## 0.0 - Introduction

The Cylinder Service Centre (CSC) required a technical document indicating the forces that act on components within a simple hydraulic cylinder. Specifically, CSC required diagrams and explanation for forces acting on the Cylinder Shaft, the Piston Head and the system which secures the Piston Head to the Shaft in the case of pressure on the annular side.

CSC Contracted a local university to produce a technical report with the required explanation of the forces. The following are extracts from that report.

## 1.0 - Summary

The basis of this report was, with respect to the example given,  to answer the CSC questions:

1. What are the forces acting on the Piston face?

2. What are the forces acting on the Nut?

This report shows that the forces vary depending on what Piston Head retention system is used.

If a circlip (or any non preloaded system) is used, the force acting to separate the Piston Head and the Cylinder Shaft shoulder is the applied pressure multiplied by the area of the Piston Head. The Piston Head and Shaft shoulder will separate and the load is fully reacted by the Piston Head Retainer.

If a preloaded system is used the force between the Cylinder Shaft and Piston Head is initially the Piston Head Retainer preload value. Once pressure is applied this force will reduce. The Piston Head and Cylinder Shaft shoulder will remain in contact unless the applied pressure x Piston Head area exceeds the preload

The maximum force the Piston Head Retainer will see is the larger of the preload and the applied pressure x full Piston Head area (Equation 13). It is interesting to note that the load on the Piston Head Retainer is greater than the external load, which is due to the reduced shaft size passing through the Piston Head.

Increasing this portion of shaft reduces the load on the Retainer.

## 2.0 - Example Cylinder

As an example the following scenario was used:

• If the cylinder was mounted vertically and 2 tonnes was hung from the cylinder (depressurised), then 2 tonnes would be reacted through the fastening system (either a nut or a circlip)
• If pressure was then applied to the annulus side of the cylinder, what would the forces be on the different parts of the system
• Note that the nut holding the piston head in place may or may not be preloaded. If it is a circlip there is no preload
• The fluid pressure acts up to the O-ring between the piston head and the shaft.
• The 'Spacer' component will be ignored

The system which secures the Piston Head to the Shaft will be referred to as the Piston Head Retainer.

An example load case has been used to illustrate the forces in the cylinder components. A tensile force applied to one end of the cylinder. Pressure supplied to compress the cylinder. Figure 1 shows the external forces acting on the cylinder. Surfaces under pressure are highlighted in orange. Figure 1 - External Forces

## 3.0 - Free Body Diagrams and Forces Acting

Free body diagrams have been prepared for the Cylinder Shaft, Piston Head and Piston Head Retainer. A free body diagram has not been included for the spacer, as it is clear of the Piston Head and therefore acted on by pressure on all sides, and has no net forces. As the parts are axisymmetric around the z-axis. radial forces as a result of pressure acting on the cylindrical surfaces have not been shown as these produce no net force.

The following colour coding has been used. Figure 2 - Diagram Colour Coding

## 3.1 Cylinder Shaft Force from Piston Head Retainer = FCS1

This could be a load on threads or on a circlip groove.

(If preload is applied to a fastener = FCS1 could be a range of values, depending on the magnitudes of the preload and cylinder pressure).

External load = Fexternal

Fastener preload force = FPRE

Force acting on Shaft shoulders:

 FCS2 = P π (Ø22) − Ø12 - eq. 1 4

 FCS3 = P π (Ø32) − Ø22 - eq. 2 4

Summation of Forces:

 Fexternal = FCS1 − FCS2 − FCS3 − FCS4 - eq. 3

From Equations 1, 2and 3:

 FCS3 = P π (Ø32) − Ø22 −FCS3 = P π (Ø32) − Ø22 - eq. 4 4 4

Therefore:

 FCS3 = Fexternal+ P π (Ø32) − Ø12 +FCS4 - eq. 5 4

If there is no preload and no pressure then the load on the Piston Head Retainer will equal the External Load.

Equation 5 shows that, when pressurised, the load on the Piston Head Retainer is greater than the applied load.

Figure3 - Cylinder Shaft free body diagram Figure 4 - Cylinder Shaft Pressure Areas

## 3.2 - Piston Head Figure 5 - Piston Head, preload, free body diagram

Fastener preload force = FPRE

If there is no fluid pressure in the Cylinder, the force acting on the bottom surface would balance the preload.

 FPH1 = FPH3 = FPRE - eq. 6

If there is no preload the Piston Head retainer force (FPH1) would balance pressure force (FPH2) acting on the bottom surface, giving:

 FCS3 = FPH2 = P π (Ø42) − Ø12 - eq. 7 4

And

 FPH3 = 0 - eq. 8

If there is preload then, as fluid fluid is increased in the annulus side of the Cylinder, the reaction force between the bottom of the Piston Head and the Cylinder Shaft shoulder (FPH3) will reduce.

Summation of forces -

 FPH1 = FPH3 + FPH3 - eq. 9

Where:

 FPH2 = P π (Ø42) − Ø12 - eq. 10 4

Therefore:

 FPH1 = P π (Ø42) − Ø12 + FPH3 - eq. 11 4

FPH1 remains approximately constant at FPH1 - FPRE until the pressure force (FPH2) exceeds the preload when Equation 7 applies. Figure 6 - Piston head retainer free body diagram

Force exerted by Piston Head Retainer i.e. fastener preload, or reaction load from a circlip = FPHR1

This force can vary significantly depending on the type of retention method used and for a heavily preloaded fastener, there may be an additional force exerted onto the shaft through this component.

Reaction force from Piston Head = FPHR2

As per section 3.2 the FPHR1 load can vary from zero to FPRE before pressure is applied to the cylinder.

Once pressure is applied, the solutions are different for each retention case.

For the case with no preload (from Equation 7):

 FPHR2 = FPHR1 = P π (Ø42) − Ø12 - eq. 12 4

For the preloaded fastener case, the maximum FPHR2 magnitude will be the greater of:

 FPHR2 = π (Ø42− Ø12) - eq. 13 4

And

 FPHR2 = FPHRE - eq. 14

## 3.4 Overall Assembly

Equation 5 gives:

 FCS1 = Fexternal + P π (Ø32− Ø12) + FCS4 4

Equation 11 gives:

 FPH1 = P π (Ø42− Ø12) + FPH3 4

 Now, FCS1 = FPH1 therefore:

 Fexternal + P π (Ø32− Ø22) +FCS4 = P π (Ø42− Ø12) +FCS4   - eq. 15 4 4

The contcat force between the Piston head (FPH3) and the Cylinder Shaft shoulder (FCS4) are variable, but equal. Therefore:

 Fexternal = P π (Ø42− Ø12) −   P π (Ø32− Ø12) - eq. 16 4 4

So:

 Fexternal = P π (Ø42− Ø32) - eq. 17 4

Which represents the case of the load being carried by the cylinder pressure.

In order to ensure that the Piston Head remains in contact with the Cylinder Shaft shoulder the preload in the Piston Head Retainer (from Equations 13 and 14) should be:

 FPRE > P π (Ø42− Ø12) - eq. 18 4

## 4.0 - Summary

The basis of this report was to answer the CSC questions:

1. What are the forces acting on the Piston face?

2. What are the forces acting on the Nut?

This report shows that the forces vary depending on what Piston Head retention system is used.

If a circlip (or any non preloaded system) is used, the force acting to separate the Piston Head and the Cylinder Shaft shoulder is the applied pressure multiplied by the area of the Piston Head. The Piston Head and Shaft shoulder will separate
and the load is fully reacted by the Piston Head Retainer.

If a preloaded system is used the force between the Cylinder Shaft and Piston Head is initially the Piston Head Retainer preload value. Once pressure is applied this force will reduce. The Piston Head and Cylinder Shaft shoulder will remain in contact unless the applied pressure x Piston Head area exceeds the preload

The maximum force the Piston Head Retainer will see is the larger of the preload and the applied pressure x full Piston Head area {Equation 13). It is interesting to note that the load on the Piston Head Retainer is greater than the external load,
which is due to the reduced shaft size passing through the Piston Head.

Increasing this portion of shaft reduces the load on the Retainer.

## 5.0 Discussion

It is likely that a cylinder will be used a significant number of times during its life and therefore fatigue needs to be considered in the design, but is outside the scope of this project.

For reference: if no preload is applied then component stress will cycle between zero and a maximum value and will generally have a shorter life than a preloaded component, In a preloaded component the stress either remains constant or cycles between two similar values resulting in longer life.