Nonlinear Characteristic Analysis of Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension System:A Theoretical and Experimental Study

Because of significantly changed load and complex and variable driving road conditions of commercial vehicles,pneumatic suspension with lower natural frequencies is widely used in commercial vehicle suspension system.How ever,traditional pneumatic suspension system is hardly to respond the greatly changed load of commercial vehicles To address this issue,a new Gas-Interconnected Quasi-Zero Stiffness Pneumatic Suspension(GIQZSPS)is presented in this paper to improve the vibration isolation performance of commercial vehicle suspension systems under frequent load changes.This new structure adds negative stiffness air chambers on traditional pneumatic suspension to reduce the natural frequency of the suspension.It can adapt to different loads and road conditions by adjusting the solenoid valves between the negative stiffness air chambers.Firstly,a nonlinear mechanical model including the dimensionless stiffness characteristic and interconnected pipeline model is derived for GIQZSPS system.By the nonlinear mechanical model of GIQZSPS system,the force transmissibility rate is chosen as the evaluation index to analyze characteristics.Furthermore,a testing bench simulating 1/4 GIQZSPS system is designed,and the testing analysis of the model validation and isolating performance is carried out.The results show that compared to traditional pneumatic suspension,the GIQZSPS designed in the article has a lower natural frequency.And the system can achieve better vibration isolation performance under different load states by switching the solenoid valves between air chambers.

Development of a Composite Suspension with a Coil and Hydro-Pneumatic Spring

A new composite suspension is developed, where a coil spring and a hydro-pneumatic spring are used in order to improve the poor reliability of off-road vehicle with pure hydro-pneumatic suspension. According to road conditions, the two springs play different roles. The method for matching the composite suspension stiffness and distributing the load is proposed. The working pressure of hydro-pneumatic spring as well as the load and stiffness characteristics of composite suspension is compared with a pure hydro-pneumatic suspension. In addition, the ISO weighted vehicle body acceleration, suspension travel and relative dynamic load of the wheels between two kinds of suspension are analyzed with a quarter vehicle mode. The simulation result shows that the developed composite suspension is more suitable for off-road vehicle than the one hydro-pneumatic suspension, because the composite suspension can reduce the working pressure, improve the reliability and keep a similar ride comfort with hydro-pneumatic suspension.

Statistical Linearization on 2 DOFs Hydropneumatic Suspension with Asymmetric Non-linear Stiffness

Most references on hydropneumatic suspension analysis regard it as harden Duffing spring and take the white noise as the system input, which is quite different from real physical model. It will introduce considerable errors to the analytical result compared with the numerical simulation which makes it impossible to give a good depiction of the hydropneumatic suspension dynamics. In this paper, the dynamic response of the hydropneumatic suspension is worked out using statistical linearization based on 2 DOFs nonlinear suspension model. The damping of the suspension and the tire stiffness are both regarded as linear components and the real road roughness spectrum is used to work out the system input. The explicit analytical equivalent stiffness, dynamic mean value offset from statistic equilibrium position and the sprung acceleration varied with parameters of hydropneumatic spring, road roughness and vehicle velocity are worked out by substituting the nonlinear stiffness of hydropneumatic spring with its first three terms Tyler series at the static equilibrium position using James formula. The comparison of the numerical simulation and analytical result both on statistical parameters and distribution shows the validity of the analysis. The explicit form provides a concise and valid method on hydropneumatic suspension design and optimization.

Control Research of Dual Chamber Hydro-Pneumatic Suspension

Vehicle riding comfort and handling stability are directly affected by suspension performance.A novel dual chamber hydro-pneumatic(DCHP)suspension system is developed in this paper.Based on the structural analysis of the DCHP suspension,an equivalent suspension model is proposed for the control purpose.A cuckoo search(CS)based fuzzy PID controller is proposed for the control of the DCHP suspension system.The proposed controller combines the advantage of fuzzy logic and PID controller,and CS algorithm is used to regulate the membership functions and PID parameters.Compared with tradition LQR controller and passive suspension system,the CSFPID controller can reduce the sprung mass acceleration,and at the same time with no deterioration of tire deflection.

Investigation of Semi-Active Hydro-Pneumatic Suspension for a Heavy Vehicle Based on Electro-Hydraulic Proportional Valve

Hydro-pneumatic suspension is widely used in heavy vehicles due to its nonlinear characteristics of stiffness and damping. However, the conventional passive hydro-pneumatic suspension can’t adjust parameters according to the complicated road environment of heavy vehicles to fulfill the requirements of the vehicle ride comfort. In this paper, a semi-active hydro-pneumatic suspension system based on the electro-hydraulic proportional valve control is proposed, and fuzzy control is used as the control strategy to adjust the?damping force of the semi-active hydro-pneumatic suspension. A 1/4?semi-active hydro-pneumatic suspension model is established, which is co-simulated with AMESim and MATLAB/Simulink. The co-simulation results show that the semi-active hydro-pneumatic suspension system can significantly reduce vibration of the vehicle body, and improve the suspension performance comparing with passive hydro-pneumatic suspension.

Control algorithm for vehicle height adjustable system of hydro-pneumatic suspension based on LuGre model

In order to control the vehicle body position precisely,1/4 nonlinear mathematical model of hydro-pneumatic suspension is established,and the influence of the frictional force in a hydraulic cylinder is analyzed.The friction characteristics are described based on the LuGre model when the piston of a hydraulic actuator is operated at a low speed.Due to the fact parameters of the friction model are effected by the system condition,an adaptive friction compensation（AFC）controller is designed through the Backstepping method,and a dual-observer has been implemented to estimate the friction state.The global asymptotic convergence of a closed-loop system is proven by the Lyapunov theorem.The simulation results show that the positional accuracy of the adaptive friction compensation yiedls a significant improvement in the vehicle height adjustment as compared to the PID control,demonstrating the effectiveness of the adaptive fiction compensation method in the vehicle height adjustable system of the hydro-pneumatic suspension.

Experimental study on wheeled vehicle hydro-pneumatic suspension fault detection

A four-channel MTS road simulation system,which is used to regenerate the acceleration signal at the axle head is presented. A new fault detection method is proposed,which is based on the remote parameter control（ RPC） technology for vehicle hydro-pneumatic suspension system. The transfer function between the drive signals and the axle head acceleration should be identified before the RPC iterative calculation on a computer. By contrasting with the desired frequency response functions（ FRF）,excited through the sample spectrum of road,the iterative convergence speed of the drive function and weighted error are used to detect faults existing in the vehicle＇s suspension. Experimental results show that during the process of regeneration of the acceleration signal at the axle head,the characteristics of failure of the hydro-pneumatic spring are changed randomly resulting in a dramatic increase in calculation of the RPC iterative,which enables relatively large iterative convergence errors. This method can quickly detect and locate a suspension fault and is a simple bench test way in suspension fault detection.

Study on Outboard Inductive Damping Valve in Hydro-pneumatic Suspension

A new outboard inductive damping valve without any electronic control system is developed. Its working principle,structure and external characteristic are studied. Its mathematical model is presented and its damping characteristic is investigated on the basis of fluid continuity equation,differential equations of motion and Bernoulli equation. The influence of the valve parameters on the damping characteristic is studied numerically. The effects of outboard inductive damping valve and common damping valve on ride and tire load are compared also. The external characteristic of the valve is verified in bench test. The results show that the valve’s mathematical model is quite accurate and the developed valve can be adjust in two stages,which can also meet the requirements of the dynamic characteristic of the vehicle suspension system.

Design and evaluation of cab seat suspension system based on negative stiffness structure

To improve the vibration-isolation performance of cab seats,the optimization model of the seat suspension system of construction machinery cabs is proposed based on the negative stiffness structure.The negative stiffness nonlinear kinetic equation is established by designing the seat negative stiffness suspension structure(NSS).Using MATLAB,the different parameters of the suspension system and their influences on the dynamic stiffness are analyzed.The ideal configuration parameter range of the suspension system is obtained.Meanwhile,the optimization model of NSS is proposed,and the vibration transmissibility characteristics are simulated and analyzed by different methods.The results show that the displacement and acceleration amplitudes of the optimized seat suspension system are evidently reduced,and the four-time power vibration dose value and root mean square calculation values in the vertical vibration direction of the seat decrease by 86%and 87%,respectively.Seat effective amplitude transmissibility(SEAT)and the vibration transmissibility ratio values also decrease.Moreover,the peak frequencies of the vibration transmitted to the driver deviate from the key frequency values,which easily cause human discomfort.Thus,the design of the seat suspension system has no effect on the health condition of the driver after being vibrated.The findings also illustrate that the NSS suspension system has good vibration-isolation performance,and the driver's ride comfort is improved.

Testing Research of Accumulator Performance in the Hydro-pneumatic Suspension of a Vehicle

Taking a 2.5 liter accumulator with hydro-pneumatic suspension in a CXP1032 crane made in Germany as the research object and taking both the overall-road simulative test-bed and the control equipment made by the Schenck Company of Germany as the testing instrument, the structure performance and mechanism are theoretically clarified and the variation of gas states are obtained. This illustrates the accumulating and releasing process of a 2.5 liter accumulator in a 32t crane in the real condition. The preliminary volume and pressure of accumulator would directly affect the stiffness performance of the hydro-pneumatic suspension in a vehicle.

Optimization design of the hydro-pneumatic suspension system for high clearance self-propelled sprayer using improved MOPSO algorithm

Large high clearance self-propelled sprayers were widely used in field plant protection due to their high-efficiency operation capabilities.Influenced by the characteristics of field operations such as high power,heavy weight,high ground clearance,and fast operation speed,the comprehensive requirements for the ride comfort,handling stability and road friendliness of the sprayer were increasingly strong.At the present stage,the chassis structure of the high clearance selfpropelled sprayer that attaches great importance to the improvement of comprehensive performance still has the problems of severe bumps,weak handling performance and serious road damage in complex field environments.Therefore,this paper proposes an optimization design method for hydro-pneumatic suspension system of a high clearance self-propelled sprayer based on the improved MOPSO(Multi-Objective Particle Swarm Optimization)algorithm,covering the entire process of configuration design,parameter intelligent optimization,and system verification of the high clearance self-propelled sprayer chassis.Specifically,chassis structure of the hydro-pneumatic suspension suitable for the high clearance self-propelled sprayer was designed,and a design method combining the improved MOPSO algorithm based on time-varying fusion strategy and adaptive update with the parameter optimization of hydro-pneumatic suspension based on this algorithm was proposed,and finally the software simulation and bench performance verification were carried out.The results show that the optimized hydropneumatic suspension has excellent vibration reduction effect,and the body acceleration,suspension dynamic deflection and tire deflection were increased by 16.5%,9.9%and 0.9%respectively,compared with those before optimization.The comprehensive performance of the hydro-pneumatic suspension designed in this study is better than that of the traditional suspension.

General Torsional Stiffness Matching of Off-road Vehicle

Increasing frame torsional stiffness of off-road vehicle will lead to the decrease of body torsional deformation, but the increase of torsional loads of frame and suspension system and the decrease of wheel adhesive weight. In severe case, a certain wheel will be out of contact with road surface. Appropriate matching of body, frame and suspension torsional stiffnesses is a difficult problem for off-road vehicle design. In this paper, these theoretically analytic models of the entire vehicle, body, frame and suspension torsional stiffness are constructed based on the geometry and mechanism of a light off-road vehicle＇s body, frame and suspension. The body and frame torsional stiffnesses can be calculated by applying body CAE method, meanwhile the suspension＇s rolling angle stiffness can be obtained by the bench test of the suspension＇s elastic elements. Through fixing the entire vehicle, using sole timber to raise wheels to simulate the road impact on a certain wheel, the entire vehicle torsional stiffness can be calculated on the geometric relation and loads of testing. Finally some appropriate matching principles of the body, frame and suspension torsional stiffness are summarized according to the test and analysis results. The conclusion can reveal the significance of the suspension torsional stiffness on off-road vehicle＇s torsion-absorbing capability. The results could serve as a reference for the design of other off-road vehicles.

Research on static bearing characteristics of magnetic-liquid double suspension bearing

Due to low viscosity of seawater,it is difficult to form a seawater-lubricated film.It is easy to cause the overload and burning phenomenon of seawater-lubrication sliding bearing,and then the operation stability and service life can be shortened seriously.Therefore,the paper introduces an electromagnetic suspension theory into the seawater lubricated sliding bearing.Then a novel magnetic-liquid double suspension bearing can be formed,which can enhance bearing capacity and stiffness greatly.Firstly,the structural characteristics,support-adjustment mechanism of magnetic-liquid double suspension bearing is analyzed.Secondly,based on force balance equation,electromagnetic equation and flow equation,the transfer functions of single DOF bearing system of magnetic-liquid double suspension bearing under constant-flow supply model are deduced.Then bearing capacity,static stiffness and total power loss are selected as static performance indexes.The influence rule of operaton and structural parameters on the static performance of single DOF bearing system will be analyzed.The results show that bearing capacity decreases with the increase of liquid film thickness and width of edge seals,bias current and coil turns decrease.Static stiffness decreases with the increase of liquid film thickness,edge seals width,bias current and coil turns.Total power loss decreases with the increase of liquid film thickness,edge seals width,bias current and coil turns decrease.And static performance indexes can not be affected by liquid viscosity.The proposed research provides some theoretical and experimental basis for the parameter design of magnetic-liquid double suspension bearing.

Dynamic Analysis of Suspension Bridges and Full Scale Testing

This paper is concerned with the earthquake analysis of suspension bridges, in which the effects of large deflections are taken into account. The first part of the study deals with an iteration scheme for the nonlinear static analysis of suspension bridges by means of tangent stiffness matrices. The concept of tangent stiffness matrix is then introduced in the frequency equation governing the free vibration of the system. At any equilibrium stage, the vibrations are assumed to take place tangent to the curve representing the force-deflection characteristics of the structure. The bridge is idealized as a three dimensional lumped mass system and subjected to three orthogonal components of earthquake ground motion producing horizontal, vertical and torsional oscillations. By this means a realistic appraisal is achieved for torsional response as well as for the other types of vibration. The modal response spectrum technique is applied to evaluate the seismic loading for the combination of these vibrations. Various numerical examples are introduced in order to demonstrate the method of analysis. The procedure described enables the designer to evaluate the nonlinear dynamic response of suspension bridges in a systematic manner.

Designing and characteristics analysis of electric suspensions with symmetrically arranged two slider-rods

An innovative design of electric suspensions was developed in this study to help realize slow active suspension easily and quickly.This design was driven by screw through double slider-rod arranged symmetrically as a substitute for two springs.Based on a mathematical modeling,suspension parameters were introduced for a certain type of wheeled vehicles.The functions and its mechanism in regulating terrain clearance and adjusting attitudes were subsequently explained respectively,together with its semi-active control mechanism and characteristics In conclusion,our data in the study show that the new mechanical design of suspensions not only could realize adjusting terrain clearance and static vehicle pose,but also had an ideal stiffness that could realize a semi-active suspension function through adjusting suspension＇s stiffness.Therefore it can bequite suitable for off-road wheeled vehicles and military wheeled vehicles.

Comparison of the vibration isolation performance of a seat suspension with various design modes

Three design modes of seat suspension,i.e.,negative stiffness elements(NSEs),damping elements(DEs),and negative stiffness-damping elements(NSDEs),are proposed to evaluate the ride performance of a vehicle.Based on a dynamic model of a seat suspension and indexes of the root mean square deformation and acceleration of the seat suspension(x RMS)and driver s seat(a RMS),the influence of the design parameters of the NSEs,DEs,and NSDEs on the driver s ride comfort is evaluated.A genetic algorithm is then applied to optimize the parameters of the NSEs,DEs,and NSDEs.The study results indicate that the design parameters of the NSEs and NSDEs remarkably influence x RMS and a RMS,whereas those of the DEs insignificantly influence x RMS and a RMS.Based on the optimal results of the NSEs,DEs,and NSDEs,the damping force of the DEs is 98.3%lower than the restoring force of the NSEs.Therefore,the DEs are ineffective in decreasing x RMS and a RMS.Conversely,the NSEs combined with the damping coefficient of the seat suspension strongly reduce x RMS and a RMS.Consequently,the NSEs can be added to the seat suspension,and the damping coefficient of the seat suspension can also be optimized or controlled to further enhance the vehicle s ride performance.

考虑主动辅助避震系统的推杆式悬架设计研究

通过设计避震器纵置式推杆悬架模型,采用悬架传力模型精确计算出悬架刚度及匹配阻尼特性;整车稳定性工况计算表明:使用纵置避震器弹簧推杆悬架结构的FSAE整车存在严重侧滑与摆尾问题,针对此问题提出一种在旋转支架摆臂反方向增加主动辅助避震器系统的设计思路、模型结构及双模糊控制算法,此设计的原理是通过抑制旋转支架摆臂的运动范围进而改变车身的振动特性,同时辅助避震器系统设计还可起到横向稳定杆的作用;均方根值显示:车身俯仰角加速度性能提升89.3%,侧倾角加速度性能提升79.3%,横摆角加速度性能提升12.1%,垂向加速度性能提升50.8%。

温度对油气弹簧工作特性影响的研究

针对油气弹簧因长时间工作温度升高影响油气弹簧工作特性的问题,考虑了密封摩擦,基于热力学理论和流体力学理论,建立出油气弹簧的数学模型,在Simulink中进行数学模型仿真。使用AMESim流体仿真软件进行虚拟模型仿真。在不同工作温度下对油气弹簧进行了台架试验,得到不同温度下的油气弹簧工作特性曲线。将仿真结果和试验结果进行了对比,验证了油气弹簧数学模型和AMESim虚拟模型的正确性。把不同温度下的试验结果进行对比,研究了温度升高对油气弹簧刚度特性和阻尼特性的影响。结果表明随温升高,油气弹簧刚度特性变化较大,阻尼特性变化较小。

基于准零刚度的坦克装甲车辆半主动惯容悬架控制策略

为了提高坦克装甲车辆悬架系统的减振性能,提出“惯容-弹簧”准零刚度的基本架构,以惯容、弹簧、阻尼三元件并联作为悬架构型,对惯容连续控制和惯容开关控制两种方案进行动力学仿真和参数优化。研究结果表明:采用准零刚度控制策略后,车体振动加速度大幅度减小,乘坐舒适性改善明显,同时降低了对阻尼系数的需求,提升了减振效率。通过分析悬架减振过程中各元件的瞬时功率,发现可变惯容起能量补偿作用,使一部分振动能量在弹簧和惯容之间反复动态地传递和转换,突破了弹簧缓冲储能、阻尼生热耗能的传统减振机理,达到了更好的减振效能。

基于目标侧倾角刚度的FSAE赛车悬架刚度研究

为提高FSAE赛车的操纵稳定性及极限侧倾加速度,提出一种基于目标侧倾角刚度的赛车双横臂悬架刚度计算方法。通过设定赛车的目标侧倾角刚度,确定了赛车单位侧倾加速度下的轮荷转移量和前后悬架侧倾角刚度的分配,并推导出前后悬架的稳定杆刚度。建立ADAMS/Car悬架模型,以最小化整车侧倾时的轮荷转移量为目标,采用隔代映射遗传算法对车轮定位参数、悬架刚度随车轮上下跳动的变化曲线进行求解。仿真和实车验证结果均表明,相比未设定目标侧倾角刚度进行悬架刚度计算,该方法可更有效地减小赛车的侧倾轮荷转移,提高赛车在极限工况下的侧倾加速度和操纵稳定性。