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Cylinder Cushion (IL)

Cushion in cylinder in isothermal liquid network

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  • Cylinder Cushion (IL) block

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:

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 πDplunger2/4, where Dplunger 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={Sleak,εxpistonLplungerSmax,εxpistonLplunger+Dplunger4SmaxSleakDplunger4(εxpistonLplunger)+Sleak,Lplunger<εxpiston<Lplunger+Dplunger4

where:

  • S is the orifice area for a given position of the piston.

  • Sleak is the Leakage area.

  • Splunger is the Cushion plunger cross-sectional area.

  • Smax is the Maximum orifice area. It is equal to Splunger.

  • xpiston is the displacement of the piston. (You must provide the initial displacement of the piston x0,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).

  • Lplunger is the Cushion plunger length.

  • Dplunger 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:

S^=(SSleak)(SmaxSleak).

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

S^smoothed=12+12S^2+(f4)212(S^1)2+(f4)2.

The smoothed orifice area is:

Ssmoothed=S^smoothed(SmaxSleak)+Sleak.

Similarly, the normalized valve pressure is:

p^=(ppcracking)(pmaxpcracking).

where:

  • pcracking is the Check valve cracking pressure differential.

  • pmax is the Check valve maximum pressure differential.

Smoothing applied to the normalized pressure is:

p^smoothed=12+12p^2+(f4)212(p^1)2+(f4)2,

and the smoothed pressure is:

psmoothed=p^smoothed(pmaxpcracking)+pcracking.

Ports

Conserving

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Entry port of the liquid to the cushion chamber.

Exit port of the liquid from the cushion chamber

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

Mechanical translational conserving port connected to the cylinder reference structure.

Parameters

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Cushion Plunger

Area of the cross-section of the cushion plunger, which is assumed to be circular. The area is equal to πDplunger2/4, where Dplunger is the diameter of the circular plunger.

Length of the cushion plunger.

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.

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 RC is positive. If this parameter is set to Pressure at A causes negative displacement of R relative to C, the piston retracts when RC is positive.

Valves

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

Total area of possible leaks when the plunger is inside the cap opening (the cushion sleeve). The area of the variable orifice modeling gap between the plunger and the cushion sleeve is equal to this leakage area when the displacement of the piston is less than or equal to the Cushion plunger length parameter.

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.

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.

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

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

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.

Introduced in R2020a