# Single-Acting Actuator (IL)

Linear conversion of pressure to actuation in an isothermal liquid system

• Library:
• Simscape / Fluids / Isothermal Liquid / Actuators

## Description

The Single-Acting Actuator (IL) block models an actuator that converts the liquid pressure at port A into a mechanical force at port R via an extending-retracting piston. The piston motion is limited by a hard stop model. The variable piston position is set by a physical signal at port P.

The Piston initial displacement, Fluid dynamic compressibility, and reference environmental pressure can be modified. Fluid and mechanical inertia are not modeled.

### Hard Stop Model

Three models are available to model the extension limit of the actuator piston. This block uses a similar formulation as the Translational Hard Stop block and models uniform damping and stiffness coefficients at both ends of the piston stroke. For more information on the hard stop model options, see the Translational Hard Stop block.

The hard stop force is modeled when the piston is at its upper or lower bound. The boundary region is within the Transition region of the Piston stroke or Piston initial displacement. Outside of this region, ${F}_{HardStop}=0.$

### Cushion

You can optionally model cushioning toward the extremes of the piston stroke. Setting Cylinder end cushioning to `On` slows the piston motion as it approaches its maximum extension, which is defined in Piston stroke. For more information on the functionality of a cylinder cushion, see the Cylinder Cushion (IL) block.

### Friction

You can optionally model friction against piston motion. When Cylinder friction is set to `On`, the resulting friction is a combination of Stribeck, Coulomb, and viscous effects. The pressure difference is measured between the chamber pressure and the environment pressure. For more information on the friction model and its limitations, see the Cylinder Friction block.

### Leakage

You can optionally model leakage between the liquid chamber and the piston reservoir. When Leakage is set to `On`, Poiseuille flow is modeled between the piston and cylinder. This block uses the Simscape Foundation Library Laminar Leakage (IL) block. The flow rate is calculated as:

`$\stackrel{˙}{m}=\frac{\frac{\pi }{128}\left({d}_{0}^{4}-{d}_{i}^{4}-\frac{{\left({d}_{0}^{2}-{d}_{i}^{2}\right)}^{2}}{\mathrm{log}\left({d}_{0}/{d}_{i}\right)}\right)}{\upsilon L}\left({p}_{A}-{p}_{env}\right),$`

where:

• ν is the fluid kinematic viscosity.

• L is the piston length, PP0.

• pA is the pressure at port A.

• penv is the environmental pressure, which is selected in the Environment pressure specification parameter.

The cylinder diameter, d0, is ${d}_{0}={d}_{i}+2c,$ where c is the Piston-cylinder clearance, and the piston diameter, di, is ${d}_{i}=\sqrt{\frac{4{A}_{P}}{\pi }},$ where AP is the Piston cross-sectional area.

### Block Sub-Components

The Single-Acting Actuator (IL) block comprises four Simscape Foundation and two Fluids Library blocks:

• Translational Hard Stop

• Laminar Leakage (IL)

• Converter

• Sensor

• Cylinder Cushion (IL)

• Cylinder Friction (IL)

Actuator Structural Diagram

## Ports

### Conserving

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Liquid entry point to the actuator chamber.

Cylinder casing reference velocity and force.

Actuator piston velocity and force.

### Output

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Piston position, in m.

## Parameters

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### Actuator

Sets the piston displacement direction. ```Fluid pressure moves R away from C``` corresponds to positive displacement, or actuator rod extension. ```Fluid pressure moves R towards C``` corresponds to negative displacement, or actuator rod retraction. Displacement is always expressed as a positive value.

Cross-sectional area of the piston rod.

Maximum piston travel distance.

Open volume in the fluid chamber when the piston is fully retracted.

User-defined environmental pressure.

#### Dependencies

To enable this parameter, set Environment pressure specification to ```Specified pressure```.

Environment reference pressure. The ```Atmospheric pressure``` option sets the environmental pressure to 0.101325 MPa.

### Hard Stop

Piston stiffness coefficient.

Piston stiffness coefficient. This value must be greater than 0.

Model choice for the force on the piston at full extension or full retraction. See the Translational Hard Stop block for more information.

Application range of the hard stop force model. Outside of this range of the piston maximum extension and piston maximum retraction, the Hard stop model is not applied and there is no additional force on the piston.

#### Dependencies

To enable this parameter, set Hard stop model to ```Stiffness and damping applied smoothly through transition region, damped rebound```.

### Cushion

Whether to model piston slow-down at maximum extension. See the Cylinder Cushion (IL) block for more information.

Area of the plunger inside the actuator cushion element.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Length of the cushion plunger.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Area of the orifice between cushion chambers.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Gap area between the cushion plunger and sleeve. This value contributes to numerical stability by maintaining continuity in the flow.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Pressure beyond which the valve operation is triggered. When the pressure difference between port A and Penv meets or exceeds the Check valve cracking pressure differential, the cushion valve begins to open.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Maximum cushion valve differential pressure. This parameter provides an upper limit to the pressure so that system pressures remain realistic.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Cross-sectional area of the cushion valve in its fully open position.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

Sum of all gaps when the cushion check valve is in a fully closed position. Any area smaller than this value is saturated to the specified leakage area. This value contributes to numerical stability by maintaining continuity in the flow.

#### Dependencies

To enable this parameter, set Cylinder end cushioning to `On`.

### Friction

Whether to model friction against piston motion. The model accounts for Coulomb, Stribeck, and viscous friction. See the Cylinder Friction block for more information.

Ratio of the breakaway force to the Coulomb friction force.

#### Dependencies

To enable this parameter, set Cylinder friction to `On`.

Threshold velocity for motion against friction force to begin.

#### Dependencies

To enable this parameter, in the Friction tab, set Cylinder friction to `On`.

Initial force in the cylinder due to seal assembly.

#### Dependencies

To enable this parameter, set Cylinder friction to `On`.

Coulomb force coefficient of friction.

#### Dependencies

To enable this parameter, set Cylinder friction to `On`.

Viscous friction coefficient.

#### Dependencies

To enable this parameter, set Cylinder friction to `On`.

### Leakage

Whether to model annular leakage between the fluid chamber and the piston reservoir at reference environment conditions. The leakage is considered laminar. See the Laminar Leakage (IL) block for more information.

Radial distance between the piston rod and cylinder casing.

#### Dependencies

To enable this parameter, set Leakage to `On`.

Annular length of the piston mounting, not including the piston rod.

#### Dependencies

To enable this parameter, set Leakage to `On`.

### Initial conditions

Neutral piston position.

Whether to model any change in fluid density due to fluid compressibility. When Fluid compressibility is set to `On`, changes due to the mass flow rate into the block are calculated in addition to density changes due to changes in pressure. In the Isothermal Liquid Library, all blocks calculate density as a function of pressure.

Starting liquid pressure for compressible fluids.

#### Dependencies

To enable this parameter, set Fluid dynamic compressibility to `On`.