In fact, the actual output thrust of the piston rod is smaller than the theoretical
thrust F th because of the mechanical friction between the inner wall of the cylinder
and the piston seal ring and the inertia force of the cylinder moving parts. If factors
such as friction force and inertia force are taken into account, the actual thrust
output of the piston is as follows:
F ¼ F th À R f þ U f
À
Á ¼ A 1 p 1 À A 2 p 2 À R f þ m
dv
dt
ð8:19Þ
or
F ¼ A 1 p 1 À A 2 p 2 À R f À m
dv
dt
ð8:20Þ
where
m Mass of piston and parts moving with piston;
v Piston speed;
R f The sum of all frictional forces in the cylinder device, including the frictional
forces at the contact surface of the sealing filler and the sliding parts of the
cylinder inner wall. The magnitude of these frictional forces is related to the
type of sealing filler, working pressure, and processing conditions of cylinder
inner wall. The frictional force is obtained by experiment and it is very difficult
to calculate by mathematical analytic method.
(2) Gas consumption per stroke
In the performance analysis or design calculation of the actuator of servo system,
the important parameter is the geometric size of the actuator or the volume of the
cylinder. Therefore, when calculating the amount of gas consumed in each stroke of
the cylinder, the volume flow is usually converted from the weight of the gas
consumed in each stroke to the volume flow of the gas under the standard atmospheric pressure. The purpose of this method is to select the standard cylinder
conveniently because the volume is directly related to the size of the cylinder.
If the single piston rod cylinder is discussed, as shown in Fig. 8.14, the amount
of gas consumed by the cylinder during driving load and no-load return can be
calculated, respectively. If the working volume of the cylinder is V 1 and V 2 ,
respectively, and the time required for each working stroke is t, according to the gas
state equation, the relationship between the gas displacement per unit stroke and the
pressure in the free state (standard atmospheric pressure) consumed by the round
trip can be obtained as follows.
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8 Pneumatic Actuators, Driving Elements and Accessories
thrust F th because of the mechanical friction between the inner wall of the cylinder
and the piston seal ring and the inertia force of the cylinder moving parts. If factors
such as friction force and inertia force are taken into account, the actual thrust
output of the piston is as follows:
F ¼ F th À R f þ U f
À
Á ¼ A 1 p 1 À A 2 p 2 À R f þ m
dv
dt
ð8:19Þ
or
F ¼ A 1 p 1 À A 2 p 2 À R f À m
dv
dt
ð8:20Þ
where
m Mass of piston and parts moving with piston;
v Piston speed;
R f The sum of all frictional forces in the cylinder device, including the frictional
forces at the contact surface of the sealing filler and the sliding parts of the
cylinder inner wall. The magnitude of these frictional forces is related to the
type of sealing filler, working pressure, and processing conditions of cylinder
inner wall. The frictional force is obtained by experiment and it is very difficult
to calculate by mathematical analytic method.
(2) Gas consumption per stroke
In the performance analysis or design calculation of the actuator of servo system,
the important parameter is the geometric size of the actuator or the volume of the
cylinder. Therefore, when calculating the amount of gas consumed in each stroke of
the cylinder, the volume flow is usually converted from the weight of the gas
consumed in each stroke to the volume flow of the gas under the standard atmospheric pressure. The purpose of this method is to select the standard cylinder
conveniently because the volume is directly related to the size of the cylinder.
If the single piston rod cylinder is discussed, as shown in Fig. 8.14, the amount
of gas consumed by the cylinder during driving load and no-load return can be
calculated, respectively. If the working volume of the cylinder is V 1 and V 2 ,
respectively, and the time required for each working stroke is t, according to the gas
state equation, the relationship between the gas displacement per unit stroke and the
pressure in the free state (standard atmospheric pressure) consumed by the round
trip can be obtained as follows.
16
8 Pneumatic Actuators, Driving Elements and Accessories