Measurement and evaluation of static characteristics of rotary hydraulic motor

The paper describes experimental equipment for measurement of static characteristics of rotary hydraulic motor. It is possible to measure flow, pressure, temperature, speed and torque by means of this equipment. It deals with measurement of static characteristics of a gear rotary hydraulic motor. Mineral oil is used as hydraulic liquid in this case. Flow, torque and speed characteristics are evaluated from measured parameters. Measured mechanical-hydraulic, flow and total efficiencies of the rotary hydraulic motor are adduced in the paper. It is possible to diagnose technical conditions of the hydraulic motor (eventually to recommend its exchange) from the experimental measurements.


Introduction
Rotary hydraulic motors belong to hydrostatic converters that work on volumetric principle.The geometric volume V gM is one of their most important properties.The volume is given by a liquid volume, which flows through an unloaded hydraulic motor within one revolution of the motor shaft.A suitable rotary hydraulic motor is chosen on the basis of static characteristics.Flow, torque and speed characteristics belong to most important characteristics of hydraulic motors.The efficiency of rotary hydraulic motors is a very important parameter too.It is possible to diagnose e.g.technical conditions of rotary motors on the basis of their efficiency.In the case of hydraulic motors, it is necessary to determine flow, mechanical-hydraulic and total efficiencies.The abovementioned parameters of rotary motors are the basis for their suitable applications [1,2].

Description of experimental equipment
The schematic diagram of the tested experimental equipment is shown in figure 1.The control hydraulic pump HP 1 is a pressure liquid source and is used in order to drive the rotary hydraulic motor HM 1 .This motor is subsequently used to driving of the hydraulic pump HP 2 .The drive of the measured rotary hydraulic motor HM 2 is realized in this manner.It is an internal-gear motor with the geometric volume V gM2 = 8.16 cm 3 , which was experimentally verified (see chapter 3).The drive consists of the manometer M and the relief valve RV, which is used to system overload protection.It is possible to adjust required flows by means of the control hydraulic pump HP 1 .The measured rotary hydraulic motor HM 2 is loaded through the hydraulic pump HP 3 and the pressure valve PV.The gear flow sensor FS is connected to a line between the pump HP 2 and the motor HM 2 .This sensor allows to measure flow (i.e. by the sensor S 2 ), temperature (i.e. by the sensor S 1 ) and pressure (i.e. by the sensor S 3 ).Speed (i.e. by the sensor S 5 ) and torque (i.e. by the sensor S 4 ) are measured on shaft between the motor HM 2 and the pump HP 3 .The pressure sensor S 6 behind the motor HM 2 makes it possible to measure the output pressure of the motor HM 2 .Mineral oil is used as working liquid in this case with the following parameters (at the temperature t o = 25ºC): the density U = 870 kgm -3 and the kinematic viscosity Q = 80 mm 2 s -1 .Measuring data were stored in memory of the measuring instrument M5050 [3].The data were subsequently processed using Hydrowin software on personal computer (PC).Mean values of quantities were determined from their measured time dependencies.These measurements were performed during the time of 30 s with the scanning interval Δt = 100 ms.All measurements were realized at the constant temperature of the working liquid.The temperature is measured by the temperature sensor S 1 and hold by means of the cooler C [4].The legend of the used hydraulic elements (see figure 1) is the following: HP 1 -control hydraulic pump, HP 2 , HP 3 -hydraulic pumps, HM 1 , HM 2 -hydraulic motors, RV -relief valve, PV -pressure valve, FS -flow sensor, T 1 , T 2 -tanks, Ccooler, M -manometer, S 1 -temperature sensor, S 2flow sensor, S 3 , S 6 -pressure sensors, S 5 -speed sensor, S 4 -torque sensor.

Determination of geometric volume
The geometric volume V gM2 of the hydraulic motor HM 2 was experimentally determined in the following way: The flow characteristic of the motor HM 2 depending on the speed s M2 (i.e.Q M2 = f(s M2 )) was measured for different values of the pressure gradient 'p M2 .Its dependence is shown in figure 4. With respect to the speed ratio s M2.2 /s M2.1 = 1.5 y 3, it is possible to determine the geometric volume of the motor from two values of the flows Q M2.1 and Q M2.2 , which are proportional to the speeds s M2.1 and s M2.2 (see figure 5).The geometric volume is defined by the formula:

Measurement methodologies of static characteristics 4.1 Flow characteristic
The flow characteristic Q M2 = f('p M2 ) of the rotary hydraulic motor HM 2 is given by the dependence of the input flow Q M2 into the motor on the pressure gradient 'p M2 through the motor at its constant speeds which are obtained by the control hydraulic pump HP 1 .The hydraulic motor HM 2 is placed on shaft together with the torque sensor S 4 and the hydraulic pump HP 3 which is loaded by the pressure valve PV.For this reason, there is torque on the shaft between the pump HP 3 and the motor HM 2 .The torque value is also proportional to the pressure gradient 'p M2 = p 1 -p 2 through the motor HM 2 .
Speed measurements are performed by means of the optical frequency speed sensor S 5 .The flow is measured by the gear flow sensor FS (i.e. by the sensor S 2 ).The input pressure p 1 and the output pressure p 2 of the motor HM 2 are obtained by the pressure sensors S 1 a S 6 .The example of the measured values at the speed s M2 = 200 min -1 is adduced in table 1 [3].

Table. 1. Example of measured values for determination of
flow characteristic at the speed s M2 = 200 min -1 . No.

Torque characteristic
The torque characteristic W M2 = f(s M2 ) is defined by the dependence of the torque W M2 on the shaft of the hydraulic motor HM 2 on the speed s M2 at the pressure gradient 'p through the motor HM 2 .The speed s M2 is regulated by the control hydraulic pump HP 1 .The required pressure gradient ‫∆‬ ெଶ is obtained by the pressure valve PV.The pressure gradient and the speed are measured in a similar manner as in the case of the above-mentioned flow characteristic measurement.The torque measurements are performed by means of the torque sensor S 4 that is placed on the shaft between the motor HM 2 and the pump HP 3 .
The example of the measured values for the pressure gradient 'p = 50 bar is adduced in table 2.
Table 2. Example of measured values for determination of torque characteristic for the pressure gradient 'p = 50 bar. No.

Speed characteristic
The speed characteristic s M2 = f(W M2 ) is given by the dependence of the speed s M2 on the torque W M2 of the motor HM 2 at the volume flow Q M2 into the motor HM 2 .
In this case, the torque on the shaft of the motor HM 2 is controlled by means of the pressure valve PV.The input flow Q M2 into the motor HM2 is maintained constant by the control pump HP 1 .The example of the measured values for the flow Q M2 = 2 dm 3 min -1 is adduced in table 3. shown in figure 6.It is evident that it is necessary to increase the flow Q M2 on the input into the motor HM 2 at increasing the pressure gradient 'p M2 through the motor HM 2 in order to maintain the constant speed s M2 [5].

Speed characteristic
The speed characteristics s M2 = f(W M2 ) of the rotary hydraulic motor HM 2 for different values of the volume flow Q M2 (i.e. 2 dm 3 min -1 , 4 dm 3 min -1 and 6 dm 3 min -1 ) are shown in figure 8.It is evident that the speed s M2 is decreasing with increasing the motor torque W M2 (see figure 8) [5].6 Determination of flow, mechanicalhydraulic and total efficiency of rotary hydraulic motor

Flow efficiency
The flow efficiency K QM2 of the investigated rotary hydraulic motor HM 2 is expressed by the equation: The flow efficiency is strongly influenced by viscosity of used liquid.Mineral oil with the kinematic viscosity Q = 80 mm 2 s -1 at the temperature t o = 25ºC was used as the working liquid.The liquid viscosity and the flow efficiency are in general decreasing with increasing the liquid temperature.
The flow efficiencies depending on the pressure gradient 'p M2 of the rotary hydraulic motor HM 2 for different values of the speed s M2 (i.e.200 min -1 , 400 min -1 , 600 min -1 and 800 min -1 ) are shown in figure 9.It is visible that the flow efficiency is decreasing with increasing the pressure gradient 'p M2 of the motor.Furthermore, the flow efficiency is increasing with increasing the motor speed [2].

Mechanical-hydraulic efficiency
Mechanical-hydraulic efficiency K mhM2 is defined by the formula: The mechanical-hydraulic efficiencies depending on the pressure gradient 'p M2 of the rotary hydraulic motor HM 2 for different values of the speed s M2 (i.e.200 min -1 , 400 min -1 , 600 min -1 and 800 min -1 ) are shown in figure 10.It was found that the mechanical-hydraulic efficiency is increasing with increasing the pressure gradient 'p M2 .On the contrary, the efficiency is decreasing with increasing the speed [2].

Total efficiency
The total efficiency K cM2 is given by the product of the flow efficiency and the mechanical-hydraulic efficiency: The total efficiencies depending on the pressure gradient 'p M2 of the rotary hydraulic motor HM 2 for different values of the speed s M2 (i.e.200 min -1 , 400 min -1 , 600 min -1 and 800 min -1 ) are shown in figure 11.

Conclusions
There is described the experimental hydraulic system for determination of static characteristics of rotary hydraulic motors in this article.Technical parameters of the investigated system are the following: p max = 160 bar,

Figure 1 .
Figure 1.Schematic diagram of hydraulic system for experimental determination of static characteristics of rotary hydraulic motor.

Figure 2 .
Figure 2. View of experimental equipment for determination of static characteristics of rotary hydraulic motor.

Figure 3 .
Figure 3.View of torque sensor S 4 and speed sensor S 5 .

Figure 4 .
Figure 4. Verification of geometric volume of hydraulic motor from speed-flow characteristic.

Figure 6 .
Figure 6.Flow characteristics of hydraulic motor HM 2 at different speeds s M2 and the oil temperature t o = 25qC.

Figure 7 .
Figure 7. Torque characteristics of hydraulic motor HM 2 for different pressure gradients 'p M2 and the oil temperature t o = 25qC.

Figure 8 .
Figure 8. Speed characteristics of hydraulic motor HM 2 for different volume flows Q M2 and the oil temperature t o = 25qC.

Figure 9 .
Figure 9. Flow efficiencies depending on pressure gradient 'p M2 of rotary hydraulic motor HM 2 at different speeds s M2 and the oil temperature t o = 25qC.

Figure 10 .
Figure 10.Mechanical-hydraulic efficiencies depending on pressure gradient 'p M2 of rotary hydraulic motor HM 2 at different speeds s M2 and the oil temperature t o = 25qC.

Figure 11 .
Figure 11.Total efficiencies depending on pressure gradient 'p M2 of rotary hydraulic motor HM 2 at different speeds s M2 and the oil temperature t o = 25qC.

Q
max = 25 dm 3 min -1 , W max = 40 Nm.The system makes it possible to measure static characteristics of rotary hydraulic motors for different working liquids at required temperatures.The flow, torque and speed characteristics were measured by this equipment.The efficiencies are strongly influenced by speed, pressure gradient and working liquid.The geometric volume of the rotary hydraulic motor was experimentally measured too.The flow, mechanical-hydraulic and total efficiencies were obtained from the measured values.The efficiencies depend on pressure gradient and speed too.For the given hydraulic motor HM 2 , the pressure gradient 'p M2 = 90 bar and the speed s M2 = 600 min -1 , the measured values of the efficiencies are the following: K QM2 = 0.95, K mhM2 = 0.73 and K cM2 = 0.695.It is possible to obtain further values of the efficiencies from the measured graphic dependencies.