Nonlinear dynamic model of air spring with a damper for vehicle ride comfort

Zhu, Hengjia; Yang, James; Zhang, Yunqing; Feng, Xiaoying; Ma, Zeyu

doi:10.1007/s11071-017-3535-9

Cited by 75 publications

(41 citation statements)

References 30 publications

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“…The relative error is calculated based on the result of the nonlinear model. Zhu et al 13 compared vertical frequency-weighted RMS acceleration values from the proposed model, the Berg’s model, and ride test results. The proposed model error is within 10%, while the Berg’s model error is over 10%.…”

Section: Influence Of Key Parameters On Dynamic Response Characteristicsmentioning

confidence: 99%

“…The air spring was assumed to be an adiabatic system in the dynamic simulation model. To correctly reproduce the air spring nonlinear characteristics, Zhu et al 13 advanced an air spring mechanical model. Docquier et al 14 considered multibody and pneumatic aspects simultaneously to model the train’s pneumatic suspension with a multidisciplinary approach.…”

Section: Introductionmentioning

confidence: 99%

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Vibration isolation characteristics and control strategy of parallel air spring system for transportation under abnormal road and eccentric load conditions

Liu

et al. 2021

Measurement and Control

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The precision equipment bears the vibration excited by the road roughness during transportation, and faces the risk of damage arising from the vibration. The parallel air spring vibration isolation system (PAVS) has an excellent vibration isolation performance, so has a good application prospect in the precision equipment transportation. But under the conditions of abnormal road and eccentric load, PAVS bears great vibration excitation, and the resulting large deformation of air spring makes the air spring stiffness nonlinear, so to obtain an excellent vibration isolation performance faces a great challenge. Aiming at this problem, based on the measured parameters, the nonlinear dynamics model of PAVS is proposed. Then, the influence of air spring under large deformation on the vibration isolation characteristics is discussed. Finally, under the condition of eccentricity of precision equipment, the vibration isolation characteristics of PAVS with equal height control strategy is investigated. The results show that PAVS with the equal height control strategy has good vibration isolation characteristics. So for the transportation of large precision equipment, PAVS is a potentially useful method.

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Section: Influence Of Key Parameters On Dynamic Response Characteristicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration isolation characteristics and control strategy of parallel air spring system for transportation under abnormal road and eccentric load conditions

Liu

et al. 2021

Measurement and Control

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“…The vertical model has a nonlinear attenuation, which depends on the rate of change in pressure in the pneumatic cylinder. There is another model of pneumatic springs Bouc-Wen [12,13,18,21], which includes not only elastic and dissipative elements describing the state of gas in the system, but also a block that simulates changes in the condition of the rubbercord shell of a pneumatic cylinder. The branch with nonlinearly elastic stiffness is used to simulate the work of air within the pneumatic spring and to describe its geometric parameters, as well as the thermodynamic processes that take place within the pneumatic spring, which can be derived in accordance with the thermodynamic equation.…”

Section: Introductionmentioning

confidence: 99%

Determination of Characteristics of Throttling Device for Pneumatic Spring

Reidemeister

Laguza

2021

STP

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Purpose. This paper focuses on determination of the dependence of the working medium flow on the capacity of the throttling device, its geometric features and the pressure difference in the pneumatic spring cylinder and in the auxiliary reservoir. Methodology. Calculation of the dependence of the working medium and pressure drop is performed in two ways: 1) by numerical simulation of a stationary gas flow through a throttling element; 2) its analytical calculation expression using empirical relationships (control calculation to evaluate the reliability of numerical simulation results). For the calculation, three models of throttling devices were chosen. Dependence of the flow rate of the working medium on the capacity of the throttling device and its geometric features was determined based on the approximation of the dependency graphs of the pressure drop against the mass flow rate of the working medium. Findings. We obtained graphical dependencies between the pressure drop and the mass flow rate of the working medium from the two calculation options. Based on the results of calculations performed with the help of a software package with visualization of the results, we calculated a proportionality coefficient that describes the dependence of the working medium flow on the throttling device capacity and its geometric features for each of the throttling elements considered, with three degrees of closure. The air flow values, obtained by numerical simulation, are greater than the flow rates obtained from semi-empirical formulas. At the same time, they are in good qualitative agreement, and the quantitative difference averages 25%, which can be regarded as confirmation of the reliability of the numerical model. Based on the calculation results, we plotted the proportionality coefficient graphs against the degree of closure of the throttling device. Originality. The work allows determining the degree of influence of the frictional component on the variation of the pressure difference in the pneumatic cylinder and the auxiliary reservoir of the pneumatic suspension system. Also, the work proposes a method to determine the dependence of the working medium on the capacity of the throttling device and its geometric features. Practical value. The ability to predict the operating parameters of the pneumatic system depending on the pneumatic resistance of the throttling device will improve the car running characteristics, increase the comfort of passenger transport, and also reduce the wear of the rolling stock and track gauge due to vehicle-track interaction.

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“…The influence of the area of the throttle orifice on the lateral and longitudinal mechanical characteristics of air spring was analyzed, and the feasibility of suspension performance control by changing the area of the throttle orifice was proposed 16 . Zhu et al studied the nonlinear dynamic characteristics of air spring with damping elements and established a mechanical model to describe its complex properties 17 . Sun et al introduced a hybrid modeling method for an air suspension system with a damping multimode switching damper and applied the model prediction control on the air suspension system 18 .…”

Section: Introductionmentioning

confidence: 99%

“…16 Zhu et al studied the nonlinear dynamic characteristics of air spring with damping elements and established a mechanical model to describe its complex properties. 17 Sun et al introduced a hybrid modeling method for an air suspension system with a damping multimode switching damper and applied the model prediction control on the air suspension system. 18 To improve control performance, Kim et al designed a sliding mode control algorithm for the nonlinearity of air suspension and applied it to improve the pitching and rolling capabilities of vehicles.…”

mentioning

confidence: 99%

Semi‐active control of air suspension with auxiliary chamber subject to parameter uncertainties and time‐delay

Zhang

Wang

et al. 2020

Intl J Robust & Nonlinear

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Suspension systems are critical to the ride comfort and handling stability of vehicles, but traditional passive suspensions fail to achieve optimal performance in the two aspects. Semi-active suspension controller changes the suspension stiffness or damping to improve the ride comfort and handling stability, which has the potential advantages of low energy consumption and high reliability. In this paper, the model of an air spring with an auxiliary chamber and a variable throttle orifice is proposed and the semi-active control strategy of air suspension is carried out. The parameters of the air spring with auxiliary chamber are optimized to improve the performance when the control system fails and to increase the basic performance for semi-active control. Based on the linear matrix inequality approach to robust H ∞ control, the semi-active control strategy of the air suspension is studied, in which parameter uncertainties and time delay are considered to improve control robustness. An inverse model of the air spring is then established to calculate the area of the variable throttle orifice, by which the desired control force is tracked accurately. Finally, the effectiveness of the semi-active control system of the air suspension is verified by numerical simulation. Comparing with the passive suspension, not only under nominal parameters, but also with parameter uncertainties, time delay, and both parameter uncertainties and time delay, the semi-active control system proposed in this paper has good control performance as well as is strong robustness to parameter uncertainties and time delay. K E Y W O R D S air suspension, parameter uncertainties, robust control, semi-active control, time delay 1 INTRODUCTION Comfort and safety are important considerations in the automotive industry, 1,2 and the ride comfort and handling stability are direct manifestations of these two properties. Suspension systems are used to transfer forces and moments between the car body and the ground. Thus, the suspension design must be improved to enhance the ride comfort and handling stability of vehicles. However, traditional passive suspensions fail to achieve optimal performance in both ride comfort and handling stability. 3,4 In recent years, in-wheel-motored electric vehicles have become a research hotspot because of their compact structure, high transmission efficiency, and 7130

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Nonlinear dynamic model of air spring with a damper for vehicle ride comfort

Cited by 75 publications

References 30 publications

Vibration isolation characteristics and control strategy of parallel air spring system for transportation under abnormal road and eccentric load conditions

Vibration isolation characteristics and control strategy of parallel air spring system for transportation under abnormal road and eccentric load conditions

Determination of Characteristics of Throttling Device for Pneumatic Spring

Semi‐active control of air suspension with auxiliary chamber subject to parameter uncertainties and time‐delay

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