Abstract：[Objective] Precise predictive control of braking torque is the foundation for autonomous driving of heavy-duty trucks. A hydraulic retarder is an auxiliary braking device widely used in these vehicles. Regulating the filling rate in its working chamber is the key to predicting and controlling the output braking torque of a hydraulic retarder. However, the working chamber is an open chamber system. The dynamic change in its filling rate is challenging to measure and characterize, which greatly affects the accurate prediction and control of the braking torque.[Methods] First, the impact of the change in the filling rate on gas pressure in the hydraulic retarder's oil storage chamber was analyzed. An increase or decrease in the filling rate corresponds to an increase or decrease in gas volume in the oil storage chamber. The gas pressure will fluctuate as the filling rate changes. Thus, measuring the dynamic variation of oil volume in the working chamber, as used in traditional methods of measuring the filling rate, was converted into monitoring gas pressure fluctuations in the oil storage chamber using pressure sensors. Subsequently, a feedforward proportional integral control algorithm with allowable deviation for the control pressure of the hydraulic retarder was designed. A new method for measuring the filling rate was established based on the target control pressure, actual control pressure, allowable deviation of the control pressure, and critical volume design parameters of the hydraulic retarder without additional flow sensors. To verify the effectiveness of the established method for measuring the filling rate, bench tests were conducted on a hydraulic retarder prototype. During the bench test, according to the four fixed gears of hydraulic retarders, four target gas pressures were set to 60, 130, 220, and 280 kPa, which allowed a deviation of 10 kPa.[Results] The measured filling rate under the four control pressures showed that at constant gas pressure, the filling rate decreased with increasing rotational speed. When the rotational speed was the same, higher gas pressure corresponded to a higher filling rate, consistent with the actual situation. Because the differences in each exhaust process were neglected, the established measurement method calculated a discontinuous filling rate during the exhaust process. However, this did not affect the overall trend in which the filling rate decreased with increasing speed. The filling rate obtained by the method in this paper was compared with the theoretical calculation method in the literature, which showed that under four different control pressures, the filling rate results obtained by the two methods exhibited the same trend and were close, indirectly confirming the effectiveness of the proposed method.[Conclusions] By monitoring the gas pressure fluctuations in the oil storage chamber using a pressure sensor, a method for measuring the filling rate of the hydraulic retarder was established. This method was based on the target control pressure, actual control pressure, allowable deviation of the control pressure, and critical volume design parameters of the hydraulic retarder, eliminating the need for additional flow sensors. The effectiveness of the established filling rate measurement method was verified through bench tests and mutual verification with the calculation results of methods in the literature. The established method for measuring the filling rate can provide critical core parameter support for accurate prediction and control of the braking torque of hydraulic retarders as well as research and development design optimization.
黄勇, 于良耀. 基于储油腔气压波动的液力缓速器工作腔充液率测量方法[J]. 清华大学学报（自然科学版）, 2025, 65(5): 940-947.
HUANG Yong, YU Liangyao. Measurement method for filling rate of hydraulic retarder working chamber based on pressure fluctuation in the oil storage chamber. Journal of Tsinghua University(Science and Technology), 2025, 65(5): 940-947.
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2025, Vol. 65 
