# GENERAL CALCULATIONS

## FORCE / PISTON DIAMETER

A: effective piston surface [mm2]

F: force [N]
p: pressure [bar]
D: piston diameter [mm]
d: rod diameter [mm]
η: efficiency of the hydraulic cylinder

The efficiency [η], which is for the most part the result of the frictional losses (seals, guides), can be approximated as 0 .8. The larger the cylinder, the smaller the effect of friction on the overall force. At speeds of less than 0 .05 m/s  (0 .164 feet/s), the friction is practically independent of the pressure.

For piston diameters of 100 mm (3 .94 inches) and larger the percentage loss is not more than 2%, even in the worst case. With even larger piston diameters it can even be regarded as insignificant.

Example:

For cylinders with a piston diameter of less than 20 mm (0 .79 inches) and an operating pressure of approx. 140 bar (2030 PSI) the frictional losses can be about 20%. For a piston diameter of 100 mm (3.94 inches) this value is reduced to 2%.

It has been noted in practice that new seals have relatively high frictional values, which however become lower as the operating time increases, thus increasing the efficiency of the hydraulic cylinder. This should be taken into account above all when the cylinders are being operated at low speeds (stick-slip effect), or low operating pressures are present.

For hydraulic cylinders, the interrelationship between the force [F], the system pressure [p] and the piston area [A] is produced by the following formula: ##### The force resulting from the system pressure is lower at the rod end than at the piston end. The effective surface is calculated as follows: As a general rule, the circular area [A] is calculated from the diameter [D] using the following formula: Alternatively from the force to be applied [F] and the pressure [p]: Determination of the piston diameter as a function of the system pressure and the required force: ## Piston speed from flow rate / pump capacity

v: piston speed [m/s]
Q: flow rate [l/min]
A: piston surface [mm2]
P: required pump capacity [KW]
p: system pressure [bar]
η: efficiency of the hydraulic system

## Required oil quantity / flow rate

Q: flow rate [l/min]
A: piston surface [mm2]
v: piston speed [m/s]
η: efficiency of the hydraulic cylinder

## Recommended flow speeds

Suction lines:

≤ 1,5 m/s

Return lines:
≤ 3 m/s

Pressure lines:

≤ 25 bar ≤ 3 m/s
25 bis 63 bar 3 – 5 m/s
63 bis 160 bar 4 – 6 m/s
160 bis 250 bar 5 – 8 m/s
> 250 bar ≤ 10 m/s

## Buckling strength

Proper dimensioning of hydraulic cylinders with pushing load makes use of the four so-called Euler buckling modes. Because the following calculations already include a quintuple safety margin, the results can be used directly.

d: Piston rod diameter [mm]
F: Axial force [N]
L: Mounting distance [mm]

First Euler buckling mode: piston rod is neither guided nor fastened – cylinder fixed

Second Euler buckling mode:
piston rod and cylinder with rotating bearing

Third Euler buckling mode:
piston rod with rotating bearing – cylinder fixed

Fourth Euler buckling mode:
piston rod guided and fastened – cylinder fixed