# 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 represents 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. When the piston position is calculated internally, it is reported at port p, and when the position is set by a connection to a Simscape™ Multibody™ joint, it is received as a physical signal at port p.

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

### Displacement

The piston displacement is measured as the position at port R relative to port C. The Mechanical orientation identifies the direction of piston displacement. The piston displacement is neutral, or `0`, when the chamber volume is equal to the Dead volume. When displacement is received as an input, ensure that the derivative of the position is equal to the piston velocity. This is automatically the case when the input is received from a Translational Multibody Interface block connection to a Simscape Multibody joint.

### 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.

### Numerically-Smoothed Area and Pressure

At the extremes of the cushion orifice area and check valve pressure range, you can maintain numerical robustness in your simulation by adjusting the block . 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:

`$\stackrel{^}{A}=\frac{\left(A-{A}_{leak}\right)}{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}.$`

where:

• Aleak is the cushion Leakage area between plunger and cushion sleeve.

• Amax is the Cushion plunger cross-sectional area.

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

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

The smoothed orifice area is:

`${A}_{smoothed}={\stackrel{^}{A}}_{smoothed}\left({A}_{\mathrm{max}}-{A}_{leak}\right)+{A}_{leak}.$`

Similarly, the normalized valve pressure is:

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

where:

• pcracking is the cushion Check valve cracking pressure differential.

• pmax is the cushion Check valve maximum pressure differential.

Smoothing applied to the normalized pressure is:

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

and the smoothed pressure is:

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

### 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.

Reference port for actuator velocity and force.

Port associated with the piston velocity and force.

### Input

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Piston position in m, received as a physical signal from a Simscape Multibody block.

#### Dependencies

To expose this port, set Piston displacement to ```Provide input signal from Multibody joint```.

### Output

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Piston position in m, returned as a physical signal.

#### Dependencies

To expose this port, set Piston displacement to ```Calculate from velocity of port R relative to port C```.

## Parameters

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### Actuator

Sets the piston displacement direction. When you set this parameter to:

• ```Pressure at A causes positive displacement of R relative to C``` the piston displacement is positive when the volume of liquid at port A is expanding. This corresponds to rod extension.

• ```Pressure at A causes negative displacement of R relative to C``` the piston displacement is negative when the volume of liquid at port A is expanding. This corresponds to rod contraction.

Cross-sectional area of the piston rod.

Maximum piston travel distance.

Volume of liquid when the piston displacement is `0`. This is the liquid volume when the piston is up against the actuator end cap.

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`.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the variable orifice and check valve are 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.

#### 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

Method for determining the piston position. The block can receive the position from a Multibody block when set to ```Provide input signal from Multibody joint```, or calculates the position internally and reports the position at port p. The position is between `0` and the Piston stroke when the mechanical orientation is positive and `0` and –Piston stroke when the mechanical orientation is negative.

Piston position at the start of the simulation.

#### Dependencies

To enable this parameter, set Piston displacement to ```Calculate from velocity of port R relative to port C```.

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`.