CALCULATION FOR CYLINDERS
Piston Force Calculations
The piston force exerted by the cylinder is dependent upon the air pressure,
the cylinder diameter and the frictional resistance of the sealing components. The
theoretical piston force is calculated by the formula:
In practice, the effective piston force is significant. When calculating this,
frictional resistance should be taken into consideration. Under normal operating
conditions (pressure range of 400 to 800 kPa / 4 to 8 bar) frictional force of approx.
10% of the theoretical piston force can be assumed.
Single-acting cylinder:
Double-acting cylinders:
Forward Stroke
Return Stroke
Feff
Feff
Feff
Feff
=
=
=
=
Feff
=
Fth - FR
(A • p) - FR
Fth - FR
(A' • p) - FR
Where:
effective piston force in newton (N)
Example 1
A double-acting cylinder with a piston diameter of 200mm and a piston rod
diameter of 25mm has an operating pressure of 6 bar. Calculate the following:
a. The theoretical piston forces (N) for both forward and return strokes
b. The effective piston forces (N) for both forward and return strokes if the friction
force is 10% of the theoretical forces.
Given:
1𝑚
D = 200mm x 1000𝑚𝑚. = 0.2m
1𝑚
d = 25mm x 1000𝑚𝑚 = 0.025 m
P = 6bar x
100,000𝑃𝑎
1𝑏𝑎𝑟
= 600,000 Pa or N/m2
FR = 10% Fth
Required:
Determine
a) Fth for forward and return strokes
b) Feff for forward and return strokes
Solution:
a. Theoretical Piston Forces
Forward Stroke
Fth = (A • p)
A = (D)2 / 4
A = (0.2m)2 / 4
A = 0.0314m2
Fth = (0.0314m2 • 600,000N/m2)
Fth = 18,840N
Return Stroke
Fth = (A' • p)
A' = (D2 – d2) / 4
A' = [(0.2m)2 – (0.025m)2] / 4
A' = 0.0309m2
Fth = (0.0309m2 • 600,000N/m2)
Fth = 18,540N
b. Effective Piston Forces
Feff = (A • p) - FR
Forward Stroke
Feff = Fth – 0.10•Fth
Feff = 0.90•Fth
Feff = 0.90 • 18,840N
Feff = 16,956N
Feff = (A' • p) - FR
Return Stroke
Feff = Fth – 0.10•Fth
Feff = 0.90•Fth
Feff = 0.90 • 18,540N
Feff = 16,686N
Example 2
A double-acting cylinder with operating pressure of 7bar produces effective forces
of 4,950N during the forward stroke and 4,900N during the return stroke. Determine the
piston diameter and the piston rod diameter of if the friction force is 10% of the theoretical
force
Given:
Forward Stroke
Feff = 4,950N
Return Stroke
Feff = 4,900N
P = 7bar x
100,000𝑃𝑎
1𝑏𝑎𝑟
= 700,000 Pa or N/m2
FR = 10% Fth
Required:
For the double acting cylinder, determine the piston diameter (D) in mm and the
piston rod diameter (d) in mm
Solution:
Forward Stroke
Feff = (A • p) - FR
4,950N= Fth – 0.10•Fth
4,950N= 0.90 • Fth
4,950N= 0.90 • (A • p)
A = 4950N / (0.90)(700,000N/m2)
A = 0.00785m2
A = (D)2 / 4
0.00785m2 = (D)2 / 4
D = 0.1m x
1000𝑚𝑚
1𝑚.
D = 100mm
Return Stroke
Feff = (A' • p) - FR
4,900N= Fth – 0.10 • Fth
4,900N= 0.90 • Fth
4,900N= 0.90 • (A' • p)
A' = 4,900N / (0.90)(700,000N/m2)
A' = 0.00777m2
A' = (D2 – d2) / 4
0.00777m2 = [(0.1m)2 – (d)2] / 4
(0.00777m2) x 4 /  = (0.1m)2 – (d)2
0.00989m2 = 0.01m2 – d2
d = 0.01049m x
1000𝑚𝑚
1𝑚.
d = 10.49mm or 10.5mm