Quarter-car Suspension Model Research Articles

IMPACT OF SHOCK ABSORBERS QUALITY ON THE SAFETY OF CAR PASSENGERS AND CARGO

The analysis of impact of properly operating shock absorbers having a substantial influence on the vehicle safety is a main issue of this paper. A "Quarter-car suspension model" has been used in creating mathematic model for dynamic processes analysis – system of differential equations. The dynamic processes taking place in the wheel suspension has been mathematically described using Quarter-car suspension model. A system of differential equations has been created and applied for programming Scilab Xcos. The results of modeling were verified by performing practical performance using automobile Volvo S80. The results of process modeling and practical car braking using shock absorbers of various quality evidently show the importance of their quality and significant impact on vehicle stability on the road. The simulation, applying Scilab X cos system allows to conclude that the mechanical oscillations during the braking process are quite significant (oscillation amplitude from 0.2, 0,1 m through 3 s period). In case of shock absorber malfunctioning the process simulation, when the damping force of the suspension system was 10 times reduced, the amplitude of moving masses grows up about twice and the period of oscillations lasts more than 3,5 times longer. That allows us to predict that these parameters could expand a braking time up to 20% - 30%, thus affecting the wheel's clamping force and, at the same time, the wheel's adhesion to the road. These factors directly affect the length of the braking distance, as well as the stability of the car's movement in the turn. Because, the results of practical measurements, proved the shock absorbers quality influence on so important parameters like vehicle stopping time and distance, quite often defining the vehicle safety on the road it‟s reasonable to stress on the importance of more strict technical quality control of shock absorbers.

Design and evaluation of self-tuning optimal control for vibration suppression of magnetorheological semi-active suspension

The objective of this paper is to enhance the vibration damping capabilities of magnetorheological (MR) semi-active suspension by utilizing a self-tuning LQG control method. Firstly, to determine the mechanical model of MR damper using the hyperbolic tangent model, mechanical experiments were performed with a damping force test machine under various input excitations. Experimental and simulation data were compared to confirm the accuracy of the mechanical model for MR damper. The MR damper is then incorporated into the vehicle’s semi-active suspension system to create a quarter-car suspension model. In order to tackle the problems associated with low control accuracy and poor dynamic adjustment in traditional LQG controllers where the weighting matrix coefficients are difficult to determine, a self-tuning LQG controller based on gravity search algorithm (GSA-LQG) was designed. Finally, the designed controller performance was evaluated by the simulation and experimental results obtained from the random and sinusoidal excitation roads. Experimental data reveal that when subjected to GSA-LQG control, the suspension control performance is considerably enhanced compared to the passive control, PID control and conventional LQG control suspension. Based on these outcome, it can be concluded that the proposed algorithm is effective and the experimental platform is feasible.

Adaptive Control for Suspension System of In-Wheel Motor Vehicle with Magnetorheological Damper

This study proposes two adaptive controllers and applies them to the vibration control of an in-wheel motor vehicle’s (electric vehicle) suspension system, in which a semi-active magnetorheological (MR) damper is installed as an actuator. As a suspension model, a nonlinear quarter car is used, providing greater practical feasibility than linear models. In the synthesis of the controller design, the values of the sprung mass, damping coefficient and suspension stiffness are treated as bounded uncertainties. To take into account the uncertainties, both direct and indirect adaptive sliding mode controllers are designed, in which the principal control parameters for the adaptation law are updated using the auto-tune method. To reflect the practical implementation of the proposed controller, only two accelerometers are used, and the rest of the state values are estimated using a Kalman observer. The designed controller is applied to a quarter car suspension model of an in-wheel motor vehicle featuring an MR damper, followed by a performance evaluation considering factors such as ride comfort and road holding. It is demonstrated in this comparative work that the proposed adaptive controllers show superior control performance to the conventional proportional–integral–derivative (PID) controller by reducing the vibration magnitude by 50% and 70% for the first and second modes, respectively. In addition, it is identified that the second mode (wheel mode) of the in-wheel motor vehicle is more sensitive than the first body mode depending on the mass ratio between the sprung and unsprung mass.

Linear Quadratic Optimal Control with the Finite State for Suspension System

The control algorithm could greatly help the suspension system improve the comprehensive performance of the vehicle. Existing control methods need to obtain the intermediate states, which are difficult to obtain directly or accurately when estimated by filters or observers. Thus, this paper proposed a new practical finite state LQR control method to deal with this problem. By combining with the output state of the finite sensor of the vehicle suspension system and weakening the unknown state as the goal, an optimization model is established with the design variables as the LQR weight coefficients. Then, the direct relationship between the current control input and the finite sensor output is obtained, and the finite state LQR control is realized. Taking the quarter-car suspension model as an example, the corresponding noise is added considering sensor accuracy, and the control performance of the four control methods is studied considering the uncertainties of suspension system parameters. In addition, the acceleration of sprung mass and the dynamic travel coefficient of suspension have been separately calculated by methods of finite state LQR control, LQR control, and PID control. The results show that there is not much difference between them under shock excitation or random excitation. However, the finite state LQR control method has the best comprehensive control performance in that its dynamic tire load coefficient is better than other methods; it could take into account the suspension work stroke coefficient, dynamic tire load coefficient, and sprung mass’ acceleration of the vehicle suspension system at the same time. In order to realize the optimal control effect with limited sensor arrangement, the finite state LQR control method only needs to obtain the current sensor output and the current control input, without estimating the unknown intermediate state. By this means, the proposed control method greatly simplifies the design of the control system and has great advantages on practical value.

Vehicle Suspension System with Integrated Inerter - Extended Analysis

Inerter devices are used in Formula 1 vehicles for a decade to reduce vertical and rolling displacement at the corner of the sharp racing curves and provide higher tire grip on racing challenges. To improve dynamics Formula SAE Car, several topological designs for suspension system are already proposed and published [1]. Based on our passive suspension system for quarter-car model, we carried out analysis for different parameters and under the impact from the road disturbance and demonstrated when integrated inerter device can increase ride comfort and decrease vertical displacement. Proposed solution system with integrated inerter mechanism can improve vehicle suspension systems development and have effects on dynamics and stability of a vehicle.

Influence of bushing flexibility and its constitutive behavior on the performance of suspension system

We study the effect of strut top mount bushing flexibility and its constitutive law on the ride comfort performance of a quarter car suspension model. A fractional Kelvin–Voigt model has been employed to capture the viscoelastic behavior of the top mount bushings. To study the effectiveness of the suspension system, we have considered sinusoidal and standard (motion over bumps) road inputs. For the sinusoidal input, the frequency response function for both the traditional and fractional Kelvin–Voigt models has been obtained using the harmonic balance method. However, we have resorted to numerical simulations for the standard base inputs for which a reduced-order system of ODEs has approximated the fractional derivative term. Convergence of the reduced system of ODEs is established by comparing the numerical results for sinusoidal forcing with those obtained analytically. We find that the bushing modeled as a traditional Kelvin–Voigt element increases the response amplitude in the resonance zone, while for higher frequencies, the response reduces. Hence, the inclusion of bushing flexibility is equivalent to decreasing the damping in the suspension. These observations also remain valid for the fractional Kelvin–Voigt model, but the effect is less pronounced than in the traditional model. Ride comfort for standard road profile is studied in terms of performance indices which suggests that a fractional Kelvin–Voigt bushing improves the ride comfort. Accordingly, bushing flexibility with an appropriate constitutive law should be accounted in the design of a suspension system for ride comfort. • Effect of strut top mount bushing (STMB) flexibility on ride comfort is studied. • Fractional Kelvin–Voigt model is employed for the viscoelastic behavior of the STMB. • Studied the suspension system response on sinusoidal and standard road inputs. • Ride comfort has been studied in terms of transmissibility and performance indices. • We find that STMB flexibility improves ride comfort especially during transient loads.

Multi-objective H2/H∞ control of uncertain active suspension systems with interval time-varying delay

The vehicle active suspension has been widely used as it could effectively improve the vehicle ride comfort. To solve the issues of actuator uncertainty and time delay existing in the active suspension system, a multi-objective non-fragile [Formula: see text] control algorithm is proposed in this work. First, to effectively describe the vehicle suspension dynamics, a quarter-car suspension model is constructed first in this study. Second, aiming at improving the ride quality and guarantee the hard constraints of the suspension system, a multi-objective H2/ H∞ performance index is proposed. Subsequently, the issues of external disturbances, actuator uncertainty and delay are considered in the design process of the suspension controller. Then, a multi-objective non-fragile control algorithm is proposed based on an effective Lyapunov functional. The control gain can be obtained by solving a convex optimization problem in terms of linear matrix inequalities. Finally, numerical simulations are implemented on MATLAB/Simulink platform to show the robustness and superiority of the proposed controller. Experiments are implemented on a quarter-car test rig to validate the practical performance of the designed controller.

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

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.

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.

A Methodology to Investigate Powered Two-Wheeler Rider’s Comfort over Road Sections with Skew Superelevation

The proper surface water drainage not only affects vehicle movement dynamics but also increases the likelihood of an accident since inadequate drainage is associated with potential hydroplaning and splash and spray driving conditions. Nine solutions have been proposed to address hydroplaning in sections with inadequate drainage e.g. augmented superelevation and longitudinal slope, reduction of runoff length, and skew superelevation. The latter has been extensively implemented in highways recently, enhancing the safety level in the applied road segments regarding the effective drainage of the rainwater. However, the concept of the skew superelevation has raised concerns regarding the level of driver’s comfort when traveling over skew superelevation sections particularly with high speeds. These concerns were alleviated through the concept of the round-up skew superelevation which reduces both the lateral and the vertical acceleration imposed on the drivers and hence, improves comfort and traffic safety. The present study investigates the behaviour of power two-wheeler riders since they are susceptible to any changes on the pavement surface and therefore a comparison between the traditional superelevation practice and the skew superelevation concept is of paramount importance. The methodology is based on the utilization of sophisticated software to design the model of the road for several values of longitudinal slopes. Based on the values of the slopes and the use of mathematical equations, the accelerations imposed on the wheel of the motorcycle were calculated. Since the final aim of the study is the influence of the skew superelevation to the rider, it was deemed necessary to convey the calculated accelerations from the wheel to the rider. That was accomplished by implementing the quarter car suspension model adjusted to the features of two-wheeler vehicles. Finally, the accelerations derived from this process evaluated according to specific thresholds based on the literature which correspond to certain levels of comfort. The most important conclusion drawn is that the comfort of the riders is not dependent to a great extent on the form of the road gradient because the vertical acceleration imposed on the riders took similar values regardless of the value of the longitudinal slope.

Combined Input–Output Finite-time Stability with H∞ Static Output-feedback Control Approach for Active Suspension

Combined input–output finite-time stability condition with static output-feedback H ∞ control is proposed in this work to effectively attenuate the short-duration road disturbance. The control problem is formulated based on the pre-defined condition of input–output finite-time stability with H ∞ bound along with pre-established quarter-car active suspension model. Then, a feasible static output-feedback controller is designed via variable substitution approach and linear matrix inequalities. Output-feedback control’s initial infeasibility issue is solved by state-feedback technique. The controller is specifically designed for the system which exposed with short-duration exogenous disturbances hence, this work prefers finite-time approach instead Lyapunov asymptotic stability condition. To enumerate the significance of the proposed controller numerical examples are presented and its response is effectively analyzed in distinct domains (time and frequency). The theoretical results denote that the combined input–output finite-time stability condition with static output-feedback H ∞ control can enhance the vehicle performance better when compared with passive and conventional static output-feedback control scheme. Additionally, the controller robustness is verified.

Analysis of a quarter car suspension based on a Kelvin–Voigt viscoelastic model with fractional-order derivative

The dynamical analysis of a quarter car suspension based on the Kelvin–Voigt​ viscoelastic model with fractional order derivative is analytically and numerically studied in this paper. Depending on the non-dimensional quadratic stiffness parameter, the potential configuration associated with the system under study is possible to obtain monostable and, asymmetric bistable configurations. Thanks to the multiple time scale method, the effects of viscoelastic parameters on the vibration amplitude of the quarter car suspension model are analytically investigated and the numerical simulations confirmed the analytical results. Moreover, the vibration amplitude of the quarter car suspension model can display periodic and dissipative chaotic behaviors by varying the non-dimensional quadratic stiffness, the fractional-order, and the road profile parameters. One scroll and double scroll chaotic attractors are generated by varying the non-dimensional quadratic stiffness parameter. Finally, the threshold conditions for the appearance of homoclinic bifurcation (left well and right well) in the case of asymmetric bistable potential are investigated using Melnikov’s criterion. Melnikov’s predictions are validated numerically by using the basin of attraction of initial conditions. It is found that the decrease of fractional order contributes to increasing the regular motion domain up to a critical value of the fractional-order and after it, decreases rather.

Estimation of Tire Normal Forces including Suspension Dynamics

Tire normal forces are difficult to measure, but information on the vehicle normal force can be used in many automotive engineering applications, e.g., rollover detection and vehicle and wheel stability. Previous papers use algebraic equations to estimate the tire normal force. In this article, the estimation of tire normal force is formulated as an input estimation problem. Two observers are proposed to solve this problem by using a quarter-car suspension model. First, the Youla Controller Output Observer framework is presented. It converts the estimation problem into a control problem and produces a Youla parameterized controller as observer. Second, a Kalman filter approach is taken and the input estimation problem is addressed with an Unbiased Minimum Variance Filter. Both methods use accelerometer and suspension deflection sensors to determine the vehicle normal force. The design of the observers is validated in simulation and a sensitivity analysis is performed to evaluate their robustness.

Vibration control of vehicle suspension with magneto-rheological variable damping and inertia

To avoid the limitation of conventional vehicle magnetorheological (MR) suspension, a variable damping and inertia device is applied in the vehicle suspension with MR technology. A semi-active adaptive MR inerter (AMRI) is discussed. A quarter car suspension model with an AMRI installed in parallel with a double-ended MR damper (D-MRD) is considered. First, the vehicle suspension with variable damping and inertia is analyzed. The prototype of D-MRD and MR variable inertia flywheel (MRVIF) are fabricated and tested respectively. Then, the control model of D-MRD and MRVIF is developed on the basis of test data. An improved Fuzzy PID controller for the semi-active suspension with D-MRD and AMRI is formulated. Numerical simulation is investigated to validate the proposed variable damping and inertia device. The results demonstrate that the performance of the semi-active suspension with D-MRD and AMRI can achieve much better ride comfort than the semi-active suspension with only D-MRD or AMRI.

Modeling of Tire Vertical Behavior Using a Test Bench

Tire models are of great importance for precise investigations of vertical vehicle dynamics, including vehicular safety and riding comfort. An adequate modeling of the tire is crucial to properly reproduce vehicle vertical behavior in simulations and to evaluate the influence of the tire in the overall performance of the suspension system. This paper introduced vehicle single-point tire models and, thereafter, investigated the influence of the excitation frequency and inflation pressure on the damping and stiffness coefficients of the proposed tires experimentally. In this manner, a test-bench was used to obtain the model parameters of a light vehicle tire and a motorcycle tire. Given the obtained results, it has been observed that both factors have a significant effect on the parameters of the proposed tire models. Moreover, a quarter car suspension model was investigated using the modelled tires to illustrate the influence of the correct characterization of the tire on the vertical suspension performance.

Adaptive fault-tolerant control for active suspension systems based on the terminal sliding mode approach

In this paper, a control system is designed for a vehicle active suspension system. In particular, a novel terminal sliding-mode-based fault-tolerant control strategy is presented for the control problem of a nonlinear quarter-car suspension model in the presence of model uncertainties, unknown external disturbances, and actuator failures. The adaptation algorithms are introduced to obviate the need for prior information of the bounds of faults in actuators and uncertainties in the model of the active suspension system. The finite-time convergence of the closed-loop system trajectories is proved by Lyapunov's stability theorem under the suggested control method. Finally, detailed simulations are presented to demonstrate the efficacy and implementation of the developed control strategy.

Sliding Mode Controller for Different Road Profiles of Active Suspension System for Quarter-Car Model

The main purpose of the vehicle suspension system is to induce more comfortable riding and well handling with the road inputs. The principal objective of this research paper is to reduce vibration and improve passenger comfort of car suspension through the sliding mode controller. The mathematical model of passive and active suspensions mechanism for a quarter car model that subjects to excitation from road profiles is obtained. The active suspension system is developed through sliding mode control for a quarter car model. The performance of the sliding mode control is evaluated through a simulation approach using MATLAB and SIMULINK toolbox. The simulated results plotted in the time domain and root mean square values. It is concluded that the active suspension using a sliding mode controller improves the ride comfort and reduces vibration.