Abstract
Hydraulic retarders are auxiliary braking devices that reduce the velocity of a vehicle, particularly when a vehicle is driven downhill. Such velocity reduction could reduce the potential risk caused by brake failure caused by the service brake working for a long time and the temperature of the brake shoe becomes extremely high. This paper introduces the construction of the hydraulic retarder and proposes two mathematical models for the hydraulic retarder. The first mathematical model is deduced by using fluid mechanics, which is used to analyze the mechanism of how braking torque is produced and the key factors that can influence the value of the braking torque. The second mathematical model is deduced by using thermodynamics, which is used to quantify the heat produced by the hydraulic retarder. This research emphasizes that the flow rate and the average velocity of the working fluid in the working chamber mainly determine the braking torque of the hydraulic retarder. The flow rate into and out of the working chamber determines the temperature rise of the working fluid. Computational fluid dynamics (CFD) simulations are conducted with the Reynolds-averaged Navier-Stokes (RANS) and Shear Stress Transport (SST) turbulent models. Experiments are carried out to justify the two mathematical models and the CFD simulations. The results show that the mathematical models are capable of describing the force analysis and energy conversion of the hydraulic retarder and SST is more accurate for CFD simulation and the error is within 6 %.
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Abbreviations
- CV :
-
control volume, m3
- CS :
-
control surface, m2
- P :
-
braking power, kW
- M :
-
braking torque, Nm
- n :
-
rotational speed of the rotor, rpm
- Q :
-
internal energy, kJ
- κ :
-
coefficient of the unit
- c :
-
specific heat, kJ/(kg·°C)
- ΔT :
-
temperature rise, °C
- \(\overrightarrow{v}\) :
-
fluid velocity, m/s
- \(\overrightarrow{v}\) r :
-
fluid velocity relative to the control surface, m/s
- l :
-
direction normal to the surface
- ṁ 1 :
-
flow rate into and out of the rotor, kg/s
- ṁ 2 :
-
flow rate into and out of the working chamber, kg/s
- v':
-
velocity of the fluid into and out of the working chamber, m/s
- v avg1 :
-
average velocity of the working fluid into and out of the rotor, m/s
- v avg2 :
-
average velocity of the working fluid into and out of the working chamber, m/s
- ρ :
-
density of the working fluid, kg/m3
- A CS1 :
-
area where the working fluid flows into the rotor, m2
- A CS2 :
-
area where the working fluid flows out of the rotor, m2
- r 1 :
-
external diameter, mm
- r 2 :
-
inner diameter, mm
- r 3 :
-
torque diameter, mm
- F 1 :
-
resultant force, N
- F 2 :
-
component force along the axial, N
- F 3 :
-
component force normal to r3, N
- F it :
-
force caused by the working fluid into and out of the rotor, N
- F io :
-
force caused by the working fluid into and out of the working chamber, N
- θ :
-
angle between the interface and the streamline, o
- f 1, f 2, f 3 :
-
function of diameter of circulation circle
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Zheng, H., Lei, Y. & Song, P. Hydraulic retarders for heavy vehicles: Analysis of fluid mechanics and computational fluid dynamics on braking torque and temperature rise. Int.J Automot. Technol. 18, 387–396 (2017). https://doi.org/10.1007/s12239-017-0039-z
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DOI: https://doi.org/10.1007/s12239-017-0039-z