Vehicle Body Vertical Acceleration Research Articles

Enhanced dynamic performance of a half-vehicle system using inerter-based nonlinear energy sink

An inerter is introduced in the traditional nonlinear energy sink (NES) to replace its mass and constitutes the novel inerter-based nonlinear energy sink (INES). The INES combines the mass amplification effect of the inerter and the vibration dissipation effect of the NES, which satisfies the lightweight design requirement and further mitigates the vibration of the main structure. Here, the INES is applied in the half-vehicle system to investigate its dynamic performance both in the vertical and pitching directions. The dynamic model of the half-vehicle system coupled with INES is established, the harmonic balance method (HBM) and pseudo arc length method (PALM) is used to obtain its dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and shock excitations is evaluated using six performance indices, which considers the vertical and pitching vibrations of the vehicle body, suspension deflection, and road holding; the vibration suppression effect of the INES and traditional NES is compared. The results show that the traditional NES can enhance the dynamic performance of the half-vehicle system slightly at the cost of a very large mass, which violates the vehicles’ lightweight design and cannot be realized in the practical engineering. For road harmonic excitation, using the INES can obtain a better dynamic performance for the front and rear suspension deflections, front and rear dynamic tire loads, vehicle body vertical acceleration in high vehicle velocity, while the vehicle body pitching acceleration is larger. For road shock excitation, applying the INES can improve the shock performance for the front and rear suspension deflections, front and rear dynamic tire loads, while the peak values of the vehicle body vertical and pitching accelerations are larger. Therefore, the INES integrates the benefits of the inerter and NES and provides a new vibration attenuation device design in the vehicle engineering.

Dynamic Vehicle and Rigid Road Interaction Analysis and Vibration Control of the Quarter Car Model Using Adaptive Neuro Fuzzy Algorithm

In this study 3-DOF quarter car model with the three bumps on the rigid road, the assumption has been modeled with the non-random irregularity. To reduce the excessive vibrations occurred on the vehicle body, an active suspension system with the linear actuator has been considered. Moreover, to control this actuator, an adaptive neuro-fuzzy algorithm is designed. The training and testing data of the ANFIS has been obtained from Proportional Integral Derivative (PID) control algorithm. After that the successful training process, a testing procedure has been applied to ANFIS for the measure of the adaptive neuro-fuzzy system with data that are not considered in the training process. Then, the performance of the ANFIS is compared by the PID algorithm and passive suspension system in terms of vehicle body vertical acceleration, vehicle body vertical displacement, and control force. The road model used in the study has been modeled according to non-random road profile mathematical formulation considering periodical and discrete road profile cases. In this formulation, one can easily determine the height, width, and number of the road defect with the series mathematical formulation. Consequently, with the results obtained from the presented study, it is proven that ANFIS is a very effective controlling algorithm to suppress vibration occurred on the vehicle body due to vehicle road interaction. Furthermore, the performance of the ANFIS has been tested with different parameters, for example, different number membership functions (MF), which used the fuzzification of the input parameters.

Design and multi-objective optimization of magnetorheological damper considering vehicle riding comfort and operation stability

Mostly, magnetorheological (MR) dampers were optimized based on individual performance, without considering the influence of structure parameters change on vehicle performance. Therefore, a multi-objective optimization scheme of MR damper based on vehicle dynamics model was proposed. The finite element method was used to analyze magnetic flux density distribution in tapered damping channel under different structure parameters. Furthermore, the damping force expression of the tapered flow mode MR damper was derived, and the damping force was introduced into the vehicle dynamics model. In order to improve the ride comfort and operation stability of the vehicle, a collaborative optimization platform combining magnetic circuit finite element analysis and vehicle dynamics model was established. Based on this platform, the optimal design variables were determined by comfort and stability sensitivity analysis. The time domain optimization objective and frequency domain optimization objective are proposed simultaneously to overcome the lack of time domain optimization objective. The results show that compared with the time domain optimization and the initial design, the suspension dynamic deflection, tire dynamic load and vehicle body vertical acceleration are decreased after the time-frequency optimization. At the same time, in the frequency domain, the amplitude of vibration acceleration in each working condition is significantly reduced.

Optimal design of the vehicle mechatronic ISD suspension system using the structure-immittance approach

There are three types of two-terminal mechanical elements, namely the inerter, the spring, and the damper in the vehicle ISD suspension system, and how to design the suspension structure has drawn much attention in automotive engineering fields. Due to the advantage of using the external electrical network to simulate the corresponding mechanical impedance output, a ball-screw mechatronic inerter is adopted in the optimal design procedure in this paper. A half vehicle dynamic model considering the vehicle body vertical motion and pitch motion is established, and the optimal design methodology of the vehicle mechatronic ISD suspension is proposed by using the structure-immittance approach to ensure the simplicity of the suspension structures. The dynamic performance indexes constraints are taken into account, and the optimal structures are discussed in detail. Numerical simulations results show that, the dynamic performance indexes, namely the RMS (root-mean square) of the vehicle body vertical acceleration and the RMS of the pitch motion acceleration of the mechatronic ISD suspensions can be reduced by 31% and 35% without constraints, and 18% and 15% with constraints by comparing to the passive suspension system. The structure-immittance approach can be easily adopted in the vehicle suspension structural design, and the research fruits will provide a new thought for the application of the inerter element in automotive engineering.

Research on the mode switching control of vehicle electromagnetic suspension employing linear motor

An electromagnetic suspension employing linear motor is able to harvest the energy otherwise wasted in the suspension vibration while the vehicle is running on rough road. A switch method of operation modes is put forward to coordinate the contradiction between energy regeneration and vibration isolation. A dynamic model is created to analyse the general properties of energy regeneration suspension under different working modes. Both simulation and experiments are conducted to verify the modelling and advantages. In energy regenerative mode, the dynamic properties of electromagnetic suspension are basically coincident with those of passive suspension, and more than 14 W of electricity is harvested while driving at 20 m s−1 on level C road. In active control mode, the RMS of vehicle body vertical acceleration and tyre dynamic load are decreased by 21.35% and 4.24% respectively, much better than passive suspension, which proves that the mode switching method is simple and effective.

Research on the mode switching control of vehicle electromagnetic suspension employing linear motor

An electromagnetic suspension employing linear motor is able to harvest the energy otherwise wasted in the suspension vibration while the vehicle is running on rough road. A switch method of operation modes is put forward to coordinate the contradiction between energy regeneration and vibration isolation. A dynamic model is created to analyse the general properties of energy regeneration suspension under different working modes. Both simulation and experiments are conducted to verify the modelling and advantages. In energy regenerative mode, the dynamic properties of electromagnetic suspension are basically coincident with those of passive suspension, and more than 14 W of electricity is harvested while driving at 20 m s−1 on level C road. In active control mode, the RMS of vehicle body vertical acceleration and tyre dynamic load are decreased by 21.35% and 4.24% respectively, much better than passive suspension, which proves that the mode switching method is simple and effective.

Optimal control and parameters design for the fractional-order vehicle suspension system

In this paper the optimal control and parameters design of fractional-order vehicle suspension system are researched, where the system is described by fractional-order differential equation. The linear quadratic optimal state regulator is designed based on optimal control theory, which is applied to get the optimal control force of the active fractional-order suspension system. A stiffness-damping system is added to the passive fractional-order suspension system. Based on the criteria, i.e. the force arising from the accessional stiffness-damping system should be as close as possible to the optimal control force of the active fractional-order suspension system, the parameters of the optimized passive fractional-order suspension system are obtained by least square algorithm. An Oustaloup filter algorithm is adopted to simulate the fractional-order derivatives. Then, the simulation models of the three kinds of fractional-order suspension systems are developed respectively. The simulation results indicate that the active and optimized passive fractional-order suspension systems both reduce the value of vehicle body vertical acceleration and improve the ride comfort compared with the passive fractional-order suspension system, whenever the vehicle is running on a sinusoidal surface or random surface.

Research on mechanics model verification and skyhook semi-active control of magneto-rheological damper

Aim at the need of vibration attenuation of some light military wheel cross-country vehicle, design valve model magneto-rheological damper (MRD) and deduce its damping force flat model. Conduct performance test of MRD and build relative mechanics model, apply the least square method to verify the model based on three indexes of relative error, relative coefficient and standard deviation. In order to test the performance of vibration attenuation of MRD, conduct platform experiment with the skyhook ON-OFF semi-active control algorithm. The result indicates that the error between the MRD model built and the result tested is small, the MRD can decrease vehicle body vertical acceleration beside vehicle body resonance area effectively, and improve ride comfort under the semi-active control.

A new method of static output-feedback H∞ controller design for 5 DOF vehicle active suspension system

In this paper, the static output-feedback control problem of 5 degrees of freedom (DOF) vehicle active suspension systems is investigated. A novel H∞ optimal controller is designed for this system to improve simultaneously ride comfort and handling ability. The actuator saturation, suspension deflection and tire deflection are considered in the controller synthesis. To minimize the seat acceleration, taking into account the vehicle body vertical acceleration and pitch acceleration, a new method for designing and solving static output-feedback H∞ optimal controllers is proposed. First of all, a 5 DOF half-vehicle active suspension including active seat system model is presented. Then a direct, easily solved and effective method for static output-feedback H∞ optimal control is presented. The controller is obtained by solving linear matrix inequality optimization problem and direct computation of related matrices. Finally, a numerical example is presented. The simulation results show that the controller proposed can achieve better performance compared with state feedback H∞ optimal controller and the validity of the design method is verified.

Ride Comfort Optimization of In-Wheel-Motor Electric Vehicles with In-Wheel Vibration Absorbers

This paper presents an in-wheel vibration absorber for in-wheel-motor electric vehicles (IWM EVs), and a corresponding control strategy to improve vehicle ride comfort. The proposed in-wheel vibration absorber, designed for suppressing the motor vibrations, is composed of a spring, an annular rubber bushing, and a controllable damper. The parameters of the in-wheel spring and rubber bushing are determined by an improved particle swarm optimization (IPSO) algorithm, which is executed under the typical driving conditions and can absorb vibration passively. To deal with negative interaction effects between vehicle suspension and in-wheel absorber, a linear quadratic regulator (LQR) algorithm is developed to control suspension damper, and meanwhile a fuzzy proportional-integral-derivative (PID) method is developed to control in-wheel damper as well. Through four evaluation indexes, i.e., vehicle body vertical acceleration, suspension dynamic deflection, wheel dynamic load, and motor wallop, simulation results show that, compared to the conventional electric wheel, the proposed suspension LQR control effectively improves vehicle ride comfort, and the in-wheel absorber exhibits excellent performance in terms of wheel and motor vibration suppression.

Investigation of Slow-Active Suspension System’s Non-linearity on The Performance of The Anti-lock Brake System

This paper presents an advanced integrated controller design for military vehicle slow-active suspension system and anti-lock brake system (ABS) considering the effect of the suspension components non-linearity on the braking dynamics. The presented investigation is applied to a quarter vehicle model using the Magic Formula tire model and the actual characteristics for suspension damper (throttle valve) and spring (gas spring). The suspension controller is designed based on LQR using a linearized vehicle model and the ABS controller is designed based on ON/OF control methodology using tire skid ratio of 15% as a reference value. The mathematical derivations as well as the control techniques are numerically implemented in MATLAB environment. Several simulation results are carried out considering typical performance measures such as stopping time, stopping distance and vehicle body vertical acceleration. The results illustrated that, the integrated controller reduces the stopping distance on different road surfaces and therefore improves the braking performance to avoid or reduce the impact of vehicle accident.

A Systematic Approach for the Study and Analysis of Vehicle Dynamics Using Design of Experiments

Suspension system design plays an important role in improving passenger comfort and road holding capabilities of the vehicle. The primary function of the vehicle suspension system is to isolate the vehicle body from road surface irregularities as well as to control the body and wheel motions. This study presents the use of analysis of variance (ANOVA) in studying the effects of vehicle design parameters, such as the spring stiffness and the shock absorber damping coefficient on the discomfort parameters which are the vehicle body vertical acceleration (Bac), suspension working space (SWS) and the dynamic tire load (DTL). The model presented in this study is a half vehicle model built in MATLAB/SIMULINK environment, and it is validated with a published work and the comparison shows very good agreement between the two models. Different values of design parameters are used as an input to the vehicle model, and the output data are analyzed using MINITAB 17 software program to plot the main and interaction effect between all design parameters and discomfort parameters. The results show that variation of both suspension stiffness & damping coefficient significantly affects the vehicle suspension working space, and have small effect on the front and rear dynamic tire loads. While, as the front suspension stiffness & damping coefficient increases the vehicle body vertical acceleration decreases for these two types of roads.

Investigation of the Ride Response of a Multi-wheeled Combat Vehicle in Pitch-Bounce Plane

Recently there is a worldwide trend to transform the heavy troops into more agile and deployable forces. These forces are based on light armored multi-wheeled combat vehicles which are demanding several challenging requirements. Furthermore, the design of suspension system of these vehicles is complex and should provide several conflicting issues such as higher mobility and cornering stability whilst maintaining a sufficient ride comfort for the crew. This paper presents a comprehensive investigation of the ride response of a typical combat vehicle in pitch-bounce plan under the effect of random road excitation. A set of mathematical passive suspension models for the vehicle with different configurations including two-axle, three-axle and four-axle are derived. The numerical simulation is carried out through the MATLAB/SIMULINK environment which aids the future development of controllable suspension systems. The ride responses of the vehicle is obtained and analyzed considering the vibration isolation, suspension deflection, and road-holding. The results show an improvement in the responses of vehicle body vertical acceleration, pitch acceleration anddynamic tire load using four-axle vehicle configuration over three-axle and two-axle ones.

Assessing the effectiveness of probe vehicle acceleration measurements in estimating road roughness

In this article, we compare roadway roughness measured using a probe vehicle with roadway roughness calculated from the measured profile using an inertial profiler. Roughness is characterised by vehicle body vertical acceleration and probe vehicle roughness index (PVRI), which approximates the international roughness index (IRI) of a full car (rather than a quarter car). The reason the PVRI is used rather than the IRI is that acceleration measurements obtained from a probe vehicle represent the response of the full car rather than a quarter car. An important aspect of this article is that the same physical quantities are compared rather than obtaining a correlation between two different physical quantities. The results suggest that the roughness calculated from probe vehicle measurements is comparable with the roughness calculated from the measured profile; however, the investigation also revealed that data sampling frequency and quarter car parameters, specifically suspension damping and tyre stiffness, can have a significant effect on the measured PVRI.

Stiffness-damping matching method of an ECAS system based on LQG control

A novel method of matching stiffness and continuous variable damping of an ECAS (electronically controlled air suspension) based on LQG (linear quadratic Gaussian) control was proposed to simultaneously improve the road-friendliness and ride comfort of a two-axle school bus. Taking account of the suspension nonlinearities and target-height-dependent variation in suspension characteristics, a stiffness model of the ECAS mounted on the drive axle of the bus was developed based on thermodynamics and the key parameters were obtained through field tests. By determining the proper range of the target height for the ECAS of the fully-loaded bus based on the design requirements of vehicle body bounce frequency, the control algorithm of the target suspension height (i.e., stiffness) was derived according to driving speed and road roughness. Taking account of the nonlinearities of a continuous variable semi-active damper, the damping force was obtained through the subtraction of the air spring force from the optimum integrated suspension force, which was calculated based on LQG control. Finally, a GA (genetic algorithm)-based matching method between stepped variable damping and stiffness was employed as a benchmark to evaluate the effectiveness of the LQG-based matching method. Simulation results indicate that compared with the GA-based matching method, both dynamic tire force and vehicle body vertical acceleration responses are markedly reduced around the vehicle body bounce frequency employing the LQG-based matching method, with peak values of the dynamic tire force PSD (power spectral density) decreased by 73.6%, 60.8% and 71.9% in the three cases, and corresponding reduction are 71.3%, 59.4% and 68.2% for the vehicle body vertical acceleration. A strong robustness to variation of driving speed and road roughness is also observed for the LQG-based matching method.

Effects of parameters on dynamics of a Nonlinear Vehicle-Road Coupled System

The nonlinear vehicle-road coupled system is modeled as a seven DOF vehicle moving along a simply supported double-layer rectangular thin plate on a nonlinear viscoelastic foundation. The vehicle suspension stiffness, suspension damping and tire stiffness are described by the nonlinear model. The material of the upper pavement surface is modeled as the nonlinear viscoelastic Leaderman constitutive relation. The dynamical response of the vehicle-road coupled system is obtained numerically by the quick direct integral method and four steps Runge-Kutta method. The effects of system parameters on vehicle body vertical acceleration and pavement displacements are also obtained. It is found that the nonlinearity of vehicle and the viscoelasticity of road material should be considered when study the vehicle-road system responses.

Investigation on dynamical interaction between a heavy vehicle and road pavement

This paper presents a model for three-dimensional, heavy vehicle-pavement-foundation coupled system, which is modelled as a seven-DOF vehicle moving along a simply supported double-layer rectangular thin plate on a linear viscoelastic foundation. The vertical tyre force is described by a single point-contact model, while the pavement-foundation is modelled as a double-layer plate on a linear viscoelastic foundation. Using the Galerkin method and quick direct integral method, the dynamical behaviour of the vehicle-pavement-foundation coupled system is investigated numerically and compared with that of traditional vehicle system and pavement system. The effects of coupling action on vehicle body vertical acceleration, suspension deformations, tyre forces and pavement displacements are also obtained. The investigation shows that the coupling action could not be neglected even on a smooth road surface, such as highway. Thus, it is necessary to investigate the dynamics of vehicle and pavement simultaneously based on the vehicle-pavement-foundation coupled system.

Development of a twin-accumulator hydro-pneumatic suspension

A twin-accumulator hydro-pneumatic suspension has been developed based on the off-road vehicle in order to meet the requirements of ride comfort. The working principle and elements construct of the developed suspension are studied. And then, a mathematical model of the developed suspension is built. The influence of twin-accumulator hydro-pneumatic suspension parameters on the vehicle body vertical acceleration, suspension travel and dynamic tyre load is studied by simulation based on a quarter off-road vehicle model. The ride comfort of the vehicle with the developed suspension is studied by a theoretical evaluation; also the ride comfort of the vehicle with twin-accumulator hydro-pneumatic suspension is compared with the one with single accumulator hydropneumatic suspension in both time domain and frequency domain. The result shows that the twin-accumulator hydro-pneumatic suspension system gives worthwhile improvements in ride comfort compared with the single accumulator hydro-pneumatic suspension, and it is more suitable for off-road vehicle.