Cylinder Cushion (IL)

Cushion in cylinder in isothermal liquid network

Since R2020a

Libraries:
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].

Diagram of cylinder cushion

As the piston moves toward the cap, which is to the left in the figure, the cushioning bush, or plunger, 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 a check valve in the gap between the cylinder and the cap The valve restricts the flow rate leaving the cylinder chamber and reduces the initial speed of the piston.

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

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

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.

You can use the Cylinder Cushion (IL) block to model actuators. A single-acting or double-acting actuator can include cylinder cushions to slow piston motion near the ends of the stroke. The cylinder cushion 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 cushions the flow rate from port B to port A. The check valve in the block is oriented from port A to port B.

Variable Orifice Area

In the variable orifice, the block assumes that when the plunger is far away from the cushion, the orifice area is fully open and equal to $π D_{p l u n g e r}^{2} / 4$ , where D_plunger is the diameter of the circular plunger. 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 towards 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. The block assumes that the orifice area changes linearly with the piston displacement between the maximum area and the leakage area. The orifice area for a given position of the piston is

$S = {\begin{cases} \begin{matrix} S_{l e a k}, & ε x_{p i s t o n} \leq \end{matrix} L_{p l u n g e r} \\ \begin{matrix} S_{m a x}, & ε x_{p i s t o n} \geq L_{p l u n g e r} + \frac{D_{p l u n g e r}}{4} \end{matrix} \\ \begin{matrix} \frac{S_{m a x} - S_{l e a k}}{\frac{D_{p l u n g e r}}{4}} (ε x_{p i s t o n} - L_{p l u n g e r}) + S_{l e a k}, & L_{p l u n g e r} < ε x_{p i s t o n} < L_{p l u n g e r} + \end{matrix} \frac{D_{p l u n g e r}}{4} \end{cases}$

where:

S is the orifice area for a given position of the piston.
S_leak is the value of the Leakage area between plunger and cushion sleeve parameter.
S_max is the maximum size of the orifice, which is equal to the value of the Cushion plunger cross-sectional area parameter.
x_piston is the displacement of the piston. The initial displacement of the piston x_0,piston is the value of the Actuator piston initial displacement parameter.
ε is 1 when the Actuator mechanical orientation parameter is Pressure at A causes positive displacement of R relative to C and is -1 when the Actuator mechanical orientation parameter is Pressure at A causes negative displacement of R relative to C.
L_plunger is the value of the Cushion plunger length parameter.
D_plunger is the value of the Cushion plunger diameter parameter.

Numerically-Smoothed Area and Pressure

You can maintain numerical robustness in your simulation by adjusting the Smoothing factor parameter. If the Smoothing factor parameter is nonzero, the block smooths the orifice area and the check valve pressure range. The block smoothly saturates the orifice area between the Leakage area between plunger and cushion sleeve and Cushion plunger cross-sectional area parameters. The valve pressure is saturated between the Check valve cracking pressure differential and Check valve maximum pressure differential parameters. For more information, see Numerical Smoothing.

Ports

Conserving

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A — Liquid entry port
isothermal liquid

Isothermal liquid conserving port associated with the liquid entry port to the cushion chamber.

B — Liquid exit port
isothermal liquid

Isothermal liquid conserving port associated with the exit liquid port of the cushion chamber.

R — Rod
mechanical translational

Mechanical translational conserving port associated with the piston plunger velocity and force.

C — Case
mechanical translational

Mechanical translational conserving port associated with the cylinder reference structure.

Parameters

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Cushion Plunger

Cushion plunger cross-sectional area — Cross-sectional area of cushion plunger
`1e-4 m^2` (default) | positive scalar

Area of the cross-section of the cushion plunger. The area is $π D_{p l u n g e r}^{2} / 4$ , where D_plunger is the diameter of the circular plunger.

Cushion plunger length — Length of cushion plunger
`1e-3 m` (default) | positive scalar

Length of the cushion plunger.

Initial actuator piston displacement — Initial displacement of attached piston
`0 m` (default) | scalar

Displacement of the piston in the cylinder at the start of simulation. This displacement determines the initial area of the variable orifice that models the variable gap between the plunger and the end cap.

Dependencies

If the Actuator mechanical orientation block parameter is set to Pressure at A causes positive displacement of R relative to C, the value of the piston initial displacement must be positive or zero.

If the Actuator mechanical orientation block parameter is set to Pressure at A causes negative displacement of R relative to C, the value of the piston initial displacement must be negative or zero.

Actuator mechanical orientation — Piston displacement direction
`Pressure at A causes positive displacement of R relative to C` (default) | `Pressure at A causes negative displacement of R relative to C`

Piston displacement direction of the connected actuator block. If this parameter is set to Pressure at A causes positive displacement of R relative to C, the piston extends when R – C is positive. If this parameter is set to Pressure at A causes negative displacement of R relative to C, the piston retracts when R – C is positive.

Valves

Cushion orifice area — Orifice area of cushioning valve
`1e-6 m^2` (default) | positive scalar

Constant orifice area of the valve through which the fluid flows. The fluid flows from the cylinder chamber to the cap chamber when the plunger is inside the opening in the cap.

Leakage area between plunger and cushion sleeve — Total leakage area when the plunger is inside the cap opening
`1e-7 m^2` (default) | positive scalar

Total area of possible leaks when the plunger is inside the cap opening or the cushion sleeve. When the displacement of the piston is less than or equal to the value of the Cushion plunger length parameter, the area of the variable orifice that models the gap between the plunger and the cushion sleeve equals the value of this parameter.

Check valve cracking pressure differential — Pressure differential at which the check valve starts to open
`0.01 MPa` (default) | positive scalar

Minimum pressure differential across the check valve at which the valve starts to open. The check valve allows free flow of the liquid from the cushion chamber to the piston chamber, but does not allow flow in the opposite direction.

Check valve maximum pressure differential — Pressure differential needed to fully open the check valve
`0.1 MPa` (default) | positive scalar

Pressure differential across the check valve needed to fully open the valve. The value of this parameter must be greater than the Check valve cracking pressure differential parameter. The check valve allows free flow of the liquid from the cushion chamber to the piston chamber, but does not allow flow in the opposite direction.

Check valve maximum area — Opening area when check valve is fully open
`1e-4 m^2` (default) | positive scalar

Passage area of the check valve when the valve is fully open.

Check valve leakage area — Total leakage area when check valve is fully closed
`1e-10 m^2` (default) | positive scalar

Total area of possible leaks when the check valve is fully closed.

Smoothing factor — Amount of smoothing to apply to check valve and variable orifice opening area functions
`0.01` (default) | positive scalar

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the valve is in near-open or near-closed positions. Set this value to a nonzero value less than one to increase the stability of your simulation in these regimes.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a

Cylinder Cushion (IL)

Description

Variable Orifice Area

Numerically-Smoothed Area and Pressure

Ports

Conserving

A — Liquid entry port isothermal liquid

B — Liquid exit port isothermal liquid

R — Rod mechanical translational

C — Case mechanical translational

Parameters

Cushion Plunger

Cushion plunger cross-sectional area — Cross-sectional area of cushion plunger 1e-4 m^2 (default) | positive scalar

Cushion plunger length — Length of cushion plunger 1e-3 m (default) | positive scalar

Initial actuator piston displacement — Initial displacement of attached piston 0 m (default) | scalar

Dependencies

Actuator mechanical orientation — Piston displacement direction Pressure at A causes positive displacement of R relative to C (default) | Pressure at A causes negative displacement of R relative to C

Valves

Cushion orifice area — Orifice area of cushioning valve 1e-6 m^2 (default) | positive scalar

Leakage area between plunger and cushion sleeve — Total leakage area when the plunger is inside the cap opening 1e-7 m^2 (default) | positive scalar

Check valve cracking pressure differential — Pressure differential at which the check valve starts to open 0.01 MPa (default) | positive scalar

Check valve maximum pressure differential — Pressure differential needed to fully open the check valve 0.1 MPa (default) | positive scalar

Check valve maximum area — Opening area when check valve is fully open 1e-4 m^2 (default) | positive scalar

Check valve leakage area — Total leakage area when check valve is fully closed 1e-10 m^2 (default) | positive scalar

Smoothing factor — Amount of smoothing to apply to check valve and variable orifice opening area functions 0.01 (default) | positive scalar