influence of the parameters of axle load, height of the centre of gravity and vehicle speed on track deterioration is investigated. Track parameters such as rail type and sleeper spacing are varied. The conclusion is that track deterioration per transported pay load increases when the axle load and loading gauge are increased. However, this can be compensated by using an improved track design.

Improvement of electromagnetic suspension elements

Voice coil type suspension elements have received much attention from many experimentalists due to the good cut-off characteristic for vibrational disturbances. To isolate experimental equipments from the storage rack in spacecraft and to realize an excellent microgravity environment, we have improved the magnet construction of a suspension element by using the axisymmetric finite element analysis. Results show that the variation of the forces can be successfully reduced and the improved suspension element provides a good cut-off characteristic.

Performance Analysis and Experience Gained with Linear and Non-Linear Wheelset Guidance Systems for Trailing and Motorised Self-Steering Bogies

This paper gives brief details of non-linear suspension elements, used to improve stability and curving performance in self-steering railway freight car bogies. A recently developed frame mounted shear stiffener is found to be an effective wheelset guidance system. The linkages provide inter-axle shear stiffness and simultaneously transmit traction and braking forces between the wheels and the bogie frame. Combined with a degressive yaw constraint device, self-steering bogies can meet modern high operating speed requirements while maintaining good curving performance and low wheel and rail wear. For the covering abstract see ITRD E117109.

STOCHASTIC OPTIMAL ACTIVE CONTROL OF A 2-DOF QUARTER CAR MODEL WITH NON-LINEAR PASSIVE SUSPENSION ELEMENTS

Active control of the time varying response to a stationary random excitation of a two-degree-of-freedom vehicle model with non-linear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive the equivalent linear model and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared damping and hysteresis type of stiffness non-linearities are considered. The performance of active suspensions with non-linear passive elements is found to be superior to the corresponding passive suspension systems. As a check on the accuracy of the equivalent linearization technique, a Monte Carlo simulation has also been performed. The results are compared with the results obtained from linearized vehicle model and good agreement between the results has been observed.

An H2Formulation for the Design of a Passive Vibration-Isolation System for Cars

SUMMARY Optimal design of an active suspension system for road vehicles can be solved using LQR techniques. Such a problem is equivalent, in the frequency domain, to determine the state feedback gain matrix that minimizes the H2 norm of a suitable transfer matrix. A passive suspension system can be seen as the physical realization of a suitable state feedback law whose gains are function of the system parameters. This law, and thus the characteristic elements of the passive suspension, can be determined as an approximation of the H2 optimal solution. This methodology allows one to choose the best controller from a constrained subset (i.e., all possible passive suspensions of a particular form) of all possible controllers.

Ventral tethering of the vagina and its role in the kinetics of urethra and bladder-neck straining.

Based on the principle that the urethra forms an integral part of the ventral wall of the vagina, the aim of this study was to determine the elements of fixation of this wall and their role in the maintenance of urethral statics during strain exertion. Eight dissections of the female pelvis were performed by a simultaneous high and low approach. The anatomic data were compared with a study of the kinetics of the urethra by dynamic MRI. The lower part of the ventral vaginal wall is tethered to the pubis and the ischiopubic rami by a complex mixed system containing elements of both suspension and support. These elements simultaneously allow a complex and asymmetric movement around the inferior border of the pubic symphysis and maintain urinary continence during straining.

Railway Vehicles With Generic Bogies Capable of Perfect Steering

SUMMARY The general form of the equations of motion of a symmetric railway vehicle with two unsymmetric two-axle bogies is derived. The equations include a generic elastic stiffness matrix that describes the nature and configuration of the structural connections between the various components of the vehicle. This matrix satisfies the condition for perfect steering (without generating creep forces) on uniform curves and the necessary condition for dynamic stability derived in previous work. The paper shows the application of these basic conditions to a class of generic unsymmetric bogies. The analysis has as its objective the derivation of the simplest rather than the most general configuration that meets the conditions imposed. The results are related to past and current practice. It is shown that perfect steering, with stability at low speeds, can be achieved by means of passive suspension elements not employing linkages, and that it is possible to simplify existing steering arrangements.

A Model for Determining Rider Induced Energy Losses in Bicycle Suspension Systems

SUMMARY The energy dissipated by the suspension systems used for off-road bicycles is a major concern due to the limited power source in cycling. Rider induced energy losses are those that arise from the muscular action of the rider. The purpose of this study was to develop and verify a dynamic model of a seated cyclist riding an off-road bicycle up a smooth road. With the absence of terrain irregularities, all suspension motion was rider induced. Knowing the stiffness and dissipative characteristics of the suspension elements, the power dissipated by the suspensions was calculated. Simulation results were compared to suspension deflections that were experimentally measured for a cyclist riding a commercially available dual suspension bicycle up a 6% grade at 6.5m/s. For this particular case, no fork motion was observed in the experiments which was consistent with the simulation results. For the rear suspension, the mean and amplitude of the largest harmonic were experimentally determined to be 6.6 and ±2...

Active control of non-stationary response of a two-degree of freedom vehicle model with nonlinear suspension

Active control of non-stationary response of a two-degree of freedom vehicle model with nonlinear passive suspension elements is considered in this paper. The method of equivalent linearization is used to derive an equivalent linear model and optimal control laws are obtained by using stochastic optimal control theory based on full state information. Velocity squared quadratic damping and hysteretic type of stiffness nonlinearities are considered. The effect of the nonlinearities on the active system performance is studied. The performance of active suspensions with nonlinear passive elements is found to be superior to the corresponding passive suspension systems.

REKEM—A design-oriented simulation program for off-road track vehicle

A design-oriented computer program, called REKEM, was developed for off-road track vehicle simulation. The equations of motion were formulated using the Lagrange approach and created automatically by a symbolic program. The model includes the detailed design and features of all suspension components, track tension, soil-track interaction, rolling resistance and soil energy dissipation. A sixth-order Runge-Kutta integration method and variable time steps were used for the solution. The output of the program includes numerical and graphical options, as well as animation of ride simulation. The simulation program is oriented for detailed design and analysis of the suspension system and for ride comfort evaluation. One of the main features of the program is the easy implementation of new suspension elements and track-soil-wheel interaction models. The source code of the model is concise in shape and size, and can be operated on work stations and personal computers with a mathematical co-processor as well. An example of ride simulation demonstrates some of the design features of the simulation model.

Electronically controlled automotive suspensions

Automotive suspension design is a compromise brought about by the conflicting demands of ride and handling. We have seen the introduction of increasingly sophisticated, electronically controlled components which redefine the boundaries of the compromise. The major elements of a motor car suspension are summarised by the author. The technology employed in automotive suspension design covers a wide range of sophistication, performance and cost and can be categorised as: adaptive suspension, semi-active suspension, low-bandwidth active suspension, and four wheel steering systems. The author considers each of these categories.

A fixed parameter optimal controller design for an active suspension system—A sensitivity analysis

The function of an automotive suspension system is to maintain passenger comfort and vehicle road handling capabilities whilst supporting the body mass of the vehicle and operating within the constraints of the suspension working space. In order to satisfy these criteria the overall suspension system is required to be ‘tuned’ to provide a satisfactory compromise; the point at which this compromise is made is an important design parameter and varies from vehicle to vehicle depending upon its application and may also be required to vary depending upon operating conditions. The paper presents results of an extensive sensitivity analysis aimed at assessing the effectiveness of an optimal control law design which is based on a low order generalised minimum variance approach applied to a low bandwidth slow active suspension system. The control law design is assessed when subjected to an increase in the body mass of the vehicle as well as variations in the tyre spring rate and the conventional suspension elements; the base vehicle under consideration being a large luxury saloon car. The results of the sensitivity analysis highlight the need for flexibility in the controller cost weightings and reinforce the appropriateness and practicability of using a fixed low order model structure in order to achieve further improvements in overall ride quality.

FREQUENCY RESPONSE ANALYSIS OF SYMMETRIC AND ASYMMETRIC NONLINEAR VEHICLE SUSPENSIONS

Frequency Response characteristics of a symmetric and asymmetric vehicle suspension are analyzed in the convenient frequency domain using a local equivalent linearization methodology. Suspension non-linearities include a progressively hardening stiffness and asymmetric damping characteristic due to a multi-phase shock absorber. The methodology, based on the principle of energy similarity, characterizes the nonlinear suspension elements by an array of local constants as function of local excitation frequency and amplitude, response and type of nonlinearity. The nonlinear behaviour of the system can thus be predicted quite accurately in the entire frequency range. The frequency response characteristics of a vehicle model with nonlinear suspension are evaluated using local linearization algorithm and compared to those established from direct integration to demonstrate the effectiveness of the algorithm for different amplitudes of excitation, in the entire frequency range.

On Mapping Cones of Suspension Elements of Finite Order in the Homotopy Groups of a Wedge of Spheres

On Mapping Cones of Suspension Elements of Finite Order in the Homotopy Groups of a Wedge of Spheres