# Dog Clutch

Clutch with toothed plates that engage when plate teeth become enmeshed

**Libraries:**

Simscape /
Driveline /
Clutches

## Description

The Dog Clutch block represents a nonslip clutch that uses the positive engagement of interlocking teeth to transfer torque between drive shafts. Dog clutches used in manual transmissions that engage and disengage power transmission by sliding two mating parts together. The ring and hub are the primary components of a dog clutch. The input shaft turns the ring, which has slots or teeth. The hub connects to an output shaft that has protruding "dogs" that fit into the slots of the ring. When you shift the transmission, the dogs on the hub engage with the slots on the ring, locking the two components and transmitting power. You shift again to disengage the clutch, which causes the dogs to disengage from the slots and allows the transmission to spin freely.

Engagement occurs when the ring and hub interlock. 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. You can control the shift linkage with
a physical signal or a mechanical translational conserving port by using the
**Torque transmission model** parameter. The torque transmission
model that you choose corresponds to a fidelity and level of abstraction:

`Two-mode`

— Fully abstracted torque transmission model based on mode charts. This setting is fast enough for real-time simulation and does not require knowledge of the clutch dimensions. You can control the shift linkage only with a physical or logic-controlled signal.`Friction clutch approximation - Suitable for HIL and linearization`

— Medium- to high-fidelity composite implementation of the Fundamental Friction Clutch block. This setting supports thermal modeling. You can control the shift linkage with either a physical signal or a mechanical translational conserving port.`Dynamic with backlash`

— High-fidelity clutch engagement model that accounts for phenomena such as backlash, torsional compliance, and contact forces between the ring and hub teeth.

Moving the ring toward the hub so that the 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

You can choose from three torque transmission models.

**Two-Mode**

To simulate an abstracted dog clutch, set **Torque transmission
model** to `Two-mode`

. The two-mode
torque transmission model uses mode charts to control whether the clutch is
engaged or disengaged. You can control the shift linkage position using
logic-based commands or a linkage position physical signal. When you use
logic-based commands, `false`

at port **X**
represents a disengaged clutch, and `true`

represents an
engaged clutch.

**Friction Clutch Approximate Model**

When you set **Torque transmission model** to
```
Friction clutch approximation - Suitable for HIL
and
```

, the block treats the clutch engagement as a friction
phenomenon between the ring and the hub. This setting is better suited for
linearization, fixed-step simulation, and hardware-in-loop (HIL) simulation. The
block uses a composite implementation of the Fundamental Friction Clutch
block.

When you use this setting, 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 switches 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 value
of the **Maximum transmitted torque** parameter.

**Dynamic Model with Backlash**

When you set **Torque transmission model** to
`Dynamic with backlash`

, the block simulates 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.

When you use this setting, 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 engagement
threshold value, the clutch transmits torque. This torque is the sum of
torsional spring and damper components, including backlash between the ring and
hub teeth, such that

$${T}_{C}=\{\begin{array}{cc}-{k}_{RH}\left(\varphi -\frac{\delta}{2}\right)-{\mu}_{R}\xb7\text{\hspace{0.17em}}\omega & \varphi >\frac{\delta}{2}\\ 0& -\frac{\delta}{2}<\varphi <\frac{\delta}{2}\\ -{k}_{RH}\left(\varphi +\frac{\delta}{2}\right)-{\mu}_{R}\omega & \varphi <-\frac{\delta}{2}\end{array},$$

where:

*k*is the torsional stiffness of the ring-hub coupling._{RH}*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. The clutch can engage in this end stop position.

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 does not engage in this end stop position.

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

$${F}_{Z}=-{k}_{K}\xb7{F}_{N}\xb7\mathrm{tanh}\left(\frac{4v}{{v}_{th}}\right)-{\mu}_{T}v,$$

where:

*F*is the net translational friction force acting on the shift linkage and ring._{Z}*k*is the kinetic friction coefficient between ring and hub teeth._{K}*F*is the normal force between ring and hub teeth, where_{N}*F*=_{N}*T*/_{C}*R*._{m}*v*is the translational velocity of the shift linkage and the ring.*v*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._{th}*μ*is the viscous damping coefficient acting on the shift linkage and the ring._{T}

### Clutch Engagement Conditions

The clutch engages when it satisfies these geometrical and dynamic conditions:

The minimum position where the ring and the hub can engage is

$$z={h}_{0}+{z}_{Gap},$$

where

*h*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_{0}The magnitude of the relative angular velocity between the ring and the hub is smaller than the maximum engagement velocity, such that

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

where

*ω*is the maximum value of the relative angular velocity at which engagement can occur._{max}If

**Torque transmission model**is`Friction clutch approximation - Suitable for HIL and linearization`

, the engagement occurs only if torque transfer between the ring and the hub is smaller than the maximum transmitted torque that the clutch supports.If

**Torque transmission model**is`Dynamic with backlash`

, the 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, such that

$${P}_{loss}=\omega \text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}{T}_{C},$$

where:

*P*is the dissipated power due to slipping._{loss}*T*is the kinetic contact torque._{C}

### Thermal Modeling

When you set **Torque transmission model** to
```
Friction clutch approximation - Suitable for HIL and
linearization
```

, you can model the effects of heat flow and
temperature change by using the optional thermal conserving port,
**T**.

### 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
```

.

## Ports

### Input

### Output

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2011a**