Dog Clutch

Clutch with toothed plates that engage when plate teeth become enmeshed

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Libraries:
Simscape / Driveline / Clutches

Description

This block represents a nonslip clutch, a mechanical device that relies on the positive engagement of interlocking teeth to transfer torque between driveline shafts. The clutch contains three key components:

• Ring

• Hub

• Shift linkage

The ring and the hub are toothed components. The ring spins with the output shaft, sliding along its longitudinal axis to engage or disengage the coaxial hub. The hub, which sits on a bearing encircling the same shaft, can spin independently until engaged.

Engagement occurs when the toothed components interlock. Once engaged, the ring and the hub spin together as a unit. To control engagement, the dog clutch contains a shift linkage that governs the position of the ring with respect to the hub.

Moving the ring towards the hub so that their teeth interlock changes the clutch state to engaged. Tooth overlap must exceed a minimum value for engagement. Moving the ring in reverse so that the two sets of teeth no longer interlock changes the clutch state back to disengaged.

Port S specifies the shift linkage position. When the clutch is fully disengaged, the shift linkage position is zero. When the clutch is fully engaged, the shift linkage position equals the sum of the tooth height and the ring-hub clearance of the fully disengaged state:

$$z=h+z_{Gap},$$

where:

• z is the shift linkage position.

• h is the tooth height.

• z_Gap is the ring-hub clearance when disengaged.

The figure shows side and front views of the dog clutch and some of its relevant variables.

Torque Transmission Models

The Dog Clutch block provides a choice of two torque transmission models.

Friction Clutch Approximate Model

Treat clutch engagement as a friction phenomenon between the ring and the hub. This model ignores special effects such as backlash, an approximation that makes the block better suited for linearization, fixed-step simulation, and hardware-in-loop (HIL) simulation. The Fundamental Friction Clutch block provides the foundation for the model.

In the friction approximate model, the clutch has three possible configurations: disengaged, engaged, and locked. When disengaged, the contact force between the ring and the hub is zero. This force remains zero until the shift linkage reaches the minimum position for engagement.

When the ring-hub tooth overlap, h, exceeds the minimum value for engagement, the contact force between the two components begins to increase linearly with the shift linkage position, z.

At full engagement, the contact force reaches its maximum value, and the clutch state switched to locked. In this state, the ring and the hub spin as a unit without slip. To unlock the clutch, the transmitted torque must exceed the maximum allowed value that you specify.

Dynamic Model with Backlash

Capture clutch phenomena such as backlash, torsional compliance, and contact forces between ring and hub teeth. This model provides greater accuracy than the friction clutch approximation.

In the dynamic model, the clutch has two possible configurations: disengaged and engaged. When disengaged, the contact force between the ring and the hub is zero. This force remains zero until the shift linkage reaches the minimum position for engagement.

When the ring-hub tooth overlap, h, exceeds the minimum value for engagement, a contact force kicks in between the two components. This force is the sum of torsional spring and damper components. Including backlash between the ring and hub teeth:

$$T_C=\{\begin{array}{cc}-k_{RH}\left(\varphi -\frac{\delta }{2}\right)-{\mu }_R·\omega & \varphi >\frac{\delta }{2}\\ 0& -\frac{\delta }{2}<\varphi <\frac{\delta }{2}\\ -k_{RH}\left(\varphi +\frac{\delta }{2}\right)-{\mu }_R\omega & \varphi <-\frac{\delta }{2}\end{array},$$

where:

• k_RH is the torsional stiffness of the ring-hub coupling.

• ϕ is the relative angle, about the common rotation axis, between the ring and the hub.

• δ is the backlash between ring and hub teeth.

• ω is the relative angular velocity between the ring and the hub. This variable describes how fast the two components slip past each other.

Compliant end stops limit the translational motion of the clutch shift linkage and the ring. The compliance model treats the end stops as linear spring-damper sets. The location of the end stops depends on the relative angle and angular velocity between the ring and hub teeth:

• If the teeth align and the relative angular velocity is smaller than the maximum value for clutch engagement, the end-stop location is the sum of the ring-hub clearance when fully disengaged and the tooth height. With the end stop at this location, the clutch can engage.

• If the teeth do not align or the relative angular velocity exceeds the maximum value for clutch engagement, the end-stop location is set to prevent the ring from engaging the hub. The clutch remains disengaged.

Translational friction opposes shift linkage and ring motion. This friction is the sum of Coulomb and viscous components:

$$F_Z=-k_K·F_N·\tanh \left(\frac{4v}{v_{th}}\right)-{\mu }_{T}v,$$

where:

• F_Z is the net translational friction force acting on the shift linkage and ring.

• k_K is the kinetic friction coefficient between ring and hub teeth.

• F_N is the normal force between ring and hub teeth.

• v is the translational velocity of the shift linkage and the ring.

• v_th is the translational velocity threshold. Below this threshold, a hyperbolic tangent function smooths the Coulomb friction force to zero as the shift linkage and ring velocity tends to zero.

• μ_T is the viscous damping coefficient acting on the shift linkage and the ring.

Clutch Engagement Conditions

The clutch engages when it satisfies a set of geometrical and dynamic conditions. These conditions specify the values that certain variables can take for clutch engagement to occur:

• The minimum position at which the ring and the hub can engage is

  $$z=h_0+z_{Gap},$$

  where h₀ is the minimum tooth overlap for clutch engagement. Adjust this parameter to minimize engagement instability, that is, the tendency of the clutch to switch rapidly between engaged and disengaged states

• The magnitude of the relative angular velocity between the ring and the hub is smaller than the maximum engagement velocity, that is:

  $$\left|\omega \right|<\left|{\omega }_{\max }\right|,$$

  where ω_max is the maximum value of the relative angular velocity at which engagement can occur.

• If using the friction clutch approximate model, engagement occurs only if torque transfer between the ring and the hub remains smaller than the maximum transmitted torque that the clutch supports.

• If using the dynamic model with backlash, engagement occurs only if the relative angular position of the ring and hub teeth allows them to interlock.

Rotational Power Dissipation

When the clutch slips under an applied torque, it dissipates power. The power loss equals the product of the slip angular velocity and the contact torque between the ring and the hub:

$$P_{loss}=\omega ·T_C,$$

where:

• P_loss is the dissipated power due to slipping.

• T_C is the kinetic contact torque.

Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, in the Clutch settings, set the Thermal port parameter to Model. Specify the associated thermal parameters for the component.

Ports

Input

S — Shift linkage

physical signal

Physical signal input port associated with the shift linkage.

Dependencies

If, in the Shift Linkage settings, the Shift linkage control parameter is set to:

• Physical signal — Input shift linkage position directly through the optional physical signal port, S.

• Conserving port — Input the shift linkage position dynamically through the optional translational conserving port, S. When you select this option, related Shift Linkage parameters are exposed.

Output

X — Clutch position

physical signal

Physical signal output port associated with clutch position.

Conserving

H — Clutch hub

mechanical rotational

Mechanical rotational conserving port associated with the clutch hub

R — Clutch ring

mechanical rotational

Mechanical rotational conserving port associated with the clutch ring.

S — Shift linkage

mechanical translational

Mechanical translational conserving port associated with shift linkage.

Dependencies

If, in the Shift Linkage settings, the Shift linkage control parameter is set to:

• Physical signal — Input shift linkage position directly through the optional physical signal port, S.

• Conserving port — Input the shift linkage position dynamically through the optional translational conserving port, S. When you select this option, related Shift Linkage parameters are exposed.

T — Heat flow

thermal

Thermal conserving port associated with heat flow.

Dependencies

This port is visible only when, in the Clutch settings, the Thermal Port parameter is set to Model.

Exposing this port makes related settings visible.

Parameters

The table shows how the specified options for parameters in both the Shift Linkage and Clutch settings affect the visibility of:

• Parameters in the Clutch, Shift Linkage, Engagement Conditions, and Initial Conditions settings

• Thermal Port settings

To learn how to read the table, see Parameter Dependencies.

Dog Clutch Parameter Dependencies

Settings	Parameters and Options
Shift Linkage	Shift linkage control
	Conserving Port			Physical signal
Clutch	Thermal port			Thermal port
	Omit		Model	Omit		Model
	Torque transmission model		-	Torque transmission model		-
	Friction clutch approximation - Suitable for HIL and linearization	Dynamic with backlash	-	Friction clutch approximation - Suitable for HIL and linearization	Dynamic with backlash	-
	-	-	Temperature vector	-	-	Temperature vector
	Maximum transmitted torque	-	Maximum transmitted torque vector	Maximum transmitted torque	-	Maximum transmitted torque vector
	-	-	Interpolation method	-	-	Interpolation method
	-	-	Extrapolation method	-	-	Extrapolation method
	Clutch teeth mean radius	Clutch teeth mean radius	Clutch teeth mean radius	Clutch teeth mean radius	-	Clutch teeth mean radius
	-	Number of teeth	-	-	Number of teeth	-
	-	Rotational backlash	-	-	Rotational backlash	-
	-	Torsional stiffness	-	-	Torsional stiffness	-
	-	Torsional damping	-	-	Torsional damping	-
Shift Linkage	Tooth height	Tooth height	Tooth height	Tooth height	Tooth height	Tooth height
	Ring-hub clearance when disengaged	Ring-hub clearance when disengaged	Ring-hub clearance when disengaged	Ring-hub clearance when disengaged	Ring-hub clearance when disengaged	Ring-hub clearance when disengaged
	Hard stop at back of shift linkage	Hard stop at back of shift linkage	Hard stop at back of shift linkage	-	-	-
	Ring stop stiffness	Ring stop stiffness	Ring stop stiffness	-	-	-
	Ring stop damping	Ring stop damping	Ring stop damping	-	-	-
	Shift linkage viscous friction coefficient	Shift linkage viscous friction coefficient	Shift linkage viscous friction coefficient	-	-	-
	-	Tooth-tooth friction coefficient	-	-	-	-
Engagement Conditions	Linkage travel direction	Linkage travel direction	Linkage travel direction	Linkage travel direction	Linkage travel direction	Linkage travel direction
	Maximum engagement speed	Maximum engagement speed	Maximum engagement speed	-	-	-
	Tooth overlap to engage	Tooth overlap to engage	Tooth overlap to engage	Tooth overlap to engage	Tooth overlap to engage	Tooth overlap to engage
Initial Conditions	Clutch initial state	Clutch initial state	Clutch initial state	Clutch initial state	Clutch initial state	Clutch initial state
	Initial shift linkage position	Initial shift linkage position	Initial shift linkage position	-	-	-
	-	Initial ring-hub offset angle	-	-	Initial ring-hub offset angle	-
Thermal Port	-	-	Thermal mass	-	-	Thermal mass
	-	-	Initial temperature	-	-	Initial temperature

Clutch

Thermal port — Thermal model

Omit (default) | Model

Model for heat flow and temperature change:

• Omit — Temperature-independent model.

• Model — Temperature-dependent model.

Dependencies

For the temperature-independent model, that is, if this parameter is set to Omit, the Torque transmission model parameter and other related parameters in the Clutch settings are visible.

For the temperature-dependent model, that is, when this parameter is set to Model, related parameters in the Clutch settings, thermal port T, and Thermal Port settings are visible.

Temperature vector — Temperature

[280, 300, 320] K (default) | increasing vector

Input values for the temperature as a vector. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension. The values in the vector must increase from left to right.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Model.

Torque transmission model — Torque transmission model

Friction clutch approximation — Suitable for HIL and linearization (default) | Dynamic with backlash

Computational framework for modeling the dynamic behavior of the dog clutch:

• Friction clutch approximation — Suitable for HIL and linearization — Model clutch engagement as a friction phenomenon between the ring and the hub. This model, based on the Fundamental Friction Clutch block, provides a computationally efficient approximation of the dog clutch.

• Dynamic with backlash — Model clutch engagement in detail, accounting for such phenomena as backlash, torsional compliance, and contact forces between ring and hub teeth. Selecting this option causes additional Shift Linkage and Initial Conditions parameters to appear.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter is set to Omit.

The visibility of related parameters in the Clutch and Shift Linkage settings is affected by the option that you select for this parameter.

Temperature vector — Temperature

[280, 300, 320] K (default) | increasing vector

Input values for the temperature as a vector. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension. The values in the vector must increase from left to right.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Model.

Maximum transmitted torque — Maximum transmitted torque

1000 N*m (default) | positive scalar

Largest torque that the clutch can transmit, corresponding to a nonslip engaged configuration. If the torque transmitted between the ring and the hub exceeds this value, the two components begin to slip with respect to each other. This torque determines the static friction limit in the friction clutch approximation

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter is set to Omit and the Torque transmission model parameter is set to Friction clutch approximation - Suitable for HIL and linearization.

Maximum transmitted torque vector — Maximum transmitted torque

[1000, 1050, 1000] N*m (default) | vector

Largest torque that the clutch can transmit, corresponding to a nonslip engaged configuration, specified as a vector. If the torque transmitted between the ring and the hub exceeds this value, the two components begin to slip with respect to each other. This torque determines the static friction limit in the friction clutch approximation. The vector has the same number of elements as the temperature vector.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Model.

Interpolation method — Interpolation method

Linear (default) | Smooth

Interpolation method for approximating the output value when the input value is between two consecutive grid points:

• Linear — Select this option to get the best performance.

• Smooth — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Model.

Extrapolation method — Extrapolation method

Linear (default) | Nearest | Error

Extrapolation method for determining the output value when the input value is outside the range specified in the argument list:

• 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 going into the extrapolation mode 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.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Model.

Clutch teeth mean radius — Clutch teeth mean radius

50 mm (default) | positive scalar

Distance from the ring or hub center to the corresponding tooth center. The mean tooth radius determines the normal contact forces between ring and hub teeth given the transmission torque between the two components. The value must be greater than zero.

Dependencies

This parameter is not visible if all of these conditions are met:

• In the Clutch settings:

  • Thermal port is set to Omit.

  • Torque transmission model is set to Dynamic with backlash.

• In the Shift Linkage settings, the Shift linkage control parameter is set to Physical control.

Number of teeth — Number of ring or hub teeth

6 (default) | positive nonzero scalar integer

Total number of teeth in the ring or the hub. The two components have equal tooth numbers. The value must be greater than or equal to one.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Omit and the Torque transmission model parameter is set to Dynamic with backlash.

Rotational backlash — Rotational backlash

10 deg (default) | positive scalar

Allowable angular motion, or play, between the ring and hub teeth in the engaged clutch configuration. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Omit and the Torque transmission model parameter is set to Dynamic with backlash.

Torsional stiffness — Torsional stiffness

10e6 N*m/rad (default) | positive scalar

Linear torsional stiffness coefficient at the contact interface between the ring and hub teeth. This coefficient characterizes the restoring component of the contact force between the two sets of teeth. Greater stiffness values correspond to greater contact forces. The value must be greater than zero. The default value is 10e6 N*m/rad.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Omit and the Torque transmission model parameter is set to Dynamic with backlash.

Torsional damping — Torsional damping

100 N*m/(rad/s) (default) | positive scalar

Linear torsional damping coefficient at the contact interface between the ring and hub teeth. This coefficient characterizes the dissipative component of the contact force between the two sets of teeth. Greater damping values correspond to greater energy dissipation during contact. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Clutch settings, the Thermal port parameter to Omit and the Torque transmission model parameter is set to Dynamic with backlash.

Shift Linkage

Shift linkage control — Shift linkage control port

Physical signal (default) | Conserving port

Port type for shift linkage control:

• Physical signal — Input shift linkage position directly through the optional physical signal port, S.

• Conserving port — Input the shift linkage position dynamically through the optional translational conserving port, S.

Dependencies

This parameter determines whether the shift linkage control port, S, is a conserving or physical signal port. Related Shift Linkage parameters are exposed if this parameter is set to Conserving port.

Tooth height — Tooth height

10 mm (default) | positive scalar

Distance between the base and crest of a tooth. Ring and hub teeth share the same height. The tooth height and the ring-hub clearance when fully disengaged determine the maximum travel span of the shift linkage. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Ring-hub clearance when disengaged — Ring-hub clearance when disengaged

3 mm (default) | positive scalar

Maximum open gap between the ring and hub tooth crests along the shift linkage translation axis. This gap corresponds to the fully disengaged clutch state. The tooth height and the ring-hub clearance when fully disengaged determine the maximum travel span of the shift linkage. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Hard stop at back of shift linkage — Hard stop model

On (default) | Off

Hard stop that prevents the shift linkage from traveling beyond the fully disengaged position:

• On — Hard stop when fully disengaged.

• Off — No hard stop when fully disengaged.

Ring stop stiffness — Ring stop stiffness

10e5 N/m (default) | positive scalar

Linear stiffness coefficient of the ring end stop. This coefficient characterizes the restoring component of the contact force that resists translational motion past the end stops. Greater stiffness values correspond to greater contact forces and a smaller end stop compliance. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Ring stop damping — Ring stop damping

1e3 N/(m/s) (default) | nonegative scalar

Linear damping coefficient of the ring end stop. This coefficient characterizes the dissipative component of the contact force that resists translational motion past the end stops. Greater damping values correspond to greater energy dissipation during contact. The value must be greater than or equal to zero

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Shift linkage viscous friction coefficient — Shift linkage viscous friction coefficient

100 N/(m/s) (default) | positive scalar

Linear damping coefficient acting on the shift linkage. This coefficient characterizes the dissipative force that resists shift linkage motion due to viscous damping. Greater coefficient values correspond to greater energy dissipation during shift linkage motion. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Tooth-tooth friction coefficient — Tooth-tooth contact kinetic friction coefficient

0.05 (default) | positive scalar

Kinetic friction coefficient at the contact interface between ring and hub teeth. This coefficient characterizes the dissipative force that resists shift linkage motion due to tooth-tooth contact during clutch engagement/disengagement.

Greater coefficient values correspond to greater energy dissipation during shift linkage motion. The value must be greater than zero.

Dependencies

This parameter is only visible when the Shift linkage control parameter is set to Conserving port and, in the Clutch settings:

• Thermal port is set to Omit

• Torque transmission model is set to Dynamic with backlash

Engagement Conditions

Linkage travel direction — Engagement condition travel direction

Positive shift linkage displacement engages clutch (default) | Negative shift linkage displacement engages clutch

Direction the shift linkage must travel in to engage the clutch. Choices include positive and negative displacements.

Maximum engagement speed — Engagement speed upper velocity threshold

inf (default) | positive scalar

Relative angular velocity between the ring and the hub above which the clutch cannot engage. The value is specific to the specific gearbox or transmission. Minimizing the value helps avoid high dynamic impact during engagement. The value must be greater than zero.

Dependencies

This parameter is visible only if, in the Shift Linkage settings, the Shift linkage control parameter to Conserving port.

Tooth overlap to engage — Tooth overlap engagement threshold

3 mm (default) | positive scalar

Overlap length between ring and hub teeth along the common longitudinal axis above which the clutch can engage. The clutch remains disengaged until the tooth overlap by at least this length. The value must be greater than zero.

Initial Conditions

Initial state — Initial clutch state

Unlocked (default) | Locked

Clutch state at the start of simulation:

• Unlocked — Clutch transmits zero torque between the ring and the hub.

• Locked — Clutch transmits torque between the ring and the hub.

Initial shift linkage position — Initial shift linkage position

0 mm (default) | scalar

Shift linkage position at simulation time zero. Values between zero and the sum of the ring-hub clearance and the tooth overlap to engage are consistent with a disengaged clutch. Larger values are consistent with an engaged clutch.

Dependencies

This parameter is only visible when both of these conditions are met:

• In the Clutch settings, the Thermal port parameter is set to Omit.

• In the Shift Linkage settings, Shift linkage control is set to Conserving port.

Initial ring-hub offset angle — Initial ring-hub offset angle

0 deg (default) | scalar

Rotation angle between the ring and the hub at simulation time zero. This angle determines whether the ring and hub teeth can interlock, and hence whether the clutch can engage. The initial offset angle must satisfy these conditions:

• If the clutch initial state is disengaged, the initial offset angle must fall in the range

  $$-\frac{{180}^{°}}{N}\le {\varphi }_0\le +\frac{{180}^{°}}{N},$$

  where N is the number of teeth present in the ring or the hub. The two components contain the same number of teeth.

• If the clutch initial state is engaged, the initial offset angle must fall in the range

  $$-\frac{\delta }{2}\le {\varphi }_0\le +\frac{\delta }{2},$$

  where δ is the backlash angle between the ring and hub teeth.

Dependencies

This parameter is only visible when, in the Clutch settings, both of these conditions are met:

• Thermal port is set to Omit.

• Torque transmission model is set to Dynamic with backlash.

Thermal Port

These settings are only visible when, in the Clutch Settings, the Thermal port parameter is set to Model.

Thermal mass — Resistance to temperature change

50 kJ/K (default) | scalar

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

Dependencies

This parameter is only visible when, in the Clutch settings, the Thermal Port parameter is set to Model.

Initial temperature — Initial temperature

300 K (default) | scalar

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses.

Dependencies

This parameter is only visible when, in the Clutch settings, the Thermal Port parameter is set to Model.

More About

Linearization

To optimize your model for linearization, use the Clutch > Torque transmission model parameter default setting, Friction clutch approximation - Suitable for HIL and linearization.

Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Clutch > Torque transmission model parameter default setting, Friction clutch approximation - Suitable for HIL and linearization.

Extended Capabilities

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

Version History

Introduced in R2011a