# Dog Clutch

Clutch with toothed plates that engage when plate teeth become enmeshed

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

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.

The translational conserving 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.

• zGap 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:

`${T}_{C}=\left\{\begin{array}{cc}-{k}_{RH}\left(\varphi -\frac{\delta }{2}\right)-{\mu }_{R}·\text{\hspace{0.17em}}\omega & \varphi >\frac{\delta }{2}\\ 0& -\frac{\delta }{2}<\varphi <\frac{\delta }{2}\\ -{k}_{RH}\left(\varphi +\frac{\delta }{2}\right)-{\mu }_{R}\omega & \varphi <-\frac{\delta }{2}\end{array},$`

where:

• kRH 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:

`${F}_{Z}=-{k}_{K}·{F}_{N}·\mathrm{tanh}\left(\frac{4v}{{v}_{th}}\right)-{\mu }_{T}v,$`

where:

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

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

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

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

• vth 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.

• μT 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 must be smaller than the maximum engagement velocity:

`$|\omega |<|{\omega }_{\mathrm{max}}|,$`

where ωmax 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:

`${P}_{loss}=\omega \text{\hspace{0.17em}}·\text{\hspace{0.17em}}{T}_{C},$`

where:

• Ploss is the dissipated power due to slipping.

• TC is the kinetic contact torque.

### Shift Linkage and Thermal Variants

The block provides four variants:

• Mechanical port shift linkage and thermal port

• Physical signal position input

• Physical signal position input and thermal port

One of the two shift linkage variants accepts the position input through a physical signal port, the other through a translational conserving port. To model thermal effects, you can add a thermal port to either of the shift linkage variants.

To change from the current variant, right-click the block in your model and, under Simscape > Block choices, and select the desired variant. Changing the variant changes the ports and parameters.

## Modeling Thermal Effects

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, right-click the block in your model and, from the context menu, select Simscape > Block choices. Choose a variant that includes a thermal port. Specify the associated thermal parameters for the component.

## Ports

`S`

Translational conserving port or physical signal port that represents the shift linkage. The port type depends on the shift linkage variant that you select.

`X`

Physical signal port for sensing the clutch position

`T`

Thermal conserving port. The thermal port is optional and is hidden by default. To expose the port, select a variant that includes a thermal port.

`R`

Rotational conserving port that represents the clutch ring

`H`

Rotational conserving port that represents the clutch hub

## Parameters

### Clutch

If you select Physical signal position input or Mechanical port shift linkage as the variant for the Dog Clutch block, parameter visibility depend on the value that you select for the Torque transmission model parameter.

Selecting a thermal variant for the Dog Clutch block, makes other Clutch parameters visible.

Tooth height

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 tooth height is greater than zero. The default value is `10` `mm`.

Hard stop at back of shift linkage

Choice of translational motion limiting device. Select whether to stop the shift linkage when fully disengaged. The default option is `Hard stop when fully disengaged`.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

Ring-hub clearance when disengaged

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 ring-hub clearance is greater than zero. The default value is `3` `mm`.

Ring stop stiffness

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 stiffness coefficient is greater than zero. The default value is `1e+6` `N/m`.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

Ring stop damping

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 damping coefficient is greater than or equal to zero. The default value is `1000` `N/(m/s)`.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

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 viscous friction coefficient is greater than zero. The default value is `100` `N/(m/s)`.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

Tooth-tooth friction coefficient

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 friction coefficient is greater than zero. The default value is `0.05`.

This parameter is only visible if you select the Mechanical port shift linkage variant for the block and set the Torque transmission model parameter to ```Dynamic with backlash```.

### Engagement Conditions

Direction the shift linkage must travel in to engage the clutch. Choices include positive and negative displacements. The default setting is `Positive shift linkage displacement engages clutch`.

Maximum engagement velocity

Relative angular velocity between the ring and the hub above which the clutch cannot engage. The maximum engagement velocity is greater than zero. The default value is `inf` (infinity) rad/s.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

Tooth overlap to engage

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 tooth overlap to engage is greater than zero. The default value is `3` mm.

### Initial Conditions

Clutch Initial state

Clutch configuration at the start of simulation. Options include:

• `Disengaged` — Clutch transmits zero torque between the ring and the hub. `Disengaged`is the default value.

• `Engaged` — Clutch transmits torque between the ring and the hub.

If you select Physical signal position input for the block variant, this parameter is only visible if you set the Torque transmission model parameter to ```Friction clutch approximation - Suitable for HIL and linearization```.

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. The default value is `0` mm.

This parameter is only visible if you select one of these variants for the block:

• Mechanical port shift linkage and thermal port

Initial ring-hub offset angle

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.

The default value is `0` deg.

This parameter is only visible if you satisfy both of these conditions:

• For the block variant, select Mechanical port shift linkage or Physical signal position input

• Set the Torque transmission model parameter to `Dynamic with backlash`.

### Thermal Port

These thermal parameters are only visible when you select a block variant that includes a thermal port.

Thermal mass

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. The default value is `25` `kJ/K`.

Initial temperature

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. The default value is `300` `K`.