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The constants '''K<sub>M</sub>''' (motor size constant) and ''' K<sub>v</sub>''' (motor velocity constant, or back EMF constant) are values use to describe characteristics of electrical motors.
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== Motor constant==
''K<sub>M</sub>'' is the ''motor constant'' Ref:<ref>http://www.motioncomp.com/pdfs/Motor_Constant_Great_Equalizer.pdf</ref>(sometimes, ''motor size constant''), defined as:
:<math>\frac{\tau}{\sqrt{P}}</math>
where
* <math>\scriptstyle \tau</math> is the motor torque (SI units, N·m)
* <math>\scriptstyle P</math> is the resistive power loss (SI units, W)
The motor constant is winding independent (as long as the same conductive material used for wires); e.g., winding a motor with 6 turns with 2 parallel wires instead of 12 turns single wire will double the velocity constant, K<sub>v</sub>, but K<sub>M</sub> remains unchanged. K<sub>M</sub> can be used for selecting the size of a motor to use in an application. K<sub>v</sub> can be used for selecting the winding to use in the motor.
 
== Motor velocity constant, back EMF constant ==
 
''K<sub>v</sub>'' is the motor velocity constant, measured in RPM per volt (not to be confused with ''kV'', the abbreviation for ''kilovolt'').<ref>[https://unitedhobbies.com/UNITEDHOBBIES/store/wikishow.asp?idwiki=4 United Hobbies: "Kv rating explained"]</ref> The K<sub>v</sub> rating of a brushless motor is the ratio of the motor's unloaded RPM to the peak (not RMS) voltage on the wires connected to the coils (the ''back-EMF''). For example, a motor of K<sub>v</sub>, 5,700&nbsp;RPM/V, supplied with 11.1&nbsp;V, will run at a nominal 63,270&nbsp;RPM (5,700&nbsp;RPM/V × 11.1&nbsp;V).
 
The terms ''K<sub>e</sub>'',<ref name="kk">{{citation| url = http://hades.mech.northwestern.edu/images/6/61/Asst7.pdf| title  =Mystery Motor Data Sheet| work = hades.mech.northwest.edu}}</ref> ''K<sub>b</sub>'' are also used,<ref>{{citation| url =http://www.smma.org/PDFs/SMMA_motor_glossary.pdf|title = GENERAL MOTOR TERMINOLOGY| work = www.smma.org}}</ref> as are the terms  ''back emf constant''.<ref>{{citation| url = http://www.mathworks.co.uk/help/toolbox/physmod/elec/ref/dcmotor.html|title =DC motor model with electrical and torque characteristics - Simulink| work =www.mathworks.co.uk}}</ref><ref>{{citation| url  =http://www.micro-drives.com/motor-calculations.aspx| title = Technical Library > DC Motors Tutorials > Motor Calculations| work = www.micro-drives.com}}</ref> or the generic ''electrical constant''.<ref name="kk"/>
 
The field flux may also be integrated into the formula:<ref>{{citation| url = http://iitd.vlab.co.in/?sub=67&brch=185&sim=470&cnt=1| title = DC motor starting and braking| work = iitd.vlab.co.in}}</ref>
 
:E<sub>b</sub> = K<sub>ω</sub>Φω
:''Where E<sub>b</sub> is back emf, K<sub>ω</sub> is the constant, Φ is the flux, and ω is the angular speed''
 
An inverse measure is also sometimes used, which may be referred to as the speed constant.<ref name="kk"/>
 
By [[Lenz's law]], a running motor generates a back-EMF proportional to the RPM. Once the motor's rotational velocity is such that the back-EMF is equal to the battery voltage (also called DC line voltage), the motor reaches its limit speed.
 
==References==
{{reflist}}
 
==External links==
*[http://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee3/bdeee3_5.aspx DC Motors], Electric motor reference center
*{{citation| url =http://biosystems.okstate.edu/home/mstone/4353/downloads/Developement%20of%20Electromotive%20Force.pdf| title = Development of Electromotive Force| work = biosystems.okstate.edu}}
 
[[Category:Electric motors]]

Revision as of 19:18, 1 March 2014

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