Gears, Clutches, and Transmissions

About Gears, Clutches, and Transmissions

In a real drivetrain, you couple an input or drive shaft to one of many output or driven shafts, or to one driven shaft with a choice of several gear ratios. The drivetrain then requires several clutches to switch between gears. You couple one of the driven shafts or one of the gear sets by engaging one of the clutches. You then switch to another output shaft or another gear ratio by disengaging one clutch and engaging another.

You can also engage more than one clutch at a time to use multiple gear sets simultaneously. Transmissions engage multiple gear sets at the same time to produce a single effective gear ratio, or drive ratio. Changing gears requires disengaging one set of clutches and engaging another set. You can specify the set of clutches to engage and disengage for each gear ratio in a clutch schedule. Designing a clutch schedule and shaping and sequencing the clutch pressure signals frequently constitute the most difficult part of transmission design. A realistic transmission model must also include losses due to friction and imperfect gear meshing.

This section explains how to model transmissions, by creating a transmission model from gears and clutches. A predesigned transmission, the CR-CR 4-speed transmission, is the basis of a second example.

Some Important Transmission Design Principles

When creating or modifying a transmission model:

  • Connect inertia blocks with nonzero inertia values to gear shafts for realistic simulation and preventing acceleration singularities when torques are applied.

  • Make sure that the clutch schedule for your transmission specifies those clutches that must be engaged and those that must be free at any instant for the transmission to be properly in gear. Set all clutch pressures to 0 only if you want to disengage the transmission completely (place it in neutral).

    Do not engage any more or fewer clutches than necessary, at any time during simulation.

  • If you want to redesign a transmission by adding or removing gears, you must consider whether you also need to add or remove clutches and redesign the clutch schedule. You also might need to add or remove gear shaft inertias.

On the relationship clutch pressure signals to solver choices and settings, see Driveline Simulation Performance.

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 Specialized Gears.

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, which can be coupled 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, a low gear like this is 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 that 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 the brake on 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
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 is similar to a real transmission where improperly constrained clutches can lead to lockup or damage to the transmission components. Changing the transmission's gear settings 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 Braking and Complete Vehicle Model.

Model a CR-CR 4-Speed Transmission Driveline with Braking

The sdl_transmission_4spd_crcr example model builds on the previous clutch and transmission models with a more realistic transmission. It uses a CR-CR 4-Speed transmission subsystem to transfer motion and torque from one shaft and inertia to another.

CR-CR 4-Speed Transmission Model

There is a constant driving torque from a torque source to the driver shaft (Inertia block on the left). Two damping subsystems apply heavy and light viscous friction to the driver and driven shafts, respectively. The two scope subsystems measure the clutch pressures. The model workspace defines essential parameters for the blocks. For information on creating, accessing, and changing model workspace variables, see Specify Source for Data in Model Workspace and Change Model Workspace Data.

The CR-CR 4-Speed transmission subsystem couples the driver to the driven shaft (Inertia block on the right). If the transmission is disengaged, a brake clutch and fixed housing allow you to brake the driven shaft.

For clarity, the model's major signal buses have been bundled as vectors and directed using Goto and From blocks. The Clutch Pressures are collected in the Scopes subsystem for convenience.

Replacing Programmed with Manually Controlled Clutch Pressures

The model represents the clutch control system using a Variant Subsystem block. Click the links in the model window to switch between the two clutch control modes that the variant provides: Programmed and Manual. During simulation, the manual subsystem provides direct control over gear changes. To switch gears in manual control mode:

  1. In the Simulink toolbar, change the simulation time to inf.

  2. Run simulation.

  3. Change gears during using the Select Gear widget.

Manual Clutch Control for CR-CR Transmission

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