Disc Friction Clutch

A friction clutch with disc plates that interlock when the pressure on the plate exceeds a threshold value.

blockType: Engee1DMechanical.Clutches.DiscFriction

Path in the library:

/Physical Modeling/1D Mechanical/Clutches/Disc Friction Clutch

Description

Block Disc Friction Clutch It is a friction clutch with two flat friction plates that come into contact for coupling. Coupling occurs when the pressure applied to the plate exceeds the threshold actuation pressure. After coupling, the plates experience a torque that allows them to transfer power between the drive and driven shafts.

The coupling can be bidirectional or unidirectional. The bidirectional coupling can slip in both positive and negative directions. The unidirectional coupling can only slip in the positive direction. The direction of slippage is positive if the driven shaft rotates faster than the driving shaft, and negative if it rotates slower. The block defines the slip rate as the difference:

where

— relative angular velocity or rate of slippage;
— angular velocity of the driven shaft;
— angular velocity of the drive shaft.

The unit has an input port P, which receives the pressure value between the clutch discs. The applied pressure must be greater than or equal to zero. If the input signal drops below zero, the unit perceives the pressure on the disk as zero.

The equations

Block Disc Friction Clutch — this is a simplified implementation of the block Fundamental Friction Clutch. For the block Fundamental Friction Clutch It is necessary to set kinetic and static moments of friction as input signals. In the block Disc Friction Clutch This is not required, since sliding friction and static friction are calculated based on the coupling parameters and the pressure input signal P.

If the port pressure value P is above the threshold then the unit can apply two types of friction to the movement of the transmission — kinetic and static. The clutch applies a kinetic moment of friction only when one transmission axis rotates relative to the other transmission axis. The clutch applies a static moment of friction when the two transmission axles lock and rotate together. The unit performs multi-step checks to determine when the clutch is locked and unlocked.

The sliding effect

The kinetic moment of friction opposes relative slippage and is applied with a minus sign. Mathematically, the kinetic moment of friction is the positive sum of the moments of viscous friction and surface contact friction.:

where

— the moment of sliding friction;
— coefficient of viscous friction;
— relative angular velocity or rate of slippage;
— contact torque.

Contact friction is the product of six coefficients:

where

— the dimensionless coefficient of sliding friction of the clutch discs, which is a function of ;
— coupling wear coefficient;
— number of friction surfaces;
— the effective radius of the torque, that is, the effective shoulder of the moment of friction force of the clutch;
— the friction ability of the clutch, such that ;
— the surface area of the clutch.

Coefficient of kinetic sliding friction It can be set as a constant or as a tabular discrete function of angular velocity. . It is assumed that the tabular function is symmetric for positive and negative values of relative angular velocity. Therefore, specify only for positive values .

The clutch applies a normal force to the piston equal to the product of the clutch’s frictional capacity and the surface area of the clutch , on each of the friction surfaces. Port pressure value must be non-negative. If less than the pressure threshold value then the coupling does not apply any friction.

Effective radius of torque — this is the effective shoulder of the friction torque of the clutch, measured from the transmission axis, at which the kinetic moments of friction act on the friction surface. It is related to the geometry of the friction surface as follows:

where, for the friction surface in the form of an annular disk,

— the outer radius of the disk;
— the inner radius of the disk.

Ratio it takes into account the wear of the coupling. For a new coupling . For a coupling approaching a state of uniform wear:

static friction

The limit of static friction is related to kinetic friction, if set set to zero and replace kinetic friction with static friction coefficient:

where

— the limiting static moment of friction, which is the product of the peak coefficient of static friction and the kinetic moment of friction as it approaches to 0;
— the dimensionless coefficient of static friction of the clutch discs;
— coupling wear coefficient;
— number of friction surfaces;
— the effective radius of the torque, that is, the effective shoulder of the moment of friction force of the clutch;
— the friction ability of the clutch, such that ;
— the surface area of the clutch.

Since , the torque , necessary to unlock the clutch by overcoming the static moment of friction, is greater than the kinetic moment of friction at the moment of unlocking, when .

The range or limits of the static friction torque are determined symmetrically:

_ Standby status: Lock and unlock_

The standby state of the disc friction clutch is identical to the standby state of the base friction clutch, with the positive sliding friction state replaced the condition of the positive frictional ability of the coupling, at which the applied pressure is equal to or exceeds the threshold pressure, that is .

The power dissipated by the coupling

The power dissipated by the clutch is equal to the absolute value of the product of the slip velocity and the kinetic moment of friction That is , . The clutch dissipates power only if it slips at the same time., , and performs sliding friction, .

Friction models that depend on speed and temperature

The Model that depends on the speed

You can simulate the effects of changing the rotation speed by selecting a velocity-dependent model. To select a speed-dependent model in the parameter group Friction set for the parameter Friction model meaning Velocity-dependent kinetic friction coefficient. For information about the friction model, which depends on both velocity and temperature, see Velocity-dependent thermal model.

For a speed-dependent model, set the parameter values in the parameter group Friction:

Relative velocity vector
Kinetic friction coefficient vector
Friction coefficient interpolation method
Friction coefficient extrapolation method

The thermal model

You can simulate the effects of heat transfer and temperature changes by selecting a temperature-dependent model. To select a temperature-dependent model in the parameter group Friction set for the parameter Friction model meaning Temperature-dependent friction coefficients. For information about the friction model, which depends on both velocity and temperature, see Velocity-dependent thermal model.

The thermal model, which depends on velocity

You can simulate the effects of changes in rotation speed and heat flow by selecting a model that depends on speed and temperature. To select a model that depends on both speed and temperature, in the parameter group Friction set for the parameter Friction model meaning Temperature and velocity-dependent friction coefficients.

Ports

Input

# P — pressure, Pa
scalar

Details

Inlet port for pressure between the clutch discs, in Pa. Values less than zero are equal to zero.

Data types	`Float64`
Complex numbers support	I don’t

Conserving

# F — driven shaft
rotational mechanics

Details

A non-directional port connected to the driven shaft.

Program usage name

follower_flange

# B — drive shaft
rotational mechanics

Details

A non-directional port connected to the drive shaft.

Program usage name

base_flange

# H — heat flow
warmth

Details

A non-directional port connected to the heat flow.

Dependencies

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

Program usage name

thermal_port

Parameters

Geometry

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

Details

Parameterization method for modeling the geometry of a friction clutch.

If this parameter is set to Define effective radius, then the value is set in the block Effective torque radius.

If this parameter is set to Define annular region, then the values are set in the block:

Friction surface outside diameter;
Friction surface inside diameter.

Values	`Define effective radius` \| `Define annular region`
Default value	`Define effective radius`
Program usage name	`geometry_parameterization`
Evaluatable	Yes

# Effective torque radius — shoulder of the moment of friction force
m | cm | ft | in | km | mi | mm | um | yd

Details

Effective radius of the moment arm , which determines the kinetic moment of friction inside the coupling.

Dependencies

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

# Number of friction surfaces — number of friction surfaces

Details

Number of contact surfaces , generating friction inside the clutch.

Default value	`4`
Program usage name	`friction_surfaces_count`
Evaluatable	Yes

# Engagement piston area — pressure application area
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Effective area The clutch piston is when the piston exerts pressure on the clutch.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.001 m^2`
Program usage name	`effective_piston_area`
Evaluatable	Yes

# Directionality — acceptable directions of slippage
Bidirectional | Unidirectional

Details

The directions of slipping of the coupling between its discs. The bidirectional coupling allows for positive and negative slip rates. The unidirectional coupling allows only positive slippage.

A unidirectional clutch is equivalent to a friction clutch connected in parallel with a one-way clutch, which is switched off only when the slip rate becomes positive. To simulate a one-way coupling with a slip in the negative direction, reverse the connections of the master and slave ports.

Values	`Bidirectional` \| `Unidirectional`
Default value	`Bidirectional`
Program usage name	`directionality`
Evaluatable	Yes

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

Details

Outer diameter the annular surface of the friction disc.

Dependencies

To use this parameter, set for the parameter Geometry model meaning 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 — the inner diameter of the friction surface
m | cm | ft | in | km | mi | mm | um | yd

Details

Inner diameter the annular surface of the friction disc.

Dependencies

To use this parameter, set for the parameter Geometry model meaning 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 — the friction model
Fixed kinetic friction coefficient | Velocity-dependent kinetic friction coefficient | Temperature-dependent friction coefficients | Temperature and velocity-dependent friction coefficients

Details

Parameterization method for modeling sliding friction coefficient:

Fixed kinetic friction coefficient — a fixed value is set for the sliding friction coefficient.
Velocity-dependent kinetic friction coefficient — the coefficient of sliding friction is determined by the table based on the relative angular velocity between the discs.
Temperature-dependent friction coefficients — the coefficient of sliding friction is determined according to the table based on temperature.
Temperature and velocity-dependent friction coefficients — the coefficient of sliding friction is determined by the table based on the 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	Yes

# Static friction coefficient — coefficient of static friction

Details

Static or peak value of the coefficient of friction. The static coefficient of friction must be greater than the kinetic coefficient of 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

# Kinetic friction coefficient — coefficient of sliding friction

Details

Coefficient of kinetic or Coulomb friction. The coefficient must be greater than zero.

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

# De-rating factor — coupling wear coefficient

Details

Dimensionless coupling wear coefficient , which takes into account the wear of the clutch disc, proportionally reducing the friction of the clutch.

Default value	`1.0`
Program usage name	`de_rating_factor`
Evaluatable	Yes

# Clutch velocity tolerance — threshold value of relative blocking speed
rpm | deg/s | rad/s

Details

The maximum slip rate at which the clutch can lock. The slip rate is defined as the difference between the angular velocities of the drive and driven shafts, that is . If the kinetic moment of friction is nonzero and the transmitted moment is within the static moment of friction, the clutch is locked if the actual slip velocity is below the threshold velocity.

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

# Engagement threshold pressure — the threshold value of the normal contact force
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Minimum pressure , at which the clutch is switched on. If the pressure input signal at port P falls below this threshold value, the coupling is automatically released.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`100.0 Pa`
Program usage name	`p_threshold`
Evaluatable	Yes

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

Details

A vector of relative velocity values. The values in the vector should increase from left to right. The minimum number of vector elements depends on the chosen interpolation method. If for the parameter Friction coefficient interpolation method the value is set:

Linear, then the minimum number of elements of the vector is two.
Smooth, then the minimum number of elements of the vector is three.

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

# Kinetic friction coefficient vector — vector of sliding friction coefficients

Details

The vector of kinetic friction coefficient values. All values must be greater than zero. The dimension of this vector must match the dimension of the vector Relative velocity vector.

Dependencies

To use this parameter, set for the parameter Friction model set to the value Velocity-dependent kinetic friction coefficient.

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

# Friction coefficient interpolation method — the interpolation method
Linear | Smooth

Details

The method used for interpolation between data table reference points:

Linear — choose this value for the lowest computational cost;
Smooth — select this value 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_method`
Evaluatable	Yes

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

Details

The method used to extrapolate the reference points in the data table. This method determines the output value when the input value is outside the range specified in the argument list.:

Linear — select this value to obtain a curve with continuous first-order derivatives in the extrapolation region and on the boundary with the interpolation region.
Nearest — Select this value to use an extrapolation that does not rise above the largest value in the data or fall below the smallest value in the data.
Error — select this value to avoid extrapolation when you want the data to be within the range of the table. If the input signal is outside the range of the table, the simulation stops and outputs an error.

Dependencies

Values	`Linear` \| `Nearest` \| `Error`
Default value	`Linear`
Program usage name	`friction_coefficient_extrapolation_method`
Evaluatable	Yes

Details

The vector of temperature values. The values in the vector should increase from left to right. The minimum number of vector elements depends on the chosen interpolation method. If for the parameter Friction coefficient interpolation method the value is set:

Linear, then the minimum number of elements of the vector is two.
Smooth, then the minimum number of elements of the vector is three.

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	`[280.0, 300.0, 320.0] K`
Program usage name	`temperature_vector`
Evaluatable	Yes

# Static friction coefficient vector — vector of static friction coefficients

Details

A vector of static or peak friction coefficients. The dimension of this vector must match the dimension of the vector Temperature vector. Each value must be greater than the value of the corresponding element in the vector. Kinetic friction coefficient vector.

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 vector — vector of sliding friction coefficients

Details

The vector of kinetic friction coefficient values. All values must be greater than zero. The dimension of this vector must match the dimension of the vector Temperature vector.

Dependencies

To use this parameter, set for the parameter Friction model set to the value Temperature-dependent friction coefficients.

Default value	`[0.3, 0.28, 0.25]`
Program usage name	`coulomb_friction_coefficient_vector_temperature`
Evaluatable	Yes

# Kinetic friction coefficient matrix — matrix of sliding friction coefficients

Details

The matrix of kinetic friction coefficient values. All values must be greater than zero. The dimension of the matrix should be (Temperature vector) on (Kinetic friction coefficient vector).

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

Viscous Losses

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

Details

Coefficient of viscous friction applied to relative slip between the driving and driven axes.

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 condition of the coupling
Unlocked | Locked

Details

The state of the coupling at the beginning of the simulation. The coupling can be in one of two states — locked and unlocked. Locked coupling (Locked) causes the drive and driven shafts to rotate at the same speed, that is, as a single unit. Unlocked coupling (Unlocked) allows the two shafts to rotate at different speeds, resulting in slippage between the clutch discs.

Values	`Unlocked` \| `Locked`
Default value	`Unlocked`
Program usage name	`initial_state`
Evaluatable	Yes

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 temperature of the component at the beginning of the simulation. The initial temperature sets the initial efficiency of the components according to the vectors specified for them, affecting the initial adhesion or friction losses.

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