How to Calculate Stretch in Cylinder Tie Rods
FLUID POWER - Design Data Sheet 16
The amount of stretch (elongation) in mechanical members under
tension is very easy to calculate with a simple formula. The method
described on this sheet can be applied to any structural member
subjected to stress. In fluid power design, it can be applied to
determine the elongation of cylinder tie rods when the cylinder is
under fluid pressure and is mounted as in Figure
1, or when severe momentary shocks pass through hydraulic
lines; it can be used to find the expected stretch in bolts holding
a component to a manifold, holding SAE flange unions together, or
holding a pipe flange to the body of a hydraulic component. It can
be used to estimate whether the tie rods or barrel of a foot
mounted cylinder may distort under pressure, binding the
Figure 1. Tie
rods elongate under fluid pressure on cylinders mounted in this
Elasticity for Common Metal (in Tension)
|Cast Iron, Gray
Gathering Data for the
Collect the following data and you will be ready to make the
calculation: (1), length of the stressed member, in inches; (2),
cross sectional area of the stressed member, in square inches; (3),
total applied force, in lbs., which is stretching the member; and
(4), the modulus of elasticity, E, of the material from which the
stressed member is constructed. This can be found from the table
under Figure 1. For other materials, refer to a
machine handbook. Since the modulus of elasticity is a ratio, it
has no units.
Simple Formula for
Elongation = (1 × F) ÷ (A × E), in
L is length, in
F is applied force, in lbs.
A is cross section, square inches;
E is modulus of elasticity (from table)
Elongation will come out in inches.
Calculation Example for
Cylinder Tie Rods
Problem: Find the stretch in the tie rods of a 6"
bore cylinder operating at 3,000 PSI. There are four steel tie rods
of 1" diameter, and they are 27" long.
Solution: First, get all your facts assembled:
Piston area of a 6" bore cylinder is 28.27 square inches. The tie
rods are the stressed members, and each rod has a sectional area of
0.785 square inches, or a total of 3.14 square inches for all rods
combined. The stressing force is 3,000 PSI × 28.27 = 84,810 lbs.
Modulus of elasticity is 30,000,000 (from table). Now apply the
Elongation = (27 × 84,810) ÷ (3.14 ×
30,000,000) = 0.0243 inches
How to Check for Over-Stressing
The stressed member will return to its normal length after the
applied force has been removed provided it was not stressed beyond
its elastic limit. To determine if a given force will over-stress a
structural member, take the force value, in lbs., and divide it by
the cross sectional area, in square inches, of the member. This
will give the stress value in PSI (lbs. per square inch). Compare
this with the elastic limit of the material as published in
machinery handbooks. As in all mechanical design, a suitable factor
of safety should be allowed.
How to Calculate Stretch Produced by Hydraulic
Pressure surges which pass through the system, even momentarily,
may over-stress and damage cylinders or other components. These
pressure surges are generated when a 4-way directional valve is
shifted, when a hydraulic motor is stopped too abruptly, when a
hydraulic cylinder is allowed to de-compress too rapidly, and by
mechanical shocks or impacts against the cylinder piston rod from
the load. The peak pressure of these surges can be determined by
instrumentation. Sometimes they can be measured by the simple
method described in
Data Sheet 14. Then, the above method can be applied,
and the member can be checked for possible over-stressing.
Short Stroke Cylinders with Long Connecting
Certain problems may develop when a short stroke cylinder is
operated through long lines from its directional control valve. If
the internal volume of the cylinder is less than the volume in the
connecting lines, the fluid in the line is never replaced by fresh
fluid coming from the supply. It circulates back and forth between
the lines and the cylinder. This may be a problem in either air or
Replenishment of oil in lines connecting valve to hydraulic
Figure 2. Hydraulic System. Oil which may
circulate back and forth between lines and cylinder without being
replaced may become overheated if cycling is rapid and regular. Hot
oil causes seals and hoses to fail prematurely. There may also be a
danger to personnel who may accidentally touch the cylinder or the
This circuit eliminates the problem. Double lines are used to
both the rod end and blind end ports, isolated with check valves.
Oil flowing toward the cylinder follows Paths A, and oil returning
from the cylinder follows Paths B. Since the check valves prevent
the oil from reversing, a new charge of oil enters the cylinder
loop on every cycle.
The idea for this method: came from Fred Miner and Jerry Snow in
Hydraulics and Pneumatics magazine.
Figure 3. Quick
exhaust valves allow oil mist to be carried into air
Figure 3. Air System. Short stroke air
cylinders may also be a problem, but for a different reason. They
are not likely to overheat, but the oil mist delivered by the
lubricator in the system may never reach the cylinder, which may
result in a shortened cylinder life.
Double connecting lines with check valves as in Figure
2 can be used with good results, but quick exhaust valves
may be a better solution. Figure 3 shows two quick
exhaust valves, although one may be sufficient. Wipe-off inside the
cylinder may provide lubrication to the entire cylinder
As in any air system excess oil mist is blown out the exhaust
and may contaminate the atmosphere. Lubricator feed rate should be
very low, as in most systems very little oil is needed.
Under-lubrication is better than over-lubrication.
Single-acting air cylinder.
Figure 4. The quick
exhaust method is also applicable to single-acting air cylinders
for keeping the barrel lubricated. Faster cylinder retraction is an
Note that the meter-out method of speed control cannot be used
in quick exhaust circuits. Nor can needle valves be installed in
valve exhaust ports for speed control. If a speed control should be
needed, install a needle valve in the air supply line, or, install
a meter-in flow control in the cylinder line just as close to the
cylinder as possible.
Download a PDF of Fluid
Power Design Data Sheet 16 - How to Calculate Stretch in Cylinder
© 1989 by Womack Machine Supply Co. This
company assumes no liability for errors in data nor in safe and/or
satisfactory operation of equipment designed from this