The example model of this section, drive_crcr_ideal, simulates a complete drivetrain. This model will help you understand how to model driveline components with SimDriveline™ blocks, connect them into a realistic model, use Simulink® blocks as well, and simulate and modify a drivetrain model.
The driveline mechanism modeled here is part of a full vehicle, without the engine or engine-drivetrain coupling, and without the final differential and wheel assembly. The model includes an actuating torque, driver and driven shafts, a four-speed transmission, and a braking clutch.
The drive_crcr_ideal model contains a driveline that accepts a driving torque and transfers this torque and the associated angular motion from the input or drive shaft to an output or driven shaft through a transmission. The model includes a CR-CR (carrier-ring–carrier-ring) four-speed transmission subsystem, based on two gears and four clutches. (The example does not use the reverse gear available in the CR-CR transmission.) You can set the transmission to four different gear combinations, allowing four different effective torque and angular velocity ratios. A fifth clutch, outside the transmission, acts as a brake on the driven shaft.
The CR-CR 4-Speed Transmission subsystem illustrates a critical feature of transmission design, the clutch schedule. To be fully engaged, the transmission, with four clutches and two gears, requires two clutches to be locked and the other two unlocked at any time. (The transmission's reverse clutch is not counted here.) The choice of which two clutches to lock determines the effective gear ratio across the transmission. The clutch schedule is the table of locked and free clutches corresponding to different gear settings. If all four clutches are unlocked, the transmission is in neutral. If the clutches are completely disengaged, no torque or angular motion at all is transferred across the transmission.
Clutch Schedule for the CR-CR 4-Speed Transmission
|Gear Setting||Clutch A State||Clutch B State||Clutch C State||Clutch D State|
L = locked, F = free
To get started quickly with the CR-CR transmission example model, follow either of these steps:
drive_crcr_ideal at the MATLAB® command
Examine the model and its structure. The main model window contains the CR-CR transmission subsystem, the input or driver shaft assembly, and the output or driven shaft assembly. Each assembly consists of a wheel with applied kinetic friction. The driver shaft transmits an externally specified torque down the driveline.
The main model also includes a brake clutch. When this clutch is locked, the driven shaft stops turning. This clutch must remain unlocked if the CR-CR transmission is engaged.
Main Model Window
Open each subsystem in turn.
The CR-CR 4-Speed Transmission subsystem is a set of four clutches, two planetary gears, and four inertias (rotating bodies). (Ignore the reverse gear and associated clutch.) Within the subsystem, open the clutch schedule block to see the four possible (forward) gear settings for the CR-CR 4-speed transmission. Exactly two clutches must be locked at any one time for the transmission to be engaged and to avoid conflicting constraints on the gear motions.
CR-CR 4-Speed Transmission Subsystem
The Clutch Control subsystem provides the pressures that lock the necessary clutches. The clutch controller is programmed to move the transmission through a fixed sequence of gears, then unlock all the transmission clutches, allowing the driven shaft to "coast" for a time, and then engage and lock the brake clutch to stop the driven shaft.
Clutch Control Subsystem
The Scopes subsystem provides Scope blocks to display the clutch pressure, driver and driven shaft velocity, and clutch mode signals.
To display the CR-CR driveline model's behavior,
Open the Scopes subsystem and then each of the Scope blocks. Close the Scopes subsystem.
Click Start. The model steps through the gears and then brakes.
Observe how the clutch pressure signals move the transmission into one gear after another, at 0, 5, 10, and 15 seconds of simulation time. Compare these clutch pressure signals to the clutch schedule in the CR-CR transmission subsystem to determine which gear settings the model is implementing. (In fact, the model steps through gears 1, 2, 3, and 4, before coasting and then braking.)
Observe the clutch modes at the same time. When a clutch mode is zero, that clutch is locked. The sequence of clutch locking and unlocking matches the sequence from the clutch schedule.
Compare the angular velocities of the driven and driver shafts. The effect of the transmission is the result of the two planetary gears coupled in different ways in the different gear settings. The effective drive ratio of output to input shafts is the reciprocal of the ratio of output to input angular velocities.
Observe what happens at 20 seconds. The transmission clutch pressures drop to zero, and the transmission disengages. The transmission ceases to transfer angular motion and torque from the driver to the driven shaft, and the driven shaft continues to spin simply from inertia. A small kinetic friction damping gradually slows the driven shaft over the next 6 seconds.
At 26 seconds of simulation time, the brake clutch pressure begins to rise from zero, and the brake clutch engages. The driven shaft decelerates more drastically now. Between 26.0 and 26.1 seconds, the brake clutch locks, and the driven shaft stops rotating completely.
You can modify this example model to explore other SimDriveline features. Here you modify and rerun the model to investigate two aspects of its motion.
Measure the effective drive ratio of the CR-CR transmission in each gear setting that it steps through.
Change the gear sequence.
The gear ratio (output to input) is the ratio of the output gear wheel radius to the input gear radius. Equivalently, the gear ratio is the ratio of the number of teeth on the output gear wheel to the number on the input wheel, or the ratio of the output torque to the input torque. The ratio of the angular velocities of output to input is the reciprocal of this gear ratio.
A transmission is a set of coupled gears. But for a particular transmission gear setting, the ratio of driven (output) shaft velocity to the driver (input) is fixed. Its reciprocal, the drive ratio, is like a gear ratio of an individual gear coupling, but for the whole transmission.
Add and connect the Simulink blocks necessary to measure the drive ratio of the transmission.
From the Simulink Math Operations library, copy a Divide block and, from the Simulink Sinks library, copy a Scope block.
From the Torque Driver subsystem outport, branch a
signal line from Motion Sensor1's angular velocity output and connect
it to the
X inport on the Divide block. From the
velocity output of Motion Sensor2, on the driven (output) shaft, again
branch a signal line. Connect it to the ÷ inport on the Divide
The effective output-to-input drive ratio is the ratio of input to output velocities.
Connect the outport of the Divide block to the Scope. Rename Scope to Drive Ratio.
CR-CR 4-Speed Model with Drive Ratio Measurement
Open the Drive Ratio scope and restart the example. Observe how the drive ratio steps through a sequence of five-second states, in parallel with the clutch pressures and clutch modes, until it reaches 20 seconds. The drive ratio measurement after 20 seconds is not meaningful because the transmission is uncoupled.
Just after 26 seconds, the driven shaft velocity drops to zero, and the Divide block produces divide-by-zero warnings at the MATLAB command line.
Look inside the CR-CR 4-Speed Transmission subsystem for the Clutch Schedule block and open it. Consult the drive ratios for each gear, 1, 2, 3, and 4, in terms of the gear ratios of the transmission's two Planetary Gears. Determine the numerical values for these drive ratios for gear settings 1, 2, 3, and 4 and check them against the values displayed in the Drive Ratio scope.
The drive ratio sequence should be 3, 5/3, 1, and 2/3, respectively, for the first, second, third, and fourth intervals of five seconds each.
The drive_crcr_ideal example, when you open it, is programmed to step through CR-CR gear settings 1, 2, 3, and 4, before disengaging. Modify it to step through settings 1, 2, 3, and 1, then disengage. The fourth gear requires A, B, C, and D to be free, locked, locked, and free, respectively. You will modify the clutch pressure signal sequence from 15 to 20 seconds so that the transmission is set in first, not fourth, gear. The first gear requires clutches A, B, C, and D to be locked, free, free, and locked, respectively.
Open the Clutch Control and CR-CR transmission subsystems. Within the transmission, open the Clutch Schedule block and review the clutch lockings for each gear setting.
Open the Signal Builder block, labeled Clutch Pressures, to view the clutch pressure signals.
Modify clutch pressure signals A, B, C, and D so that, between 15 and 20 seconds, clutches A and D are locked (not free) and clutches B and C are free (not locked). Sufficient pressure will lock the clutches, while zero input pressure leaves a clutch unlocked.
Modified CR-CR 4-Speed Transmission Clutch Pressures
Restart the model. Observe that between 15 and 20 seconds of simulation time the clutch pressures, the clutch modes, and the driven shaft velocity are now different from the original version of the model.
Check the effective drive ratio between 15 and 20 seconds to confirm that the CR-CR transmission during that time is set in gear 1, not gear 4. This fourth interval of five seconds should exhibit a drive ratio of 3 instead of 2/3.