Page 445 - Mechatronics with Experiments

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JWST499-c07
JWST499-Cetinkunt
ELECTROHYDRAULIC MOTION CONTROL SYSTEMS 431
l
Q
0 d

FIGURE 7.19: Hydraulic circuit where sudden
closure of valve results in pressure spikes due to
the inertia of the moving fluid.

Similarly, the diode and the check valve analogy is that they allow flow of electricity
and fluid in one direction, and block it in the opposite direction,
i = i V ≥ V o (7.49)
i
o
i
= 0.0 V < V o (7.50)
i
Q = Q p ≥ p o (7.51)
i
o
i
= 0.0 p < p (7.52)
i o
where i , i are input and output current, V , V are input and output voltage, repectively.
i o i o
Similar notation applies for Q , Q , p , p for flow rate and pressure.
o i i o
1
Example Consider the hydraulic circuit shown in Figure 7.19 . The dimensions of
the pipe are shown in the figure, d = 20 mm, l = 10 m. Assume that there is a constant
3
flow rate in steady-state, Q = 120 l∕min = 2l∕s = 0.002 m ∕s. The mass density of fluid
0
3
is = 1000 kg∕m . Then, the valve closes suddenly, over a period of Δt = 10 ms, which
results in a pressure spike. This phenomenon is also known as water hammering. Assume
that the relief valve does not open.
The change in pressure due to the inertial deceleration of the fluid due to sudden
closure of the valve is determined by
Δp = p − p = L ⋅ Q ̇ (7.53)
1 2
⋅ l Q 0
= (7.54)
A Δt
1000 ⋅ 10 0.002
= (7.55)
2
(0.02) ∕4 0.01
0.2 8 2
= 10 Nt∕m (7.56)

20
= MPa = 6.36 MPa (7.57)

Notice that in this example we neglected the pressure change due to the compressibility of
the fluid. A long pipe (inductor equivalent) and accumulator (capacitor equivalent) pair can
be used as the LC filtering effect on the pressure in hydraulic circuits.
7.2.2 Energy Loss and Pressure Drop in Hydraulic
Circuits
Anytime there is a pressure drop and flow in a hydraulic circuit, there is energy loss. The lost
energy is converted to heat at the loss point. Recall that hydraulic power is equal to pressure
difference times the flow rate between two points. Hence, the energy differential between

1 Courtesy of Mr. Daniele Vecchiato.