# Double-Sided Synchronizer

Back-to-back dog-cone clutch pairs assembled symmetrically about a translational detent to provide smooth gear engagement

**Libraries:**

Simscape /
Driveline /
Clutches

## Description

The block represents a double-sided synchronizer that contains two back-to-back dog
clutches, two back-to-back cone clutches, and one translational detent. Shift linkage
translation along the negative direction causes the clutches to engage the ring with hub
*A*. Shift linkage translation along the positive direction causes
the clutches to engage the ring with hub *B*. When the magnitude of the
shift linkage translation is smaller than the cone clutch ring-hub gap, the synchronizer
is in neutral mode and does not transmit torque.

The schematic illustrates a double-sided synchronizer in the disengaged state. In this
state, the ring, **R**, and hub,
**H _{A}** and

**H**, shafts can spin independently at different speeds. As the shift linkage,

_{B}**S**, translates in the negative direction, the faces of cone clutch

*A*(

**CC**) come into contact. The friction in the cone clutch decreases the difference in rotational speed between the shafts. When the force on the shift linkage exceeds the peak force of detent,

_{A}**D**, the dog clutch teeth,

**T**, can engage. The detent peak force should be such that the cone clutch has enough time and normal force to bring the shafts to sufficiently similar speeds to allow engagement of the dog clutch. Similarly, translating the shift linkage along the positive direction allows the faces of cone clutch

*B*(

**CC**) to come into contact, and can allow the shaft of the ring to engage with the shaft of the hub

_{B}*B*

**(H**.

_{B})The model implements two Dog Clutch blocks, two Cone Clutch blocks, and one Translational Detent block. Refer to each block reference page for more information on the corresponding block function.

Connections **R**, **H _{A}**,
and

**H**are mechanical rotational conserving ports that represent the ring,

_{B}**R**, hub

*A*(

**H**), and hub

_{A}*B*(

**H**), respectively. Connection

_{B}**S**is a mechanical translational conserving port that represents the ring shifter handle.

Connections **X1** and **X2** are physical signal
ports that output the shift linkage positions of the dog clutches and cone clutches,
respectively. The tables provide the values of *X1* and
*X2* in common clutch engagement cases.

Dog Clutch State | X1 |
---|---|

Disengaged | 0 |

Fully engaged with hub A | Negative sum of ring-hub gap and tooth height |

Fully engaged with hub B | Positive sum of ring-hub gap and tooth height |

Cone Clutch State | X2 |
---|---|

Disengaged | 0 |

Fully engaged with hub A | Negative value of ring-hub gap |

Fully engaged with hub B | Positive value of ring-hub gap |

The values of *X1* and *X2* are zero when the
synchronizer is fully disengaged. When the dog clutch is fully engaged with hub
*A*, *X1* is equal to the negative sum of its
ring-hub gap and tooth height. When the dog clutch is fully engaged with hub
*B*, *X1* is equal to the positive sum of its
ring-hub gap and tooth height. When the cone clutch is fully engaged with hub
*A*, *X2* is equal to the negative of its ring-hub
gap. When the cone clutch is fully engaged with hub *B*,
*X2* is equal to its ring-hub gap.

### 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, select a
temperature-dependent setting tor the **Friction model** parameter.
Specify the associated thermal parameters for the component.

## Assumptions and Limitations

The model does not account for inertia effects. You can add a Simscape™ Inertia block at each port to add inertia to the synchronizer model.

## Ports

### Output

**X1** — Dog clutch translation

physical signal

Physical signal output port that measures the magnitude of the dog clutch translation.

**X2** — Cone clutch translation

physical signal

Physical signal output port that measures the magnitude of the cone clutch translation.

### Conserving

**HA** — Clutch hub *A*

mechanical rotational

Mechanical rotational conserving port associated with the clutch hub
*A* shaft.

**HB** — Clutch hub *B*

mechanical rotational

Mechanical rotational conserving port associated with the clutch hub
*B* shaft.

**R** — Clutch ring

mechanical rotational

Mechanical rotational conserving port associated with the clutch ring.

**S** — Shift linkage

mechanical rotational

Mechanical rotational conserving port associated with shift linkage.

**T** — Heat flow

thermal

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only if, in the **Friction**
settings, the **Friction model** parameter is set
to ```
Temperature-dependent friction
coefficients
```

or ```
Temperature and
velocity-dependent friction coefficients
```

.

## Parameters

The table shows how the specified options for parameters in both the **Cone
Clutch** and **Dog Clutch** settings affect the visibility of:

Parameters in the

**Cone Clutch**,**Dog Clutch**, and**Initial Conditions**settings**Thermal Port**settingsThermal port

**T**

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

**Double-Sided Synchronizer Block Parameter
Dependencies**

Settings | Parameters and Options | |||||
---|---|---|---|---|---|---|

Cone Clutch | Contact surface maximum
diameter | |||||

Contact surface minimum
diameter | ||||||

Cone half
angle | ||||||

Friction
model | ||||||

```
Fixed kinetic friction
coefficient
``` | ```
Velocity-dependent kinetic friction
coefficient
``` | ```
Temperature-dependent friction
coefficients
``` | ```
Temperature and velocity-dependent friction
coefficients
``` | |||

- | - | Exposes: Conserving port **T****Thermal Port**settings
| Exposes: Conserving port **T****Thermal Port**settings
| |||

- | Relative velocity
vector | Relative velocity vector | ||||

- | - | Temperature vector | Temperature vector | |||

Static friction
coefficient | Static friction
coefficient vector | Static friction coefficient vector | Static friction coefficient matrix | |||

Kinetic friction
coefficient | Kinetic friction
coefficient vector | Kinetic friction coefficient vector | Kinetic friction coefficient matrix | |||

- | Friction coefficient
interpolation method | Friction coefficient interpolation
method | Friction coefficient interpolation
method | |||

- | Friction coefficient
extrapolation method | Friction coefficient extrapolation
method | Friction coefficient extrapolation | |||

Velocity
tolerance | Velocity
tolerance | Velocity tolerance | Velocity tolerance | |||

Threshold
force | Threshold
force | Threshold force | Threshold force | |||

Dog Clutch | 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 | - | Maximum transmitted torque vector | 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 | Clutch teeth mean radius | |

- | Number of teeth | - | Number of teeth | |||

Rotational backlash | Rotational backlash | |||||

- | Torsional stiffness | - | Torsional stiffness | |||

- | Torsional damping | - | Torsional damping | |||

- | Tooth-tooth friction coefficient | - | Tooth-tooth friction coefficient | |||

Initial Conditions | Initial state | Initial state | Initial state | Initial state | Initial state | Initial state |

Dog clutch initial shift linkage
position | Dog clutch initial shift linkage
position | Dog clutch initial shift linkage
position | Dog clutch initial shift linkage
position | Dog clutch initial shift linkage
position | Dog clutch initial shift linkage
position | |

Cone clutch initial shift linkage
position | Cone clutch initial shift linkage
position | Cone clutch initial shift linkage
position | Cone clutch initial shift linkage
position | Cone clutch initial shift linkage
position | Cone clutch initial shift linkage
position | |

- | Initial dog clutch A ring-hub offset
angle | - | Initial dog clutch A ring-hub offset
angle | - | - | |

- | Initial dog clutch B ring-hub offset
angle | - | Initial dog clutch B ring-hub offset
angle | - | - | |

Thermal Port | - | - | - | - | Thermal mass | Thermal mass |

- | - | - | - | Initial temperature | Initial temperature |

### Cone Clutch

**Contact surface maximum diameter** — Outer diameter

`150`

`mm`

(default) | positive scalar

Outer conical diameter *d _{o}*.

**Contact surface minimum diameter** — Inner diameter

`100`

`mm`

(default) | positive scalar

Inner conical diameter
*d _{i}*.

**Cone half angle** — Cone half angle

`12`

`deg`

(default) | positive scalar

Half opening angle *α* of the cone geometry.

**Friction model** — Friction model

```
Fixed kinetic friction
coefficient
```

(default) | ```
Velocity-dependent kinetic friction
coefficient
```

| ```
Temperature-dependent friction
coefficients
```

| ```
Temperature and velocity-dependent friction
coefficients
```

Parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the friction model that you select for the block. The options are:

`Fixed kinetic friction coefficient`

— Provide a fixed value for the kinetic friction coefficient.`Velocity-dependent kinetic friction coefficient`

— Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between disks.`Temperature-dependent friction coefficients`

— Define the kinetic friction coefficient by table lookup based on the temperature.`Temperature and velocity-dependent friction coefficients`

— Define the kinetic friction coefficient by table lookup based on the temperature and the relative angular velocity between disks.

#### Dependencies

The friction model setting affects the visibility of other parameters, settings, and ports.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Relative velocity vector** — Relative velocity

`[0, 100, 1000]`

`rad/s`

(default) | vector

Input values for the relative velocity as a vector. The values in the vector must increase from left to right. 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.

#### Dependencies

This parameter is visible only if the **Friction
model** parameter is set to
```
Velocity-dependent kinetic friction
coefficient
```

or ```
Temperature and
velocity-dependent friction coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 the **Friction
model** parameter is set to
```
Temperature-dependent friction
coefficients
```

or ```
Temperature and
velocity-dependent friction coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Static friction coefficient** — Static friction coefficient

`0.35`

(default) | scalar

Static or peak value of the friction coefficient. The static friction coefficient must be greater than the kinetic friction coefficient.

#### Dependencies

this parameter is visible only if the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Static friction coefficient vector** — Static friction coefficient

`[.4, .38, .36]`

(default) | vector

Static, or peak, values of the friction coefficient as a vector. The vector must have the same number of elements as the temperature vector. Each value must be greater than the value of the corresponding element in the kinetic friction coefficient vector.

#### Dependencies

This parameter is visible only if the **Friction
model** parameter is set to
```
Temperature-dependent friction
coefficients
```

or ```
Temperature and
velocity-dependent friction coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Kinetic friction coefficient** — Kinetic friction coefficient

`0.3`

(default) | positve scalar

The kinetic, or Coulomb, friction coefficient. The coefficient must be greater than zero.

#### Dependencies

This parameter is visible only if the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Kinetic friction coefficient vector** — Kinetic friction coefficient

`[.3, .22, .19]`

(default) | `[.3, .28, .25]`

| vector

Output values for kinetic friction coefficient as a vector. All values must be greater than zero.

If the **Friction model** parameter is set to

`Velocity-dependent kinetic friction coefficient`

— The vector must have same number of elements as relative velocity vector.`Temperature-dependent friction coefficients`

— The vector must have the same number of elements as the temperature vector.

#### Dependencies

This parameter is visible only if the **Friction
model** parameter is set to
```
Velocity-dependent kinetic friction
coefficient
```

or ```
Temperature-dependent
friction coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Kinetic friction coefficient matrix** — Kinetic friction coefficient

```
[.34, .32, .3; .3, .28, .25; .25, .2,
.15]
```

(default) | matrix

Output values for kinetic friction coefficient as a matrix. All the values must be greater than zero. The size of the matrix must equal the size of the matrix that is the result of the temperature vector × the kinetic friction coefficient relative velocity vector.

#### Dependencies

This parameter is visible only if the **Friction
model** parameter is set to ```
Temperature
and velocity-dependent friction
coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Friction coefficient 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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Velocity-dependent kinetic friction
coefficient
```

, ```
Temperature-dependent
friction coefficients
```

, or ```
Temperature
and velocity-dependent friction
coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Friction coefficient 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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Velocity-dependent kinetic friction
coefficient
```

, ```
Temperature-dependent
friction coefficients
```

, or ```
Temperature
and velocity-dependent friction
coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Velocity tolerance** — Relative velocity locking threshold

`0.001`

`rad/s`

(default) | scalar

Relative velocity below which the two surfaces can lock. The surfaces lock if the torque is less than the product of the effective radius, the static friction coefficient, and the applied normal force.

**Threshold force** — Normal contact force threshold

`1`

`N`

(default) | scalar

The normal force is applied only if the amount of force exceeds the
value of the **Threshold force** parameter. Forces
below the **Threshold force** are not applied so there
is no transmitted frictional torque.

### Dog Clutch

The methods that are available for parameterizing the torque transmission depend whether the friction model is temperature-dependent.

The friction model is determined, in the **Cone Clutch**
settings, by the **Friction model** parameter setting:

`Fixed kinetic friction coefficient`

— Temperature independent`Velocity-dependent kinetic friction coefficient`

— Temperature independent`Temperature-dependent friction coefficients`

— Temperature dependent`Temperature and velocity-dependent friction coefficients`

— Temperature dependent

For a temperature-independent model, parameterize the block using one of the
options for the **Torque Transmission Model** parameter.

**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.

#### Dependencies

This parameter is visible only if, in the **Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent friction
coefficients
```

.

The visibility of related parameters in the **Dog
Clutch** and **Initial Conditions**
settings is affected by the option that you select for this
parameter.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Temperature-dependent friction
coefficients
```

or ```
Temperature and
velocity-dependent friction coefficients
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Friction
clutch approximation - Suitable for HIL and
linearization
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Temperature-dependent kinetic friction
coefficient
```

or ```
Temperature and
velocity-dependent kinetic friction
coefficient
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Temperature-dependent kinetic friction
coefficient
```

or ```
Temperature and
velocity-dependent kinetic friction
coefficient
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to
```
Temperature-dependent kinetic friction
coefficient
```

or ```
Temperature and
velocity-dependent kinetic friction
coefficient
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in the **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Dynamic with
backlash
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in the **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Dynamic with
backlash
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 **Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in the **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Dynamic with
backlash
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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

**Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in the **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Dynamic with
backlash
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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

**Cone
Clutch** settings, the **Friction
model** parameter is set to ```
Fixed kinetic
friction coefficient
```

or
```
Velocity-dependent kinetic friction
coefficient
```

and, in the **Dog
Clutch** settings, the **Torque transmission
model** parameter is set to ```
Dynamic with
backlash
```

.

For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

### Detent

**Peak force** — Peak shear force

`500`

`N`

(default) | nonnegative scalar

Peak shear force of the detent.

**Notch width** — Notch width

`3`

`mm`

(default) | nonnegative scalar

Width of the region where the detent exhibits shear force.

**Viscous friction coefficient** — Viscous friction coefficient

`0.1`

`N/(m/s)`

(default) | nonnegative scalar

Viscous friction coefficient at the contact surface of the detent. The value must be greater than or equal to zero.

**Friction to peak force ratio** — Friction to peak force ratio

`0.01`

(default) | nonnegative scalar

Ratio of the kinetic friction to the peak shear force of the detent. The parameter is used to set the value of the kinetic friction. The parameter must be greater than or equal to zero.

**Friction velocity threshold** — Kinetic friction velocity threshold

`0.05`

`m/s`

(default)

Velocity required for peak kinetic friction at the contact surface of
the detent. The parameter ensures the force is continuous when the
travel direction changes, increasing the numerical stability of the
simulation. The parameter must be greater than zero. The default value
is `0.05`

`m/s`

.

### Shift Linkage

**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.

**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.

**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.

**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.

**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.

**Dog clutch ring stop stiffness** — Dog clutch ring stop stiffness

`10e5`

`N/m`

(default) | positive scalar

Stiffness of the hard stops on both sides of the dog clutch ring. The
model assumes the ring and stops behave elastically. Contact deformation
is proportional to the applied force and the reciprocal of the contact
stiffness. The value of the stiffness must be assigned with reference to
the parameter **Tooth overlap to engage**. Too low a
stiffness could cause the deformation to exceed the required overlap and
initiate a false engagement. The parameter must be greater than zero.

**Cone clutch ring stop stiffness** — Cone clutch ring stop stiffness

`10e5`

`N/m`

(default) | positive scalar

Stiffness of the hard stops on both sides of the cone clutch ring. The model assumes the ring and stops behave elastically. Contact deformation is proportional to the applied force and the reciprocal of the contact stiffness.

**Dog clutch ring stop damping** — Dog clutch ring stop damping

`1e3`

`N/(m/s)`

(default) | nonegative scalar

Translational contact damping between the dog clutch ring and the hub. The value of the damping is inversely proportional to the number of oscillations that occur after impact. The parameter must be greater than zero.

**Cone clutch ring stop damping** — Cone clutch ring stop damping

`1e3`

`N/(m/s)`

(default) | nonegative scalar

Translational contact damping between the cone clutch ring and the hub. The value of damping is inversely proportional to the number of oscillations that occur after impact. The parameter must be greater than zero.

**Shift linkage viscous friction coefficient** — Shift linkage viscous friction coefficient

`100`

`N/(m/s)`

(default) | positive scalar

Viscous friction coefficient for the relative translational motion between the hub and the ring. The value of the parameter depends on lubrication state and quality of contacting surfaces. The coefficient must be greater than or equal to zero.

### Initial Conditions

**Initial state** — Initial clutch state

```
All clutches
unlocked
```

(default) | ```
Cone clutch A and dog clutch A
locked
```

| `Cone clutch A locked`

| `Cone clutch B locked`

| ```
Cone clutch B and dog clutch B
locked
```

Beginning configuration of cone and dog clutches:

`Cone clutch A and dog clutch A locked`

— Cone clutch*A*and dog clutch*A*transmit torque between the ring and hub shafts.`Cone clutch A locked`

— Cone clutch*A*transmits torque between the ring and hub shafts.`All clutches unlocked`

— Cone and dog clutches transmit zero torque between the ring and hub shafts.`Cone clutch B locked`

— Cone clutch*B*transmits torque between the ring and hub shafts.`Cone clutch B and dog clutch B locked`

— Cone clutch*B*and dog clutch*B*transmit torque between the ring and hub shafts.

**Dog clutch initial shift linkage position** — Dog clutch initial shift linkage position

`0`

`mm`

(default) | scalar

Initial position of the shift linkage section that attaches to the dog clutch. The value of the parameter has these restrictions:

Dog Clutch State | Parameter Restriction |
---|---|

Dog clutch A Initially engaged | Negative of the parameter value must be greater than
the sum of parameters Ring-hub clearance when
dog clutch disengaged and Tooth
overlap to engage |

Dog clutch A Initially disengaged | Negative of the parameter value must be smaller than
the sum of parameters Ring-hub clearance when
dog clutch disengaged and Tooth
overlap to engage |

Dog clutch B Initially engaged | Parameter value must be greater than the sum of
parameters Ring-hub clearance when dog clutch
disengaged and Tooth overlap to
engage |

Dog clutch B Initially disengaged | Parameter value must be smaller than the sum of
parameters Ring-hub clearance when dog clutch
disengaged and Tooth overlap to
engage |

**Cone clutch initial shift linkage position** — Cone clutch initial shift linkage position

`0`

`mm`

(default) | scalar

Initial position of the shift linkage section that attaches to the cone clutch. The value of the parameter has these restrictions:

Cone Clutch State | Parameter Restriction |
---|---|

Cone clutch A initially engaged | Negative of parameter must be greater than the value
of Ring-hub clearance when cone clutch
disengaged |

Cone clutch A initially disengaged | Negative of parameter must be smaller than the value
of Ring-hub clearance when cone clutch
disengaged |

Cone clutch B initially engaged | Parameter must be greater than the value of
Ring-hub clearance when cone clutch
disengaged |

Cone clutch B initially disengaged | Parameter must be smaller than the value of
Ring-hub clearance when cone clutch
disengaged |

**Initial dog clutch A ring-hub offset angle** — Initial dog clutch *B* ring-hub offset angle

`0`

`deg`

(default) | scalar

Rotation angle between the ring and the hub of dog clutch
*B* 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

$$-\frac{{180}^{\xb0}}{N}\le {\varphi}_{0}\le +\frac{{180}^{\xb0}}{N},$$

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 both of these conditions are met:

In the

**Cone Clutch**settings, the**Friction model**parameter is set to`Fixed kinetic friction coefficient`

or`Velocity-dependent kinetic friction coefficient`

.In the

**Dog Clutch**settings, the**Torque transmission model**is set to`Dynamic with backlash`

.

**Initial dog clutch B ring-hub offset angle** — Initial dog clutch *A* 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

$$-\frac{{180}^{\xb0}}{N}\le {\varphi}_{0}\le +\frac{{180}^{\xb0}}{N},$$

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 both of these conditions are met:

In the

**Cone Clutch**settings, the**Friction model**parameter is set to`Fixed kinetic friction coefficient`

or`Velocity-dependent kinetic friction coefficient`

.In the

**Dog Clutch**settings, the**Torque transmission model**is set to`Dynamic with backlash`

.

### Thermal Port

**Thermal Port** settings are visible only if, in the **
Cone Clutch** settings, the **Friction model **
parameter is set to ```
Temperature-dependent friction
coefficients
```

or ```
Temperature and velocity-dependent
friction coefficients
```

. For more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**Thermal mass** — Thermal mass

`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 ** Cone
Clutch** settings, the **Friction model
** parameter is set to ```
Temperature-dependent
friction coefficients
```

or ```
Temperature
and velocity-dependent friction coefficients
```

. For
more information, see Double-Sided Synchronizer Block Parameter Dependencies.

**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 ** Cone
Clutch** settings, the **Friction model
** parameter is set to ```
Temperature-dependent
friction coefficients
```

or ```
Temperature
and velocity-dependent friction coefficients
```

. For
more information, see Double-Sided Synchronizer Block Parameter Dependencies.

### Thermal Port

These thermal parameters are only visible when you select a temperature-dependent friction model.

**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

`100`

`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`

.

## More About

### Linearization

To optimize your model for linearization, use the **Dog 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 **Dog 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 R2012b**

## See Also

### Simscape Blocks

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