# Bearing

**Libraries:**

Simscape /
Driveline /
Couplings & Drives

## Description

The Bearing block represents a ball- or roller-type bearing
or a journal bearing. These bearings constrain a shaft in the transverse plane so the
shaft may only rotate axially in the bearing. Bearings also contribute torque to the
system due to friction. You can add bearing friction to a mechanical rotational network
by connecting the network to only port **B** or by connecting the
bearing in series with other components using ports **B** and
**F**.

You can use either a constant or variable load on the bearing, *F*.
When you set **Radial load specification** to
`Constant`

, the block uses the value of the **Load
on bearing** parameter. When you set **Radial load
specification** to `Variable`

, the block takes a
physical signal input from port **Load** and smooths the signal such that

$$F={\left({F}_{input}^{2}+{F}_{Thr}^{2}\right)}^{1/2},$$

where:

*F*is the physical signal input at the_{input}**Load**port.*F*is the_{Thr}**Force threshold**parameter.

The block calculates the torque due to friction such that

$${T}_{f}=\mu \cdot F\cdot r,$$

where:

*μ*is the coefficient of friction.*F*is the friction force acting on the bearing._{f}*r*is the**Bearing radius**parameter.

How the block calculates *μ* depends on the type of
bearing that you simulate.

### Ball- or Roller-Type Bearings

When you set **Bearing type** to ```
Ball or
Roller
```

, the block calculates the overall friction coefficient
depending on the **Coefficient of friction specification**
parameter. When you set this parameter to `Constant`

, the
block calculates a constant coefficient of friction throughout the simulation. The
block uses a hyperbolic tangent function to smooth the zero-crossing transition.
When you set **Coefficient of friction specification** to
`Variable`

, the block uses a 1-D lookup table where
*μ* functions with the angular velocity, *ɷ*
such that

$$\mu =\text{tablelookup}\left(\stackrel{\rightharpoonup}{\omega},\stackrel{\rightharpoonup}{\mu},\omega ,\text{interpolation}=\mathrm{interp}\_method\_1,\text{extrapolation}=extrap\_method\_1\right),$$

where:

$$\stackrel{\rightharpoonup}{\omega}$$ is the

**Bearing angular speed vector, N**parameter.$$\stackrel{\rightharpoonup}{\mu}$$ is the

**Coefficient of friction, f(N)**parameter.

The block uses linear interpolation and extrapolation by default. You
can use the **Interpolation method** and **Extrapolation
method** parameters to change the interpolation and extrapolation,
respectively.

### Journal Bearings

When you set **Bearing type** to `Journal`

, the
block uses the Hersey number a lookup table to define the coefficient of friction,
such that

$$\mu =\text{tablelookup}\left(\stackrel{\rightharpoonup}{H}\cdot K,\stackrel{\rightharpoonup}{\mu}\cdot {\mu}_{min},H,\text{interpolation}=\mathrm{interp}\_method\_2,\text{extrapolation}=extrap\_method\_2\right),$$

where:

$$\stackrel{\rightharpoonup}{H}$$ is the optional

**Normalized Hersey number vector**parameter.$$\stackrel{\rightharpoonup}{\mu}$$ is the optional

**Normalized viscous coefficient vector**parameter.*K*is the bearing modulus, which is the value of*H*where*μ*occurs._{min}*μ*is the_{min}**Minimum coefficient of friction**parameter.

The block defines the bearing characteristic number, or Hersey number, as

$$H=\frac{\mu \omega}{P},$$

where *P* is the bearing lubricant pressure such that

$$P=\frac{F}{2rl},$$

where *r* is the **Radius**
parameter and *l* is the **Length**
parameter.

### Faults

To model a fault in the Bearing block, in the
**Faults** section, click the **Add fault** hyperlink next
to the fault that you want to model. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

When the block experiences a fault, it increases the bearing friction using the value of
the **Faulted damping coefficient multiplier** parameter. When
you trigger a fault, the block calculates the friction coefficient such that

$${\mu}_{fault}=\mu \cdot \text{faultfactor,}$$

where *fault factor* is the **Faulted
damping coefficient multiplier** parameter.

### Assumptions and Limitations

The block assumes that the bearing lubricant is a Newtonian fluid with zero-slip boundary conditions.

## Ports

### Input

### Conserving

## Parameters

## References

[1] Mckee, S. A., and T. R. Mckee. “Journal-Bearing Friction in the Region of Thin-Film Lubrication,” 320009, 1932. https://doi.org/10.4271/320009.

[2] Shigley, Joseph Edward,
Charles R. Mischke, and Richard G. Budynas. *Mechanical Engineering
Design.* 7th ed. McGraw-Hill Series in Mechanical Engineering. New York,
NY: McGraw-Hill, 2004.

## Extended Capabilities

## Version History

**Introduced in R2023a**