Units/de: Difference between revisions

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Hier einige Artikel zu Einheiten:

Einige Artikel zu Einheiten:
*[https://de.wikipedia.org/wiki/Metrologie Metrologie] (Meßwesen)
*[https://de.wikipedia.org/wiki/Internationales_Einheitensystem SI System]
*[https://de.wikipedia.org/wiki/Internationales_Einheitensystem SI System]
*[https://de.wikipedia.org/wiki/Angloamerikanisches_Ma%C3%9Fsystem Angloamerikanisches Maßsystem (Imperiale Einheiten)]
*[https://de.wikipedia.org/wiki/Angloamerikanisches_Ma%C3%9Fsystem Angloamerikanisches Maßsystem (Imperiale Einheiten)]
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== Unterstützte Einheiten ==
== Unterstützte Einheiten ==
Eine vollständige Liste aller unterstützten Einheiten kann [[Expressions/de#Einheiten |hier zu finden]] sein.

== Ziele und Grundsätze: Vorschlag für eine Erweiterung des Einheitenverwaltungssystems ==

Eine Erweiterung des Einheitenverwaltungssystems wird in den folgenden Abschnitten vorgeschlagen und das Konzept eines ''Einheitensystems'' entwickelt, das während einer laufenden FreeCAD-Instanz aktiviert wird.
Das Interesse an der Definition eines neues Konzepts ist es, einfacher mit einer größtmöglichen Anzahl von '''physischen''' Einheiten arbeiten zu können (selbst mit benutzerdefinierten), ohne die Komplexität der Einheitenverwaltung für den Benutzer oder die FreeCAD-Entwickler zu erhöhen.

Kurzgesagt werden Ereignisse von Einheitenskalierung präzise lokalisiert und in einer generischen Weise ausgeführt.

Die Erreichung solch einer Flexibilität ist insbesondere dann erforderlich, wenn man mit Materialeigenschaften hantiert, die sehr unterschiedlich sein können, und sie manuell schwierig zu verarbeiten sind.

Die vorgeschlagene Argumentation erlaubt die Behandlung von Einheiten wie in [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)] und [http://physics.nist.gov/Pubs/SP330/sp330.pdf The International System of Units (SI)] beschrieben, beide vom NIST.

In diesem Vorschlag wird im Abschnitt [[Units/de#Brainstorming|Ideenfindung]] zunächst daran erinnert, welche möglichen Kontexte für eine Einheitenverwaltung erforderlich sind.

Im [[Units/de#Organizing|Organisieren]] Abschnitt stellen wir das Datenmodell vor, das zur Erreichung der Einheitenverwaltung beibehalten wurde, basierend auf 3 Objekten, der ''Einheit'', dem ''Einheitenwörterbuch'' und dem ''Einheitensystem''.
Schließlich wird auch eine kurze API eines 4. Objekts namens ''Einheitenverwalter'' vorgestellt.

== Ergebnis ==
Dank dieser Erweiterung soll die Skalierung von Einheiten, die zwischen verschiedenen geschäftlichen Aufgaben auftreten können, erleichtert werden. Beispielsweise können technische Zeichnungen im Standard Einheitensystem erstellt werden, während die FE Modellierung in einem dafür besser geeigneten Einheitensystem verwaltet werden kann.

Der Datenaustausch zwischen diesen beiden Arten von Aktivitäten wird mit dieser Erweiterung einfacher.

== Ideenfindung ==
In diesem Abschnitt werden die Anwendungszusammenhänge eines solchen Einheitenverwaltungssystems hervorgehoben.
Anhand dieser Zusammenhänge können wir dann seine technischen Spezifikationen festlegen.

Im Wesentlichen werden 2 Zusammenhänge als Beispiel angeführt.

=== Zusammenhang 1: Öffnen einer Datendatei ===
Dieser Fall ist wahrscheinlich der häufigste Fall.
Du erhältst eine Datei, die zum Beispiel ein geometrisches Modell enthält oder ein Material mit ziemlich vielen Eigenschaften beschreibt. Das geometrische Modell wird in Metern oder die Materialeigenschaften nach dem internationalen Einheitensystem ausgedrückt.

Wie schade...

Du bist ein Experte für FE Modellierung und arbeitest normalerweise mit Millimeter für Länge, MegaPascal für Spannung, Tonne für Masse...

In diesem Zusammenhang ist das Einheitenmanagement erforderlich, um Daten von einem in der Eingabedatei definierten Anfangseinheitensystem auf ein benutzerdefiniertes Zieleinheitensystem zu skalieren.

=== Context 2: switching the unit system at runtime ===
In this case, you can be at the same time the guy that carries out a drawing, and the guy that will manage the FE modelling. Similarly to the previous case, the unit systems for these 2 tasks are not the same, and you need to switch the initial unit system at runtime to your favorite one.

== Organisieren ==

=== Logic of unit scaling ===
In the [[Units#Brainstorming|Brainstorming]] section have been presented 2 contexts when using unit scaling.
Some items should be highlighted from these two contexts.

==== Unit coherence throughout the FreeCAD running instance ====
The system proposed is based on a primary assumption: the user is working in a coherent unit system.
For instance, this means that if the user expresses length in millimeters, necessarily areras will be expressed in terms of squared millimeters, not squared meters.
This is '''hypothesis one'''.

==== Unit system ====
Because of ''hypothesis one'', it is possible and relevant to define an unit system.
An unit system applies to:
* a running FreeCAD instance into which you are working
* or it may also apply globally to the content of an input file
According [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)] from NIST, they are 7 physical base units.
We chose to express a unit system in terms of these 7 base units.

When working within an instance of FreeCAD, the user has thus to define first the unit system according to which she/he is working before she/he decides to switch to another unit system, or before importing data from an input file.

This unit system will apply till the user decides to change it. If she/he does, all data with dimensions will be scaled.

Considering ''hypothesis one'', all data that the user will input manually in FreeCAD are assumed to be coherent with the chosen unit system.

The benefit to work with a ''unit system'' defined at a FreeCAD running instance level, or at data file level (instead of ''unit'' which are defined at the data level) is then that unit management is considerably simplified.

Here are some examples of unit systems.
* meter, kilogram, second, ampere, Kelvin, mole, candela
* millimeter, tonne, millisecond, ampere, Kelvin, mole, candela
* millimeter, kilogramme, millisecond, ampere, Kelvin, mole, candela
*...

==== Base and derived units ====
Derived units are created by combination of base units. For instance, an acceleration (m/s) combines at the same time length and time. An interesting picture presenting the relationships between base and derived units can be seen [http://physics.nist.gov/cuu/pdf/SIDiagramColorAnnot.pdf here] also from NIST.

Thanks to the definition of ''unit system'', it is possible for the user to work with any kind of derived units, without the need for FreeCAD developpers to foresee them in advance.

==== Base and derived unit symbols ====
According to [http://physics.nist.gov/Pubs/SP330/sp330.pdf The International System of Units (SI)], the symbols to specify a units are officially approved. Two consequences can be highlighted from this.
* it is not easy for a computer program to work with unit symbols because some are greek letters for instance. Hence they can be a bit difficult to process by a program
* while some units and their symbols can be used widely, they may be not approved officially, like for instance ''tonne'' unit (see p32 of [http://physics.nist.gov/Pubs/SP330/sp330.pdf The International System of Units (SI)])

To overcome these limitations and remain flexible, the proposed system favors the use of unit magnitudes instead of unit symbols, which remain nonetheless available for an ergonomy reason.

=== Data model ===
The three core objects of the unit management system are presented, namely the ''unit'', the ''unit dictionary'' and the ''unit system''.

==== Unit ====
As a foreword, it is important to highlight that a ''unit'' object in itself only indicates a '''dimension''' like length, mass, time... It doesn't specify a '''magnitude''' like meter, millimeter, kilometer... This last information is specified through the unit system.

===== Dimension =====
Compulsory string indicating the ''dimension'' of the unit. The ''dimension'' of the 7 base units are indicated below (from [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)]).
* LENGTH
* MASS
* TIME
* ELECTRIC CURRENT
* THERMODYNAMIC TEMPERATURE
* AMOUNT OF SUBSTANCE
* LUMINOUS INTENSITY

''Dimension'' attribute allows identifying the unit.
Two units cannot share the same ''dimension''.

===== Signature =====

Compulsory integer array of size 7 (number of base units) that defines what the unit is.
The signature of the 7 base units are:
* LENGTH: [1,0,0,0,0,0,0]
* MASS: [0,1,0,0,0,0,0]
* TIME: [0,0,1,0,0,0,0]
* ELECTRIC CURRENT: [0,0,0,1,0,0,0]
* THERMODYNAMIC TEMPERATURE: [0,0,0,0,1,0,0]
* AMOUNT OF SUBSTANCE: [0,0,0,0,0,1,0]
* LUMINOUS INTENSITY: [0,0,0,0,0,0,1]

From these 7 units, we are then able to express all derived units defined in [http://physics.nist.gov/cuu/pdf/sp811.pdf Guide for the Use of the International System of Units (SI)] and create new ones as needed such as for instance:
* MASS DENSITY: [-3,1,0,0,0,0,0]
* AREA: [0,2,0,0,0,0,0]

''Signature'' is the attribute thanks to which unit scaling can be achieved in a generic way.

===== Symbols =====
Array of [real, string] (meaning [''magnitude'', ''symbol'']) that lists all ''symbols'' known by FreeCAD.
Thanks to this array, the unit scaling API becomes more ergonomic because ''symbols'' and related ''magnitudes'' are linked.

This array can be extended as required.

For instance, the list of ''symbols'' of the LENGTH unit, and their related ''magnitudes'' is:

[1e+12,"Tm"],[1e+09,"Gm"],[1e+06,"Mm"],
[1e+03,"km"],[1e+02,"hm"],[1e+01,"dam"],
[1e+00,"m"],[1e-01,"dm"],[1e-02,"cm"],
[1e-03,"mm"],[1e-06,"µm"],[1e-09,"nm"],
[1e-12,"pm"],[1e-15,"fm"]

Standard ''symbols'' can be found on [http://physics.nist.gov/cuu/Units/units.html NIST website] and p23 to 26 and p32 (''metric ton'' or ''tonne'') of [http://physics.nist.gov/Pubs/SP330/sp330.pdf The International System of Units (SI)].

==== Unit dictionary ====
All the units available in FreeCAD, and new ones created by the user, should be stored in ''unit dictionary'', which is an XML file (FreeCAD configuration file), so as to be retrieved when needed, i.e. when achieving unit scaling.

===== Units =====
Array of units, contained in the ''unit dictionary''.

==== Unit system ====
A ''unit system'' is the object that allows the user defining the current unit ''magnitude'' of each base units with which she/he is working.
For instance, knowing that the user is working with millimeter, tonne, and second, thanks to the use of a unit system, FreeCAD can know that energy is expressed in terms of milliJoule, force in terms of Newton, and stress in terms of MegaPascal.
Hence a unit system is only defined by a ''name'' (for instance ''Standard unit system'') and a ''magnitude table'' specifying for each of the 7 base units, what is its corresponding ''magnitude''.

===== Name =====
String allowing to the user identifying what is the unit system.

===== Magnitudes =====
By specifying the magnitude of the 7 base units, a unit system is defined.

For instance [1e-03, 1e+03, 1, 1, 1, 1, 1], meaning millimeter, tonne, second, ampere, Kelvin, mole, candela

==== Unit management API ====
Only the logic of some methods is presented, in order to highlight some features.
These methods could belong to an object called ''Unit manager''.

===== Checking the unit dictionary =====

====== isValid ======
The unit dictionary can be an XML file (FreeCAD configuration file). It contains a list of defined units.
Such a dictionary is required for the proposed unit management system to work.

It must fulfills some conditions that should be checked before activating the unit management system.
These conditions are:
* check that all base units are defined
* check that a ''dimension'' is not defined twice through the units
* check that a ''symbol'' is not defined twice in all the existing symbols
* check that the ''signatures'' of all units have all the same size
* chacke that a ''standard symbol'' (for which ''magnitude'' is 1) is defined for all units

====== isCompatibleWithThisSignature ======
A unit dictionary defines a set of units and their known magnitudes.
When managing a unit, it is relevant to check that its signature is compatible with the set of units registered in the unit dictionary, so as to process it.
This check includes:
* check that the input ''signature'' length is of the same size than the unit dictionary unit ''signatures''

===== Scaling units =====

====== scaleUnitFromSymbolToSymbol ======
Knowing a value, an initial unit by its symbol, the target unit by its symbol, scale the value.

====== scaleUnitFromSymbolToUnitSystem ======
Knowing a value, an initial unit by its symbol, the target unit system, scale the value.

====== scaleUnitFromUnitSystemToSymbol ======
Knowing a value, an initial unit system, the target unit by its symbol, scale the value.

==== Motivations for such a management: example of application ====
Let's assume that we are going to setup a finite element model.
To build our model, we need the mesh, material properties, and to define numerical parameters.
Considering that they can be tens of material properties to manage, expressed with different units, sometimes not always very common, it is interesting for the user to only have to specify a global unit system, without caring much.

FreeCAD would then just do the job.

As FreeCAD developpers and FreeCAD users do not necessarily know all units that can be defined in the material property files, it is interesting to rely on a generic system.

Let's assume that in such a file we have a fair number of exotic material properties expressed with exotic units, and that we want to work in a specific unit system.

It is easy with the proposed extension to scale any of these properties by knowing their signatures, magnitudes, and the target unit system.

For each of the properties, the scaling is obtained by multiplying the initial property value with the factor <math>\frac{initialMagnitude}{targetMagnitude}</math>.


Eine vollständige Liste aller unterstützter Einheiten kann man [[Expressions/de#Einheiten |hier]] finden.
The ''targetMagnitude'' is then simply obtained with the operation <math>\prod_{bu} targetMagnitude_{bu}^{signature_{bu}}</math>, ''bu'' standing for ''base unit''.


== Siehe auch ==
It becomes thus very easy to manage any number of properties with any kind of units with very few lines of Python.


* Die Seite [[Expressions/de#Einheiten|Ausdrücke]] für eine Auflistung aller bekannten Einheiten.
== Next actions ==
* Die Dokumentation der [[Quantity|Größen]].
* Das Werkzeug [[Std_UnitsCalculator/de|Std Einheitenrechner]].


* Implementing Quantity and Unit classes (mostly done)
* Implementing InputField as User front end (in progress)
* UnitsCalculator as test bed (in progress)
* [[Quantity|Quantity]] documentation
* [[Std_UnitsCalculator|Std UnitsCalculator]] documentation
* Update Material framework to work only with Quantities
* Test Cases


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Latest revision as of 18:36, 28 November 2022

Other languages:

Einige Artikel zu Einheiten:

Beispiele

# -- some examples of the FreeCAD unit translation system --
# make a shortcut for the examples
pq = FreeCAD.Units.parseQuantity

# 10 meters in internal numbers
pq('10 m')

# doing math
pq('3/8 in')

# combined stuff
pq('100 km/h')

# transfer to other units
pq('100 km/h')/tu('m/s')

# derived units (Ohm)
pq('m^2*kg*s^-3*A^-2')

# or
pq('(m^2*kg)/(A^2*s^3)')

# angles 
pq('2*pi rad') # full circle

# as gon
pq('2*pi rad') / tu('gon')

# more imperial
tu('1ft (3+7/16)in')

# or 
pq('1\' (3+7/16)"') # the ' we have to escape because of python

# trigonometry
pq('sin(pi)')

# Using translated units as parameters, this command will create a 50.8mm x 20mm x 10mm box
b = Part.makeBox(pq('2in'), pq('2m')/100, 10)

Unterstützte Einheiten

Eine vollständige Liste aller unterstützter Einheiten kann man hier finden.

Siehe auch


Power user documentation
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