Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects

Demonstrates the usage of 1-dim. rotational elements with all 3-dim. effects included

Information

This package demonstrates the usage of elements of the Mechanics.Rotational library by taking into account all 3-dim. effects. The reason for this type of modeling is to speedup the simulation drastically. This is possible if moving bodies have rotational symmetry. A typical application area are drive trains, driving joints of a multi-body system.

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name	Description
GyroscopicEffects	Demonstrates that a cylindrical body can be replaced by Rotor1D model
ActuatedDrive	Demonstrates usage of models Rotor1D and Mounting1D
MovingActuatedDrive	Demonstrates usage of model Rotor1D mounted on a moving body
GearConstraint	Demonstrate usage of GearConstraint model
BevelGear1D	Demonstrates the usage of a BevelGear1D model and how to calculate the power of such an element

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects.GyroscopicEffects

Demonstrates that a cylindrical body can be replaced by Rotor1D model

Information

This example consists of a body that is attached to the world system with a spherical joint. On this body, a "rotor", i.e., a body with rotational symmetry is present. Two kinds of models are shown:

• In the upper part of the diagram layer, only multi-body components are used.
• In the lower part of the diagram layer, the same model is implemented, but by a different modeling of the cylindrical body: The cylindrical body is included, but it is rigidly attached to its mount. This part takes into account the movement of the center of mass and of the inertia tensor of the cylindrical body. Note, since the cylindrical body has rotational symmetry, its center of mass and its inertia tensor is independent of the angle of the inertia and can therefore be rigidly attached to its mount. Additionally, with a "MultiBody.Parts.Rotor1D" model, a primarily 1-dim. inertia is included that takes into account the additional effects when the cylindrical body is moving relatively to its mounts

The simulation reveals that both the kinematic movement and the reaction forces on the environment (object "world" and "fixed" respectively) are identical for both models.

A typical usage scenario is to model a complete drive train of a vehicle, including the automatic gearbox, with elements of the "Mechanics.Rotational" library, but using the "Rotor1D" model instead of the "Rotational.Components.Inertia" component. This drive train model can be mounted on a 3-dim. multi-body model of the vehicle. Additionally, one rigid body has to be fixed to the vehicle that has the mass, center of mass and inertia tensor of the complete drive train. Both models together, give exactly the same effect, as if every part of the drive train would have been modelled solely with mult-body components. One benefit of this modeling is that the simulation is much faster.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects.ActuatedDrive

Demonstrates usage of models Rotor1D and Mounting1D

Information

This example demonstrates how to utilize the Rotor1D and Mounting1D models and compares the implementation with a standard multi-body implementation. Note, the solution with Rotor1D is much more efficient.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects.MovingActuatedDrive

Demonstrates usage of model Rotor1D mounted on a moving body

Information

This model demonstrates how a moving drive train modelled with 3-dim. multi-body elements (revolute, bodyCylinder) can alternatively be modeled with component rotor1D to speed up simulation. The movement of the two systems is identical and also the cut-torques in the various frames (such as: r1.frame_b.t and r2.frame_b.t).

The driving joints (r1, r2) with rotation axis {0,1,0} are modelled to be driven by a motor torque along the {1,0,0} axis. Basically, this means that an idealized bevel gear is used to drive the axes of the revolute joints.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects.GearConstraint

Demonstrate usage of GearConstraint model

Information

This model demonstrates the usage of the GearConstraint model to model a gearbox with multi-body elements. The formulation is compared with a one-dimensional model that is mounted with an Mounting1D element.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Modelica.Mechanics.MultiBody.Examples.Rotational3DEffects.BevelGear1D

Demonstrates the usage of a BevelGear1D model and how to calculate the power of such an element

Information

This model consists of a drive train with two inertias that are coupled by a bevel gear (with 90 degree angle between the two gear flanges). This drive train is mounted on a body that is rotated along three axes. The drive train is modeled with 1D rotational elements that take into account 3D effects.

The bevelGear component consists of two rotational flanges (for the gear flanges) and one 3D frame (for the support/mounting). Since the bevelGear does not store energy, the power balance must hold (the total sum of inflowing and outflowing energy must be zero). One has to be careful, when computing the energy flow of hybrid 1D/3D component: The angular velocities of rotational flanges are with respect to the support frame (so the moving body on which the drive train is mounted). Therefore, when computing the energy flow, first the absolute angular velocities of the flanges have to be calculated. In this example model, this is performed in the following way (na and nb are the axes of rotations of the gear flanges, and ws is the angular velocity of the support frame):

  import Modelica.Mechanics.MultiBody.Frames;

  SI.Power           bevelGearPower;
  SI.AngularVelocity ws[3] = Frames.angularVelocity2(bevelGear.frame_a.R);
equation
  bevelGearPower = (ws + der(bevelGear.flange_a.phi)*na)*bevelGear.flange_a.tau*na +
                   (ws + der(bevelGear.flange_b.phi)*nb)*bevelGear.flange_b.tau*nb +
                   ws*bevelGear.frame_a.t;

The total energy flow bevelGearPower must be zero. If a relative tolerance of 1e-4 is used for simulation, bevelGearPower is in the order of 1e-8 (and smaller for a smaller relative tolerance).

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters