# Determination of the optimum steady-state performance of an open-loop and a closed-loop valve-controlled hydro-motor drive: a design approach

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## Abstract

This article analyses the steady-state performance of an open-loop and a closed-loop proportional valve-controlled hydro-motor drive. The drives considered for the analysis consist of HSLT and LSHT hydro-motors. In this respect, considering the flow and torque losses of the valve and the hydro-motors, the system equations are deduced from the model. They are made non-dimensionalised, from where the expressions of the performance parameters in terms of the speed, efficiency and power transfer of the drives are determined. From the explicit design equations, the conditions for the maximum efficiency and the power transfer are obtained. The drives performances are analysed in both open-loop and closed-loop configurations and compared with the test data. Using the explicit design equations developed from the model, the effects of the losses of the hydro-motors and the control gain on the performance of the drives are studied. Using the simplified set of design equations developed in the model, the drive’s performance can be determined within its reasonable operating zone from a limited amount of test data.

## Keywords

Steady state Proportional valve Open loop Closed loop Flow losses High-speed, low-torque (HSLT) hydro-motor Low-speed, high-torque (LSHT) hydro-motor## List of Symbols

*C*Energy storage capacitive element used in bond graph model

*C*_{1}Constant in flow equations

*C*_{2}Closed-loop gain

*C*_{d}Discharge coefficient of the proportional valve

*G*_{a}Proportional amplifier gain

*H*_{t}Speed sensor gain

*i*_{v}Input voltage signal to the Proportional valve

*k*_{v}Proportional flow constant

*N*_{m}Generalised speed of the hydro-motor speed (rpm)

*N*_{m}(*0*)No-load motor speed (rpm)

- \(\overline{N}_{mp}\), \(\overline{N}_{ma}\)
Non-dimensional predicted and actual speed, respectively

*P*_{l}, \(\overline{P}_{l}\)Load pressure (bar) and its non-dimensional value

*P*_{s}Supply pressure (bar)

*P*_{t}Sump pressure (bar)

*P*_{1},*P*_{2}, \(\overline{P}_{1}\), \(\overline{P}_{2}\)Line pressures (bar) and its non-dimensional values

*Q*_{lv}Cross port leakage of the proportional valve (lpm)

*Q*_{mean}Mean flow rate (lpm)

*Q*_{1},*Q*_{2}, \(\overline{Q}_{1}\), \(\overline{Q}_{2}\)Line flow rates (lpm) and its non-dimensional values

*R*Energy dissipative element used in bond graph model

*R*_{ilkg}Hydro-motor cross port leakage coefficient (Ns/m

^{5})*R*_{lv}Cross port leakage resistance of the proportional valve (Ns/m

^{5})*R*_{lkg}Hydro-motor external leakage coefficient (Ns/m

^{5})*R*_{m}Equivalent leakage resistance of hydro-motor (Ns/m

^{5})*R*_{ln}Line resistance (Ns/m

^{5})*SE*Source of effort element used in bond graph model

*SF*Source of flow element used in bond graph model

*TF*Multi-port element that transforms mechanical to hydraulic power and vice versa used in bond graph model

*T*_{l}Load torque (N m)

*T*_{ls}, \(\overline{T}_{ls}\)Torque loss (N m) and its non-dimensional value

*V*_{m}Displacement of hydro-motor (cc/rev)

- \(\overline{W}_{mp}\), \(\overline{W}_{ma}\)
Non-dimensional predicted and actual Power transfer to motor, respectively

*φ*Motor flow coefficient

*γ*Internal flow loss coefficient of the proportional valve

- ξ
External flow loss coefficient of the hydro-motor

*η*_{mp},*η*_{ma}Predicted and actual efficiency of the hydro-motor drive, respectively.

- 1
Common flow bond graphic junction

- 0
Common effort bond graphic junction

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