# Cylinder Cushion (IL)

Cushion in cylinder in isothermal liquid network

**Library:**Simscape / Fluids / Isothermal Liquid / Actuators / Auxiliary Components

## Description

The Cylinder Cushion (IL) block models a cylinder cushion in an isothermal liquid network. The cushion decelerates the cylinder rod as it approaches the end of a stroke by restricting the flow rate leaving the cylinder chamber. This figure below shows a typical cylinder cushion design [1].

**Typical Cylinder Cushion Design**

As the piston moves toward the cap (to the left in the figure), the plunger (the cushioning bush) enters the chamber in the cap and creates an additional resistance to the fluid leaving the cylinder chamber. The piston deceleration starts when the plunger enters the opening in the cap and closes the main fluid exit. In this state, the fluid flows through the gap between the cylinder and the cap through a cushioning valve. This restricts the flow rate leaving the cylinder chamber and reduces the initial speed of the piston.

The device contains a check valve between the cylinder and the cap. The check valve eases piston response during retraction by providing a flow path between the cap and cylinder chamber.

The cylinder cushion is a composite of a variable orifice, a fixed orifice, and a check valve. The variable orifice provides a variable opening between the plunger and end cap cavity. The fixed orifice connects the piston chamber to the cushion chamber. The check valve provides a flow path between the cushion chamber and the piston chamber during piston retraction only.

The Cylinder Cushion (IL) block is a composite component that consists of these blocks shown in the figure:

A Local Restriction (IL) block that models the cushioning valve.

A Check Valve (IL) block that models the check valve.

An Orifice (IL) block that models the variable gap between the plunger and the end cap.

An Ideal Translational Motion Sensor block that converts the separation between the plunger and the cavity in the end cap into a physical signal. This signal controls the opening of the Orifice (IL) block.

The Cylinder Cushion (IL) block is an actuator building block. A single-acting or double-acting actuator can optionally include cylinder cushions to slow piston motion near the ends of the stroke. This prevents extreme impacts when the piston is stopped by the end caps.

Ports **A** and **B** are isothermal liquid conserving
ports associated with the chamber inlet and outlet, respectively. Port
**R** is a mechanical translational conserving port connected with
the piston plunger. Port **C** is a mechanical translational conserving
port that corresponds to the cylinder clamping structure. The block develops a
cushioning effect for the flow rate from port **B** to port
**A**. The check valve in the block is oriented from port
**A** to port **B**.

### Equation for Area of Variable Orifice

In the variable orifice, it is assumed that when the plunger is far away from the cushion,
the orifice area is fully open and equal to $$\pi {D}_{plunger}{}^{2}/4$$, where
*D*_{plunger} is the
diameter of the circular plunger. Also, when the plunger is in the cushion, the
orifice is fully closed and the orifice area is equal to the leakage area. As the
plunger moves close to the cushion, the fluid flows radially from the cylinder
chamber to the cap chamber through the gap between the plunger and the opening in
the cap. Therefore, it can be assumed that the orifice area changes linearly with
piston displacement between the maximum area and the leakage area. The orifice area
for a given position of the piston is calculated as:

$$S=\{\begin{array}{l}\begin{array}{cc}{S}_{leak},& \epsilon {x}_{piston}\le \end{array}{L}_{plunger}\\ \begin{array}{cc}{S}_{max},& \epsilon {x}_{piston}\ge {L}_{plunger}+\frac{{D}_{plunger}}{4}\end{array}\\ \begin{array}{cc}\frac{{S}_{max}-{S}_{leak}}{\frac{{D}_{plunger}}{4}}(\epsilon {x}_{piston}-{L}_{plunger})+{S}_{leak},& {L}_{plunger}<\epsilon {x}_{piston}<{L}_{plunger}+\end{array}\frac{{D}_{plunger}}{4}\end{array}$$

where:

*S*is the orifice area for a given position of the piston.*S*_{leak}is the**Leakage area**.*S*_{plunger}is the**Cushion plunger cross-sectional area**.*S*_{max}is the**Maximum orifice area**. It is equal to*S*_{plunger}.*x*_{piston}is the displacement of the piston. (You must provide the initial displacement of the piston*x*_{0,piston}as a block parameter.)*ε*is the**Actuator mechanical orientation**of the cylinder cushion (`1`

if the displacement indicates positive motion,`-1`

if the displacement moves in the negative direction).*L*_{plunger}is the**Cushion plunger length**.*D*_{plunger}is the**Cushion plunger diameter**.

### Numerically-Smoothed Area and Pressure

At the extremes of the orifice area and check valve pressure range, you can maintain
numerical robustness in your simulation by adjusting the block **Smoothing
factor**. A smoothing function is applied to all calculated areas and
valve pressures, but primarily influences the simulation at the extremes of these
ranges.

The normalized orifice area is calculated as:

$$\widehat{S}=\frac{\left(S-{S}_{leak}\right)}{\left({S}_{\mathrm{max}}-{S}_{leak}\right)}.$$

The **Smoothing factor**, *f*,
is applied to the normalized area:

$${\widehat{S}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{S}}_{}^{2}+{\left(\frac{f}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\widehat{S}-1\right)}^{2}+{\left(\frac{f}{4}\right)}^{2}}.$$

The smoothed orifice area is:

$${S}_{smoothed}={\widehat{S}}_{smoothed}\left({S}_{\mathrm{max}}-{S}_{leak}\right)+{S}_{leak}.$$

Similarly, the normalized valve pressure is:

$$\widehat{p}=\frac{\left(p-{p}_{cracking}\right)}{\left({p}_{\mathrm{max}}-{p}_{cracking}\right)}.$$

where:

*p*is the_{cracking}**Check valve cracking pressure differential**.*p*is the_{max}**Check valve maximum pressure differential**.

Smoothing applied to the normalized pressure is:

$${\widehat{p}}_{smoothed}=\frac{1}{2}+\frac{1}{2}\sqrt{{\widehat{p}}_{}^{2}+{\left(\frac{f}{4}\right)}^{2}}-\frac{1}{2}\sqrt{{\left(\widehat{p}-1\right)}^{2}+{\left(\frac{f}{4}\right)}^{2}},$$

and the smoothed pressure is:

$${p}_{smoothed}={\widehat{p}}_{smoothed}\left({p}_{\mathrm{max}}-{p}_{cracking}\right)+{p}_{cracking}.$$

## Ports

### Conserving

## Parameters

## References

[1] Rohner, P. *Industrial
Hydraulic Control*. Fourth edition. Brisbane: John Wiley & Sons,
1995.

**Introduced in R2020a**