User manual MATLAB SIMDRIVELINE 1

[. . . ] SimDrivelineTM 1 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. SimDrivelineTM User's Guide © COPYRIGHT 2004­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] It includes these basic steps: · The basic elements of a driveline diagram: 3-14 Connection lines Dynamic elements and internal torques Constraints Importing and exporting information into and from your driveline · Sensors and actuators Analyzing Degrees of Freedom - Terminating DoFs With these pieces, you can enumerate all the DoFs of any driveline. The section closes with an example of how to do this. Identifying Degrees of Freedom In a SimDriveline model, all mechanical motions are rotational. Because absolute angles are not used in SimDriveline software, it is simplest to identify a driveline degree of freedom (DoF) with an angular velocity. (Some blocks use the relative angle between two driveline shafts to determine the torques generated by internal driveline dynamic elements. ) A DoF represents a single, distinct angular velocity. Each DoF responds to the torques acting on the inertias making up the driveline. Integrating Newton's equations of rotational motion determines the angular motions. In fundamental terms, mechanical DoFs are properties of rotating inertias. It is consistent and simpler to identify a single SimDriveline DoF as a driveline axis (idealized driveshaft) with its connected inertias, because the inertias are rigidly attached to their idealized shaft. Thus, to identify and count DoFs in a driveline, you need to look at a SimDriveline diagram starting with its Physical Modeling driveline connection lines first, before considering its blocks. Driveline blocks modify the DoFs represented by connection lines by · Imposing torques that act relatively between driveline axes · Adding constraints among the driveline axes · Imposing externally actuated torques and motions Fundamental Degrees of Freedom The basic unit of driveline motion is the degree of freedom (DoF) represented by an unbroken driveline connection line. Such lines represent idealized massless and perfectly rigid driveshafts. Rotating bodies with rotational inertias, represented by Inertia blocks, are rigidly attached to these lines and rotate with the axes. 3-15 3 Advanced Methods Driveline Axes as Fundamental Degrees of Freedom A driveline connection line anchored by driveline connector ports represents an idealized driveline axis. The connection line enforces the constraint that the two connected driveline components rotate at the same angular velocity. You measure the angular velocity of an axis with a Motion Sensor block. For the SimDriveline analysis of a single axis, only angular velocity is important. The absolute angle of an axis is internally undefined. Measuring Driveline Axis Motion with a Motion Sensor 3-16 Analyzing Degrees of Freedom Defining Relative and Absolute Angles. Relative angle is sometimes necessary to compute internally generated torques between pairs of axes (see "Connected Degrees of Freedom" on page 3-18). To determine a relative angle, the block integrates the relative angular velocity of the pair of axes and adds the result to the initial relative angle that you specify in the cases where it is needed. You can define an absolute angle of rotation for a single axis only when you measure its motion with a Motion Sensor block. The sensor defines the absolute angle by integrating the angular velocity of the axis and adding an arbitrary absolute reference angle that you provide in the Motion Sensor dialog. Rigidly Rotating Inertias Attached to Driveline Axes By itself, a driveline connection line represents a single DoF. You cannot subject this DoF to any torques, because it lacks rotational inertia. The other basic element needed to construct a functioning driveline model is one or more Inertia blocks. [. . . ] You specify the first derivative of the variable gear ratio as a function of time with the Simulink input signal v. Axis Motion and Constraint The Variable Ratio Gear imposes a single constraint, specified by the variable gear ratio gFB(t), on the motions and torques of the two axes: ±gFB(t) = B/F = F/B Warning All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a SimDriveline simulation stops with an error. Effect of Coriolis Acceleration With the Variable Ratio Gear block, you can choose to include or not include the effect of Coriolis acceleration on the gear motion. If you choose to include it, you must supply the first derivative, dgFB/dt, of the gear ratio as another Simulink input signal v. The Coriolis acceleration is a nonlinear effect proportional to the angular velocity and the first derivative of the gear ratio: dB/dt = gFB·dF/dt + F·dgFB/dt 5-115 Variable Ratio Gear Caution If you do not include the Coriolis acceleration, simulation with the Variable Ratio Gear block will be inaccurate by an error proportional to dgFB/dt. [. . . ]