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 needed, 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_simple_transmission 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_engage 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 (blocks D1 and D2). 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 is engaged, the driven shaft is stopped.) There are now two selectable gears to couple the two axes, instead of one. (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 respective clutch. Coupling one gear requires engaging and locking its 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 Simple Gear 5:1 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 Simple Gear 2:1 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   You must check every transmission's clutch schedule to implement its transmission states correctly and to avoid motion conflicts among gear sets. You must also check clutch pressure signal profiles to make sure that any transmission's clutches are engaged, locked, unlocked, and disengaged in a realistic and conflict-free manner. Unphysical or conflicting clutch schedules and clutch pressure signals lead to simulation errors in Simscape™ Driveline™ models and can damage or destroy a real transmission.

For the sdl_simple_transmission 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

In this simplified and unrealistic clutch control model, the clutch pressure signals are constants: 1 to engage and lock a clutch; 0 to disengage it. (A clutch pressure signal is normalized to equal 1 when the surface friction force equals the peak normal force specified in the clutches.) For each transmission state, the table of these constants is contained in the Clutch Schedule Table block, customized from the Direct Lookup Table (n-D) block. Open the Clutch Schedule Table block to see this table.

The table is indexed in both row and column, starting from zero. An input signal of 0 causes the block to output the first column of table values; a value of 1 outputs the second column; a value of 2, the third column. The Terminator block prevents the first element of each column (that is, the entire first row of values) from leaving the subsystem.

The first column applies zero pressure to the two gear clutches. The second column applies full pressure to the low gear clutch and zero pressure to the high gear. The third column applies full pressure to the high gear clutch and zero pressure to the low gear.

These different table columns are activated by changing the positions of the Gear switch and Neutral switch, while leaving the Brake switch off. With the neutral switch off, the Gear switch signal can pass to the Clutch Schedule Table. This signal is 1 for the low gear and 2 for the high gear. Turning the neutral switch on prevents the Gear switch signal from reaching the clutch controller.

Turning on the Brake switch also prevents the Gear switch signal from reaching the clutch controller. At the same time, switching on the brake directly applies locking pressure to the Brake clutch.

Running the Model, Switching Gears, and Braking

To see how gear switching works:

  1. Start the model and open the two scopes.

    Its initial transmission state is low gear, with the Gear switch to the left, transmitting a signal value of 1. The driven shaft spins at one-fifth the rate of the driver shaft, in the opposite direction.

  2. Change the Gear switch from low to high (left to right, signal value of 1 to 2), and observe how the driven shaft velocity increases in the Speeds and torques scope.

    The driven-to-driver ratio is now one-half. (The driver shaft velocity decreases slightly, because it experiences the damping torque on the driven shaft differently depending on which gear is engaged.)

  3. Change the Gear switch back to low (right to left, 2 to 1), then observe that the driven shaft again spins more slowly.

    At the same time, while you switch the gears back and forth, the clutches, as shown in the Clutch modes scope, switch from Low gear clutch being locked, to the High gear clutch being locked, and back. When one is locked, the other is unlocked.

  4. Apply immediate braking by switching the Brake switch to on (left to right, 0 to 1). The driven shaft comes to an immediate and complete stop. The driver shaft continues to spin.

    Then release the brake, moving the Brake switch to off (right to left, 1 to 0).

  5. Change the Neutral switch to the right position, transmitting a signal value of 0.

    The two gear clutches unlock and disengage. The Brake clutch remains unengaged. The driven shaft, subject to very light damping, now slows gradually.

  6. By turning the Brake switch to on, you can switch the Brake clutch to the locked mode and bring the driven shaft to a stop. The driver shaft continues to spin.

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. It is critical for the Simscape and Simulink solvers to determine transmission motion for exactly two clutches to always remain locked, or for all four to be unlocked, at any time in the simulation. 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_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

A Torque Driver subsystem feeds a constant driving torque from a torque source to the driver shaft (Inertia1). Two damping subsystems apply heavy and light viscous friction to the driver and driven shafts, respectively. The two Scopes measure the shaft velocities and clutch pressures, respectively. The model pre-load function defines essential parameters in the workspace. (You can view this pre-load function. Open the model File > Model Properties > Model Properties dialog box. Then, click the Callbacks tab).

The CR-CR 4-Speed transmission subsystem couples the driver to the driven shaft (Inertia2). If the transmission is disengaged, a brake clutch and fixed housing allow you to brake the driven shaft. When you first open the model, the Clutch Control subsystem contains a set of programmed clutch signals for shifting the CR-CR transmission through a preconfigured gear and braking sequence over 30 seconds.

For clarity, the model's major signal buses have been bundled as vectors and directed using Goto and From blocks. The Scopes 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. This block provides two clutch control modes, or variants: manual and programmed. To switch to manual control mode:

  1. Right-click Clutch Control.

  2. In the context menu, select Variant > Override using > Variant1 (Manual)

  3. Double-click Clutch Control and then Manual. During simulation, the Manual subsystem provides direct control over gear changes.

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

  5. Run simulation.

To change gears during simulation, use the Manual Switch blocks. Bit 2 Switch controls clutches A and B, while Bit 1 Switch controls clutches C and D. The table summarizes the clutch responses when toggling a switch up or down.

Manual Switch BlockSwitch-Up ResponseSwitch-Down Response
Bit 2 SwitchLock clutch A, release clutch BRelease clutch A, lock clutch B
Bit 1 SwitchLock clutch D, release clutch CRelease clutch D, lock clutch C

Manual Clutch Control for CR-CR Transmission

Configuring the CR-CR Transmission Subsystem

The CR-CR 4-Speed transmission subsystem uses certain parameters set to realistic values. These parameters are referenced to variables defined in the workspace when the model opens. These variables are used in the four CR-CR Clutch blocks A, B, C, and D.

CR-CR 4-Speed Transmission Clutch Variables

Workspace VariableDescription
num_fric_surfNumber of frictional surfaces in each clutch
eff_tor_radEffective torque radius in each clutch (m)
peak_normalPeak normal force on clutch surfaces (N)
fric_coeff (matrix)Kinetic friction coefficient as a function of the relative angular velocity of the clutch shafts

The clutch schedule of the CR-CR transmission subsystem is a table of gear settings, clutch lockings, and gear ratios. There are four distinct (forward) gear settings, each with a different effective gear ratio. For the transmission to be properly engaged and transmit torque and motion, exactly two clutches must be locked at any instant. Unlocking all the clutches simultaneously puts the transmission into neutral (no motion or torque transfer). The transmission contains two planetary gears, five clutches, and four inertias.

Clutch Schedule for the CR-CR 4-Speed Transmission

Gear SettingClutch A StateClutch B StateClutch C StateClutch D StateClutch R StateDrive Ratio
1LFFLF1 + go
2LFLFF1 + go/(1 + gi)
4FLLFFgi/(1 + gi)

  • L = locked

  • F = free

  • gi = Input Planetary Gear ring-to-sun gear ratio

  • go = Output Planetary Gear ring-to-sun gear ratio

The main model's Damping subsystems use these variables for frictional damping of the driving (engine) and driven shafts coupled across the transmission.

Drive Shaft Damping Coefficients

Workspace VariableDescription
eng_dampingDriver (engine) shaft kinetic friction coefficient (N-m/(rad/s))
driven_dampingDriven shaft kinetic friction coefficient (N-m/(rad/s))

Programming the Clutch Schedule Logic

For this and the following sections, switch the default programmed Clutch Control subsystem to the manually controlled configuration. See Replacing Programmed with Manually Controlled Clutch Pressures.

From the main model, open the Clutch Control subsystem. The Clutch Schedule Logic block provides the CR-CR 4-Speed clutch schedule as a truth table for the four forward gears. Each row represents a different gear setting. You select a particular row for output by inputting a set of 1s and 0s that specify the row value as a binary number.

CR-CR 4-Speed Clutch Schedule Logic

Gear SettingTruth Table RowTruth Table Value
1002 = 01 0 0 1 0
2012 = 11 0 1 0 0
3102 = 21 1 0 0 0
4112 = 30 1 1 0 0

In the order of the CR-CR Clutches—A, B, C, and D, respectively—the sequence of 1s and 0s indicates which clutches are locked (1) and which are free (0). These Boolean values are then converted into normalized clutch pressure signals. The fifth value in each row represents the disengaged reverse gear Clutch R.

Programming the Reverse Gear.  By default, the Forward/Reverse Switch is set to the up position, placing the transmission in forward motion. If you want to engage the reverse gear, set the switch to the down position.

Open the corresponding Reverse block to see the reverse gear clutch schedule as a truth table.

CR-CR Reverse Gear Clutch Schedule Logic

Gear SettingTruth Table Value
Reverse0 0 0 1 1

Running the CR-CR Transmission Model — Changing Gears

You are now ready to run the model.

  1. Open the Scopes subsystem, then the individual Scope blocks. Close the Scopes subsystem.

    With the Scopes, you can observe the angular velocities of the driving and driven shafts, and the input pressures of the four clutches.

  2. Open the Clutch Control subsystem, which should be set to manual control. Ensure that the Forward/Reverse Switch is set to up and the Neutral Switch is set to down.

    Also ensure that the simulation time is inf.

  3. Start the model. You can change the forward gear settings by changing the Bit1 and Bit2 Switch blocks and moving through truth table entries corresponding to each setting, as summarized in the table, CR-CR 4-Speed Clutch Schedule Logic.

Switching from one gear setting to another unlocks some clutches and locks others, but always leaves two clutches locked. As you change between gear settings, the transmission transfers motion and torque at different ratios. You can disengage the CR-CR transmission completely and engage the Brake by setting the Neutral Switch to up. If you brake, the driven shaft velocity immediately drops to 0. The braking here works the same way as in the previous examples.

You can put the CR-CR transmission into reverse by keeping the Neutral Switch set to down and by setting the Forward/Reverse Switch to down. As with a real transmission, it is best to transition the transmission model through neutral and bring the driven shaft to a rest before putting the transmission into reverse gear.

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