Suspension Damping Research Articles

Uncertainties Investigation and µ-Synthesis Control Design for a Full Car with Series Active Variable Geometry Suspension

Linear robust control schemes, for example the H∞ control, are commonly utilized in the control design of an active suspension system, with a linearized and time-invariant state-space model of the system adopted. However, the vehicle parameter uncertainties are mainly ignored and their effect on the control robustness is not investigated. In this paper, a µ-synthesis-based control scheme is synthesized for a full car with the recently introduced Series Active Variable Geometry Suspension (SAVGS), to mainly enhance the ride comfort and road holding performance, with two significant practical uncertainties in the sprung mass and the suspension damping taken into account. Numerical simulations with a high fidelity nonlinear vehicle model are performed, with the cases of the fixed and swept values of the sprung mass tested, to assess the control robustness and performance of the developed scheme against the passive suspension as well as the H∞ -controlled SAVGS. The proposed µ-synthesis control scheme is proved to be more effective for realistic applications as it is capable of maintaining the suspension performance improvement regardless of variations of system parameters associated with the uncertainties, while the H∞ control performance tends to deteriorate when a notable deviation from the nominal values occurs.

Multi-objective optimization of a sports car suspension system using simplified quarter-car models

In this paper, first, the vibrational governing equations for the suspension system of a selected sports car were derived using Lagrange's Equations. Then, numerical solutions of the equations were obtained to find the characteristic roots of the oscillating system, and the natural frequencies, mode shapes, and mass and stiffness matrices were obtained and verified. Next, the responses to unit step and unit impulse inputs were obtained. The paper compares the effects of various values of the damping coefficient and spring stiffness in order to identify which combination causes better suspension system performance. In this regard, we obtained and compared the time histories and the overshoot values of vehicle unsprung and sprung mass velocities, unsprung mass displacement, and suspension travel for various values of suspension stiffness (KS ) and damping (CS ) in a quarter-car model. Results indicate that the impulse imparted to the wheel is not affected by the values of CS and KS . Increasing KS will increase the maximum values of unsprung and sprung mass velocities and displacements, and increasing the value of CS slightly reduces the maximum values. By increasing both KS and CS we will have a smaller maximum suspension travel value. Although lower values of CS provide better ride quality, very low values are not effective. On the other hand, high values of CS and KS result in a stiffer suspension and the suspension will provide better handling and agility; the suspension should be designed with the best combination of design variables and operation parameters to provide optimum vibration performance. Finally, multi-objective optimization has been performed with the approach of choosing the best value for CS and KS and decreasing the maximum accelerations and displacements of unsprung and sprung masses, according to the TOPSIS method. Based on optimization results, the optimum range of KS is between 130 000–170 000, and the most favorable is 150, and 500 is the optimal mode for CS .

Pneumohydraulic spring with adaptive self-adjusting damper for suspension of a high-speed tracked vehicle and its calculation procedure

Currently, a further increase in the mobility of high-speed vehicles is largely limited by the existing suspension systems, which mainly have unregulated characteristics, and the developed adjustable suspension systems with external control are very complex, expensive and less reliable. Therefore, the development of relatively simple and reliable self-adjusting suspensions for high-speed machinery is an urgent task. At the Department of Automatic Installations of Volgograd State Technical University an original design of an air-hydraulic spring (AHS) with an adaptive self-regulating damper for suspension of a high-speed tracked vehicle (HSTV) was developed. A feature of its adaptive damper is the provision of a two-stage inelastic resistance depending on the amplitude, frequency and direction of oscillation, which can significantly reduce the acceleration of the «shaking» and heating of AHS when the HSTV moves along small irregularities, as well as practically eliminate suspension breakdowns when large vertical and angular vibrations occur at the vehicles body when driving on large bumps or springboards with a takeoff of the rollers from the supporting surface. These modes of operation are ensured by installing two spring-loaded step plungers in the serial AHS body, which in a static position and with small spring lift open an additional throttle channel, which significantly reduces the inelastic resistance of the suspension, and at large strokes they block this channel, thereby significantly increasing damping fluctuations. Due to the fact that these plungers are equipped with a system for delaying their movement in the opposite direction, the increased resistance is maintained for several periods of oscillation. The article also presents an engineering methodology and a numerical example of determining the parameters of the main elements of an adaptive self-regulating damper, the elastic and damping characteristics of the AHS taking into account the operation of the pressure relief valve and the rebound check valve.

An adjustable damper for cab suspension

An adjustable damper for cab suspension

LMI-based designs for robust state and output derivative feedback guaranteed cost controllers in reciprocal state space form

In some practical problems, state derivative variables are more easily obtained than state variables. Solution of guaranteed cost control problem using derivative feedback for continuous, linear time-invariant systems in Reciprocal State Space form with or without polytopic uncertainties, is presented in this paper. Sufficient conditions on stability and performance are derived in terms of Linear Matrix Inequalities. State derivative and output derivative feedback gain matrices are found to minimise non-standard quadratic cost. Vibration attenuation performance of the proposed controllers are examined on an active suspension of a car seat example in the presence of suspension damping element failure. Numerical simulation results verify the superiority of guaranteed cost robust derivative feedback controllers over existing derivative feedback linear quadratic regulator controllers which are given in literature.

Interaction between asymmetrical damping and geometrical nonlinearity in vehicle suspension systems improves comfort

This work explores the role of asymmetrical damping and geometrical nonlinearities in the suspension system of a simplified vehicle model in order to improve comfort. Improving comfort for passengers is a constant challenge for the automotive industry. Although technologies have been introduced for this purpose, many vehicles still use suspension systems which are less effective in vibration isolation due to cost restrictions. To improve comfort at relatively low cost, the use of asymmetrical suspension dampers has been explored. It has been shown that different asymmetry ratios can be advantageous to improve comfort at different frequency ranges. Models which include the suspension geometry can help to better understand the vehicle dynamical response, as it also depends on the geometrical arrangement of its components. As a contribution to the current literature, this paper proposes a study on asymmetrical damping considering a Double Wishbone suspension geometry. A nonlinear single-degree-of-freedom system subject to harmonic base excitation is used. The combination of asymmetry and geometry nonlinearities is investigated for varying asymmetry ratio, geometrical parameters and vehicle velocity. The numerical and experimental results show that the geometrical nonlinearity induces changes in the spring and damping forces because of different inclinations of the spring–damper assembly during expansion and compression, resulting in changes in acceleration amplitude and resonance frequency. This effect is superimposed on the effect of asymmetrical damping coefficient alone, ultimately influencing the acceleration of the suspended mass. Therefore, these two effects must be considered carefully when designing a suspension system with comfort criteria.

Optimal response of half car vehicle model with sky-hook damper based on LQR control

This paper addresses the problem of determining the optimal parameters of a sky-hook damper type suspension in the control of the stationary response of half car vehicle models traversing a rough road. The optimal values of the sky-hook damper suspension parameters are obtained by equating the active suspension control force using linear quadratic regulator (LQR) with that of the sky-hook damper suspension force. Results show that the performance of half car model with optimal sky-hook damper suspension is almost close to the performance of half car model with LQR control.

Critical points numerical analysis of ride comfort of the flexible railway carbody

Ride comfort is one of the criteria for evaluating the dynamic behaviour in railway vehicles, through which the complex sensation triggered by the vibrations in the railway vehicle carbody upon passengers is being described. The behaviour of vibrations along the vehicle carbody is not uniform and the point where the ride comfort is the least convenient can be considered as the carbody critical point. The paper examines the ride comfort along the carbody and the position of the ride comfort critical points in correlation with the speed, carbody flexibility and suspension damping. To this purpose, there are used the results from numerical simulations regarding the ride comfort index calculated along the carbody and the ride comfort index in three points deemed relevant in terms of evaluating the ride comfort at the center of carbody and above the bogies.

The Effect of Masses in the Determination of Optimal Suspension Damping Coefficient

The proper design of the suspension damper determines the ride quality and road holding performance of the suspension system against the road excitation. The objective of the present study is to investigate the effect of both sprung and unsprung masses on the root-mean-square vertical acceleration experienced by the occupants to determine the optimal value of the damping coefficient. Road excitation, 2-DOF mathematical model, and ISO 2631 weighting function were numerically modelled into three different cases in Matlab platform. The responses in root-mean-square value of acceleration were then evaluated. Further, the results were compared and the analysis was performed to determine the optimal value of the damping coefficient for the proposed suspension model. The obtained results indicate that varying the sprung masses with the proportional value of unsprung masses does not affect the root-mean-square value, but it increases the value of optimum damping coefficient by 131.5 Ns/m. Making the sprung mass constant increases the root-mean-square value by 0.005 m/s2 for each chosen unsprung mass. However, fixing the unsprung mass influences both acceleration and the value of damping coefficient.

The Effect of Masses in the Determination of Optimal Suspension Damping Coefficient

The proper design of the suspension damper determines the ride quality and road holding performance of the suspension system against the road excitation. The objective of the present study is to investigate the effect of both sprung and unsprung masses on the root-mean-square vertical acceleration experienced by the occupants to determine the optimal value of the damping coefficient. Road excitation, 2-DOF mathematical model, and ISO 2631 weighting function were numerically modelled into three different cases in Matlab platform. The responses in root-mean-square value of acceleration were then evaluated. Further, the results were compared and the analysis was performed to determine the optimal value of the damping coefficient for the proposed suspension model. The obtained results indicate that varying the sprung masses with the proportional value of unsprung masses does not affect the root-mean-square value, but it increases the value of optimum damping coefficient by 131.5 Ns/m. Making the sprung mass constant increases the root-mean-square value by 0.005 m/s2 for each chosen unsprung mass. However, fixing the unsprung mass influences both acceleration and the value of damping coefficient.

An Innovative Design of Magnetorheological Lateral Damper for Secondary Suspension of a Train

This article delivered an innovative idea of a magnetorheological (MR) damper for secondary suspension of train bogie. The valve inside MR damper adopted meandering of both fluid flow and magnetic flux for improving magnetization area. In this work, the design and working principle of the MR valve were presented including a mathematical model to predict the pressure drop. In the early stage, the finite element method magnetics software (FEMM) simulation could predict the magnetic flux density across the passages. Based on the amount of magnetic flux, the corresponding shear yield stress could be determined from its basic physical properties. The mathematical model covered pressure drop prediction for both off-state and on-state. The FEMM simulation results showed that the meandering flow and serpentine flux design could improve the effective area of magnetization. Consequently, the pressure drop of the valve could have wider ranges and achieve a high value of pressure differences. This result could be potentially improving the performance of the damping forces of the lateral damper in a bogie train.

Lyapunov Exponents of Early Stage Dynamics of Parametric Mutations of a Rigid Pendulum with Harmonic Excitation

This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions.

Numerical study on the influence of suspension damping on the bogie vertical vibration

The paper presents a study on the influence of suspension damping (SD) on bogie vertical vibrations generated by vertical track irregularities. The study is based on the results of the numerical simulations developed on the basis of a linear model with seven-degree of freedom of the bogie-track system, that takes into account the rigid vertical vibration modes of the bogie – bounce and pitch, vertical displacements of the wheels and rails, and the wheel-rail contact elasticity. The bogie vibration behaviour is assessed based on the dynamic response of the bogie chassis, expressed as the power spectral density of the vertical acceleration (PSD acceleration) at three reference points – at the bogie chassis centre and over the axles, and root mean square of vertical acceleration (RMS acceleration). It is highlighted the main characteristics of the bogie vibration behaviour according to the SD in correlation with the speed and quality of the railway track.

Vertical bending vibration analysis of the car body of railway vehicle

The paper features the analysis of the symmetrical vertical bending of the car body railway vehicle, when vehicle is running along on a track with vertical irregularities described in the form of the power spectral density (PSD). The analysis relies on the numerical simulations results, developed based on a rigid-flexible coupled vehicle model, with seven-degree freedom, where the car body is modelled as an Euler-Bernoulli type equivalent beam. The vibration behaviour of the car body is evaluated based on the PSD of the car body acceleration (PSD acceleration), calculated at the car body centre and above the bogies. The main characteristics of the car body bending vibration are pointed in correlation with velocity, the secondary suspension damping and the car body elasticity characteristics.

Energy-harvesting variable/constant damping suspension system with motor based electromagnetic damper

Energy-harvesting suspension is very important to improve the energy efficiency of vehicles, especially for electric vehicles. A novel energy-harvesting variable/constant damping suspension system with motor based electromagnetic damper is proposed in this paper. The method attempts to make following contributions: The vehicle vibration energy is not only harvested from the suspension system, but also controlled to store in the battery for further usage. Moreover, the damping of the suspension system is able to be controlled as wish, to be constant or to vary with road conditions. The performance comparison with conventional suspension equipped with an oil damper is carried out by simulation and experiments. The effect of the moment of inertia on the suspension performance is investigated. To experimentally validate the proposed method, a scaled quarter car suspension validation platform is established. The experimental results show that the damping can be controlled to be constant as the conventional oil damper, and also be variable as wish. The proposed energy-harvesting suspension can recover energy from vehicle vibration to store in the battery for further usage with high efficiency, which is as high as 35.24% improvement compared with previous studies. Meanwhile, the damping coefficient can also be regulated in real-time accurately.

Stability Analysis of Magneto-Rheological Damper for Suspension of Commercial Vehicles

This paper aims at improving the efficiency of magneto-rheological dampers, which utilizes a smart material in the form of magneto-rheological fluid, over the typical-build conventional dampers. The proposed design has been modeled for its implementation in commercial vehicles which extensively relies on conventional shock-absorbers for the safety and comfort of its occupants, considering the space available for mounting the system. Dimensional constraints based on commercial vehicles pertaining to the hatchback segment have been taken in COMSOL® and analyzed to generate a considerable amount of damping force for realizable inputs. As the analysis requires a profound consideration of highly coupled physics interface, COMSOL® Multi-physics is chosen as the relevant platform which makes it suitable to fulfill the criteria at hand. The damping forces achieved in the model are determined based on the linear Bingham model and the non-linear hysteretic Bou c-Wen model. A rigorous analysis was conducted to realize the variation in damping force values on account of the hysteresis losses induced in the system. Optimization based on Taguchi’s mixed level design approach is used to attain the optimal design parameters of MR damper. MRF-140 CG fabricated by Lord Corporation is adopted to introduce the rheological effect of MR fluid on the proposed model.

Dynamic characteristics analysis of nonlinear suspension system of automobile with seven degree of freedom

The application of MATLAB/SIMULINK to establish the mechanical simulation model of seven-degree-of-freedom vehicle linear and non-linear suspension system. Realization of system response under simulated road excitation, the dynamic characteristics of the non-linear suspension are studied, the non-linear spring and damping are simulated, and the parameter ε is introduced to change the degree of nonlinearity. The root mean square values of acceleration and displacement of linear suspension, non-linear stiffness suspension and non-linear damping suspension are analyzed and compared under different pavement conditions. The results show that: The mean square root of the acceleration of the body mass center and the pitch angle of the non-linear suspension are reduced by 14.3% and 17.0% respectively compared with the linear acceleration of the body mass center and the pitch angle; The root mean square value of pitch acceleration of non-linear suspension damping is 31.2% less than that of linear acceleration, which improves ride comfort and safety to a certain extent.

Torque response characteristics of a controllable electromagnetic damper for seat suspension vibration control

Abstract In this paper, a novel resistance switching method is proposed to control an electromagnetic damper (EMD) system of a vehicle seat suspension, and torque response characteristics of the EMD system are investigated in detail. First, the relationship between electromagnetic torque and circuit resistance of the EMD system is established. The basic parameters of the EMD system are identified by least squares fitting, and the resistance distribution is optimized to meet the demand damping of seat suspension. Second, the electromagnetic torque response time and the continuously dynamic torque tracking performance of the EMD system are investigated experimentally. The time required for the torque change from its initial to 80% of the final state and the final state is measured, respectively. The results show that the response time required for torque decrease is shorter than the response time required for torque increase; the EMD system has excellent torque response and torque tracking performance and is suitable for seat suspension vibration control. Finally, two typical vehicle body vibration excitations are exerted on the EMD seat suspension. The test results verify that the EMD seat suspension has excellent controllable damping and can significantly isolate the vibration of driver body when applying a sliding mode control method.

Modeling and dynamic analysis of a vehicle-flexible pavement coupled system subjected to road surface excitation

Increased road traffic combined with heavy vehicle loads leads to deterioration of pavements and reduces the life span of the paved roads. As a result, large amounts of financial resources are spent each year to improve and maintain road infrastructure around the world. Vehicle dynamics and pavement dynamics are strongly coupled through their contact points. This research focuses on the dynamic analysis of pavement-vehicle interaction system and the effect of coupling action on the response. The system response due to the moving vehicular load on rough road supported by a linear visco-elastic foundation was investigated. The vehicle is modeled as a two-degree-of-freedom quarter-vehicle model, and the pavement-foundation system is described by a simply supported Euler-Bernoulli beam resting on Pasternak foundation, while the tire is coupled to the flexible pavement with a single point contact. Galerkin method was used to develop a system of governing differential equations for a coupled system in the time domain. Direct numerical integration method using Newmark-β based on linear average acceleration method was then used to solve the governing equations and evaluate the response of the coupled system. The results were validated with previous research works and compared with conventional uncoupled systems. Finally, the effects of parameters such as vehicle speed, road roughness, soil stiffness and suspension damping on the responses were investigated.

Modeling and Control of a Shear-Valve Mode MR Damper for Semiactive Vehicle Suspension

Aiming at demonstrating the feasibility and capability of applying magnetorheological (MR) dampers to the vehicle vibration control, the hyperbolic tangent model is established to characterize the performance of a shear-valve mode MR damper that was developed for a vehicle suspension system in this study. An experimentally derived differential evolution (DE) algorithm is used to find the optimal parameters of the model. To demonstrate the effectiveness of the MR damper for semiactive suspension systems, a model was constructed of a quarter-car suspension system with the damper. A fuzzy control algorithm with a correction factor was adopted to control the output force of the damper and obtain better overall control of the performance of the suspension system. Simulation results indicate that the improved fuzzy control algorithm provides a better ride comfort than normal fuzzy control and passive control. Furthermore, the semiactive suspension system displayed effectively vibration suppression thanks to the MR damper combined with corresponding control algorithms.