Page 187 - The Mechatronics Handbook

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10.5 Hydraulic Cylinders

A hydraulic cylinder transfers the potential energy of the pressurized fluid into mechanical energy to
drive the operating device performing linear motions and is the most common actuator used in hydraulic
systems. A hydraulic cylinder consists of a cylinder body, a piston, a rod, and seals. Based on their
structure, hydraulic cylinders can be classified as single acting (applying force in one direction only),
double acting (exerts force in either direction), single rod (does not have a rod at the cap side), and
double rod (has a rod at both sides of the piston) cylinders.
Cylinder Parameters

A hydraulic cylinder transfers energy by converting the flow rate and pressure into the force and velocity.
The velocity and the force from a double-acting double-rod cylinder can be determined using the
following equations:
4q
v = ------------------------- (10.16)
p D –( 2 d )
2

--- D –(
F = p 2 d ) P 1 – P 2 ) (10.17)
(
2
4
The velocity and the force from a double-acting single-rod cylinder should be determined differently
for extending and retracting motions. In retraction, the velocity can be determined using Eq. (10.16),
and the force can be determined using the following equation:
(
2
2
F = P 1 p D – d ) P 2 pD 2 (10.18)
-------------------------- –
---------
4 4
In extension, the velocity and exerting forces can be determined using the following equations:
4q
v = --------- (10.19)
pD 2
2 2
p D
F = ( P 1 – P 2 )---------- + P 2 pd (10.20)
--------
4 4
The hydraulic stiffness, k h , of the cylinder plays an important role in the dynamic performance of a
hydraulic system. It is a function of fluid bulk modulus (β), piston areas (A 1 , A 2 ), cylinder chamber
volumes (V 1 , V 2 ), and the volume of hydraulic hoses connected to both chambers (V L1 , V L2 ). For a double-
acting single-rod cylinder, the stiffness on both sides of the piston acts in parallel (Skinner and Long,
1998). The total stiffness of the cylinder is given by the following equation:

2
2

k h = b -------------------- + --------------------   (10.21)
A 1
A 1

V L1 +
V L2 +
V 1
V 2
The natural frequency, ω n , of a hydraulic system is determined by the combined mass, m, of the
cylinder and the load using the following equation:
w n = k h (10.22)
----
m
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