Modelica.Mechanics.Translational.Examples

Demonstration examples of the components of this package

Information

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

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

Package Content

Name	Description
SignConvention	Examples for the used sign conventions
InitialConditions	Setting of initial conditions
WhyArrows	Use of arrows in Mechanics.Translational
Accelerate	Use of model accelerate
Damper	Use of damper models
Oscillator	Oscillator demonstrates the use of initial conditions
Sensors	Sensors for translational systems
Friction	Use of model Stop
PreLoad	Preload of a spool using ElastoGap models
ElastoGap	Demonstrate usage of ElastoGap
Brake	Demonstrate braking of a translational moving mass
HeatLosses	Demonstrate the modeling of heat losses
EddyCurrentBrake	Demonstrate the usage of the translational eddy current brake
Vehicle	One-dimensional vehicle with driving resistances
GenerationOfFMUs	Example to demonstrate variants to generate FMUs (Functional Mock-up Units)
Utilities	Utility classes used by translational example models

Modelica.Mechanics.Translational.Examples.SignConvention

Examples for the used sign conventions

Information

If all arrows point in the same direction, a positive force results in a positive acceleration a, velocity v and position s.

For a force of 1 N and a mass of 1 kg this leads to

a = 1 m/s2
v = 1 m/s after 1 s (SlidingMass1.v)
s = 0.5 m after 1 s (SlidingMass1.s)

The acceleration is not available for plotting.

System 1) and 2) are equivalent. It doesn't matter whether the force pushes at flange_a in system 1 or pulls at flange_b in system 2.

It is of course possible to ignore the arrows and connect the models in an arbitrary way. But then it is hard see in what direction the force acts.

In the third system the two arrows are opposed which means that the force acts in the opposite direction (in the same direction as in the two other examples).

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

Modelica.Mechanics.Translational.Examples.InitialConditions

Setting of initial conditions

Information

There are several ways to set initial conditions. In the first system the position of the mass m3 was defined by using the modifier s(start=4.5), the position of m4 by s(start=12.5). These positions were chosen such that the system is at rest. To calculate these values start at the left (fixed2) with a value of 1 m. The spring s2 has an unstretched length of 2 m and m3 an length of 3 m, which leads to

  1   m (fixed2)
+ 2   m (spring s2)
+ 3/2 m (half of the length of mass m3)
-------
  4,5 m = s(start = 4.5) for m3
+ 3/2 m (half of the length of mass m3)
+ 4   m (springDamper sd2)
+ 5/2 m (half of length of mass m4)
-------
 12,5 m = s(start = 12.5) for m4

This selection of initial conditions can prioritize the selection of those variables (m3.s and m4.s) as state variables.

In the second example, the lengths of the springs are given start values but they cannot be used as state for pure springs (only for the spring/damper combination). In this case the system is not at rest.

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

Modelica.Mechanics.Translational.Examples.WhyArrows

Use of arrows in Mechanics.Translational

Information

When using the models of the translational sublibrary it is recommended to make sure that all arrows point in the same direction because then all component have the same reference system. In the example the distance from flange_a of Rod1 to flange_b of Rod2 is 2 m. The distance from flange_a of Rod1 to flange_b of Rod3 is also 2 m though it is difficult to see that. Without the arrows it would be almost impossible to notice. That all arrows point in the same direction is a sufficient condition for an easy use of the library. There are cases where horizontally flipped models can be used without problems.

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

Modelica.Mechanics.Translational.Examples.Accelerate

Use of model accelerate

Information

Demonstrate usage of component Sources.Accelerate by moving a mass with a predefined acceleration.

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

Modelica.Mechanics.Translational.Examples.Damper

Use of damper models

Information

Demonstrate usage of a translational damper component in various configurations.

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

Modelica.Mechanics.Translational.Examples.Oscillator

Oscillator demonstrates the use of initial conditions

Information

A spring - mass system is a mechanical oscillator. If no damping is included and the system is excited at resonance frequency infinite amplitudes will result. The resonant frequency is given by omega_res = sqrt(c / m) with:

c … spring stiffness and
m … mass.

To make sure that the system is initially at rest the initial conditions s(start=-0.5) and v(start=0) for the sliding masses are set. If damping is added the amplitudes are bounded.

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

Modelica.Mechanics.Translational.Examples.Sensors

Sensors for translational systems

Information

These sensors measure

force f in N
position s in m
velocity v in m/s
acceleration a in m/s2

In this example, the measured velocity and acceleration is independent of the flange the sensor is connected to. In contrast, the measured position depends on the flange (flange_a or flange_b) and the length L of the component. Plot positionSensor1.s, positionSensor2.s and mass.s to see the difference.

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

Modelica.Mechanics.Translational.Examples.Friction

Use of model Stop

Information

1. Simulate and then plot stop1.f as a function of stop1.v This gives the Stribeck curve.
2. The same model is also available by modeling the system with a Mass and a SupportFriction model. The SupportFriction model defines the friction characteristic with a table. The table is constructed with function Examples.Utilities.GenerateStribeckFrictionTable(…) to generate the same friction characteristic as with stop1. The simulation results of stop1 and of model mass are therefore identical.
3. Model stop2 gives an example for a hard stop. However there can arise some problems with the used modeling approach (use of reinit(…), convergence problems). In this case use the ElastoGap to model a stop (see example Preload).

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

Modelica.Mechanics.Translational.Examples.PreLoad

Preload of a spool using ElastoGap models

Information

When designing hydraulic valves it is often necessary to hold the spool in a certain position as long as an external force is below a threshold value. If this force exceeds the threshold value a linear relation between force and position is desired. There are designs that need only one spring to accomplish this task. Using the ElastoGap elements this design can be modelled easily. Drawing of spool.

Simulate for 100 s and plot the spool position spool.s as a function of working force force.f. For positive force, the spool moves in positive direction - in figure below the start value spool.s.start influences the offset.

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

Modelica.Mechanics.Translational.Examples.ElastoGap

Demonstrate usage of ElastoGap

Information

This model demonstrates the effect of ElastoGaps on eigenfrequency: Plot mass1.s and mass2.s as well as mass1.v and mass2.v to see that effect.

While mass1 is moved by both spring/damper forces all the time, this is not the case for mass2 since elastoGap1 lifts off at s > -0.5 m and elastoGap2 lifts off at s < +0.5 m. Therefore, mass2 moves freely as long as -0.5 m < s < +0.5 m.

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

Parameters

Modelica.Mechanics.Translational.Examples.Brake

Demonstrate braking of a translational moving mass

Information

This model consists of a mass with an initial velocity of 1 m/s. After 0.1 s, a brake is activated and it is shown that the mass decelerates until it arrives at rest and remains at rest. Two versions of this system are present, one where the brake is implicitly grounded and one where it is grounded explicitly.

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

Modelica.Mechanics.Translational.Examples.HeatLosses

Demonstrate the modeling of heat losses

Information

This model demonstrates how to model the dissipated power of a Translational model, 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 and transported to the environment is present in variable convection.fluid.

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

Modelica.Mechanics.Translational.Examples.EddyCurrentBrake

Demonstrate the usage of the translational eddy current brake

Information

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

Modelica.Mechanics.Translational.Examples.Vehicle

One-dimensional vehicle with driving resistances

Information

Vehicles vehicle and vehicle1 are accelerated and decelerated by a driving torque. Nominal torque is defined as the sum of driving resistances at nominal velocity vNom times wheel radius R.

Starting at 5 s, the vehicle is accelerated by a multiple of nominal torque until it nearly reaches nominal velocity, then driven by nominal torque. Between 20 s and 25 s, an inclination of 5 % occurs and driving torque is increased to a multiple of nominal torque temporarily. Between 50 s and 55 s, the driving torque is set below zero, causing the vehicle to decelerate. After 55 s, the vehicle decelerates due to the driving resistances.

Coupling the trailer with the same data but without drive, the driving torque of vehicle1 has to be doubled to achieve the same acceleration and velocity. Force and power between the two vehicles is measured.

Note

Since the trailer is coupled tightly with the vehicle1, initialization of the trailer has to be removed.

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

Parameters

Modelica.Mechanics.Translational.Examples.GenerationOfFMUs

Example to demonstrate variants to generate FMUs (Functional Mock-up Units)

Information

This example demonstrates how to generate an input/output block (e.g. in form of an FMU - Functional Mock-up Unit) from various Translational 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 masses
The upper part (DirectMass, InverseMass) demonstrates how to export two masses and connect them together in a target system. This requires that one of the masses (here: DirectMass) is defined to have states and the position, velocity and acceleration are provided in the interface. The other mass (here: InverseMass) is moved according to the provided input position, velocity and acceleration.

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

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

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