# Synchronizer

Cone clutch, dog clutch, and translational detent assembled to provide smooth gear engagement

• Library:
• Simscape / Driveline / Clutches

## Description

The block represents a synchronizer that contains a dog clutch, a cone clutch, and a translational detent. The shift linkage first translates to engage the cone clutch. Frictional torque causes the shift linkage and cone clutch shaft to rotate at equal speed. When the force acting on the shift linkage exceeds the detent force, the dog clutch can engage.

The schematic illustrates a synchronizer in the disengaged state. In this state, the ring (R) and hub (H) shafts can spin independently at different speeds. To synchronize ring and hub shaft speeds, the shift linkage (S) translates toward the hub shaft to engage the cone clutch. The friction surfaces of the cone clutch produce a frictional torque that equalizes the rotational speeds of the ring and hub shafts. The dog clutch teeth (T) can engage when the translational force acting on the shift linkage exceeds the peak detent force. The peak detent force should allow sufficient time and normal force to equalize ring and hub shaft speeds so that the dog clutch can engage.

The model implements the Dog Clutch, Cone Clutch, and Translational Detent blocks. Refer to each block reference page for more information on the corresponding block function. You can use a similar approach to model customized versions of the synchronizer. One example is the Transmission (Detailed) subsystem in the model sdl_vehicle_manual_transmission.

Connections R and H are mechanical rotational conserving ports that represent the ring (R) and hub (H), respectively. Connection S is a mechanical translational conserving port that represents the ring shifter handle.

Connections X1 and X2 are physical signal outputs that report the shift linkage positions of the dog clutch and cone clutch, respectively. The shift linkage positions are zero when the clutch is fully disengaged. When the dog clutch is fully engaged, the dog clutch shift linkage position has a magnitude equal to the sum of the dog clutch ring-hub gap and the tooth height. When cone clutch is fully engaged, the cone clutch shift linkage position has a magnitude equal to the cone clutch 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

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

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

### Conserving

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Mechanical rotational conserving port associated with the clutch hub

Mechanical rotational conserving port associated with the clutch ring.

Mechanical rotational conserving port associated with shift linkage.

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```.

## Parameters

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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 settings

• Thermal port T

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

Synchronizer Block Parameter Dependencies

SettingsParameters and Options
Cone ClutchContact 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 vectorTemperature vector
Static friction coefficientStatic friction coefficient vectorStatic friction coefficient vectorStatic friction coefficient matrix
Kinetic friction coefficientKinetic friction coefficient vectorKinetic friction coefficient vectorKinetic friction coefficient matrix
-Friction coefficient interpolation methodFriction coefficient interpolation methodFriction coefficient interpolation method
-Friction coefficient extrapolation methodFriction coefficient extrapolation methodFriction coefficient extrapolation
Velocity toleranceVelocity toleranceVelocity toleranceVelocity tolerance
Threshold forceThreshold forceThreshold forceThreshold force
Dog ClutchTorque transmission modelTorque 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 vectorTemperature vector
Maximum transmitted torque-Maximum transmitted torque-Maximum transmitted torque vectorMaximum transmitted torque vector
----Interpolation methodInterpolation method
----Extrapolation methodExtrapolation method
-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 ConditionsInitial stateInitial stateInitial stateInitial stateInitial stateInitial state
-Initial dog clutch ring-hub offset angle-Initial dog clutch ring-hub offset angle--
Thermal Port----Thermal massThermal mass
----Initial temperatureInitial temperature

### Cone Clutch

Outer conical diameter do.

Inner conical diameter di.

Half opening angle α of the cone geometry.

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.

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 when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature and velocity-dependent friction coefficients```.

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 when the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```.

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 when the Friction model parameter is set to ```Fixed kinetic friction coefficient``` or ```Velocity-dependent kinetic friction coefficient```.

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 when the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```.

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

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Fixed kinetic friction coefficient```.

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 when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature-dependent friction coefficients```.

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 when the Friction model parameter is set to ```Temperature and velocity-dependent friction coefficients```.

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 when, 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```.

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 when, 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```.

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.

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.

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.

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```.

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```.

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```.

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```.

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```.

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.

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```.

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```.

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```.

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 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```.

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 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```.

### Detent

Peak shear force of the detent.

Width of the region where the detent exhibits shear force.

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

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.

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`.

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

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.

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.

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.

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 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.

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.

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.

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.

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.

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

Beginning configuration of cone and dog clutches:

• `All clutches unlocked` — Cone and dog clutches transmit zero torque between the ring and hub shafts.

• `Cone clutch locked` — Cone clutch transmits torque between the ring and hub shafts.

• `All clutches locked` — Cone and dog clutches transmit torque between the ring and hub shafts.

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

Linkage Travel Direction Dog Clutch StateParameter Restriction
```Positive shift linkage displacement engages clutch```Initially engagedParameter must be greater than the sum of parameters Ring-hub clearance when dog clutch disengaged and Tooth overlap to engage
Initially disengagedParameter must be smaller than the sum of parameters Ring-hub clearance when dog clutch disengaged and Tooth overlap to engage
```Negative shift linkage displacement engages clutch```Initially engagedNegative of the parameter must be greater than the sum of parameters Ring-hub clearance when dog clutch disengaged and Tooth overlap to engage
Initially disengagedNegative of the parameter must be smaller than the sum of parameters Ring-hub clearance when dog clutch disengaged and Tooth overlap to engage

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

Linkage Travel Direction Dog Clutch StateParameter Restriction
```Positive shift linkage displacement engages clutch```Initially engagedParameter must be greater than the value of Ring-hub clearance when cone clutch disengaged
Initially disengagedParameter must be smaller than the value of Ring-hub clearance when cone clutch disengaged
```Negative shift linkage displacement engages clutch```Initially engagedNegative of the parameter must be greater than the value of Ring-hub clearance when dog cone disengaged
Initially disengagedNegative of the parameter must be smaller than the value of Ring-hub clearance when dog cone disengaged

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 visible only if 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 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 Synchronizer Block Parameter Dependencies.

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 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 Synchronizer Block Parameter Dependencies.

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 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 Synchronizer Block Parameter Dependencies.

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