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Model a Two-Speed Transmission with Braking

The example model sdl_transmission_2spd contains a driveline system that makes up a simple yet complete transmission.

Simple Transmission with Two Gear-Clutch Pairs and Braking

The model is built on the sdl_clutch_acc_brake example model. This model contains two driveline shafts or axes, with a constant actuating torque of 1 Newton-meter applied to the driver shaft. Both the driver and the driven shafts are subject to small viscous damping torques. The viscous torque constant μ is 0.001 newton-meters/(radians/second). In the steady state, the driving and damping torques balance one another; the two shafts spin at constant rates, the driver shaft at (1 N-m)/(0.001 N-m/(rad/s)) = 1000 rad/s. If braking occurs, the driven shaft stops. There are now two selectable gears to couple the two axes, instead of one. For more information on modeling viscous losses with nonideal gear bearings instead of dampers, see Model Gears with Losses and Constant and Load-Dependent Gear Efficiencies.

This transmission model couples the gears in a simple way, with each gear and the brake associated with its own clutch. Coupling one gear requires engaging and locking the corresponding clutch, while ensuring that the other two clutches are disengaged. The brake clutch is directly activated by its own switch.

Setting Up the Gears, Clutches, and Brake

The two gears are Simple Gear blocks with different gear ratios, each connected in series with its corresponding clutch. The two gear-clutch pairs are coupled in parallel. This parallel assembly then couples the driver shaft to the driven shaft, with their two spinning inertias. One gear is a “low” gear, the other a “high” gear. Following common usage for automobile gears, the “low” and “high” labels refer to the angular velocity ratios.

Note

The ratio of speeds in a gear is the reciprocal of the gear ratio.

  • The low gear is the Gear High block. You can couple the low gear by engaging its corresponding clutch, modeled by the Low gear clutch block. The gear ratio is 5:1, so that the ratio of output to input (follower to base) angular speeds is 1/5. Such a gear has a high torque transfer ratio of 5, from base to follower. In an automobile, such low gears are used to accelerate the vehicle from a stop by transferring a large torque down the drivetrain from the engine.

  • The high gear is the Gear Low block, coupled by engaging its own clutch, represented by the High gear clutch block. The gear ratio is 2:1, and the angular velocity ratio of follower to base is 1/2, or 5/2 times the ratio in the low gear. The torque transfer ratio is only 2 from base to follower. An automotive high gear is used for milder acceleration or coasting once a vehicle is moving at a significant speed. The vehicle acceleration generated by this gear is less than the acceleration that is generated by the low gear.

Switching on either the Neutral switch or the Brake switch disengages both gear clutches. In either case, the driver shaft continues to spin, approaching a steady velocity, subject to the competing driving and damping torques.

  • Switching the transmission to neutral leaves the brake clutch disengaged and the driven shaft free to spin. But without a driving torque, damping gradually brings the driven shaft to a stop.

  • Switching on the brake immediately locks the brake clutch and stops the driven shaft.

This simple transmission is based on mapping each transmission state one-to-one with an engaged clutch. You cannot engage more than one clutch at a time without creating conflicts between gear ratios or between the driver shaft and the rotational ground.

Controlling the Transmission State with a Clutch Schedule

The requirement to engage a certain clutch or set of clutches and disengage others, both to implement transmission functions and to avoid motion conflicts between gears, is the basis for all clutch schedules. Simulink® provides a number of ways to implement clutch schedules, depending on the complexity of the transmission and how much realism you require for the clutch pressure signals.

Caution

To ensure that the transmission states are implemented correctly and to avoid motion conflicts among gear sets, check the clutch schedule for the transmission. To make sure that the clutches are engaged, locked, unlocked, and disengaged in a realistic and conflict-free manner, check the clutch pressure signal profiles. Unphysical or conflicting clutch schedules and clutch pressure signals lead to simulation errors in Simscape™ Driveline™ models.

For the sdl_transmission_2spd model, avoiding such conflicts leads to a unique clutch schedule.

Clutch Schedule for the Simple Two-Speed Transmission

Transmission StateBrake Clutch StateLow Gear Clutch StateHigh Gear Clutch State
Neutral/BrakedDisengaged/LockedDisengagedDisengaged
Low GearDisengagedLockedDisengaged
High GearDisengagedDisengagedLocked

The model contains a simple Clutch Control subsystem to implement the clutch schedule and to output the clutch pressure signals to lock each clutch as needed.

Clutch Control Subsystem for Simple Transmission Model

Adding Realistic Clutch Signals

The clutch control subsystem of this example is adequate for a simple model, but not realistic. It contains unrealistic clutch pressure signals that rise and fall sharply. A full clutch control model requires realistic clutch pressure signals that rise from and fall back to zero in a smooth way. Greater realism requires a potentially more complex model. During simulation, the Simscape and Simulink solvers can determine transmission motion only if exactly two clutches are locked, or if all four clutches are unlocked. This model is similar to a real transmission where improperly constrained clutches can lead to lockup or damage to the transmission components. Changing the gear settings for the transmission while maintaining this requirement is an example of the central problem of transmission design.

For transmission and car examples with smoothed clutch pressure signals, see Model a CR-CR 4-Speed Transmission Driveline with Brakingand Complete Vehicle Model.

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