Cone Clutch

A conical coupling with plates that interlock when the normal force exceeds a threshold value.

blockType: Engee1DMechanical.Clutches.Cone

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/Physical Modeling/1D Mechanical/Clutches/Cone Clutch

Description

Block Cone Clutch It is a friction clutch with a conical contact surface. The conical contact surface reduces the normal force required to engage the clutch, creating jamming between the coupling components: the cone element and the conical landing surface. Bevel couplings are used in synchronous gearboxes that synchronize the rotational speeds of the drive and driven shafts to ensure smoother engagement between the transmission gears.

The conical landing surface is rigidly connected to the drive shaft and rotates with it as a single unit. The cone element is rigidly connected to the driven shaft, which is located coaxially with the drive shaft. The coupling is activated when the cone element slides towards the conical seating surface and presses tightly against it. Friction on the conical contact surface allows the coupling to transfer torque between the drive and driven shafts. The friction model of this unit includes the contribution of static friction and sliding friction, the latter of which leads to power dissipation during sliding between the conical element and the conical landing surface.

Block Cone Clutch based on the block Fundamental Friction Clutch. See the full model of the friction clutch in the block Fundamental Friction Clutch. This section discusses the specialized model implemented in the block Cone Clutch.

When you apply normal force , block Cone Clutch It 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.

Coupling geometry and variables

The figure shows the geometry of the conical coupling.

cone clutch 1

Variables that define the coupling:

— the outer diameter of the conical contact surface;
— the inner diameter of the conical contact surface;
— half of the opening angle of the cone;
— relative angular velocity: ;
— threshold value of the relative blocking speed;
— the normal force applied to the conical surfaces. This force is applied if it is greater than the threshold value. ;
— the effective radius of the torque, that is, the effective shoulder of the moment of friction force of the clutch;
is the dimensionless coefficient of sliding friction of conical surfaces, which is a function of ;
— dimensionless coefficient of static friction of conical surfaces;
— the moment of sliding friction;
— the limiting static moment of friction, is defined as the product of the peak value of the coefficient of static friction and the moment of sliding friction at .

The equations

Block Cone Clutch based on 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 Cone Clutch This is not required, since sliding friction and static friction are calculated based on the coupling parameters and the input signal of the normal force N.

The sliding effect

The kinetic moment of friction is the result of the product of four coefficients:

The kinetic moment of friction opposes relative slippage and is applied with a minus sign. It changes sign when changes the sign.

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 .

Effective radius of torque is the effective radius measured from the transmission axis at which sliding friction forces are applied to the friction surfaces. It is related to the geometry of the conical friction surface as follows:

where and are the maximum and minimum diameters of the contact surface, respectively.

static friction

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

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:

Range is used by the block Fundamental Friction Clutch.

conditions of coupling and locking

The clutch turns on (transmits torque) when a positive normal force acts on the conical friction surfaces and sliding friction occurs.: and .

The clutch locks if and only if it is engaged, and the slip is less than the threshold speed.: .

The power dissipated by the coupling

The power dissipated by the coupling is . The clutch dissipates power only if it slips at the same time., , and performs sliding friction, ( ).

A speed-dependent model

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.

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.

Velocity-dependent thermal model

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

Conserving

# B — drive shaft
rotational mechanics

Details

A mechanical non-directional port connected to the drive shaft. The movement of the clutch is defined as slipping , the angular velocity of the driven shaft relative to the drive shaft.

Program usage name

base_flange

# F — driven shaft
rotational mechanics

Details

A mechanical non-directional port connected to the driven shaft.

Program usage name

follower_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 meaning Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Program usage name

thermal_port

# S — gearshift lever
rotational mechanics

Details

A mechanical non-directional port connected to the gearshift lever.

Dependencies

To use this port, set the parameter Shift linkage control meaning Conserving port.

Program usage name

shift_linkage_flange

Input

# N — normal strength
scalar

Details

Input port for normal power. This value is either positive or zero. Values less than zero are equal to zero.

Dependencies

To use this port, set the parameter Shift linkage control meaning Physical signal.

Data types	`Float64`
Complex numbers support	No

Output

# X — gearshift lever position
scalar

Details

The output port associated with the position of the gearshift lever.

Dependencies

To use this port, set the parameter Shift linkage control meaning Conserving port.

Data types	`Float64`
Complex numbers support	No

Parameters

Geometry

# Contact surface maximum diameter — Outer diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

Outer diameter of the cone .

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

# Contact surface minimum diameter — inner diameter
m | cm | ft | in | km | mi | mm | um | yd

Details

Inner diameter of the cone .

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

# Cone half angle — half of the opening angle of the cone
deg | rad | rev | mrad

Details

Half of the opening angle of the cone .

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`12.0 deg`
Program usage name	`cone_half_angle`
Evaluatable	Yes

# Shift linkage control — gearshift model
Physical signal | Conserving port

Details

Gearshift lever control model:

Physical signal — the F port is used for normal power;
Conserving port — A non-directional port S is used, which is connected to the gearshift lever and an output port X, which outputs data on the position of the gearshift lever.

Values	`Physical signal` \| `Conserving port`
Default value	`Physical signal`
Program usage name	`shift_linkage_model`
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 the coefficient of sliding friction. The parameters and default values for this parameter depend on the friction model you select for the block. The following options are possible:

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 search table based on the 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	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

# 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 surfaces are fixed if the torque at ports B and F is less than the product of the effective radius, 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 — the threshold value of the normal contact force
N | kN | lb | mN | dyn | lbf

Details

The normal force on the port N is applied to the contact surface only if its value exceeds the value of the parameter Threshold force. The strength is below the value Threshold force no friction torque is applied and not transmitted.

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

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

Details

Coefficient of viscous friction.

Units	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`0.0 N*m/(rad/s)`
Program usage name	`rotational_viscous_coefficient`
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 get 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 Kinetic friction coefficient vector 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

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

# Initial shift linkage position — the initial position of the gearshift lever
m | cm | ft | in | km | mi | mm | um | yd

Details

The initial position of the gearshift lever.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.0 mm`
Program usage name	`delta_p_start`
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

Shift Linkage

# Hard stop at back of shift linkage — hard focus

Details

A hard stop at the rear of the gearshift lever.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Default value	`true (switched on)`
Program usage name	`enable_hard_stop`
Evaluatable	Yes

# Ring-hub clearance when disengaged — the gap between the ring and the hub
m | cm | ft | in | km | mi | mm | um | yd

Details

The gap between the ring and the hub when uncoupling.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`3.0 mm`
Program usage name	`ring_hub_backlash`
Evaluatable	Yes

# Ring stop stiffness — rigidity of the annular stop
N/m | lbf/ft | lbf/in

Details

The rigidity of the annular stop.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Units	`N/m` \| `lbf/ft` \| `lbf/in`
Default value	`1.0e6 N/m`
Program usage name	`k`
Evaluatable	Yes

# Ring stop damping — damping coefficient of the annular stop
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The damping coefficient of the annular stop.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`1000.0 N/(m/s)`
Program usage name	`C`
Evaluatable	Yes

# Shift linkage viscous friction coefficient — coefficient of viscous friction of the gearshift lever
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

Coefficient of viscous friction of the gearshift lever.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`100.0 N/(m/s)`
Program usage name	`translational_viscous_coefficient`
Evaluatable	Yes

# Linkage travel direction — the direction of movement of the gearshift lever
Positive shift linkage displacement engages clutch | Negative shift linkage displacement engages clutch

Details

The direction of movement of the lever that disables the clutch.

Dependencies

To use this parameter, set for the parameter Shift linkage control meaning Conserving port.

Values	`Positive shift linkage displacement engages clutch` \| `Negative shift linkage displacement engages clutch`
Default value	`Positive shift linkage displacement engages clutch`
Program usage name	`linkage_travel_direction`
Evaluatable	Yes