cylinder, the initial position of the piston, and the change of the gas state in
cylinder. In addition, the friction between the moving parts and the resistance at the
sealing filler are also related. If these factors affecting piston motion characteristics
at the same time are regarded as independent variables, the theoretical calculation
results of piston motion characteristics under different conditions can be obtained.
In order to investigate the influence of various factors on piston motion characteristics, the following dimensionless quantities and parameters are introduced.
1. B ¼ C v1 =C v2 represents the flow coefficient ratio of the inlet and exhaust passages of the cylinder. B value is large, indicating that the flow coefficient C v1 of
the inlet port is large, that is, the flow resistance of the inlet port is small, that is
to say, the amount of gas entering the working chamber ① of the cylinder
through the inlet port increases in unit time. A small B value indicates that the
throttling loss at the outlet passage of the cylinder is large, and it becomes an
outlet throttling circuit.
2. I ¼ A 1 p s =M
ð
Þ z p =v
2
0
À
Á
, when the action area A 1 , the supply pressure p s , the
piston working stroke z p , and the piston average velocity v 0 are known, the
dimensionless quantity is proportional to the reciprocal of the mass M of the
cylinder moving parts. It shows that the smaller the I value, the greater the
inertia of the cylinder moving parts.
3. S 0 ¼ z 0 =z p represents the ratio of the initial position of the piston before starting
to the working stroke z p of the piston. The smaller the S 0 value is, the closer the
piston’s starting position is to the side of the inlet port, that is to say, the volume
of cylinder working chamber ① is the smallest, while that of cylinder working
chamber ② on the other side of the piston is the largest, and vice versa.
4. T a ¼ z p =v 0 represents the time required to complete a working stroke z p at the
piston average velocity v 0 .
5. W t represents the total load acting on the piston (including frictional force).
According to the dimensionless quantities p 1 =p s , p 2 =p s , v=v 0 , t=T a quoted previously and the newly defined dimensionless quantities B, I, S 0 as well as the
parameters T a and load W t , the gas state in the cylinder is calculated according to
three different changing processes, that is, adiabatic process, variable process and
isothermal process, and the calculated piston motion characteristics (i.e., the relationship between pressure p 1 , p 2 and piston velocity v and time t) and the experimental results are drawn together on the dimensionless coordinate diagram.
Figures 8.21 and 8.22 are the theoretical curves and experimental results of the
motion characteristics of cylinder and piston based on the above method (the dots in
the figure represent the measured values).
From Figs. 8.21 and 8.22, it can be seen that the theoretical calculation results
are in good agreement with the measured results, if the gas state in cylinder is
calculated according to the multivariate process (n ¼ 1:2). Therefore, in practical
calculation, it is reasonable to regard the change of gas state in cylinder as a variable
process (n ¼ 1:2).
24
8 Pneumatic Actuators, Driving Elements and Accessories
cylinder. In addition, the friction between the moving parts and the resistance at the
sealing filler are also related. If these factors affecting piston motion characteristics
at the same time are regarded as independent variables, the theoretical calculation
results of piston motion characteristics under different conditions can be obtained.
In order to investigate the influence of various factors on piston motion characteristics, the following dimensionless quantities and parameters are introduced.
1. B ¼ C v1 =C v2 represents the flow coefficient ratio of the inlet and exhaust passages of the cylinder. B value is large, indicating that the flow coefficient C v1 of
the inlet port is large, that is, the flow resistance of the inlet port is small, that is
to say, the amount of gas entering the working chamber ① of the cylinder
through the inlet port increases in unit time. A small B value indicates that the
throttling loss at the outlet passage of the cylinder is large, and it becomes an
outlet throttling circuit.
2. I ¼ A 1 p s =M
ð
Þ z p =v
2
0
À
Á
, when the action area A 1 , the supply pressure p s , the
piston working stroke z p , and the piston average velocity v 0 are known, the
dimensionless quantity is proportional to the reciprocal of the mass M of the
cylinder moving parts. It shows that the smaller the I value, the greater the
inertia of the cylinder moving parts.
3. S 0 ¼ z 0 =z p represents the ratio of the initial position of the piston before starting
to the working stroke z p of the piston. The smaller the S 0 value is, the closer the
piston’s starting position is to the side of the inlet port, that is to say, the volume
of cylinder working chamber ① is the smallest, while that of cylinder working
chamber ② on the other side of the piston is the largest, and vice versa.
4. T a ¼ z p =v 0 represents the time required to complete a working stroke z p at the
piston average velocity v 0 .
5. W t represents the total load acting on the piston (including frictional force).
According to the dimensionless quantities p 1 =p s , p 2 =p s , v=v 0 , t=T a quoted previously and the newly defined dimensionless quantities B, I, S 0 as well as the
parameters T a and load W t , the gas state in the cylinder is calculated according to
three different changing processes, that is, adiabatic process, variable process and
isothermal process, and the calculated piston motion characteristics (i.e., the relationship between pressure p 1 , p 2 and piston velocity v and time t) and the experimental results are drawn together on the dimensionless coordinate diagram.
Figures 8.21 and 8.22 are the theoretical curves and experimental results of the
motion characteristics of cylinder and piston based on the above method (the dots in
the figure represent the measured values).
From Figs. 8.21 and 8.22, it can be seen that the theoretical calculation results
are in good agreement with the measured results, if the gas state in cylinder is
calculated according to the multivariate process (n ¼ 1:2). Therefore, in practical
calculation, it is reasonable to regard the change of gas state in cylinder as a variable
process (n ¼ 1:2).
24
8 Pneumatic Actuators, Driving Elements and Accessories