In view of requirements for better positionaccuracy, response time and stability of hydraulic system, it ismore important than ever to pay attention to bulk modulus ofhydraulic oil. In this paper, the effects of the bulk modulus ofhydraulic oil on system performance and the entrapped air onbulk modulus have been analyzed. A method of online vacuumdegassing in a sealed system has been used to increase theeffective bulk modulus of hydraulic oil, and a device has beendeveloped to measure oil bulk modulus online. The experimentalresults show that the bulk modulus of hydraulic oil can becontrolled in real system effectively by the method mentionedabove.
* This work is supported by National Science Fund for Distinguished Young Scholars of China #50425518 and National Basic Research Program of China #2007CB714004.
Abstract - In view of requirements for better position accuracy, response time and stability of hydraulic system, it is more important than ever to pay attention to bulk modulus of hydraulic oil. In this paper, the effects of the bulk modulus of hydraulic oil on system performance and the entrapped air on bulk modulus have been analyzed. A method of online vacuum degassing in a sealed system has been used to increase the effective bulk modulus of hydraulic oil, and a device has been developed to measure oil bulk modulus online. The experimental results show that the bulk modulus of hydraulic oil can be controlled in real system effectively by the method mentioned above.
Index Terms - Hydraulic system; Bulk modulus of hydraulic oil; Vacuum degassing; Online measurement
I. INTRODUCTION
Bulk modulus is a very important physical parameter of hydraulic oil. It can seriously affect hydraulic system performance in relation to position, power level, response time, and stability [1]. During the process of dynamic analysis, modeling and simulation of hydraulic system, it is important to decide the value of oil bulk modulus reasonably and accurately. At present, in design and research of hydraulic system, the bulk modulus of hydraulic oil is usually estimated as a constant value and has nothing to with the state of system. Researchers found that the simplification makes the results of dynamic analysis and simulation very different from practice [2][3]. As the demand to the power and response time of hydraulic system increasing, more attention should be paid to bulk modulus of hydraulic oil. Which factors are related to oil bulk modulus and how much each affects? How to increase bulk modulus of hydraulic oil? How to get the value of bulk modulus of hydraulic oil in real system? Researches have been done on these questions as follows.
II. INFLUENCE OF OIL BULK MODULUS ON HYDRAULIC SYSTEM PERFORMANCE
A. Power Loss Because most fluids are compressible, the oil in an actuator must be compressed before the cylinder or piston will move a load. In other words, an amount of oil equal to the compressed volume must be added to an actuator before a load will move. Because this process does not do useful work, it is lost work:
LW p V= Δ × Δ 1
where 0
e
V pVB× ΔΔ = 2
so: 2
0L
e
p VWB
Δ ×= 3
Lost power: 2
0L
e
p VPB t
Δ ×=×
4
where p=change in pressure V0=initial volume of oil in cylinder Be=effective bulk modulus of oil B. Response Time Before the useful work, the lost work will be done. From the expression of lost power, we can see that when power is a constant, the bulk modulus is larger, the response time is shorter. C. Position Control If a cylinder moves a load at a uniform velocity, the cylinder has momentum that the oil and the system must absorb when a valve controlling upstream and downstream is suddenly closed. The downstream oil pressure will rise from some nominal value to some peak pressure as energy is absorbed. Assuming the cylinder and hydraulic lines to be rigid, and a linear rise in pressure, the bulk modulus of oil will determine peak pressure. Thus, for a specific maximum pressure, the stiffer the oil, the less energy is absorbed and the less overshoot. Oil with higher valves of bulk modulus have less energy absorption and less piston overshoot, which translates to better position accuracy. D. Stability Hydraulic natural frequency:
24 eh
t
B AV m
ω = 5
A low modulus lowers the natural frequency of a system and reduces the stability of a system. So, in order to lower the power loss, shorten the response time, increase the position accuracy and system stability, the bulk modulus of oil in hydraulic system should be improved.
III. EFFECT OF AIR ON OIL BULK MODULUS
The expression of bulk modulus of oil with entrapped air is deduced below.
Proceedings of the 2008 IEEE/ASMEInternational Conference on Advanced Intelligent Mechatronics
July 2 - 5, 2008, Xi'an, China
For pure oil:
f f
dp BdV V
= − 6
where B=bulk modulus of pure oil Vf=volume of pure oil P=pressure The result of the equation is:
( )0 /0
p p Bf fV V e− −= 7
where Vf0=volume of pure oil at atmosphere Consider the process of compression to be adiabatic, the air entrapped in oil should meet the following equation of state:
0
0
'a a
a
V Vpp V
λ� �−= � �� �
8
where p0=atmospheric pressure Va0 =total volume of bubbles at atmosphere Va’=dissolved volume of air when pressure changes from p0 to p Va=total volume of bubbles under pressure p
λ=adiabatic index Total volume of oil with air entrapped under pressure p:
( ) ( )0
1//0
0 0'
a f
p p Ba a f
V V V
pV V V ep
λ− −
= +
� �= − +� �
� �
9
Tangent bulk modulus of oil with entrapped air:
( ) ( )
( ) ( )
0
0
1//0
0 0
1//00 0
'
' 1
eT
p p Ba a f
p p Bfa a
dpB VdV
pV V V ep
VV V p ep p B
λ
λ
λ
− −
− −
= −
� �− +� �� �=
− � � +� �� �
10
As bulk modulus of pure oil is much larger than (p-p0), and ( )0 / 1p p Be −− ≈ , the above can be simplified:
The simulation results are shown in Fig.1. B is set to 1800MPa. The green short dash lines present air content at atmosphere is 0.2%, and following the direction of the arrow the dissolution of the bubbles is 0%-90%. The red long dash lines present air content at atmosphere is 2%, and following the direction of the arrow the dissolution of the bubbles is 0%-90%. The blue continuous lines present air content at atmosphere is 10%, and following the direction of the arrow the dissolution of the bubbles is 0%-90%.
Fig. 1 Tangent bulk modulus of oil with entrapped air changes with pressure.
Secant bulk modulus of oil with entrapped air:
( )
( )
( ) ( )( )
( )( )
0
0
00
0
0 00
0 0
0 001/
/00 0 0 0
0
001/
/0 0 0
0 0
12
'
1
'1
eS
a f
a f a f
a f
p p Ba a f a f
a
f
p p Ba a a
f f
VB p pV V
V Vp p
V V V VV V
p ppV V V e V Vp
VV
p pV V V p eV V p
λ
λ
− −
− −
= − −−
+= − −
+ − −
+= − −
� �− + − −� �� �
+= −
� �−+ − −� �� �
��
The simulation results are shown in Fig.2. B is set to 1800MPa. The green short dash lines present air content at atmosphere is 0.05%, and following the direction of the arrow the dissolution of the bubbles is 0%-99%. The red long dash lines present air content at atmosphere is 0.1%, and following the direction of the arrow the dissolution of the bubbles is 0%-99%. The blue continuous lines present air content at atmosphere is 0.2%, and following the direction of the arrow the dissolution of the bubbles is 0%-99%. From Fig.1 and Fig.2, we can see that when the pressure is the same, less the air content at atmosphere, larger the bulk modulus. More over, when the pressure changes, less the air content at atmosphere, smaller the changes of bulk modulus with pressure. Less the air content at atmosphere, smaller the effect of resolution of bubbles on bulk modulus. All these show that in order to improve the bulk modulus of oil in hydraulic systems, air content in oil should be as low as possible. There are two ways to decrease air content of oil in hydraulic system. One is that oil should be degassed before they start to work, and the other is to prevent air entering into hydraulic systems during the process of work.
0.2 2 10%
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Fig. 2 Secant bulk modulus of oil with entrapped air changes with pressure.
. MEASURES OF DEGASSING IN HYDRAULIC SYSTEMS
A. Pressure-sealed Reservoir The reservoir is sealed, so the air in the atmosphere can not be entrained to oil in system. The reservoir is pressurized, so the solubility of gas in oil is increased, less air will separate out from oil. This is very benefit to increase the effective bulk modulus of oil and to reduce cavitations erosion. But the problems of oil supplement and tank pressure control should be resolved. The methods are not expounded here for the paper length limits. B. Online Vacuum Degassing The principle of the vacuum degassing device is shown in Fig.3.
First, the air cylinder pulls the piston of the piston accumulator moving to the left, and the oil level in the reservoir descends, so the inside of the reservoir becomes vacuum. Then, open the integrated driven ball valve to connect the reservoir and the vacuum pump. When the pressure in the reservoir is lower than the oil-gas separation pressure, the dissolved air separates from oil. After the air is released from oil, the vacuum pump suctions the air rapidly. Control the pressure in the reservoir always higher than saturation vapour pressure of oil to prevent the oil atomizing. During the process of vacuum degassing pre-treatment, the pressure-sealed reservoir works as a vacuum vessel. While in the period of hydraulic system working, the reservoir is sealed by the integrated driven ball valve and pressurized by the air cylinder.
. OIL BULK MODULUS ONLINE MEASUREMENT
In order to test the effect of vacuum degassing and to find out the bulk modulus of oil in system, an online oil bulk modulus auto-measuring device is designed. Its principle is shown in Fig.4.
(1) Loading cylinder and piston; (2) Check valve;(3) Pressure sensor;
(4) Testing chamber;(5) Displacement sensor; (6) Two-position four-way directional control valve; (7) Pilot relief valve; (8) Two-position two-way directional control valve; (9) Direct relief valve;
(10) Two-position two-way directional control poppet valve (11) Pressure reducing valve; (12) Gas holder; (13) Air cylinder;
Fig. 4 Schematic diagram of oil bulk modulus measurement.
Base on the definition of bulk modulus. Pressurize oil in the sealed testing chamber by the piston rod of loading cylinder. The value of the pressure is controlled by the two stage pressure control circuit. The volume of the oil in the testing chamber is changed with the pressure. Using pressure sensor and displacement sensor to record the change of pressure and volume of the oil in the testing chamber, compute the value of the bulk modulus. The characteristics of the device is that, auto measuring process, online measurement, circulation of the oil in the testing chamber before measuring to make sure that the result presents the actual situation of the oil in system, and the result not effected by friction force.
1
2
3 4 5
6
7 8 9
14
15
16
17 13
12
11
10
0.050.1 0.2
9
8
6
5
7
10
3
4
2
1
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. CONTROL FLOW OF VACUUM DEGASSING PRE-TREATMENT
Before hydraulic systems start to work, vacuum degassing pre-treatment will be done to control of bulk modulus of oil in systems. The control flow of the process of vacuum degassing
pre-treatment is shown in Fig.5. The numbers of the components in Fig. 5 are corresponding to the numbers in Fig.3.
Fig. 5 Control flow of vacuum degassing pre-treatment
. EXPERIMENT RESEARCH The experiments were carried out on the hydraulic driven system of motion simulator of comprehensive test bed for docking mechanism.
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The picture of the pressure-sealed reserv-oir is shown in Fig.6, which is used as a vacuum vessel in the process of vacuum de-gassing pre-treatment.
The picture of the oil bulk modulus mea-surement device is shown in Fig.7, which is used to control the process of vacuum de-gassing pre-treatment.
For the effects of air content at atmosphere and of resolution of bubbles on bulk modulus are obvious under low pressure, the experiments were mainly done with the pressure in testing chamber below 3MPa. Several groups of testing data are given in Tab.1.
The method called ‘parallel secant method’ has been used to evaluate results. The principle involved may be seen from Fig.8, which represents a compression curve for oil. The points 0, A, B and C correspond to pressures of zero, p1, p2 and p3 (where p3=p1+p2), to relative volume changes of zero, R1, R2 and R3 and to secant bulk modulus of B0, B1, B2 and B3. It follows from the definition of secant bulk modulus that B3 is equal to the slope of 0C. The slope of the line AB is denoted by B3
’; it is termed the ‘parallel secant modulus at pressure p3’ because, provided that p1 is small compared with p2, AB is almost parallel with 0C. Consequently, B3
’ is a good approximation to B3.
Pre
ssur
e p
Fig. 8 Principle of the parallel secant method.
By this method, the secant bulk modulus and the corresponding pressure of oil in the system can be found with the data in Tab.1. The evaluating data are given in Tab.2.
Tab.2 evaluating data of secant bulk modulus Group
No. State description BeS
(MPa) p
(MPa) T
( ) 1 Before vacuum degassing 907.3 2.170 42.72 After vacuum degassing 960.3 2.314 41.73 Before air entering into
the system 1073.3 3.530 35.6
4 After air entering into the system
929 3.623 35.9
Found the data in Tab.2 on the Fig.9 of secant bulk modulus of oil with entrapped air changes with pressure. From above to below the curves respectively present air content at atmosphere of 0.1% to 0.2% with incremental change of 0.02%.
Fig. 6 Picture of the pressure-sealed reservoir.
Fig. 7 Picture of the oil bulk modulus measurement device.
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Fig. 9 Secant bulk modulus of oil with entrapped air changes with pressure.
From Fig.9, we can see that after a short time of vacuum degassing about 30 minutes, the air content decreases from 0.13% to 0.12%. After air entering into the system, the air content increases from 0.2% to 0.14%. These show that air content in oil affects the bulk modulus apparently. By the means of vacuum degassing, the air content in oil decreases and the bulk modulus of oil increases. There is a point should be noted during the process that the time of vacuum degassing shouldn’t be too short. Other wise, the dissolved air is separated out from oil rapidly in vacuum environment and has no enough time to be gathered to form big bubbles and to be pumped out the system. So if the process ends in this condition and the pressure changes to be normal, the air which has been separated out from oil but not
pumped out is not easy to be dissolved and makes the bulk modulus of oil decreasing instead.
. CONCLUSIONS
1) The analysis of the effect of air on oil bulk modulus shows that the oil in hydraulic systems should be degassed before they start to work and prevent air entering into hydraulic systems during the process of work. 2) The method of vacuum degassing before system works and reservoir pressurized and sealed when system works, increases the bulk modulus of oil in system effectively. 3) The designed oil bulk modulus online measuring device accurately reflects the effect of the vacuum degassing.
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it important” Hydraulics & Pneumatics, no. 7, pp. 34-39, July 2007. [2] Ali Volkan Akkaya, “Effect of bulk modulus on performance of a
hydrostatic transmission control system” Sadhana, vol. 31, pp. 543-556, 2006.
[3] K A Edge, “Cylinder pressure transients in oil hydraulic pumps with sliding plate valves” Proc. Int. Mech. Eng., vol. 200, pp. 45-54, 1986.
[4] A. T. J. Hayward, “How to measure the isothermal compressibility of liquids accurately” Journal of Physics D: Applied Physics, vol. 4, no.7, pp.938-950, 1971.
[5] Karjalainen, J-P, Karjalainen, R., “Fluid dynamics-comparison and discussion on system-related differences” Proc.10th SICFP, Tampere University of Tech, vol. 2, pp. 371–381, 2007.
[6] H. R. Li, “Hydraulic control systems” Defense Industry Press, Beijing, pp.147-152, 1981.
[7] Y. X. Lu, “Hydraulic pneumatic technical manual” China Machine Press, Beijing, pp. 230-232, 2002.
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