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Modeling dissipative heating of hydraulic dampers under consideration of stochastic uncertainties in their geometric parameters

  • Ke Chen
  • Xiaopeng Yu
  • Hongmei Zheng
  • Yuanyuan Wang
  • Guojun Zhang
  • Rui Wu
Technical Paper
  • 59 Downloads

Abstract

To obtain a hydraulic damper thermodynamic model that is much more realistic than the thermodynamic model of literature, research is carried out by introducing the stochastic uncertainty theory. The geometric variables of the hydraulic damper are defined as uncertain variables. The stochastic variables are defined with the stochastic factor method, and the stochastic thermodynamic model is established with the algebraic synthesis method. The results of the experiment are considered as the standards for verifying the correctness and superiority of the stochastic thermodynamic model. The results of the stochastic thermodynamic model and the thermodynamic model of literature are compared with the experimental results, respectively. The oil temperature at the stable state of the stochastic thermodynamic model is close to that of the experiment, indicating that the stochastic thermodynamic model is correct. The oil temperature curve of the stochastic thermodynamic model is much closer to that of the experiment than that of the thermodynamic model of the literature, indicating that the stochastic thermodynamic model is superior to the thermodynamic model of literature.

Keywords

Hydraulic damper Stochastic uncertainty theory Thermodynamic model Stochastic factor The experimental results 

List of symbols

mo

Mass of the hydraulic oil

co

Specific heat capacity of the hydraulic oil

T

Oil temperature

Fd

Damping force

t

Time

v(t)

Velocity of the oil

T

Temperature of the air

R1

Heat transfer resistance of the forced convection in the working cylinder

Rc

Heat transfer resistance from the working cylinder inner wall to the storage cylinder outer wall

R4

Heat transfer resistance of the forced convection out of the storage cylinder

ρo

Density of the hydraulic oil

Vr

Piston velocity of the recovery process

Ap

Cross-sectional area of the piston

Apo

Cross-sectional area of the piston rod

Ar

Area of thin holes in the recovery process

Vc

Piston velocity of the compression process

Ac

Area of thin holes in the compression process

Cq

Flow coefficient of the thin holes

lr

Symbol for replacing an expression

lc

Symbol for replacing an expression

k1

Symbol for replacing an expression

k2

Symbol for replacing an expression

b1

Symbol for replacing an expression

b2

Symbol for replacing an expression

W

Thermal energy generated in a cycle

A

Vibration amplitude of the outer excitation

f

Vibration frequency

Tn

End oil temperature of the nth cycle

Tn−1

Initial oil temperature of the nth cycle

Tp

Iterative period

ht

Heat transfer coefficient in the working cylinder

A1

Heat transfer area in the working cylinder

λo

Heat conductivity coefficient of the hydraulic oil

Reo

Reynolds number of the hydraulic oil

Pro

Prandtl number of the hydraulic oil

uo

Average velocity of the hydraulic oil

vo

Kinematic viscosity of the hydraulic oil

hr

Radiation heat transfer coefficient of the storage cylinder outer wall

δ

Stefan–Boltzmann constant

ε

Radiation emissivity of the storage cylinder outer wall

\(T_{{d_{4} }}\)

Temperature of the storage cylinder outer wall

ha

Heat transfer coefficient of the forced convection out of the storage cylinder

A4

Heat transfer area out of the storage cylinder

λa

Heat conductivity coefficient of the air

Rea

Reynolds number of the air

Pra

Prandtl number of the air

ua

Average velocity of the air

va

Kinematic viscosity of the air

λc

Heat conductivity coefficient of the cylinder material

λq

Heat conductivity coefficient of the nitrogen

d1

Inner diameter of the working cylinder

d2

Outer diameter of the working cylinder

d3

Inner diameter of the storage cylinder

d4

Outer diameter of the storage cylinder

L

Length of the heat transfer

dp

Diameter of the piston

dpo

Diameter of the piston rod

\(\bar{d}_{1}\)

Mean value of the working cylinder inner diameter

\(\bar{d}_{2}\)

Mean value of the working cylinder outer diameter

\(\bar{d}_{3}\)

Mean value of the storage cylinder inner diameter

\(\bar{d}_{4}\)

Mean value of the storage cylinder outer diameter

\(\bar{L}\)

Mean value of the heat transfer length

\(\bar{d}_{\text{p}}\)

Mean value of the piston diameter

\(\bar{d}_{\text{po}}\)

Mean value of the piston rod diameter

r1

Inner radius of the working cylinder

r2

Outer radius of the working cylinder

r3

Inner radius of the storage cylinder

r4

Outer radius of the storage cylinder

Te

Oil temperature at the stable state

E

Expected value

σ

Mean square error

i

Variation coefficient

Notes

Acknowledgements

We thank the Digital Design and Manufacture Key Laboratory of Anhui Province at the Hefei University of Technology for supporting this research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringHefei University of TechnologyHefeiPeople’s Republic of China

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