Half Car Research Articles

Study of a Half Car Suspension Model

In this paper, a model with four degrees of freedom is studied to assess the discomfort of car passengers due to vibrations. The response of the half car model due to road irregularities is presented in order to attain a control method for the dampers. For the analytical study, the differential equations of the motion were written in order to determine the critical frequencies. The resulted model takes into account both the forced and damped solution for a numerical case, thus giving a more detailed overview of the phenomena. Using this numerical case, a control method can be developed to reduce the passenger discomfort, based on the motion diagrams.

Input advanced control of semi active half car heave model

This paper deals with an input-based half car vehicle model moving with constant velocity over a terrain surface, where MR damper is fixed in both the wheels. The half car model fixed in a rolling dynamometer is operated with various input frequencies corresponding to various speeds. To design and develop control algorithms that will give optimum benefits of the unique features of the MR damper, models have been developed which adequately characterize the damper’s genuine, natural nonlinear behavior. The controller controls both the dampers according to variations in parameters of road surface, speed and load etc., with an advanced time with a particular time bound, through input (pre-programmed) based skyhook on/off control system. Comparison of experimental results of input based and ordinary skyhook on/off results indicates that the model is more functional and rewarding for vibration suppression over a wide range of operating conditions and is passable for control design and analysis.

Optimisation of the Nonlinear Suspension Characteristics of a Light Commercial Vehicle

The optimum functional characteristics of suspension components, namely, linear/nonlinear spring and nonlinear damper characteristic functions are determined using simple lumped parameter models. A quarter car model is used to represent the front independent suspension, and a half car model is used to represent the rear solid axle suspension of a light commercial vehicle. The functional shapes of the suspension characteristics used in the optimisation process are based on typical shapes supplied by a car manufacturer. The complexity of a nonlinear function optimisation problem is reduced by scaling it up or down from the aforementioned shape in the optimisation process. The nonlinear optimised suspension characteristics are first obtained using lower complexity lumped parameter models. Then, the performance of the optimised suspension units are verified using the higher fidelity and more realistic Carmaker model. An interactive software module is developed to ease the nonlinear suspension optimisation process using the Matlab Graphical User Interface tool.

Application of Independent Component Analysis for Road Profile Estimation

An application method of Independent Component Analysis (ICA) on vibration of an automobile considering dynamical properties is introduced and its performance is examined through a numerical simulation using a half car model. ICA is categorized in blind source separation method, and originally invented to separate significant signals buried in mixed signals. The proposed method separates road irregularity profile from mixed signals; data set of measured accelerations and calculated double integral of accelerations (displacements), integral of accelerations (velocities), differential accelerations (jerk) and double differential of accelerations. The advantage of proposed method is considering dynamical properties, while original ICA assumes a static mixture. So, it is effective on analysis of source separation in mechanical system including springs and dampers. Also, methods for fixing order of independent components and amplitude are proposed for the estimation of road irregularity. By applying the proposed method, road irregularity with information of amplitude is estimated without knowing parameters such as mass and spring constant.

An investigation on the ride comfort of a vehicle subjected to the random road excitation

In this paper, considering the random road excitation as the input, the Root Mean Square Acceleration Response (RMSAR) of the vehicle body and the driver seat has been derived to investigate the ride comfort. To this end, the DOF of the driver seat is added to the widely used 2-DOF half car model in which the actual vibration sensed by the driver can be investigated. Moreover, a realistic Power Spectral Density (PSD) function is proposed to formulate the actual random road excitation. Using the mentioned model and the proposed PSD function, the variation of the RMSAR of the vehicle body and the driver seat against the excitation frequency and the vehicle velocity are illustrated in appropriate diagrams. The results show that the RMSAR of the driver seat which is sensed directly by the driver, in general, is different from that of the vehicle body, and one can select appropriate values for the vibration parameters of the driver seat to enhance the ride comfort.

VIBRATION OPTIMIZATION OF A PASSIVE SUSPENSION SYSTEM VIA GENETIC ALGORITHM

In this paper, we have formulated mathematical models to optimize the bouncing transmissibility of the sprung mass of the half car system with passengers' seat suspensions considering different road conditions. The corresponding problem has been solved with the help of advanced real coded Genetic Algorithm (GA). The nonlinearity of suspension spring and damper, which are the most important characteristics of the suspension, has been taken into account in order to validate the model to real applications. The nonlinear cubic polynomial has been used to describe the spring characteristic and a quadratic polynomial has been used to describe the damper characteristic. The coefficients of each polynomial represent the design parameters of the suspension system and are to be determined. To find these parameters we have formulated a nonlinear optimization problem in which the bouncing transmissibility of the sprung mass at the center of mass has been minimized with respect to technological constraints and the constraints which satisfy the performance as per ISO 2631 standards. The advanced real coded GA has been used to solve this problem in time domain and the results obtained have been compared to those obtained using the existing design parameters. The objective function and the constraints have been evaluated by simulating the vehicle model over two roads with multiple bumps at uniform velocity.

Numerical integration approach to the problem of simulating damage in an asphalt pavement

A road develops permanent deformation or fatigue damage because of the stress and strain induced in its structure by surface loading and environmental change. Dynamic tyre forces generated by the vibration of moving heavy vehicles excited by the road surface profile are strongly influenced by vehicle speed and dynamic properties. A mechanistic-empirical approach is implemented here to simulate the deterioration of a pavement, taking account of dynamic excitation of the axles. This paper highlights the importance of statistical spatial repeatability in damage evolution during the pavement life. Numerical integration of the distribution of forces at each point is shown to be sufficient to predict the changing road surface and elastic modulus. This results in an approximate 100-fold increase in computational efficiency. Finally, the pattern of the forces generated by the axles of a half car is found to be a little less damaging than that of independent quarter cars. In the examples considered, the quarter car reduces calculated pavement life by an average of 6%.

Decentralized neuro-fuzzy control for half car with semi-active suspension system

In this paper, a decentralized neuro-fuzzy controller has been created in order to improve the ride comfort and increase the stability for half car suspension system, which used the magneto-rheological damper as a semi-active device. Firstly, relative gain array and relative disturbance gain methods have been used for deriving a relation between inputs, disturbances and outputs to select pairing with minimum interaction to design a decentralize controller. Secondary, decentralized neuro-fuzzy controllers for front and rear chassis are designed to predict the required damping force taking the acceleration of the sprung mass and desired acceleration obtained by using pole-placement method as inputs. To predict the control voltage required for producing the force predicted by the controller, the inverse neuro-fuzzy model of MR damper has been designed. Simulation by using MATLAB programs has been created. The results show that the ride comforts and vehicle stability have been improved in comparison with the passive system.

Intelligent semi-active vehicle suspension systems using neural networks

A methodology is proposed for designing intelligent vehicle suspension systems which implement the magneto-rheological damper as an active element. The adaptive control law is constructed based on the neural network methodology and Taylor series approximation. The controller commands the current of the magneto-rheological damper and controls directly the damper force. The neural network is trained with respect to a developed road disturbance scenario and its parameters are obtained using a global numerical optimisation technique. The proposed control law has a novel structure capable of sensing the interactions between the variables and thus can adjust the feedback gains with respect to the existing conditions. It takes into consideration the actuator’s dynamics and avoids limit cycling which is caused by the hysteretic behaviour of the MR dampers. The performance of the intelligent system is evaluated by means of simulations in MATLAB for quarter and half car models.

On the influence of design parameters and nonlinearities in vehicle suspensions on road deformation

AbstractAmong others, two main objectives of modern vehicle design are road friendliness and ride comfort. Both aspects are strongly related since the dynamical tire forces depend on the vertical acceleration of the vehicle. In order to investigate the influence of design and operation parameters, different car models are considered which move with constant velocity on a rippled road. First, a linear half car model is examined and the influence of different design parameters is discussed. Second, nonlinear suspensions with Coulomb friction due to sealings as well as with bilinear shock absorbers are taken into account. The vertical dynamics of the vehicle model and the dynamic tire forces between vehicle and road are calculated using analytical methods. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Surface prediction and control algorithms for anti-lock brake system

Anti-lock brake system (ABS) has been designed to achieve maximum deceleration by preventing the wheels from locking. The friction coefficient between tyre and road is a nonlinear function of slip ratio and varies for different road surfaces. In this paper, methods have been developed to predict these different surfaces and accordingly control the wheel slip to achieve maximum friction coefficient for different road surfaces. The surface prediction and control methods are based on a half car model to simulate high speed braking performance. The prediction methods have been compared with the results available in the literature. The results show the advantage of ABS with surface prediction as compared to ABS without proper surface identification. Finally, the performance of the controller developed in this paper has been compared with four different ABS control algorithms reported in the literature. The accuracy of prediction by the proposed methods is very high with error in prediction in a range of 0.17–2.4%. The stopping distance is reduced by more than 3% as a result of prediction for all surfaces.

Investigation of Vibration on Vehicle Suspension System using Half-car-model

Vibration of the suspension system of a vehicle is crucial for comfort of the passenger. In this paper, a mathematical model of the suspension system is presented with half car model with four degrees of freedom. Vibration characteristics due to different pitch line excitation and different damping coefficients are investigated for heavy vehicle suspension system. The model is simulated in MATLAB SIMULINK for this investigation. ANSYS Structural software has also been used to determine the resonance frequency and mode shape of vehicle bounce and pitch motion.

337 鉄道車両の脱線後まくらぎ上走行縮尺模型試験とその運動シミュレーション

Upon a train derails, its dynamic motion should be affected by the change of running resistance when the wheels run over sleepers. Therefore, it is important to determine the change of running resistance experimentally and theoretically. Authors made a model vehicle of 1 to 10 scale, and carried out running tests under which the vehicle ran colliding against model iron sleepers varying the initial running speed of the vehicle and the width of model sleepers. We found from the tests that the running resistance increased during the vehicle speed from Okm/h to about 20km/h, once decreased during the vehicle speed from approximately 20km/h to 70km/h, increased again exceeding 70km/h with the increasing of the vehicle speed. Authors also constructed half car and full car dynamics models to describe the motion of the vehicle in which the force acting between wheels and sleepers when the both collide with each other was considered, and executed running simulations varying parameters considered in our wheels and sleepers collision model. The calculated results of running resistance were consistent with the test results satisfactorily regardless of the sleeper type, and indicated that the maximum contact force between wheels and sleepers was the most affective for the running resistance among three parameters considered in the collision model.

Influência da suspensão na segurança e no conforto de um pulverizador autopropelido

Para avaliar o comportamento da suspensão do pulverizador autopropelido, foram desenvolvidos modelos físicos e matemáticos em função da excitação ocasionada pelas irregularidades do solo. Neste trabalho, estas irregularidades são representadas por obstáculos de uma pista normalizada segundo a norma ISO 5008. As equações do movimento são obtidas a partir dos modelos matemáticos de meio veículo. As simulações numéricas são executadas nos softwares Matlab® e Simulink®. A partir da entrada conhecida, podem-se determinar as características dos elementos da suspensão para obter níveis desejáveis de conforto e segurança. Foram analisadas quatro diferentes configurações do sistema, variando-se a relação de rigidez a partir de um modelo considerado padrão. Constatou-se que o aumento da relação de rigidez resulta na redução da aceleração vertical e no aumento do curso da suspensão, melhorando o conforto e diminuindo a segurança.

A New Optimal Nonlinear Approach to Half Car Active Suspension Control

A New Optimal Nonlinear Approach to Half Car Active Suspension Control

An evaluation of LQR and fuzzy logic controllers for active suspension using half car model

The application of the linear quadratic regulator (LQR) and fuzzy logic controller (FLC) in the field of active vibration isolation for a vehicle suspension system is presented to overcome the limitation of passive suspension system and the performances of the two active controllers are compared with the passive system. Results show that the performance of the LQR controller is better than the FLC at the expense of control force. The performances of both active controllers are better than the passive system in terms of settling time.

Modeling and Vibration Analysis of Road Profile Measuring System

During a vehicle development program, load data representing severe customer usage is required. The dilemma faced by a design engineer during the design process is that during the initial stage, only predicted loads estimated from historical targets are available, whereas the actual loads are available only at the fag end of the process. At the same time, changes required, if any, are easier and inexpensive during the initial stages of the design process whereas they are extremely costly in the latter stages of the process. The use of road profiles and vehicle models to predict the load acting on the whole vehicle is currently being researched. This work hinges on the ability to accurately measure road profiles. The objective of the work is to develop an algorithm, using MATLAB Simulink software, to convert the input signals into measured road profile. The algorithm is checked by the MATLAB Simulink 4 degrees of freedom half car model. To make the whole Simulink model more realistic, accelerometer and laser sensor properties are introduced. The present work contains the simulation of the mentioned algorithm with a half car model and studies the results in distance, time, and the frequency domain.

59355 Numerical Study on the Derailment of Rail Vehicle due to Large Earthquakes and the Effect of Anti-derailing Guard Rails(Railroad System Dynamics)

At Mid Niigata Prefecture Earthquake in October 2004, a Shinkansen train was derailed while being operated at the speed of 200km/h, which was the first case of the derailment of a Japanese high speed train under commercial operation through the long history. As reported, the horizontal ground motion of the earthquake was concluded to be the major cause of the derailment. Based on the reports and facts, we believe that we should study the derailment mechanism of a high speed railway vehicle due to large earthquakes, and pursue to develop an effective measure to minimize the risk of railway system against large earthquakes. In this research, a vehicle-track dynamics simulation program is developed and then employed to numerically examine the derailment mechanism and the function of Anti-derailing guard rails. The 16 DoF vehicle-track dynamics model is composed of a 10 DoF half car model and a 6 DoF track model to capture the entire dynamic response of a vehicle and rails. This reasonably simplified dynamics model should be suitable for studying the derailment mechanism and effect of guard rails. Also for more comprehensive understanding on the derailment mechanism and guard rail function for high speed railway vehicle, derailment process should be directly verified. Therefore, we also arrange an experimental setup with 1/10 scale vehicle and roller rig providing both conditions of high speed wheel/rail rolling contact and large amplitude excitations. Through the numerical analysis and experiment, we obtained the flowing outcomes. Firstly, as with the derailment pattern and process, rocking derailment is the cause of derailment due to large earthquakes. Secondly, as the measure to minimize the derailment risks, guard rails work effectively to the rocking derailments in times of large earthquakes.

Optimal semi-active preview control response of a half car vehicle model with magnetorheological damper

The control of the stationary response of a half car vehicle model moving with a constant velocity over a rough road with magnetorheological (MR) dampers is considered. The MR damper is modelled by the modified Bouc–Wen model. The MR damper parameters adopted in the vehicle model correspond to an actual fabricated damper and are determined so that the MR damper model characteristics match with experimental characteristics. The random road excitation is considered as the output of a first-order linear shaping filter to white noise excitation. The control and response statistics of the nonlinear vehicle model with MR damper are obtained using the equivalent linearization method in an iterative manner and the results are verified by Monte-Carlo simulation. The MR damper performance is sought to be improved by suitable choice of input currents to the levels of performance of an active suspension based on H ∞ control without and with preview by a mean square equivalence of respective control forces. The H ∞ optimal control with preview minimizes a performance index which is a weighted sum of vehicle performance measures such as sprung mass acceleration, pitch acceleration, front and rear suspension strokes, road holding and control forces with the weights obtained by solving a multi-objective optimization problem using a non-dominated sorting genetic algorithm II (NSGA II).

Optimization of Speed Control Hump Profiles

In this study, the goal attainment method is implemented for the optimization of speed control hump profiles. Basic dimensions for a number of hump profile functions are optimized for single vehicles classified in five categories and for a specified distribution of these vehicles. Objective functions are selected as combinations of the longitudinal and vertical acceleration components at pre-specified points on the vehicle body. The main objective is to minimize vehicle response functions below the hump crossing speed limit and to maximize them above the speed limit. Typical characteristics of a series of two axle vehicles, described by the half car model, are used and the performances of various hump profiles are assessed.