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| R2012a Documentation → SimDriveline Version 1 | |
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About Torques, Motions, and Actuation Modeling the Effect of a Variable Inertia Actuating a Driveline with Torques |
A SimDriveline simulation solves, from the torques applied to spinning inertias, a driveline's dynamics for its motions. However, it can also accept motions imposed on a driveline and solve for the torques needed to produce those motions. A driveline simulation is typically a mixture of these two requirements, solving dynamics both forward (torque to motion) and inverse (motion to torque). Imposing motions and applying torques are together forms of driveline actuation.
This section discusses actuating drivelines with time-varying inertias, torques, motions, and motion initial conditions. All of these actuation types (except for initial conditions) require input Simulink signals to define time-varying functions.
In all cases, you should exercise care as you apply a mixture of actuations to a driveline and its degrees of freedom (DoFs), as discussed in greater detail by the section, Analyzing Degrees of Freedom in the Advanced Methods chapter. The complete effect of the actuations must be such that
Driveline DoFs actuated by torques are not also subject to motion actuations. (They can be subject to motion initial condition actuation.)
Driveline DoFs actuated by motions are not also subject to torque actuations.
For a SimDriveline model to successfully simulate nontrivial motion, torque and motion actuations must exactly complement one another to account consistently for the motion of all the DoFs, no more and no less. If this criterion is not satisfied, one of these outcomes results.
The motion of the driveline is trivial, staying in its initial motion state for the entire simulation.
The actuations are inconsistent with each other, and the simulation stops with an error.
The actuations leave the driveline underdetermined or overdetermined, and the simulation stops with an error.
For more about driveline simulation errors, see Troubleshooting Simulation Errors in the Advanced Methods chapter.
To actuate a physical system modeled by blocks, you often need to differentiate an incoming Simulink signal.
Simulink provides a Derivative block for numerical differentiation of a signal. However, this block's output is sometimes not stable or accurate enough for physical modeling purposes. Recommended alternatives to the Derivative block include the following.
Integrating Higher Derivative Signals. Start by specifying the highest derivative signal (such as an acceleration), then integrate this signal to obtain lower derivative signals (such as a velocity) using the Integrator block.
Transforming Signals with Transfer Functions. To differentiate a signal, use a transfer function block (Transfer Fcn). This block actually performs a Laplace transform convolution to smooth the output, which is not exactly the derivative.
You can eliminate this drawback by filtering the original signal f, then defining exact derivatives dF/dt, etc., of the filtered signal F by adding higher orders to the transfer function numerator. The order of the denominator should be equal to or greater than the number of output signals. Use the filtered signal F (instead of f), as well as the filtered derivatives.
In this example, the constant τ represents a smoothing time. The transfer functions define a filtered signal and its first derivative, two signals in all. Therefore, the transfer function denominator should be second order or higher.
You cannot vary the inertia value of an Inertia block during a simulation. However, you can model a time-varying inertia indirectly with a Variable Ratio Gear block. This method relies on the conservation of angular momentum.
Place a Variable Ratio Gear between a shaft and an Inertia.
Connect this constant Inertia to the Gear's base (B) or follower (F) port.
Vary the gear ratio of the Variable Ratio Gear with an incoming Simulink signal.
By changing the gear ratio, you change the effective inertia on the shaft from the constant Inertia.
Effective inertia = (constant inertia)•(variable gear ratio)
if
the B port is connected to Inertia
Effective inertia = (constant inertia)/(variable gear
ratio)
if
the F port is connected to Inertia
Effective Variable Inertia with a Variable Ratio Gear
You can apply a torque to a driveshaft
Directly, with a Torque Actuator block
Indirectly, with a block that generates torque, using a Torque Actuator as part of a larger subsystem. Such blocks include:
Dynamic elements such as clutches, torque converters, and engines
Transmissions, which contain clutches
In any case, a Torque Actuator accepts an incoming Simulink signal and originates, from its driveline connector port, a driveline connection line carrying that torque.
The SimDriveline simulation solves for the motion of the spinning driveshaft, given the torque it is subject to. Therefore you cannot, in addition, subject that same driveshaft to motion actuation.
Caution A driveline actuated by a torque must have a nonzero inertia, represented by one or more connected Inertia blocks. A torque-actuated driveline without any inertia experiences a singular acceleration. In this case, the SimDriveline simulation will stop with an error. |
You can apply a motion to a driveshaft directly, with a Motion Actuator block.
A Motion Actuator accepts an incoming Simulink signal and originates, from its driveline connector port, a driveline connection line spinning with the specified motion.
The SimDriveline simulation solves for the torque carried by the spinning driveshaft, given its motion. Therefore you cannot, in addition, subject that same driveshaft to torque actuation.
When driveline simulation starts, the complete driveline determines the initial motion of all driveshafts by a combination of constraints, motion actuators, and initial condition actuators. If, after the application of the complete driveline's constraints and actuators, one or more of the driveshaft motions remain undetermined, these driveshafts start simulation with zero angular velocity by default.
You can exercise direct control over how a driveshaft starts motion during simulation by connecting it to an Initial Condition actuation block. You set the initial velocity of the driveshaft in the block's dialog.
For more about constraints and degrees of freedom, see Analyzing Degrees of Freedom in the Advanced Methods chapter.
Caution You must ensure that whatever initial conditions you impose on the driveshafts in your driveline are consistent with all of the driveline's constraints and motion actuators. If an inconsistency occurs, the SimDriveline simulation stops with error. |
A simple gear has two ports and imposes one constraint between them, leaving one independent DoF. Once one port is connected to a driveshaft, the motion of the other port's driveshaft is determined.
A complex gear has three or more ports and imposes one or more constraints among them. A complex gear can have any number of independent DoFs, including none.
For more about complex gears, see Representing and Transferring Driveline Motion and Torque previously.
Tip If a simulation apportions the initial motions of a complex gear in an unsatisfactory way, determine how you want the overall initial motion divided up and enforce that division with one or more Initial Condition blocks on one or more of the complex gear shafts. However you divide the initial motion among the gear shafts, ensure that this division is consistent with all constraints in your driveline, as well as any motion actuators. |
 | Representing and Transferring Driveline Motion and Torque | Controlling Gear Couplings with Clutches |  |
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