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Nonlinear dynamic analysis and experiments of a pressure self-regulating device for hydraulically interconnected suspension systems

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Abstract

Hydraulically interconnected suspension (HIS) systems have increasingly drawn attention because of its superiority on improving anti-rollover stability and ride comfort, but due to inevitable inner leakage, the unwanted static tilt of vehicle body caused by the pressure difference between two independent hydraulic circuits limits its application. This tilt problem will greatly reduce the driving safety and even lead to the rollover accident. In this study, a new pressure self-regulating (PSR) device is proposed to address this tilt problem, including its system design, manufacture and experimental validation. The structure and pressure self-regulating principle for this PSR device are introduced in detail first, and the nonlinear model is developed based on mechanical-hydraulic coupling equations. Moreover, the developed model is validated by bench tests; based on this, the parametric analysis is implemented to reveal the impacts of the key parameters of PSR device, including equivalent stiffness and clearance height, on the pressure difference threshold and the time delay. Also, the simulations and experiments from the perspective of the whole vehicle integrated with PSR device are carried out, which demonstrates that PSR device can automatically eliminate the tilt of the vehicle body by balancing the pressure between two hydraulic circuits of HIS system without deteriorating the anti-rollover stability and ride comfort.

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Abbreviations

\({\text{m}}_{\text{s}}\) :

The mass of the spool (kg)

\({\ddot{x}}_{\text{s}}\) :

The acceleration of the spool movement (m/s2)

\({\text{p}}_{1}(i=\mathrm{1,2})\) :

The pressures in the spool chamber i (MPa)

\({A}_{\text{pi}}\) :

The equivalent cross-sectional area of the spool chamber i (m2)

ke :

The spring rate of belleville spring (N/m)

xe :

The initial compression of belleville spring (m)

x s :

The displacement of spool movement (m)

lm :

The maximum limit that the spool can reach (m)

ls :

The length of spool (m)

μ:

The oil viscosity coefficient (N s/m2)

\({\dot{x}}_{\text{s}}\) :

The velocity of the spool movement (m/s)

h g :

The clearance height of the gap (m)

dp :

The inner diameter of the valve seat and (m)

dr :

The outer diameter of the spool (m)

\({\text{P}}_{\text{A}}\) :

The pressure of Port A (MPa)

\({\text{c}}_{\text{d}}\) :

The throttling coefficient of equivalent orifice

ρh :

The density of hydraulic oil (kg/m3)

\({\text{A}}_{\text{oi}}\) :

The equivalent area of the orifice i (m2)

\({\text{P}}_{\text{B}}\) :

The pressure of the Port B (MPa)

P c :

The fluid pressure in the piston-side chamber (MPa)

P r :

The fluid pressure rod-side chamber (MPa)

Q c :

The flow rate of the piston-side chamber (m3/s)

Q r :

The flow rate of the rod-side chamber (m3/s)

A c :

The cross section area of the piston-side chamber (m2)

A r :

The cross section area of the rod-side chamber (m2)

\({\dot{x}}_{\text{h}}\) :

The relative velocity of the corresponding hydraulic cylinder (m/s)

β F :

The bulk modulus of fluid (MPa)

V com :

The volume changes of the piston-side chamber (m3)

V reb :

The volume changes of the rod-side chamber (m3)

V c 0 :

The initial volume of the piston-side chamber (m3)

V r 0 :

The initial volume of the rod-side chamber (m3)

x h :

The relative displacement of the hydraulic cylinder (m)

k q :

The leakage coefficient (m3/Pa s)

l p :

The length of the pipeline unit (m)

r :

The radius of the pipeline unit (m)

\({\overline{P} }_{\text{p}}\) :

The pre-charge pressure in the accumulator (MPa)

\({\overline{V} }_{\text{p}}\) :

The volume of gas in the accumulator (m3)

\({P}_{\text{a}}\) :

The instantaneous fluid pressure in the accumulator (MPa)

\({Q}_{\text{a}}\) :

The flow rate in the accumulator (m3/s)

γ :

The polytropic exponent

Q v :

The flow rate through the damping valve (m3/s)

A v :

The equivalent cross-sectional area of the orifice (m2)

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Funding

The authors appreciate the support from National Natural Science Foundation of China (Grant No. 52075465), Science and Technology Innovation Program of Hunan Province (Grant No. 2020JJ5686) which made this research possible.

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Authors and Affiliations

  1. School of Mechanical Engineering, Xiangtan University, Xiangtan, 411105, China

    Bohuan Tan & Jingang Liu

  2. School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei, 230009, China

    Nong Zhang

  3. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China

    Hengmin Qi & Bangji Zhang

  4. Bus Technical Department, CRRC Electric Vehicle CO., LTD, Zhuzhou, 412007, China

    Kunjun Wang

Authors
  1. Bohuan Tan
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Correspondence to Bangji Zhang.

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Tan, B., Zhang, N., Qi, H. et al. Nonlinear dynamic analysis and experiments of a pressure self-regulating device for hydraulically interconnected suspension systems. Nonlinear Dyn 111, 4173–4190 (2023). https://doi.org/10.1007/s11071-022-08090-2

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  • DOI: https://doi.org/10.1007/s11071-022-08090-2

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