# Hydraulic Cylinder Calculations

Hydraulic cylinders are the muscle of a hydraulic system.  In this article we'll present the equations for hydraulic cylinder calculations and discuss efficiency.

## Cylinder Equations - SI

These are the formulas for SI units.  All formulas are for theoretical values.

## Cylinder Equations - US

These are the formulas for US units.  All formulas are for theoretical values.

## Hydraulic Cylinder Efficiency

There are three types of efficiency associated with a hydraulic cylinder.

1. Volumetric efficiency.
2. Mechanical/hydraulic efficiency.
3. Total efficiency.

Volumetric efficiency accounts for the leakage of fluid from the cylinder that doesn't do any work.  Unless the cylinder is leaking, volumetric efficiency is basically 100% and disregarded.

Mechanical/hydraulic efficiency accounts for friction losses.  There is mechanical friction associated with the piston and rod seals.  There is also fluid friction as fluid enters and exits the cylinder.

Total efficiency is volumetric efficiency X mechanical/hydraulic efficiency.  Since volumetric efficiency is assumed to be 100%, total efficiency is a function of mechanical/hydraulic efficiency.  Therefore, we are most concerned with mechanical/hydraulic efficiency, at least in theory.

## Why Efficiency is Not Useful

Sizing cylinders using the concept of efficiency is not very useful.  As we stated earlier, assuming 100% volumetric efficiency is valid, so we'll focus on mechanical/hydraulic efficiency.

Fluid friction is dependent on port size and piston speed (flow rate).  The cylinder ports must be sized to minimize losses to an acceptable level and the pressure entering the cylinder must be enough to overcome losses and deliver the desired force.

The other factor is seal friction.  This friction is independent of the working pressure, and hence the forces transmitted by the cylinder.  This friction is referred to as the breakloose pressure.  That is, it's the pressure required to overcome seal friction and get the piston moving.

The idea of efficiency loses it's appeal when you consider it doesn't account for the actual forces that are transmitted by the cylinder.  Let's consider two different applications of the same cylinder that pushes a load.  The cylinder has a 2 inch bore and a breakloose pressure of 20 psi.  The piston area is 3.14 square inches.

For the first example, the load on the cylinder is 300 pounds.  The pressure required for the load is:

P = 300/3.14 = 95.5 psi

The cylinder efficiency is:

η = 95.5/(20 + 95.5) = .827 or 82.7%

For the second example, the load on the cylinder is 600 pounds.  The pressure required for the load is:

P = 600/3.14 = 191.1 psi

The cylinder efficiency is:

η = 191.1/(20 + 191.1) = .905 or 90.5%

There is almost an 8% difference in efficiency and it is entirely dependent on the load.  Therefore, speaking in terms of efficiency is not very useful.  It's better to calculate the theoretical pressure required and add the breakloose pressure.

Another method would be to measure the force required to move the piston and add it to the load.  Then the actual pressure required can be calculated.

MEboost can easily perform hydraulic cylinder calculations.  To learn more, visit the MEboost page.