Loaded-Contact Rotational Friction

Loaded contact friction between two rotating surfaces.

loaded contact rotational friction

Description

Block Loaded-Contact Rotational Friction Simulates friction between two rotating surfaces loaded with a normal force.

The block is implemented as a structural component based on the block Fundamental Friction Clutch. From the locked state, the two surfaces unlock if the transmitted torque exceeds the static friction, determined by the static coefficient of friction and the current normal force. For details on how locking and unlocking are modelled, see block Fundamental Friction Clutch.

The torque is transmitted at a normal force that exceeds the parameters Threshold force.

Equations

This block models the friction between two rotating surfaces loaded by a normal force. When the two rotating surfaces are not locked, the transmitted torque is determined using the following equations:

where

- is the transmitted torque;
- normal force;
- friction coefficient;
- effective radius;
- outer surface radius;
- inner surface radius;
- relative angular velocity;
- viscous friction torque;
- viscous friction coefficient.

Velocity-dependent model

You can simulate the effects of rotational speed changes by selecting a speed-dependent model. To select a velocity-dependent model, set the Friction parameters in the Friction parameters to Friction model value Velocity-dependent kinetic friction coefficient. For a friction model that depends on both speed and temperature, see Speed dependent thermal model.

Thermal model

You can model the effects of heat flow and temperature change by selecting a temperature-dependent model. To select a temperature-dependent model, set the Friction parameters to Friction model value Temperature-dependent friction coefficients. For a friction model that depends on both velocity and temperature, see Velocity Dependent Thermal Model.

Speed dependent thermal model

You can model the effects of varying rotational speed and heat flux by selecting a speed-dependent and temperature-dependent model. To select a model that depends on both speed and temperature, set the Friction parameters to Friction model value Temperature and velocity-dependent friction coefficients.

Limitations and assumptions

The model does not account for inertia. If necessary, add external inertia terms to B and F ports.
The model calculates torque assuming a uniform distribution of normal force.

Ports

Conserving

# F — mechanical rotation of the follower
`rotational mechanics

Details

A non-directional port associated with a driven (moving) surface.

Program usage name

follower_flange

# B — base
`rotational mechanics

Details

A non-directional port associated with a drive (base) surface.

Program usage name

base_flange

# H — heat flux
`heat

Details

A non-directional port associated with heat flow.

The heat port allows modelling the heat flow between the unit and the connected network.

Dependencies

To use this port, set the parameters to Friction model value Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Program usage name

thermal_port

Input

# N — normal force
scalar

Details

An input physical signal associated with a normal force. This signal can be positive or zero. A signal less than zero is interpreted as zero.

Data types	`Float64`.
Complex numbers support	No

Parameters

Geometry

# Geometry model — parameterization method
Define effective radius | Define annular region

Details

A parameterization method for the load-contact friction model. Defined as:

Define effective radius - specify the value of the effective friction radius.
Define annular region - define the radius of the effective friction surface area by specifying the inner and outer diameters of the friction surface.

Values	`Define effective radius` \| `Define annular region`
Default value	`Define effective radius`
Program usage name	`geometry_parameterization`
Evaluatable	No

# Effective torque radius — radius of effective friction surface
m | cm | ft | in | km | mi | mm | um | yd

Details

Radius of effective friction surface, . The value should be .

Dependencies

To use this parameter, set parameter Geometry model set to Define effective radius.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`130.0 mm`
Program usage name	`effective_radius`
Evaluatable	Yes

# Friction surface outside diameter — external diameter of the friction surface
m | cm | ft | in | km | mi | mm | um | yd

Details

External diameter of the friction surface, . The value should be .

Dependencies

To use this parameter, set parameter Geometry model set to Define annular region.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`150.0 mm`
Program usage name	`outer_diameter`
Evaluatable	Yes

# Friction surface inside diameter — internal diameter of the friction surface
m | cm | ft | in | km | mi | mm | um | yd

Details

Internal diameter of the friction surface, . The value must lie in the range .

Dependencies

To use this parameter, set parameter Geometry model set to Define annular region.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`100.0 mm`
Program usage name	`inner_diameter`
Evaluatable	Yes

Friction

# Friction model — friction model
Fixed kinetic friction coefficient | Velocity-dependent kinetic friction coefficient | Temperature-dependent friction coefficients | Temperature and velocity-dependent friction coefficients

Details

A model of friction in a transmission. Defined as:

Fixed kinetic friction coefficient - Provide a fixed value for the coefficient of sliding friction.
Velocity-dependent kinetic friction coefficient - determine the sliding friction coefficient by a one-dimensional interpolation table based on the relative angular velocity between the discs.
Temperature-dependent friction coefficients - determine the coefficient of sliding friction by an interpolation table based on temperature.
Temperature and velocity-dependent friction coefficients - determine the coefficient of sliding friction by an interpolation table based on temperature and the relative angular velocity between the discs.

Values	`Fixed kinetic friction coefficient` \| `Velocity-dependent kinetic friction coefficient` \| `Temperature-dependent friction coefficients` \| `Temperature and velocity-dependent friction coefficients`
Default value	`Fixed kinetic friction coefficient`
Program usage name	`kinetic_friction_coefficient_type`
Evaluatable	No

# Relative velocity vector — relative speed
rpm | deg/s | rad/s

Details

Values of relative velocity given as a vector. The values in the vector should be monotonically increasing.

The minimum number of values depends on the chosen interpolation method. For linear interpolation, specify at least two values in each dimension. For smooth interpolation, specify at least three values per measurement.

Dependencies

To use this parameter, set the parameters to Friction model value Velocity-dependent kinetic friction coefficient or Temperature and velocity-dependent friction coefficients.

Units	`rpm` \| `deg/s` \| `rad/s`
Default value	`[0.0, 100.0, 1000.0] rad/s`
Program usage name	`delta_w_vector`
Evaluatable	Yes

Details

The temperature given as a vector. The values in the vector should increase monotonically.

The minimum number of values depends on the chosen interpolation method. For linear interpolation, specify at least two values per measurement. For smooth interpolation, specify at least three values per measurement.

Dependencies

To use this parameter, set the parameters to Friction model value Velocity-dependent kinetic friction coefficient or Temperature and velocity-dependent friction coefficients.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[280.0, 300.0, 320.0] K`
Program usage name	`temperature_vector`
Evaluatable	Yes

# Static friction coefficient — static friction coefficient

Details

The static, or maximum, value of the coefficient of friction. The static coefficient of friction must be greater than the sliding coefficient of friction.

Dependencies

To use this parameter, set parameter Friction model value Fixed kinetic friction coefficient or Velocity-dependent kinetic friction coefficient.

Default value	`0.35`
Program usage name	`static_friction_coefficient`
Evaluatable	Yes

# Static friction coefficient vector — vector of static friction coefficients

Details

The static, or maximum, values of the vector of friction coefficients. The vector must have the same number of elements as the temperature vector. Each value must be greater than the value of the corresponding element in the sliding friction coefficient vector.

Dependencies

To use this parameter, set the parameters to Friction model value Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Default value	`[0.4, 0.38, 0.36]`
Program usage name	`static_friction_coefficient_vector`
Evaluatable	Yes

# Kinetic friction coefficient — sliding friction coefficient

Details

Coefficient of sliding friction. The value must be .

Dependencies

To use this parameter, set parameter Friction model value Fixed kinetic friction coefficient.

Default value	`0.3`
Program usage name	`coulomb_friction_coefficient`
Evaluatable	Yes

# Kinetic friction coefficient vector — vector of sliding friction coefficients

Details

Vector of sliding friction coefficients. All values must be .

Dependencies

To use this parameter, set parameter Friction model value Velocity-dependent kinetic friction coefficient or Temperature-dependent friction coefficients.

Default value	`[0.3, 0.22, 0.19]`
Program usage name	`coulomb_friction_coefficient_vector`
Evaluatable	Yes

# Kinetic friction coefficient matrix — matrix of sliding friction coefficients

Details

Matrix of sliding friction coefficients. All values must be . The size of the matrix should be equal to the size of the matrix that is the product of the product of the temperature vector by the relative velocity vector multiplied by the sliding friction coefficient.

Dependencies

To use this parameter, set parameter Friction model value Temperature and velocity-dependent friction coefficients.

Default value	`[0.34 0.32 0.3; 0.3 0.28 0.25; 0.25 0.2 0.15]`
Program usage name	`coulomb_friction_coefficient_matrix`
Evaluatable	Yes

# Friction coefficient interpolation method — interpolation method
Linear | Smooth

Details

An interpolation method for approximating the output value when the input value is between two consecutive grid points. Defined as:

Linear - select this option to get the best performance.
Smooth - select this option to get a continuous curve with continuous first order derivatives.

Dependencies

To use this parameter, set the parameters to Friction model value Velocity-dependent kinetic friction coefficient, Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Values	`Linear` \| `Smooth`
Default value	`Linear`
Program usage name	`friction_coefficient_interpolation_method`
Evaluatable	No

# Friction coefficient extrapolation method — extrapolation method
Linear | Nearest

Details

Extrapolation method to determine the output value when the input value is outside the range specified in the argument list. Defined as:

Linear - select this option to obtain a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.
Nearest - select this option to get an extrapolation that does not rise above the highest point in the data or below the lowest point in the data.

Dependencies

To use this option, set the parameters to Friction model value Velocity-dependent kinetic friction coefficient, Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Values	`Linear` \| `Nearest`
Default value	`Linear`
Program usage name	`friction_coefficient_extrapolation_method`
Evaluatable	No

# Velocity tolerance — surface rotation locking threshold
rpm | deg/s | rad/s

Details

The relative speed below which two surfaces can lock. The surfaces are locked if the torque through the rotary ports B and F is less than the product of the radius of the effective friction surface, the coefficient of static friction and the applied normal force.

Units	`rpm` \| `deg/s` \| `rad/s`
Default value	`0.001 rad/s`
Program usage name	`w_slip_threshold`
Evaluatable	Yes

# Threshold force — normal contact force threshold
N | kN | lb | mN | dyn | lbf

Details

The normal force applied to the scalar port N is applied to the contact only if the magnitude of the force exceeds the value of the parameters Threshold force. Forces smaller than the value of the parameters Threshold force are not applied, so no frictional torque is transmitted.

Units	`N` \| `kN` \| `lb` \| `mN` \| `dyn` \| `lbf`
Default value	`1.0 N`
Program usage name	`F_vertical_threshold`
Evaluatable	Yes

Viscous Losses

# Viscous drag torque coefficient — viscous drag torque
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Viscous drag coefficient, , for calculating torque. The coefficient depends on the type of working fluid, the fluid temperature and the maximum distance between surfaces.

Units	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`0.0 N*m/(rad/s)`
Program usage name	`viscous_coefficient`
Evaluatable	Yes

Initial Conditions

# Initial state — initial state of coupling
Unlocked | Locked

Details

The state of the indoor unit Fundamental Friction Clutch at the beginning of the simulation.

Unlocked - rotary ports B and F initially slide relative to each other.
Locked - rotary ports B and F are initially locked together.

Values	`Unlocked` \| `Locked`
Default value	`Unlocked`
Program usage name	`initial_state`
Evaluatable	No

Thermal Port

# Thermal mass — heat capacity
J/K | kJ/K

Details

The heat energy required to change the temperature of a component by one degree. The greater the heat capacity, the more resistant the component is to temperature change.

Dependencies

To use this parameter, set the parameters to Friction model value Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Units	`J/K` \| `kJ/K`
Default value	`50.0 kJ/K`
Program usage name	`thermal_mass`
Evaluatable	Yes

Details

The initial temperature given as a scalar.

Dependencies

To use this parameter, set the parameters to Friction model value Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`300.0 K`
Program usage name	`temperature_start`
Evaluatable	Yes