Mathematical Modelling and Simulation of a Simple Quarter Car Vibration Model (original) (raw)
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Analysis of Active and Passive Suspension System of Half Car model using MatlabTM - Simulink®
International Journal of Engineering Sciences & Research Technology, 2014
The concept of using an active suspension system for vehicles is to provide the best performance of car controlling. A fully active suspension system aim is to control the suspension over the range of excitation signals. It is considered to be the way of increasing load carrying, handling and ride quality. The purpose of this research paper is to construct a half car model with a linear control design which is the Proportional Integral Derivatives (PID).This paper compares the passive suspension response with active suspension response. The response of the system is simulated by MATLAB™ Simulink®. To evaluate the performance of this system, PID is chosen as a control strategy and will be compared with the uncontrolled, by performing a MATLAB™ Simulink® simulation.
Analysis of a Passive Linear Quarter Car Suspension System using Matlab/Simulink
This paper discusses the suspension of a two-degree-of-freedom (2-DOF), Linear Quarter Car, vehicle system. MATLAB/Simulink environment is used to analyze response of the quarter car. The quarter car model is subjected to various inputs like step input, sine, random, saw tooth, ramp etc... To study the system, first the governing equations for a linear quarter car model are derived. Then a Differential Equation approach, State Space approach and Transfer Function approach was used using Simulink blocks. For all the approaches the results matches to each other.
2015
Suspension system of an automobile not only supports the body of the vehicle, engine and passengers but also absorbs shocks arising from the roughness of the road. So, tremendous research carried out on vibrational analysis for active and passive suspension system. This paper includes review of vibrational analysis for active and passive suspension for linear and nonlinear system. Vibrational analysis usually carried out with quarter car, half car and full car model. Also uses various optimization techniques for optimum parameters for suspension system. KEYWORDS— Passive and active suspension system, Quarter, half car model, FFT analyser, PID controller, MATLAB. INTRODUCTION Conventionally Automobile suspension strategies have been a compromise among three contradictory criteria of road holding, rattle space requirements and ride comfort of passenger. The suspension arrangement need to take care of the vehicle handling parameters during vehicle moving over a terrain and be responsib...
The three main objectives that a suspension system of an automobile must satisfy are ride comfort, vehicle handling and suspension working space. Ride comfort is directly related to the vehicle acceleration experienced by the driver and the passengers. Lesser vertical acceleration, higher is the level of comfort. The aim of the Project was to design and analyze the semi active suspension system models using skyhook, ground hook and hybrid control for quarter car. The project work includes modeling of semi-active suspension system in MATLAB simulink, using 2 degree of freedom quarter car model. The skyhook on-off, ground hook and hybrid control strategies were designed using control laws stated in literatures. Simulated results have been compared with passive system for time response analysis of body vertical displacement and vertical displacement of quarter car. Simulation was carried out for various road conditions such as random road excitation, road bump excitation, step input etc. The simulated results for quarter car model are shows similar trends and within range when compared with reference research paper.
Suspension system of an automobile not only supports the body of the vehicle, engine and passengers but also absorbs shocks arising from the roughness of the road. So, tremendous research carried out on vibrational analysis for active and passive suspension system. This paper includes review of vibrational analysis for active and passive suspension for linear and nonlinear system. Vibrational analysis usually carried out with quarter car, half car and full car model. Also uses various optimization techniques for optimum parameters for suspension system
International Journal of Modelling, Identification and Control, 2009
Several control policies of semi-active system, namely skyhook, groundhook and hybrid controls are presented using a half-car model, as a continuation of the previous work on quarter-car model. Their ride comfort, suspension displacement and road-holding performances are analysed and compared with passive system. The analysis covers both transient and steady state responses in time domain and transfer function in frequency domain. The results show that the hybrid control policy yields better comfort than a passive suspension, without reducing the road-holding quality or increasing the suspension displacement for typical passenger cars. The hybrid control policy is also shown to be a better compromise between comfort, road-holding and suspension displacement than the skyhook and groundhook control policies.
Modeling, Simulation, and Control of Half Car Suspension System Using Matlab/Simulink
Abstract: The modeling, simulation, and control of linear half car suspension system with different control algorithms are studied using Matlab programming package. The model has four degrees of freedom; comprising of heave movements of the front and rear axle, pitch and heave motions of the unsprung mass of the vehicle. Different controllers developed and implemented in this study such as PID, Fuzzy and Fuzzy-PID. Each controller was widely simulated for linear half car models hydraulically actuated for active suspension system. The aim of each controller was to minimize the deflection and the acceleration of the suspension system in the presence of road disturbances, modeled by step input excitation wheels. Comparisons between passive and active, linear simulation models have been carried out with different control schemes. The result of these comparisons was that performance of the linear model was attuned better than the linear model, and the Fuzzy-PID controller suggest in this work was the best among other controllers used in analysis. Shows the superior performance of response amplitude, shorter settling time, small overshot, high steady precision, and good dynamic performance
Validation of Simulation of Nonlinear Passive Vehicle Suspension System
international journal for research in applied science and engineering technology ijraset, 2020
In this paper the nonlinear behaviour of passive suspension system for quarter car is studied. The mathematical model is developed with the help of equations of motions. In the actual practice, all system behaves nonlinearly but for simplification purpose it consider as linear. A linear system can capture basic performances of vehicle suspension such as body displacement, body acceleration, wheel displacement, wheel deflection, suspension travels. Performance of suspension system is determined by the ride comfort and vehicle handling. It can be measured by car body displacement and wheel deflection performance. Two types of road profiles are used as input for the system. The quarter car two degree of freedom and MATLAB-SIMULINK model is developed for the nonlinear quarter car passive suspension system. I. INTRODUCTION Vehicle suspensions are mainly classified into three types i.e., passive, semi active and active suspensions, which depend on the operation mode to improve vehicle ride comfort, vehicle safety, road damage minimization and the overall performance. This paper presents mathematical modelling of nonlinear quarter car. The nonlinear quarter car model consists of quadratic tyre stiffness and cubic stiffness in suspension spring as nonlinearities. It also reduces the vibrations passing to the vehicle body. The quarter car (1/4th) model of suspension system is developed for the analysis purpose [2]. The passive vehicle suspension system has spring and damper. The motivation behind damper to disperse the energy while spring acts as an energy storing element. Both the elements never add energy to system such type of automobile suspension systems called as passive suspension system. There are fixed parameters in this system, which select to get a specific level of trade-off between ride comfort, road holding and load conveying. The main problem in this suspension system is that designed of the damper. If the damper is heavy then it will throw the car on unbalanced of road. If the damper is light in design then its effect on stability of the vehicle while turning or changing lane. Sometimes car may be swing due to such design. The road profiles plays important role in the performance suspension system. In the passive suspension system, if spring stiffness increases then the ride comfort decreases and vice versa [5]. Daniel Fischer et al [1] derived the mathematical models for suspensions with variable dampers and springs as well as active components for fault detection and diagnosis of the damper by combining parameter estimation and parity equation methods.
suspensıons, 2018
Quarter-car model is in use for years to study the car dynamics. The objection of this paper is to examine the dynamics of a car passing a circular hump for sake maintaining ride comfort for the passengers. Passive suspension elements are considered with suspension damping coefficient in the range 1 to 15 kNs/m. Car speed in the range 5 to 25 km/h is considered when passing the hump. Important phenomenon evolved from the analysis of the car dynamics which is performed using MATLAB. The mathematical model of the quarter-car model is derived in the state form and the dynamics are evaluated in terms of the sprung mass displacement and acceleration. The effect of suspension damping and car speed on the sprung-mass displacement and acceleration is examined. The study shows that for ride comfort the car speed has not to exceed 6.75 km/h when passing a circular hump depending on the suspension damping. .
Modelling and simulation of motor vehicle suspension system
IOP Conference Series: Materials Science and Engineering, 2021
In this work, using a quarter-car model was adopted, the equations of motion were derived for a passive and then the sky-hook semi-active suspension systems. The derived differential equations, solved using the Dormand-Prince pair numerical formula, was then used to simulate values of displacements as affected by damping coefficients and the sky-hook constant. The simulated results showed that the maximum amplitude of the sprung mass, which is linked to ride discomfort, increases while those of unsprung masses, which affects the road holding ability, decreases with increasing depth of pothole. Furthermore, displacements for both sprung and unsprung masses varied directly with damping coefficient. Finally, as the sky-hook constant of the semi active system model increases, values of amplitudes of unsprung masses decreases while those of sprung masses increases. It was, thus, shown that the vertical displacements of vehicle bodies and wheels are dependent on the depth of potholes, dam...