Suspension Damping Research Articles

Comfort Improvement of a Novel Nonlinear Suspension for a Seat System Based on Field Measurements

This paper describes improved ride comfort of a novel nonlinear suspension for seat system based on field measurements. For the novel nonlinear suspension proposed, a rubber spring is used as its elastic element which has highly nonlinear characteristics to adapt various working conditions, and an asymmetrical damper is designed to yield asymmetric damping characteristics. Previous seat models were not very suitable for the system; thus, a nonlinear mathematical model was built to describe it better. Then, based on field measurements, the model parameters were identified, and the suspension damping coefficients were tuned under the practical constraints, to achieve satisfactory ride comfort to the greatest extent possible. Finally, the bench test was carried out, and the results show that, after the coefficients tuning, the seat vertical frequency-weighted root mean square (RMS) acceleration values are decreased by about 10% and 8% under the driving conditions on the highway and the gravel road, respectively, which proves the damping coefficients tuned are workable. The novel nonlinear suspension and the method of the damping coefficients tuning provide a valuable reference for further improving ride comfort to better protect the driver’s health.

Predictive vehicle ride discomfort model based on <i>in</i>-<i>situ</i> Stevens power law parameters

The current dynamic ride comfort mathematical models do not use Maxwell arrangement of vehicle suspension occurring due to top mount and the discomfort weightings used are based on the shaker table tests which ignore the influence of vehicle dynamics, for example the effect of seat cushion. A refined integrated vehicle-occupant, 10 degrees of freedom model that includes top mounts is developed to estimate the occupant response to given harmonic input. The dynamic responses are combined with experimentally obtained in-situ discomfort indices for a car that incorporates the effects of features such as seat cushion. The Stevens power law parameters are estimated and compared with previous studies; the perception model is then used to predict discomfort index as a function of frequency. The influence of the relative stiffness of the top mount and suspension damping on the resonance frequencies is discussed. The acceleration in wheel hop mode can be ~3 times larger than that when top mount is not included. The influence of resonance frequencies suggests importance of not just using frequency average discomfort index while optimising suspension and seat parameters.

Predictive vehicle ride discomfort model based on <i>in-situ</i> Stevens power law parameters

The current dynamic ride comfort mathematical models do not use Maxwell arrangement of vehicle suspension occurring due to top mount and the discomfort weightings used are based on the shaker table tests which ignore the influence of vehicle dynamics, for example the effect of seat cushion. A refined integrated vehicle-occupant, 10 degrees of freedom model that includes top mounts is developed to estimate the occupant response to given harmonic input. The dynamic responses are combined with experimentally obtained in-situ discomfort indices for a car that incorporates the effects of features such as seat cushion. The Stevens power law parameters are estimated and compared with previous studies; the perception model is then used to predict discomfort index as a function of frequency. The influence of the relative stiffness of the top mount and suspension damping on the resonance frequencies is discussed. The acceleration in wheel hop mode can be ~3 times larger than that when top mount is not included. The influence of resonance frequencies suggests importance of not just using frequency average discomfort index while optimising suspension and seat parameters.

Network synthesis and parameter optimization for vehicle suspension with inerter

In order to design a comfortable-oriented vehicle suspension structure, the network synthesis method was utilized to transfer the problem into solving a timing robust control problem and determine the structure of “inerter–spring–damper” suspension. Bilinear Matrix Inequality was utilized to obtain the timing transfer function. Then, the transfer function of suspension system can be physically implemented by passive elements such as spring, damper, and inerter. By analyzing the sensitivity and quantum genetic algorithm, the optimized parameters of inerter–spring–damper suspension were determined. A quarter-car model was established. The performance of the inerter–spring–damper suspension was verified under random input. The simulation results manifested that the dynamic performance of the proposed suspension was enhanced in contrast with traditional suspension. The root mean square of vehicle body acceleration decreases by 18.9%. The inerter–spring–damper suspension can inhibit the vertical vibration within the frequency of 1–3 Hz effectively and enhance the performance of ride comfort significantly.

Electromagnetics Car Suspension System

Car suspension system play important role to determine the comfort of car subject to the road profile. For mechanical car suspension system, to improve the suspension, the spring and hydraulic damper are elements that need to be studied. In this research, we change the spring in the suspension system with an electromagnetic suspension. To study the effect of electromagnetic suspension, a simple mathematical model of electromagnetic car suspension is formulated. The model is solved using analytical method. The analysis of the solution of the model are presented and interpreted.

The use of a linear half-vehicle model for the optimization of damping in the passive suspension system of a railway car

The paper presents a methodology of optimizing the parameters of the passive suspension system of a railway vehicle. A linear half-vehicle model and an example of the procedure carried out to optimize a selected parameter of the model have been demonstrated. A method of the selection of damping in the suspension system of a railway vehicle, based on over 40-year achievements of the cited authors of publications in the field of motor vehicles, has been shown. The optimization of linear damping in the secondary suspension system of a passenger carriage moving on a track with random profile irregularities has been described in detail. The algorithms adopted for the calculations have a wider range of applicability; especially, they may be used for determining the optimum values of the other parameters of the railway vehicle model under analysis, i.e. stiffness of the secondary suspension system as well as stiffness and damping of the primary suspension system.

Energy-harvesting potential of automobile suspension

ABSTRACTThis study is aimed quantify dissipated power in a damper of automobile suspension to predict energy harvesting potential of a passenger car more accurately. Field measurements of power dissipation in a regenerative damper are still rare. The novelty is in using the broad database of real road profiles, a 9 degrees-of-freedom full-car model with real parameters, and a tyre-enveloping contact model. Results were presented as a function of road surface type, velocity and road roughness characterised by International Roughness Index. Results were calculated for 1600 test sections of a total length about 253.5 km. Root mean square of a dissipated power was calculated from 19 to 46 W for all four suspension dampers and velocity 60 km/h and from 24 to 58 W for velocity 90 km/h. Results were compared for a full-car model with a tyre-enveloping road contact, full-car and quarter-car models with a tyre–road point contact. Mean difference among three models in calculated power was a few per cent.

Optimization of Automotive Suspension System by Design of Experiments: A Nonderivative Method

A lot of health issues like low back pain, digestive disorders, and musculoskeletal disorders are caused as a result of the whole body vibrations induced by automobiles. This paper is concerned with the enhancement and optimization of suspension performance by using factorial methods of Design of Experiments, a nonderivative method. It focuses on the optimization of ride comfort and determining the parameters which affect the suspension behavior significantly as per the guidelines stated in ISO 2631-1:1997 standards. A quarter car test rig integrated with a LabVIEW based data acquisition system was developed to understand the real time behavior of a vehicle. In the pilot experiment, only three primary suspension parameters, that is, spring-stiffness, damping, and sprung mass, were considered and the full factorial method was implemented for the purpose of optimization. But the regression analysis of the data obtained rendered a very low goodness of fit which indicated that other parameters are likely to influence the response. Subsequently, steering geometry angles, camber and toe and tire pressure, were included in the design. Fractional factorial method with six factors was implemented to optimize ride comfort. The resultant optimum combination was then verified on the test rig with high correlation.

SIDE FORCE ANALYSIS OF SUSPENSION STRUT UNDER VARIOUS LOAD CASES

This paper presents the side forces extraction of a Macpherson suspension strut under extreme load cases using multibody dynamics model. Inevitable side forces subjected to the Macpherson suspension system during vehicle driving cause the damper rod and top mounting failure. Bending moment generated could increase the friction of damper piston and inner tube and simultaneously decrease the ride comfort of the vehicle, or in a more severe condition, failure occurs. In this study, the side forces magnitude subjected to the Macpherson strut under various severe load events were obtained through a quasi-static multibody dynamics half vehicle model simulation. Outcomes of the multibody simulation that showing the forces exerted on the suspension Macpherson strut were derived into three axes which were vertical, lateral and longitudinal. The lateral and longitudinal side forces on the strut were highest during the pothole striking event which achieved 11052 N. The extracted force provided useful information for suspension linkages design and damper friction analysis to prevent failure.

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Employing theory on vehicle–track coupled dynamics, the equation of motion of a vehicle–track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle–track vertical coupled system was calculated under the excitation of the German low-interference spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German low-interference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel–rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle–track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the low-frequency vibrations of the vehicle system and track structure. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel–rail vertical force and track structure decrease at 50–80 Hz, while the mid-frequency and high-frequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel–rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel–rail vertical force and track structure.

A semi-active vehicle suspension based on pneumatic springs and magnetorheological dampers

Semi-active and active suspensions can improve both ride comfort and handling compared to passive suspensions. The authors have proposed a suspension comprising a pneumatic system capable of changing the stiffness of the suspension and a semi-active magnetorheological damper capable of controlling the suspension damping. Eight configurations of this magnetorheological/pneumatic suspension result from combining two possible stiffnesses (compliant and stiff) and four possible means of producing damping (constant low, constant high, on-off skyhook control and on-off balance control). The minimization of a cost function, which considers both ride comfort and handling, leads to decision maps which indicate the most appropriate configuration depending on vehicle velocity and two pieces of information about the road: the international roughness index and the curve radius. All this information can be gathered from a GPS system and toggling between set-ups is fast, efficient, and easily done by simply opening or closing pipes in the pneumatic system and modifying the current supply in the magnetorheological dampers. The proposed magnetorheological/pneumatic suspension achieves the same roll angle levels as in a comparable passive vehicle while improving ride comfort by reducing acceleration by up to 30%.

Influence of Spring Ratio on Variable Stiffness and Damping Suspension System Performance

The variable stiffness and damping (VSVD) suspension system offers an interesting option to improve driver comfort in an energy efficient way. The aim of this study is to analyze the influence of the spring ratio on the VSVD. The realization of the VSVD is obtained by the application of variable damping with magnetorheological (MR) damper. In this study, the nonlinear damping force characteristic of the MR damper is modeled with the Bouc-Wen model and the road disturbance is modeled by a stationary random process with road displacement power spectral density. It is shown from simulation that VSVD has a potential benefit in improving performance of vehicle suspension.

Optimization of nonlinear quarter car suspension–seat–driver model

In this paper a nonlinear quarter car suspension–seat–driver model was implemented for optimum design. A nonlinear quarter car model comprising of quadratic tyre stiffness and cubic stiffness in suspension spring, frame, and seat cushion with 4 degrees of freedom (DoF) driver model was presented for optimization and analysis. Suspension system was aimed to optimize the comfort and health criterion comprising of Vibration Dose Value (VDV) at head, frequency weighted RMS head acceleration, crest factor, amplitude ratio of head RMS acceleration to seat RMS acceleration and amplitude ratio of upper torso RMS acceleration to seat RMS acceleration along with stability criterion comprising of suspension space deflection and dynamic tyre force. ISO 2631-1 standard was adopted to assess ride and health criterions. Suspension spring stiffness and damping and seat cushion stiffness and damping are the design variables. Non-dominated Sort Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization – Crowding Distance (MOPSO-CD) algorithm are implemented for optimization. Simulation result shows that optimum design improves ride comfort and health criterion over classical design variables.

Combining Design of Vibration Absorbing and Isolation for a Power Equipment Based on 2 Degrees of Freedom

When power equipments are suspended under the under-frame of a rail train vehicles, dynamic and vibration characteristics of the car body will be changed. In order to study suspended parameters of the car body dynamic system, the vertical dynamic coupling model of rigid car body and power equipment under different exciting force was established. Results showed: when the exciting force of suspended power equipment is zero, the elastic suspension stiffness and damping can be designed according to the principle of Dynamic Vibration Absorber (DVA); when the exciting force acting on the rigid car body is zero, the vibration isolation problem of equipment is consistent to the base isolation problem, a good vibration isolation effect can be obtained as; when the body and power equipment simultaneously be excited, vibration absorbing and isolation must be simultaneously designed: the DVA is meet on at first, when ,the suspension isolation system appeared two different frequency peaks, but only , a good vibration isolation can be obtained for suspension system.

Investigation on cornering brake stability of a heavy-duty vehicle based on a nonlinear three-directional coupled model

A nonlinear three-directional coupled lumped parameters (TCLP) model is proposed for a heavy-duty vehicle to investigate the longitudinal, lateral and vertical dynamics of vehicles simultaneously. The nonlinear property of suspension damping is described by a fitted exponent model from experimental data. The nonlinear tire forces in different directions are modeled by the nonlinear Gim model and the vertical single dot contact model with square nonlinearity. The system responses are calculated by numerical integration and compared with the Functional Virtual Prototyping (FVP) model and the test data, so as to verify the validity of this new vehicle model. With Lateral-Load Transfer Ratio (LTR) and yaw rate as evaluation indexes, the influences of system parameters on cornering brake stability are analyzed. The critical vehicle speed table is also obtained. The study shows that high vehicle running speed, large front wheel steering angle, large tire cornering stiffness or small braking moment is harmful to yaw stability and roll stability. Road surface frictional coefficient mainly influences yaw stability, and vertical tire stiffness and road surface roughness mainly influence roll stability.

Prototyping design and experimental validation of membranous dual-cavity based amplitude selective damper

This paper designs a membranous dual-cavity based amplitude sensitive damper (shorted as MASD) for road vehicle suspension to better compromise ride comfort and driving safety. A specially designed sleeve, separated into two cavities by a rubber membrane, is centrally placed along the main piston of conventional twin-tube damper. The volume change of dual-cavity caused by membrane deformation accommodates partial oil flow in the condition of small piston displacement, which results in a reduced damping ratio. Due to the attached rubber embossments on both sides of rubber membrane, this MASD can switch smoothly between low and high damping forces at the final stage of membrane deformation. This design prevents the damper from additional impact when switching between higher damping ratio to lower one. After elaborating the working principle of MASD, its dynamic model is derived by combining first-principle modeling of hydraulic components and empirical modeling of membranous valve. A prototyping MASD is finally developed and tested on a damper test rig to demonstrate its effectiveness.

Dynamic response of high speed vehicles and sustaining curved bridges under conditions of resonance

This paper examines the dynamic response of vehicle(s) moving at high speeds and the sustaining horizontally curved (simple, continuous or multi-unit) bridges, when each subsystem is set into resonance. The bridge is simulated by finite elements and each vehicle as a multibody system. The coupling contact forces, between the vehicle and the bridge, are derived by adopting a rigid contact assumption. Key feature of the present study is the simulation of the three-dimensional (3D) dynamics of a vehicle running over a horizontally curved path. This simulation allows the examination of deformation modes of the 3D multibody vehicle model (e.g. related to lateral-rolling and yawing degrees of freedom) for the first time. In all cases, the numerical results agree well with pertinent analytical solutions. From the parametric study, the followings are observed: (1) The impact factors show the same pattern for the vertical and the radial directions. (2) The suspension damping can alleviate the resonance response of the car body even when the vehicle’s resonance condition is met. (3) The feedback effect of the bridge’s resonance to the vehicle response is large, but the vehicle’s resonance effect on the bridge response is quite small, especially along the vertical direction. (4) No resonance of the middle span of the continuous bridge occurs for the second mode in the vertical and the radial directions. (5) The increase in the number of spans results in both smaller displacement and lower impact factor.

Vibration Analysis of 5-DOF Vehicle Model under Stochastic Road Surface Excitation

Considering human body vertical motion, vehicle body vertical motion, pitch movement and vertical jump of front and rear wheels, a five-degree-of-freedom vehicle model is established to study basic driving characteristics of the vehicle. Using Fourier transform method, acceleration power spectral density of the seat and the mean square value curves of seat vertical weighted acceleration are obtained by numerical simulation. Combined with comfort provision standards, the influence of vehicle model parameters and speed on seat acceleration power spectral density and vertical root-mean-square value of seat weighted acceleration are analyzed. Results show that the stiffness and damping of the seat have no significant effect on seat acceleration power spectral density, and seat acceleration PSD increases with increasing front or rear suspension stiffness, but it decreases with increasing front or rear suspension damping. It should also be concluded that the model stiffness and the mean square value of seat vertical weighted acceleration present positive correlation in general, but seat vertical weighted acceleration decrease first and then increase when model damping increase. Such analysis results can provide reference for the parameter optimization design of the automobile.

Evaluation of Stability in Railway Vehicles on Basis of Bogie Lateral Acceleration

The paper focuses on evaluating the stability of the railway vehicle during running on a track horizontal irregularities and investigating the possibilities to improve the dynamic behavior on a lateral direction. The evaluation method for the stability relies on the homologation specifications of the railway vehicles from the perspective of the dynamic behavior included in the UIC 518 Leaflet, where the lateral accelerations of the bogies represent evaluation units for the stability. The lateral accelerations are derived from numerical simulations, developed on a non-linear complex model of the vehicle/track system, where the vehicle is described by a mechanical system with 21 degrees of freedom. The results thus presented outline the possibilities of improving the vehicle stability by adopting the best values of the lateral damping of the secondary suspension or of the lateral stiffness of the primary suspension that will lead to the minimizing of the lateral acceleration in a bogie.

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.