# Dog Clutch

Clutch with toothed plates that engage when plate teeth become enmeshed

**Library:**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:

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

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. 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:

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

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._{N}*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 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

*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, that is:

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

where

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

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

where:

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

### Thermal Modeling

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

### Output

### Conserving

## Parameters

## More About

## Extended Capabilities

## See Also

### Simscape Blocks

**Introduced in R2011a**