Quarter Car Model Research Articles

Bridge frequency identification based on relative displacement of axle and contact point using tire pressure monitoring

The identification of bridge frequency (BF) using the responses of moving vehicles has received growing interest in recent years. In this study, a two-stage framework was developed to extract the BF using the tire pressure of a vehicle crossing it. The first step was to establish and calibrate a tire pressure model, which facilitates the interpretation of the relationship between the tire pressure change and relative displacement of the axle and contact point (RD of A-CP). To satisfy the field test requirements, a quarter-car model representing the rear axle system of a half-car model was adopted; thus, the excitation from the front suspension vibration could be neglected. In the second stage, the calibrated tire pressure model was used to identify BFs, by combining it with field measurements of the rear tire pressure change of a traversing vehicle. The A-CP displacement estimation method was formulated using the estimated rear axle RD of the A-CP. In addition, a residual displacement method was proposed to eliminate the adverse effects of road roughness; this used the estimated CP displacement of the rear tire over two runs, and the BF could be identified from the residual response. From numerical simulations, we verified that the proposed CP displacement estimation and road roughness elimination methods were reliable, allowing the identification of BFs with satisfactory accuracy. Finally, the performance of the proposed two-stage framework was comprehensively determined in both laboratory experiments and field tests using a real inspection vehicle. Thelimitations of the present study and recommendations for future workwerealso addressed.

Multiphysics Design of an Automotive Regenerative Eddy Current Damper

This research presents a finite element multi-physics design methodology that can be used to develop and optimise the inherent functions and geometry of an innovative regenerative eddy current (REC) damper for the suspension of B class vehicles. This methodology was inspired by a previous work which has been applied successfully for the development of an eddy current (EC) damper used for the same type of applications. It is based on a multifield finite element coupled model that can be used to fulfil the electromagnetic, thermal, and fluid dynamic field properties and boundary conditions of a REC damper, as well as its non-linear material properties and boundary conditions, while also analysing its damping performance. The proposed REC damper features a variable fail-safe damping force, while electric power is advantageously regenerated at high suspension frequencies. Its damping performance has been benchmarked against that of a regular hydraulic shock absorber (selected as a reference) by analysing the dynamic behaviour of both systems using a quarter car suspension model. The results are expressed in terms of damping force, harvested power, thermal field, comfort and handling, with reference to ISO-class roads. The optimisation analysis of the REC damper has suggested useful guidelines for the harmonisation of damping and regenerative power performances during service operation at different piston speeds.

The estimation of frequency response of nonlinear quarter car model and bilinear model of damper characteristics

The paper presents proposed and tested methods of estimation of frequency response of nonlinear quarter car suspension model and comparison with method for linear model used for research of vehicle vertical dynamics. Linear quarter car suspension model is widely used for estimation of comfort and safety performance of passive and semiactive suspensions. The real suspension - especially shock absorbers - are non-linear in three aspects: static characteristics, hysteresis and the presence of friction. Testing linear suspension model is possible with the use of analytical transfer function formulas but testing real suspension on a testing stand or even virtual but nonlinear suspension needs to use methods of transfer function estimation. It was necessary to design appropriate input signal allowing to get useful response signals. With the use of obtained frequency responses a method of linear estimation of nonlinear suspension for a given range of working condition was proposed. Also the bilinear model of damper characteristic estimation was proposed and tested proving to be good alternative to nonlinear characteristic.

Simulating porpoising effect on quarter-car suspension model

Simulating porpoising effect on quarter-car suspension model

Control of Semi-Active Suspension System Using Kalman Observer

Optimal control methods are increasingly used in automatic control systems, especially in automotive suspension system. However, the optimal control algorithm only achieves the highest efficiency in suspension control system when the required number of sensors is sufficient, corresponding to the number of states in the system. The arrangement of sufficient number of sensors depends on the capacity, economic conditions and responsiveness of the sensor. The Kalman observer is designed to reliably estimate the required parameters in the control where the number of sensors is limited. The article focuses on analyzing the theory of building a quarter-car model, developing and determining the optimal control matrix, the Kalman observer design method. The findings of the article reveal the effectiveness of automotive body vibration suppression and the required force for control corresponding to LQG control and LQR control, under the influence of square pulse road surface, when using two similar sensors are installed on the sprung and unsprung, thereby providing a choice of sensor type and the location on the semi-active ¼ suspension.

Safety-critical Policy Iteration Algorithm for Control under Model Uncertainty

Safety is an important aim in designing safe-critical systems. To design such systems, many policy iterative algorithms are introduced to find safe optimal controllers. Due to the fact that in most practical systems, finding accurate information from the system is rather impossible, a new online training method is presented in this paper to perform an iterative reinforcement learning based algorithm using real data instead of identifying system dynamics. Also, in this paper the impact of model uncertainty is examined on control Lyapunov functions (CLF) and control barrier functions (CBF) dynamic limitations. The Sum of Square program is used to iteratively find an optimal safe control solution. The simulation results which are applied on a quarter car model show the efficiency of the proposed method in the fields of optimality and robustness.

A Lyapunov Stability Analysis of Modified HOSM Controllers Using a PID-Sliding Surface Applied to an ABS Laboratory Setup

The antilock braking system (ABS) is a mechatronic system that helps a driver maintain the maneuverability of a vehicle while braking by preventing wheel lock-ups. However, the design of high-performance controllers for this type of system is complicated because of its highly nonlinear dynamics. The problem becomes even more difficult to resolve when uncertainties in the parameters appear in its dynamics. In this paper, an ABS laboratory setup mimicking a quarter car model is considered. A modified high-order sliding mode (HOSM) controller using a proportional-integral-differential (PID) control as a sliding surface was designed. This controller provides a reference value of a tire slip. The proposed controller uses a tracking error to define the slip surface through the PID controller structure, and the modified HOSM controller holds the system on the previously designed slip surface. The closed-loop system stability has been proven in the sense of Lyapunov. Finally, the ABS laboratory setup allows for experimentally checking the performance of the modified HOSM controller using a PID-sliding surface, showing a considerable increase in the efficiency of the control system compared with a PID-like controller.

Stochastic optimal preview control response of a quarter-car nonlinear suspension model using spectral decomposition method

This paper considers a two degree of freedom quarter-car model of a four wheel vehicle with nonlinear spring travelling at a constant speed on a random road surface with a preview control to obtain the optimal vehicle response. The nonlinear spring behavior is assumed as a hysteresis and modelled by the Bouc–Wen model. This nonlinear vehicle model is linearized by using statistical linearization approach. The root mean square values of the control force, suspension stroke and road holding characteristics are determined by spectral decomposition method. The results obtained for the equivalent linearized model using the SDM are validated with Monte Carlo simulation, and the results show that the vehicle performs better using preview control.

Observer-based robust gain-scheduled control for semi-active air suspension systems subject to uncertainties and external disturbance

In this paper, an observer-based robust gain-scheduled control scheme is designed for a semi-active air suspension (SAAS) system subject to uncertainties and external disturbance. Since the air spring in SAAS system is a highly nonlinear component and its stiffness relies on the spring interior pressure and displacement, an air spring model is constructed based on aerothermodynamics theory. Aiming at comprehensive and simplified expression of air spring nonlinear dynamics, the air spring model is expressed as linear-parameter-varying (LPV) form and further integrated into a quarter car semi-active air suspension model. To identify system states under the noisy condition with lower cost, a LPV-Kalman filter is proposed to estimate the states which are difficult to be measured or physically unmeasurable in the semi-active air suspension. With the proposed observer, a robust gain-scheduled controller is developed to overcome complex nonlinear dynamics, actuator uncertainties and external disturbance. To realize a better transient response, the control law is improved by constraining eigenvalues of the closed-loop system in desired linear matrix inequality (LMI) region. At last, simulations and experiments are conducted to illustrate the effectiveness of proposed control scheme in a quarter car test rig.

Modeling and Simulation of PID Controller-Based Active Suspension System for A Quarter Car Model

The most common automotive suspension systems have been used passive components with fixed damping coefficient and spring constant. They are two separate functions to reach a compromise between drive quality and handling performance. Because of the limit of structures, the passive suspension system could hardly enhance the two features at the same time. In recent years, the active suspension system has been widely used in a vehicle which can overcome the limitations of the passive suspension systems. Since there are many advantages to make the vehicle operate safer and quieter than the passive suspension system. The aim of this study is to develop a linear mathematical model of active and passive suspensions systems for quarter car models subjected to different road profiles using a Proportional Derivative Integral (PID) controller. After modeling and simulation of the suspension system using Matlab/Simulink, this study has been able to determine the parameter of PID controllers of active suspension in many different road surfaces and vehicle speeds to improve driving comfort. Another new point of this study is the Graphical User Interfaces to be a successful design. The users can enter the input parameters for Matlab processing and get the results, which can make system analysis faster and more convenient. The main outcomes of this paper are performed to investigate and compare the response between active and passive suspension systems. Through the analysis of the simulation results, this research has demonstrated the feasibility, reliability, and they can be applied to propose a further improvement of the kinematic and dynamic characteristics of the vehicle active suspension system.

Neural Network Modeling and Dynamic Analysis of Different Types of Engine Mounts for Internal Combustion Engines.

This paper presents the results of studies on reducing the amount of vibrations in different frequency ranges generated by a combustion engine through the use of different types of engine mounts. Three different types of engine supports are experimentally and numerically analyzed, namely an elastomeric engine mount, an elastomeric engine mount with a hydraulic component and standard decoupling, and an elastomeric engine mount with a hydraulic component and a modified decoupler—with this engineering design being a novelty in the literature. Experimental tests that considered different excitation frequencies were performed for the three types of engine mounts. Experimental data for stiffness and damping were used to obtain nonlinear mathematical models of the two systems with hydraulic components through the use of an Artificial Neural Network (ANN). For the results, all of the mathematical models presented coefficients of determination, R2, greater than 0.985 for both stiffness and damping, showing an excellent fit for the nonlinear experimental data. Numerical results using a quarter-car suspension model showed a large reduction in vibration amplitudes for the first vibration model when using the hydraulic systems, with values ranging between 48.58% and 66.47%, depending on the tests. The modified system presented smaller amplitudes and smoother behavior when compared to the standard hydraulic model.

Nonlinear control of an antilock braking system in the presence of tire–road friction uncertainties

An Antilock Braking System (ABS) is characterized by nonlinear dynamics, which render more difficult the design of a controller for high performance. The problem is even harder due to the uncertainties on the parameters appearing in its dynamics. In this paper, an ABS laboratory setup is considered, which mimics a quarter car model. A super–twisting controller is proposed to overcome the problem due to parameter uncertainties. This controller is designed in order to impose a reference value of the tire slip. Two cases are considered: in the first, nominal ABS parameters are used in the controller, whereas in the second the controller embeds an estimator of the tire–road friction coefficient, which is one of most critical parameters. The friction coefficient is estimated in finite–time by means of a high–order sliding mode differentiator. The original contributions of the paper are the real–time implementation of the super–twisting controller for the laboratory setup under study, and the use of a super–twisting estimator to provide a finite–time estimation of the friction coefficient between the tire and the road, along with a comparison with classical PI–like and super–twisting controllers, available in the literature. The ABS laboratory setup allows checking experimentally the performance of the proposed nonlinear dynamic controller, showing a considerable increase of the efficiency of the control system.

A Review on PID Control System Simulation of the Active Suspension System of a Quarter Car Model While Hitting Road Bumps

A Review on PID Control System Simulation of the Active Suspension System of a Quarter Car Model While Hitting Road Bumps

Dynamic responses of a damaged double Euler-Bernoulli beam traversed by a 'phantom' vehicle.

SummaryIn this paper, the dynamic response of a damaged double‐beam system traversed by a moving load is studied, including passive control using multiple tuned mass dampers. The double‐beam system is composed of two homogeneous isotropic Euler–Bernoulli beams connected by a viscoelastic layer. The damaged upper beam is simulated using a double‐sided open crack replaced by an equivalent rotational spring between two beam segments, and the lower primary beam is subjected to a moving load. The load is represented by a moving Dirac delta function and by a quarter car model, respectively. Road surface roughness (RSR) is classified as per ISO 8606:1995(E). The effect of vehicle speed of the moving oscillator and variable RSR profiles on the dynamics of this damaged double Euler–Bernoulli beam system for different crack‐depth ratios (CDRs) at various crack locations is studied. It is observed that coupling of two beams leads to a vehicular effect on the damaged beam, even when no vehicle on it is present. The effects of single and multiple tuned mass dampers to control the vibrational responses of the primary beam due to damage on the secondary beam is studied next. The performance of tuned mass dampers to reduce the transverse vibrations of the damaged double‐beam system and of the quarter car is investigated. The paper links the coupling between the two levels of double beam with the inertial coupling of the vehicle to the double‐beam system.

Design, Parameter Optimisation, and Performance Analysis of Active Tuned Inerter Damper (TID) Suspension for Vehicle

The inherent inertia of active actuators can adversely affect the performance of vehicle suspension systems, which has been a long-standing problem in suspension design. To overcome this problem, an active tuned inerter damper (TID) suspension is designed based on a combination of an active actuator and an inerter, merging the inherent inertia of the former into the inertia of the latter. However, several parameters are involved in active TID suspension, requiring much time and resource to optimise via numerical method. Based on the H2-norm of a quarter-car model, an analytical-solution-based parameter optimisation method that simplifies the process of obtaining the optimal suspension parameters is proposed. Stability analysis is performed algebraically using the Hurwitz criterion, verifying that the parameters obtained using this method can ensure the stability of the suspension. The advantages of active TID suspensions are demonstrated via performance comparison against a variety of suspensions. The results show that the active TID suspension can change the actuator inertia from a harmful to a favourable factor, greatly improve the ultimate capacity of the suspension, and improve vehicle comfort without changing the tire load.

Design of Static Output Feedback Controllers for an Active Suspension System

This paper presents a method by which to design linear quadratic (LQ) static output feedback (SOF) controllers with a 2-DOF quarter-car model for an active suspension system. Generally, it is challenging to implement linear quadratic regulator (LQR), designed with a full-car model, in actual vehicles because doing so requires 14 state variables to be precisely measured. For this reason, LQR has been designed with a quarter-car model and then applied to a full-car model. Although this requires far fewer state variables, some of them are still difficult to measure. Thus, it is necessary to design a LQ SOF controller which uses available sensor signals that are relatively easily measured in real vehicles. In this paper, a LQ SOF controller is designed with a quarter-car model and applied to a full-car model for ride comfort. To design the controller, an optimization problem is formulated and solved by a heuristic optimization method. A frequency domain analysis and a simulation with a simulation package show that the proposed LQ SOF controllers effectively improve the ride comfort with an active suspension system.

Investigation of Vibrations Energy Harvesting from Passive Car Suspension Using Quarter Car Model Under Bump Excitation

This paper aims to evaluate the voltage and the electrical power harvested from the car suspension system under bump excitation using a piezoelectric stack. For this purpose, a quarter car system equipped with a piezoelectric stack installed parallel to the suspension's damper is modelled and investigated in temporal domain using MATLAB/Simulink. The studied system is excited, considering different bump amplitudes to evaluate the harvested voltage and power at different speeds. The effect of the suspension's damping coefficient on the harvested voltage and power is also studied and quantified.

Fuzzy control of active suspension system based on quarter car model

In this paper, the performance of model-free intelligent Fuzzy Controller analyzed with the model-based conventional controller concerning body displacement and body acceleration. The development of a mathematical model for active suspension is quite difficult which increases the difficulty of designing a model-based controller for active suspension. So, the model-free intelligent adaptive fuzzy controller has been proposed for active suspension. The Fuzzy Controller predicts and controls the performance of active suspension better than a conventional controller. The results obtained from the simulation of the road profile show that the proposed fuzzy control performs better than the conventional controller in terms of body displacement and body acceleration.

Ride comfort investigation of semi-active seat suspension integrated with quarter car model

A method for parameter identification of the magnetorheological damper (MRD) model with an improved firefly algorithm (IFA) is proposed, and a semi-active seat control system with three-degree-of-freedom (3-DOF) is established by combining with a quarter car model to investigate the ride comfort. The dynamic characteristics of the MRD were analyzed by experimental method. Combined with the IFA, the parameters of the MRD phenomenon model were identified, and the forward model of the MR damper was constructed. The semi-active control model of a 3-DOF seat suspension was established. The MRD controller and suspension system controller were designed. The passive control, PID control, and Fuzzy-PID control on the vibration reduction of the semi-active seat suspension were compared and analyzed, under different road excitation. The simulation results show that the semi-active seat suspension controlled by the PID and Fuzzy-PID can effectively reduce the seat acceleration and dynamic stroke, which significantly improve the ride comfort and operation safety compared to the passive seat suspension.

Structural and dynamic analysis of automotive quarter car model suspension system for different materials

The suspension system is a group of mechanical components that links the wheels to the frame or chassis. Suspension systems have received a significant deal of engineering attention as part of an ongoing effort to improve vehicle ride and handling as well as passenger comfort and safety. As the noise, vibration and harshness (NVH) issues are at the forefront of the customers perspective, the vehicle comfort and stability have been considered. In the passenger four-wheelers, shock absorption and vibration due to random excitation are prevalent. The suspension effects play a major role in absorbing the shocks. Hence, this work attempts to model a car suspension and analyzed the dynamic behaviour due to external excitation forces. Among the investigated materials, the epoxy based composites ended-up with the larger deformations and higher stresses compared to the aluminium and steel.