Loaded-Contact Rotational Friction

Loaded contact friction between two rotating surfaces.

blockType: Engee1DMechanical.Brakes.LoadedContactRotationalFriction

Path in the library:

/Physical Modeling/1D Mechanical/Brakes & Detents/Rotational/Loaded-Contact Rotational Friction

Description

The Loaded-Contact Rotational Friction block simulates friction between two rotating surfaces loaded by 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.

Torque is transmitted at a normal force greater than 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 speed-dependent model, in the Friction parameters, set Friction model to . Velocity-dependent kinetic friction coefficient. For information on a friction model that depends on both speed and temperature, refer to Thermal model that depends on velocity.

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, in the Friction parameters, set Friction model to . Temperature-dependent friction coefficients. For information on a friction model that depends on both velocity and temperature, see . Thermal model that depends on velocity.

Thermal model that depends on velocity

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, in the Friction parameters, set Friction model to . 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

Parameterization method for the load-contact friction model. Set as:

Define effective radius – specify the value of the effective friction radius.
Define annular region – determine 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 the effective friction surface
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

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

Dependencies

To use this parameter, set for the parameter Geometry model the value is set Define effective radius.

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

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

Details

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

Dependencies

To use this parameter, set for the parameter Geometry model the value is set Define annular region.

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

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

Details

The inner diameter of the friction surface, . The value must be in the range .

Dependencies

To use this parameter, set for the parameter Geometry model the value is set Define annular region.

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

Friction

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

Details

The model of friction in transmission. Set as:

Fixed kinetic friction coefficient – provide a fixed value for the sliding friction coefficient.
Velocity-dependent kinetic friction coefficient – determine the coefficient of sliding friction by using 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 using an interpolation table based on temperature.
Temperature and velocity-dependent friction coefficients – determine the coefficient of sliding friction from an interpolation table based on temperature and 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

Details

Relative velocity values, set as a vector. The values in the vector should increase monotonously.

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 for the parameter Friction model meaning Velocity-dependent kinetic friction coefficient or Temperature and velocity-dependent friction coefficients.

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

Details

The temperature set as a vector. The values in the vector should increase monotonously.

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 for the parameter Friction model meaning 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 — coefficient of static friction

Details

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

Dependencies

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

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

# Static friction coefficient vector — vector of static friction coefficients

Details

Static or maximum values of the coefficient of friction vector. 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 vector of sliding friction coefficients.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 — coefficient of sliding friction

Details

Coefficient of sliding friction. The value should be .

Dependencies

To use this parameter, set for the parameter Friction model meaning Fixed kinetic friction coefficient.

Default value	`0.3`
Program usage name	`coulomb_friction_coefficient_const`
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 for the parameter Friction model meaning Velocity-dependent kinetic friction coefficient or Temperature-dependent friction coefficients.

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

# Kinetic friction coefficient matrix — matrix of sliding friction coefficients

Details

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

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 — the interpolation method
Linear | Smooth

Details

An interpolation method for approximating the output value when the input value is between two consecutive grid points. Set 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 for the parameter Friction model meaning 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_type`
Evaluatable	No

# Friction coefficient extrapolation method — the extrapolation method
Linear | Nearest | Error

Details

An extrapolation method for determining the output value when the input value is outside the range specified in the argument list. Set as:

Linear – select this option to get a curve with continuous first-order derivatives in the extrapolation domain and on the boundary with the interpolation domain.
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

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

Details

The relative velocity below which two surfaces can lock. The surfaces are blocked 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	`rad/s` \| `deg/s` \| `rad/min` \| `deg/min` \| `rpm` \| `rps`
Default value	`0.001 rad/s`
Program usage name	`w_slip_threshold`
Evaluatable	Yes

# Threshold force — threshold of normal contact force
N | nN | uN | mN | kN | MN | GN | dyn | lbf | kgf

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 parameter Threshold force. Forces are less than the parameter value Threshold force they are not applied, so the friction torque is not transmitted.

Units	`N` \| `nN` \| `uN` \| `mN` \| `kN` \| `MN` \| `GN` \| `dyn` \| `lbf` \| `kgf`
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

Coefficient of viscous resistance, , to calculate the torque. The coefficient depends on the type of working fluid, the temperature of the fluid, and the maximum distance between the 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 — the initial state of the clutch
Unlocked | Locked

Details

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

Unlocked – the rotary ports B and F are initially sliding relative to each other.
Locked – The 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 thermal energy required to change the temperature of a component by one degree. The higher the heat capacity, the more resistant the component is to temperature changes.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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, set as a scalar.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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