Page 188 - The Mechatronics Handbook

0066_frame_C10 Page 8 Wednesday, January 9, 2002 4:10 PM

10.6 Fluid Power Systems Control

System Steady-State Characteristics

The steady-state characteristics of a fluid power system determine loading performance, speed control
capability, and the efficiency of the system. Modeling a hydraulic system without loss of generality, a
system consisting of an open-center four-way directional control valve and a single-rod double acting
cylinder is used to analyze the steady-state characteristics of the system (Fig. 10.1). In this system, the
orifice area of the cylinder-to-tank (C-T) port in the control valve is always larger than that of the pump-
to-cylinder (P-C) port. Therefore, it is reasonable to assume that the P-C orifice controls the cylinder
speed during extension (Zhang, 2000).
Based on Newton’s Law, the force balance on the piston is determined by the head-end chamber pressure,
P 1 , the head-end piston area, A 1 , the rod-end chamber pressure, P 2 , the rod-end piston area, A 2 , and the
external load, F, when the friction and leakage are neglected.

P 1 A 1 – P 2 A 2 = F (10.23)

If neglecting the line losses from actuator to reservoir, the rod-end pressure equals zero. Then, the
head-end pressure is determined by the external load to the system.

F
P 1 = ----- (10.24)
A 1
In order to push the fluid passing the control valve and entering the head-end of the cylinder, the
discharge pressure, P P , of the hydraulic pump has to be higher than the cylinder chamber pressure.
The difference between the pump discharge pressure and the cylinder chamber pressure is determined
by the hydraulic resistance across the control valve. Based on the orifice equation, the flow rate entering
the cylinder head-end chamber is

2
q = C d A o --- P P –( P 1 ) (10.25)
r

Using a control coefficient, K, to represent C d and ρ, the cylinder speed can be described using the
following equation:

F
v = KA o ----- (10.26)
--------- P P –
A 1 A 1
Equation (10.13) describes the speed-load relationship of a hydraulic cylinder under a certain fluid
passing area (orifice area) of the control valve. Depicted in Fig. 10.4, the cylinder speed decreases as the
external load applied to the cylinder increases. When there is no external load, the cylinder speed reaches
a maximum. Conversely, when the external load researches the valve of F = P P A 1 , then the cylinder will
stall. The stall load is independent of the size of the fluid passing area in the valve. Such characteristics
of a fluid power system eliminate the potential of overloading, which makes it a safer power transmission
method.
In system analysis, the speed stiffness, k v , is often used to describe the consistency of the cylinder speed
under changing system load (Li et al., 2000).

1
k v = – ----- = 2 P P A 1 –( F) (10.27)
----------------------------
∂ v v
-------
∂F
©2002 CRC Press LLC