Page 60 - Fluid Power Engineering

Hydraulic Oils and Theor etical Backgr ound 37

D ⎞
in ∑
∫ (∑ Q − Q ) dt = V ⎛ 1 + 4 5 Eh⎠ ⎟ Δ P = Δ (2.79)
⎜
C P
⎝
out
B
D ⎞
where C = V ⎛ 1 + 4 5 Eh⎠ ⎟ (2.80)
⎜
⎝
B
Example 2.1 Apply the continuity equation to both chambers of the shown
hydraulic cylinder.

dy V dP
Q − A = A A , where V = V + A y
A P dt B dt A Ao p
dy V dP B where V = V − A y
A − Q = B B Bo r
r dt B B dt

where A = Piston area, m 2
P
A = Piston rod side area, m 2
r
V = Volume of oil in chamber A, m 3
A
V = Initial volume of piston side chamber, m 3
Ao
V = Volume of oil in chamber B, m 3
B
V = Initial volume of rod side chamber, m 3
Bo
y = Piston displacement, m
2.2.4 Thermal Expansion
The hydraulic liquids are subjected to volumetric thermal expan-
sion. Generally, the volume of liquids changes with temperature as
follows:
ΔV =α V ΔT
T (2.81)
where V = Initial volume of oil, m 3
α= Thermal expansion coefficient, for typical mineral oil
α= 0.0007 K −1
ΔT = Temperature variation, °C
ΔV = Oil volume variation due to thermal expansion, m 3
T
In the case of oil trapped in a rigid vessel for a long period, the
pressure may increase to enormous values due to the rise in oil tem-
perature. Considering a volume of oil trapped in a hydraulic cylinder,