Modelica.Mechanics.Rotational.Examples

Information

This package contains example models to demonstrate the usage of the Modelica.Mechanics.Rotational package. Open the models and simulate them according to the provided description in the models.

Package Content

Name	Description
First	First example: simple drive train
FirstGrounded	First example: simple drive train with grounded elements
Friction	Drive train with clutch and brake
CoupledClutches	Drive train with 3 dynamically coupled clutches
LossyGearDemo1	Example to show that gear efficiency may lead to stuck motion
LossyGearDemo2	Example to show combination of LossyGear and BearingFriction
LossyGearDemo3	Example that failed in the previous version of the LossyGear version
ElasticBearing	Example to show possible usage of support flange
Backlash	Example to demonstrate backlash
RollingWheel	Demonstrate coupling Rotational - Translational
HeatLosses	Demonstrate the modeling of heat losses
SimpleGearShift	Simple Gearshift
GenerationOfFMUs	Example to demonstrate variants to generate FMUs (Functional Mockup Units)
Utilities	Utility components used by the example models

Modelica.Mechanics.Rotational.Examples.First

Information

The drive train consists of a motor inertia which is driven by a sine-wave motor torque. Via a gearbox the rotational energy is transmitted to a load inertia. Elasticity in the gearbox is modeled by a spring element. A linear damper is used to model the damping in the gearbox bearing.

Note, that a force component (like the damper of this example) which is acting between a shaft and the housing has to be fixed in the housing on one side via component Fixed.

Simulate for 1 second and plot the following variables:
angular velocities of inertias inertia2 and 3: inertia2.w, inertia3.w

Parameters

Name	Description
amplitude	Amplitude of driving torque [N.m]
freqHz	Frequency of driving torque [Hz]
Jmotor	Motor inertia [kg.m2]
Jload	Load inertia [kg.m2]
ratio	Gear ratio
damping	Damping in bearing of gear

Modelica.Mechanics.Rotational.Examples.FirstGrounded

Information

The drive train consists of a motor inertia which is driven by a sine-wave motor torque. Via a gearbox the rotational energy is transmitted to a load inertia. Elasticity in the gearbox is modeled by a spring element. A linear damper is used to model the damping in the gearbox bearing.

Note, that a force component (like the damper of this example) which is acting between a shaft and the housing has to be fixed in the housing on one side via component Fixed.

Simulate for 1 second and plot the following variables:
angular velocities of inertias inertia2 and 3: inertia2.w, inertia3.w

Parameters

Name	Description
amplitude	Amplitude of driving torque [N.m]
freqHz	Frequency of driving torque [Hz]
Jmotor	Motor inertia [kg.m2]
Jload	Load inertia [kg.m2]
ratio	Gear ratio
damping	Damping in bearing of gear

Modelica.Mechanics.Rotational.Examples.Friction

Information

This drive train contains a frictional clutch and a brake. Simulate the system for 1 second using the following initial values (defined already in the model):

   inertia1.w =  90 (or brake.w)
   inertia2.w =  90
   inertia3.w = 100

Plot the output signals

   tMotor      Torque of motor
   tClutch     Torque in clutch
   tBrake      Torque in brake
   tSpring     Torque in spring

as well as the absolute angular velocities of the three inertia components (inertia1.w, inertia2.w, inertia3.w).

Parameters

Name	Description
startTime	Start time of step [s]

Modelica.Mechanics.Rotational.Examples.CoupledClutches

Information

This example demonstrates how variable structure drive trains are handled. The drive train consists of 4 inertias and 3 clutches, where the clutches are controlled by input signals. The system has 2^3=8 different configurations and 3^3 = 27 different states (every clutch may be in forward sliding, backward sliding or locked mode when the relative angular velocity is zero). By invoking the clutches at different time instances, the switching of the configurations can be studied.

Simulate the system for 1.2 seconds with the following initial values:
J1.w = 10.

Plot the following variables:
angular velocities of inertias (J1.w, J2.w, J3.w, J4.w), frictional torques of clutches (clutchX.tau), frictional mode of clutches (clutchX.mode) where mode = -1/0/+1 means backward sliding, locked, forward sliding.

Parameters

Name	Description
freqHz	Frequency of sine function to invoke clutch1 [Hz]
T2	Time when clutch2 is invoked [s]
T3	Time when clutch3 is invoked [s]

Modelica.Mechanics.Rotational.Examples.LossyGearDemo1

Information

This model contains two inertias which are connected by an ideal gear where the friction between the teeth of the gear is modeled in a physical meaningful way (friction may lead to stuck mode which locks the motion of the gear). The friction is defined by an efficiency factor (= 0.5) for forward and backward driving condition leading to a torque dependent friction loss. Simulate for about 0.5 seconds. The friction in the gear will take all modes (forward and backward rolling, as well as stuck).

You may plot:

Inertia1.w,
Inertia2.w : angular velocities of inertias
powerLoss  : power lost in the gear
gear.mode  :  1 = forward rolling
              0 = stuck (w=0)
             -1 = backward rolling

Modelica.Mechanics.Rotational.Examples.LossyGearDemo2

Information

This model contains bearing friction and gear friction (= efficiency). If both friction models are stuck, there is no unique solution. Still a reliable Modelica simulator, such as Dymola, should be able to handle this situation.

Simulate for about 0.5 seconds. The friction elements are in all modes (forward and backward rolling, as well as stuck).

You may plot:

Inertia1.w,
Inertia2.w          : angular velocities of inertias
powerLoss           : power lost in the gear
bearingFriction.mode:  1 = forward rolling
                       0 = stuck (w=0)
                      -1 = backward rolling
gear.mode           :  1 = forward rolling
                       0 = stuck (w=0)
                      -1 = backward rolling

Note: This combination of LossyGear and BearingFriction is not recommended to use, as component LossyGear includes the functionality of component BearingFriction (only peak not supported).

Modelica.Mechanics.Rotational.Examples.LossyGearDemo3

Information

This example demonstrates a situation where the driving side of the LossyGear model is not obvious. The version of LossyGear up to version 3.1 of package Modelica failed in this case (no convergence of the event iteration).

Modelica.Mechanics.Rotational.Examples.ElasticBearing

Information

This model demonstrates the usage of the bearing flange. The gearbox is not connected rigidly to the ground, but by a spring-damper-system. This allows examination of the gearbox housing dynamics.

Simulate for about 10 seconds and plot the angular velocities of the inertias housing.w, shaft.w and load.w.

Modelica.Mechanics.Rotational.Examples.Backlash

Information

This model demonstrates the effect of a backlash on eigenfrequency, and also that the damping torque does not lead to unphysical pulling torques (since the ElastoBacklash model takes care of it).

Modelica.Mechanics.Rotational.Examples.RollingWheel

Information

This model demonstrates the coupling between rotational and translational components:
A torque (step) accelerates both the inertia (of the wheel) and the mass (of the vehicle).
Du to a speed dependent force (like driving resistance), we find an equilibrium at 5 m/s after approx. 5 s.

Modelica.Mechanics.Rotational.Examples.HeatLosses

Information

This model demonstrates how to model the dissipated power of a drive train, by enabling the heatPort of all components and connecting these heatPorts via a convection element to the environment. The total heat flow generated by the elements of the drive train and transported to the environment is present in variable convection.fluid.

Modelica.Mechanics.Rotational.Examples.SimpleGearShift

Information

This model shows how an automatic gear shift is built up from a planetary gear, a brake and a clutch.

• In the beginning, the clutch is free and the brake fixes the ring of the planetary. Thus we obtain a gearRatio = 1/(1 + planetary.ratio).
• At time = 2 s, the brake frees the ring of the planetary, whereas the clutch blocks the ring and the sun. Thus we obtain a gearRatio = 1.

Modelica.Mechanics.Rotational.Examples.GenerationOfFMUs

Information

This example demonstrates how to generate an input/output block (e.g. in form of an FMU - Functional Mockup Unit) from various Rotational components. The goal is to export such an input/output block from Modelica and import it in another modeling environment. The essential issue is that before exporting it must be known in which way the component is utilized in the target environment. Depending on the target usage, different flange variables need to be in the interface with either input or output causality. Note, this example model can be used to test the FMU export/import of a Modelica tool. Just export the components marked in the icons as "toFMU" as FMUs and import them back. The models should then still work and give the same results as a pure Modelica model.

Connecting two inertias
The upper part (DirectInertia, InverseInertia) demonstrates how to export two inertias and connect them together in a target system. This requires that one of the inertias (here: DirectInertia) is defined to have states and the angle, angular velocity and angular acceleration are provided in the interface. The other inertia (here: InverseInertia) is moved according to the provided input angle, angular velocity and angular acceleration.

Connecting a force element that needs angles and angular velocities
The middle part (SpringDamper) demonstrates how to export a force element that needs both angles and angular velocities for its force law and connect this force law in a target system between two inertias.

Connecting a force element that needs only angles
The lower part (Spring) demonstrates how to export a force element that needs only angles for its force law and connect this force law in a target system between two inertias.