# Air Spring

Sealed translational air spring

• Library:
• Simscape / Driveline / Couplings & Drives

## Description

The Air Spring block represents a generic sealed translational pneumatic spring that isolates equipment from shocks and vibrations. The compressibility of gas gives air springs desirable isolation performance. Air springs are common in automotive and industrial applications where low spring rate and low natural frequency are beneficial. Air springs can help you to:

• Reduce wear and tear on the sprung mass.

• Reduce the wear and tear that the unsprung mass deals to infrastructure.

• Lighten suspension systems to allow for greater total mass.

• Filter out specific unwanted frequencies.

Air springs consist of bellows that confine a column of compressed air or other gas. The air bears the force of the load, and the bellows hold the air. Sealed air springs maintain a constant mass of air, so the increasing load lowers the volume of air and the resulting spring rate. The reverse is also true. The natural frequency of a sealed air spring system also depends on this relationship. Due to the large amount of variability in air spring requirements and performance, manufacturers commonly provide pressure characteristic tables for each model.

Based on the data that you possess, you can set Parameterization to `Load as a function of height` or ```Stiffness as a function of height```. The Air Spring block uses the information that you enter to create a lookup table. The lookup table allows the block to simulate the nonlinear force response of an arbitrary air spring. This is the effective force to achieve a given height, which is equivalent to the Load vector parameter or the element-wise product of the Stiffness vector parameter and the Height vector parameter. For more information about using lookup tables in Simscape™, see `tablelookup`.

The block takes the relative translational motion between port R and port C to evaluate the air spring height and velocity and uses this information to find the appropriate lookup table entry. The block computes the nonlinear effective force response ΣF(x(t),t), such that:

`$\sum F\left(x\left(t\right),t\right)=-c\left(x\left(t\right)\right)\stackrel{˙}{x}\left(t\right)-k\left(x\left(t\right)\right)x\left(t\right)+{F}_{external},$`

where

• x(t) is the height of the spring relative to the undisturbed position.

• ẋ(t) is the velocity of the spring.

• -c(x(t))ẋ(t) is the viscous damping force. The damping coefficient c varies with spring height.

• -k(x(t))x(t) is the stiffness force. The spring coefficient k varies with spring height.

• Fexternal is the force transmitted through the ports.

You can choose whether to implement hard stops in your model on the Hard Stops tab. When you set Hard stop at full extension or Hard stop at full compression to `On`, you can specify a boundary height, the stiffness and damping at that height, and the length of the transition region. The hard stops are equivalent to the Translational Hard Stop block.

### Variables

Use the Variables tab to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

The sign of the Force variable is negative when the load is positive.

## Ports

### Conserving

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Mechanical translational conserving port associated with the follower of the air spring. Positive physical signals travel from R to C.

Mechanical translational conserving port associated with the base end of the air spring. Positive physical signals travels from R to C.

## Parameters

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### Spring

Option to parameterize by height or load. Obtain data for your air spring from manufacturer-supplied specifications or experimental results.

Vector of spring heights. These values correspond to either the load or stiffness values, depending on the way you choose to parameterize the spring. You must specify a vector that has at least three elements.

Vector of spring loads. This vector must be the same length as the Height vector parameter.

#### Dependencies

To enable this parameter, set Parameterization to ```Load as a function of height```.

Vector of spring stiffness values. This vector must be the same length as the Height vector parameter.

#### Dependencies

To enable this parameter, set Parameterization to ```Stiffness as a function of height```.

Vector of spring damping values. This vector must be the same length as the Height vector parameter.

Lookup table breakpoint interpolation. The block uses the `tablelookup` function to model nonlinearity by using array data to map input values to output values:

• `Linear` — Select this option for the lowest computational cost.

• `Smooth` — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information, see `tablelookup`.

Lookup table breakpoint extrapolation. This method determines the output value when the input value is outside the range specified in the argument list. The block uses the `tablelookup` function to model nonlinearity by using array data to map input values to output values:

• `Linear` — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• `Error` — Select this option to avoid extrapolating when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

For more information, see `tablelookup`.

### Hard Stops

Option to enable a hard stop when the air spring is fully extended. The hard stop occurs as the spring reaches the value of the Maximum height parameter. For more information, see Translational Hard Stop.

Maximum spring height. This parameter determines the location of the full-extension hard stop.

#### Dependencies

To enable this parameter, set Hard stop at full extension to `On`.

Stiffness to apply as the spring reaches full extension.

#### Dependencies

To enable this parameter, set Hard stop at full extension to `On`.

Damping to apply as the spring reaches full extension.

#### Dependencies

To enable this parameter, set Hard stop at full extension to `On`.

Option to enable a hard stop when the air spring is fully extended. The hard stop occurs as the spring reaches the value of the Minimum height parameter. For more information, see Translational Hard Stop.

Minimum spring height. This parameter determines the location of the full-compression hard stop.

#### Dependencies

To enable this parameter, set Hard stop at full compression to `On`.

Stiffness to apply as the spring reaches full compression.

#### Dependencies

To enable this parameter, set Hard stop at full compression to `On`.

Damping to apply as the spring reaches full compression.

#### Dependencies

To enable this parameter, set Hard stop at full compression to `On`.

Stiffness and rebound options for the hard stop model. You can choose from the following options:

• ```Stiffness and damping applied smoothly through transition region, damped rebound```

• ```Full stiffness and damping applied at bounds, undamped rebound```

• ```Full stiffness and damping applied at bounds, damped rebound```

#### Dependencies

To enable this parameter, set Hard stop at full extension or Hard stop at full compression to `On`.

Distance from full compression or full extension where the effects of stiffness and damping are partially applied. When you set Hard stop model to ```Stiffness and damping applied smoothly through transition region, damped rebound```, the block will smoothly transition the onset of stiffness and damping as the spring approaches full extension or full compression.

#### Dependencies

To enable this parameter, set Hard stop at full extension or Hard stop at full compression to `On`, and set Hard stop model to ```Stiffness and damping applied smoothly through transition region, damped rebound```.

## Version History

Introduced in R2021a