# Bearing

Bearing that provides trans-axial support to freely rotating shaft

Since R2023a

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:

• Finput is the physical signal input at the Load port.

• FThr is the 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.

• Ff is the friction force acting on the bearing.

• 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

`$\mu =\text{tablelookup}\left(\stackrel{⇀}{\omega },\stackrel{⇀}{\mu },\omega ,\text{interpolation}=\mathrm{interp}_method_1,\text{extrapolation}=extrap_method_1\right),$`

where:

• $\stackrel{⇀}{\omega }$ is the Bearing angular speed vector, N parameter.

• $\stackrel{⇀}{\mu }$ 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

`$\mu =\text{tablelookup}\left(\stackrel{⇀}{H}\cdot K,\stackrel{⇀}{\mu }\cdot {\mu }_{min},H,\text{interpolation}=\mathrm{interp}_method_2,\text{extrapolation}=extrap_method_2\right),$`

where:

• $\stackrel{⇀}{H}$ is the optional Normalized Hersey number vector parameter.

• $\stackrel{⇀}{\mu }$ is the optional Normalized viscous coefficient vector parameter.

• K is the bearing modulus, which is the value of H where μmin occurs.

• μmin is the 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. When the Add Fault window opens, you can to specify the fault properties. 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

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

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Physical signal input port associated with the load on the bearing, in N.

#### Dependencies

To enable this port, set Radial load specification to `Variable`.

### Conserving

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Mechanical rotational conserving port associated with the base end of the shaft.

Mechanical rotational conserving port associated with the follower end of the shaft. This port maintains the same angular velocity as port B.

#### Dependencies

To enable this port, select Enable follower port.

Mechanical rotational conserving port associated with the bearing casing. When this port is enabled, the block assumes the casing reference is stationary.

#### Dependencies

To enable this port, select Enable case port.

## Parameters

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### Mechanical Properties

Type of bearing that the block behaves as during the simulation.

Whether to enable the follower port.

Whether to enable the case port.

Radius of the interface between the bearing and the shaft.

Length of the interface between the bearing and the shaft.

Whether the block uses a constant load or you specify a variable load using the Load port.

Constant load that the shaft imparts on the bearing.

#### Dependencies

To enable this parameter, set Radial load specification to `Constant`.

Load threshold above which the block applies a load to the bearing.

#### Dependencies

To enable this parameter, set Radial load specification to `Variable`.

Angular velocity threshold above which the block applies bearing friction.

#### Dependencies

To enable this parameter, set Bearing type to `Ball or Roller`.

Whether the block coefficient is constant or varies with the bearing speed.

#### Dependencies

To enable this parameter, set Bearing type to `Ball or Roller` and Coefficient of friction specification to `Constant`.

Constant coefficient of friction.

#### Dependencies

To enable this parameter, set Coefficient of friction specification to `Constant`.

Method to use for 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`.

Method to use for 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.

Bearing angular velocity.

Coefficient of friction for a given bearing angular velocity. The elements in this vector must correspond one-to-one with the Bearing angular speed vector, ω parameter.

### Fluid Properties

To enable these parameters, set Bearing type to `Journal`.

Whether to customize the bearing friction curve.

#### Dependencies

To enable this parameter, set Bearing type to `Journal`.

Dynamic viscosity of the bearing lubricant.

#### Dependencies

To enable this parameter, set Bearing type to `Journal`.

Lowest coefficient of friction the block uses for any angular velocity.

#### Dependencies

To enable this parameter, set Bearing type to `Journal`.

Journal bearing modulus.

#### Dependencies

To enable this parameter, set Bearing type to `Journal` and select Customize friction curve.

Normalized Hersey number.

#### Dependencies

To enable this parameter, set Bearing type to `Journal` and select Customize friction curve.

Normalized viscous friction coefficients. The elements in this vector correspond one-to-one with the Normalized Hersey number vector parameter.

#### Dependencies

To enable this parameter, set Bearing type to `Journal` and select Customize friction curve.

Method to use for 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`.

#### Dependencies

To enable this parameter, set Bearing type to `Journal` and select Customize friction curve.

Method to use for 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.

#### Dependencies

To enable this parameter, set Bearing type to `Journal` and select Customize friction curve.

### Faults

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

Whether to model a fault in the bearing. To add a fault, click the Add fault hyperlink.

Damping coefficient when a fault is triggered.

#### Dependencies

To enable this parameter, enable faults for the block by clicking the hyperlink.

## 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.

## Version History

Introduced in R2023a

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