Page 442 - Mechatronics with Experiments

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of the hydraulic fluid. The heat exchanger transfers heat between two separate fluids (i.e.,
hydraulic fluid and water, or hydraulic fluid and air). If the heat is transferred from the
hydraulic fluid to the other fluid (i.e., to cold water), it functions as a cooler. If the heat is
transferred from the other fluid (i.e., from hot water) to the hydraulic fluid, it is used as a
heater. In most applications, the hydraulic fluid needs to be cooled. However, in very cold
environment temperatures, it is necessary to heat the hydraulic fluid instead of cooling it. A
typical heat exchanger uses a temperature sensor in the hydraulic fluid reservoir in order to
control the temperature in closed loop control mode. A regulator (analog or digital) controls
a valve (which modulates the flow rate of the second fluid) based on the temperature sensor
signal and the desired temperature value. In general, the viscosity of oil increases (oil gets
thicker and resists flow more) as temperature decreases. As the oil viscosity increases, the
flow rate of pumps reduces due to the fact that oil is less fluid and the suction action of the
pump cannot pull-in as much oil.

Bulk Modulus Bulk modulus, , represents the compressibility of the fluid volume,
and is defined as
dp
=− (7.24)
dV∕V
where the negative sign indicates that the volume gets smaller as the pressure increases. The
bulk modulus has the same units as pressure. It is an indication of the stiffness of the fluid.
The higher the bulk modulus of the fluid is, the less compressible it is. It is also a function
of pressure and temperature. The nominal value of bulk modulus for hydraulic fluids is
around = 250 000 psi. Entrapped air in fluid can drastically reduce the bulk modulus
of a hydraulic line. Hence, the hydraulic circuit becomes softer and the system motion
bandwidth gets slower. Therefore, it is important to take care in design and operation of
hydraulic circuits that there is no entrapped gas in the hydraulic fluid lines. The overall
system would lose its stiffness significantly.

Example Consider a hydraulic fluid with bulk modulus of = 250 000 psi, a nominal
3
volume of V = 100 in . If the fluid is compressed from atmospheric pressure level to the
0
2500 psi level, find the change in the fluid volume.
Since,
dp
=− (7.25)
dV∕V
0
Then,
V ⋅ dp
0
dV =− (7.26)

100 ⋅ 2500
=− (7.27)
250 000
=−1in 3 (7.28)
= 1%V 0 (7.29)

which shows that a typical hydraulic fluid will contract about one percent in volume under
a 2500 psi increase in pressure. The negative sign indicates that the volumetric change is a
decrease.
Entrapped gas (i.e., air) in hydraulic oil significantly reduces the effective bulk
modulus of the hydraulic fluid. The more entrapped gas there is, the lower the bulk modulus
will be. For instance, consider this example with entrapped air in the hydraulic fluid such
that the bulk modulus is 1∕2 the previous case without entrapped gas. For the same load