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:

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

• F_Thr 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.

• F_f 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

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

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_min occurs.

• μ_min 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

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

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

Load — Variable load input, N

physical signal

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

B — Base

mechanical rotational

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

F — Follower

mechanical rotational

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.

C — Case

mechanical rotational

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

Mechanical Properties

Bearing type — Bearing option

Ball or Roller (default) | Journal

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

Enable follower port — Follower port option

off (default) | on

Whether to enable the follower port.

Enable case port — Case port option

off (default) | on

Whether to enable the case port.

Radius — Bearing interface radius

30 mm (default) | positive scalar

Radius of the interface between the bearing and the shaft.

Length — Bearing interface length

100 mm (default) | positive scalar

Length of the interface between the bearing and the shaft.

Radial load specification — Option to control radial load

Constant (default) | Variable

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

Load on bearing — Constant bearing load

10 N (default) | positive scalar

Constant load that the shaft imparts on the bearing.

Dependencies

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

Force threshold — Load threshold

0.001 N (default)

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 — Angular velocity threshold

0.001 rev/s (default)

Angular velocity threshold above which the block applies bearing friction.

Dependencies

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

Coefficient of friction specification — Option to specify coefficient of friction

Constant (default) | Variable

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.

Coefficient of friction — Coefficient of friction

0.002 (default) | positive scalar

Constant coefficient of friction.

Dependencies

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

Interpolation method — Method of interpolation between breakpoint values

Linear (default) | Smooth

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.

Extrapolation method — Method of handling input values that fall outside range of breakpoint data set

Linear (default) | Nearest | Error

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 speed vector, ω — Bearing angular velocity

[10, 2500, 5000, 10000, 25000] rpm (default) | vector of length N

Bearing angular velocity.

Coefficient of friction, f(ω) — Coefficient of friction

[.004, .001, .0005, .00025, .000125] (default) | vector of length N

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.

Customize friction curve — Option to customize bearing friction curve

off (default) | on

Whether to customize the bearing friction curve.

Dependencies

To enable this parameter, set Bearing type to Journal.

Dynamic viscosity — Lubricant dynamic viscosity

0.29 Pa*s (default) | positive scalar

Dynamic viscosity of the bearing lubricant.

Dependencies

To enable this parameter, set Bearing type to Journal.

Minimum coefficient of friction — Minimum coefficient of friction

0.002 (default) | positive scalar

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

Dependencies

To enable this parameter, set Bearing type to Journal.

Bearing Modulus — Journal bearing modulus

7.2519e-08 rev (default) | positive scalar

Journal bearing modulus.

Dependencies

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

Normalized Hersey number vector — Normalized Hersey number

[.4306, .6124, .6651, .7512, .866, 1, 1.1962, 1.4354, 3.8517] (default) | vector of length M

Normalized Hersey number.

Dependencies

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

Normalized viscous coefficient vector — Normalized viscous friction coefficient

[3.6621, 1.672, 1.3397, 1.1811, 1.0743, 1, 1.0358, 1.1173, 2.2792] (default) | vector of length M

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.

Interpolation method — Method of interpolation between breakpoint values

Linear (default) | Smooth

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.

Extrapolation method — Method of handling input values that fall outside range of breakpoint data set

Linear (default) | Nearest | Error

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.

Damping fault — Option to model bearing failure

Add fault

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

Faulted damping coefficient multiplier — Damping multiplier

5 (default) | positive scalar

Damping coefficient when a fault is triggered.

Dependencies

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Version History

Introduced in R2023a

R2024a: Model faults with the Simscape faults interface

The Bearing block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.