查看“︁馬達常數”︁的源代码

'''馬達尺寸常數'''''K<sub>M</sub>''、'''[[反電動勢]]常數'''''K<sub>v</sub>''及'''轉矩常數'''''K<sub>T</sub>''都是常用來描述[[電動機|馬達]]特性的數值。.

== 馬達常數==

''K<sub>M</sub>''是'''馬達常數'''<ref>{{Cite web |url=http://www.motioncomp.com/pdfs/Motor_Constant_Great_Equalizer.pdf |title=存档副本 |access-date=2016-02-22 |archive-date=2021-04-13 |archive-url=https://web.archive.org/web/20210413125847/http://www.motioncomp.com/pdfs/Motor_Constant_Great_Equalizer.pdf |dead-url=yes }} {{Wayback|url=http://www.motioncomp.com/pdfs/Motor_Constant_Great_Equalizer.pdf |date=20210413125847 }}</ref>或'''馬達尺寸常數'''。若用[[國際單位制]]表示，其單位為[[牛頓|N]]⋅[[公尺|m]]/sqrt([[瓦特|W]]))：	
:<math>K_\mathrm{M} =\frac{\tau}{\sqrt{P}}</math>
 	
其中
	
* <math>\scriptstyle \tau</math>為馬達[[轉矩]]。（SI制單位為N·m）	
* <math>\scriptstyle P</math>為馬達[[銅損|熱損失]]。（SI制單位為W）
 	
只要馬達用的導線材料不變，馬達常數和繞線方式無關。像繞馬達時，用2條平行線繞6圈，其速度常數K<sub>v</sub>會是單線繞12圈的二倍，但K<sub>M</sub>不會變化。K<sub>M</sub>可以用來選擇符合特定應用的馬達大小，而K<sub>v</sub>可以用來決定其繞線方式。

==馬達速度常數、反電動勢常數==

''K<sub>v</sub>''是馬達速度常數，其單位為[[每分鐘轉速|RPM]]/[[伏特|V]]（容易和表示千伏特的''kV''混淆）<ref>[https://unitedhobbies.com/UNITEDHOBBIES/store/wikishow.asp?idwiki=4 United Hobbies: "Kv rating explained"]{{dead link|date=2018年5月 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>。[[永磁同步馬達|無刷馬達]]的K<sub>v</sub>是馬達無載的轉速除以在馬達線圈上的峰端電壓（[[反電動勢]]，非RMS電壓）。例如，一個無載時K<sub>v</sub>, 5,700&nbsp;rpm/V的馬達，若供電電壓為11.1&nbsp;V，其轉速為63,270&nbsp;rpm（5,700&nbsp;rpm/V × 11.1&nbsp;V）。

也會用''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| accessdate = 2016-02-22| archive-date = 2021-05-06| archive-url = https://web.archive.org/web/20210506140440/http://hades.mech.northwestern.edu/images/6/61/Asst7.pdf| dead-url = no}} {{Wayback|url=http://hades.mech.northwestern.edu/images/6/61/Asst7.pdf |date=20210506140440 }}</ref>及''K<sub>b</sub>''等符號表示馬達速度常數<ref>{{citation| url =http://www.smma.org/pdf/SMMA_motor_glossary.pdf| title =GENERAL MOTOR TERMINOLOGY| work =www.smma.org| accessdate =2016-02-22| archive-date =2015-04-21| archive-url =https://web.archive.org/web/20150421082412/http://www.smma.org/pdf/SMMA_motor_glossary.pdf| dead-url =no}} {{Wayback|url=http://www.smma.org/pdf/SMMA_motor_glossary.pdf |date=20150421082412 }}</ref>，也會表示為'''反電動勢常數'''<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| deadurl = yes| archiveurl = https://web.archive.org/web/20120404160332/http://www.micro-drives.com/motor-calculations.aspx| archivedate = 2012-04-04}} {{Wayback|url=http://www.micro-drives.com/motor-calculations.aspx |date=20120404160332 }}</ref>或泛用的'''馬達常數'''<ref name="kk"/>。和''K<sub>V</sub>''相反，''K<sub>e</sub>''在SI制下的單位常表示為<math>\frac{V\cdot s}{rad}</math>，因此和''K<sub>V</sub>''成反比<ref>{{Cite web |url=http://www.precisionmicrodrives.com/tech-blog/2014/02/02/reading-the-motor-constants-from-typical-performance-characteristics |title=存档副本 |access-date=2016-02-22 |archive-date=2016-04-08 |archive-url=https://web.archive.org/web/20160408102614/http://www.precisionmicrodrives.com/tech-blog/2014/02/02/reading-the-motor-constants-from-typical-performance-characteristics |dead-url=no }} {{Wayback|url=http://www.precisionmicrodrives.com/tech-blog/2014/02/02/reading-the-motor-constants-from-typical-performance-characteristics |date=20160408102614 }}</ref>。有時會表示為非SI制單位krpm/V<ref>{{Cite web |url=http://www.smma.org/pdf/SMMA_motor_glossary.pdf |title=存档副本 |access-date=2016-02-22 |archive-date=2015-04-21 |archive-url=https://web.archive.org/web/20150421082412/http://www.smma.org/pdf/SMMA_motor_glossary.pdf |dead-url=no }} {{Wayback|url=http://www.smma.org/pdf/SMMA_motor_glossary.pdf |date=20150421082412 }}</ref>。

也可以將馬達的[[磁通]]整合到上述公式中<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| accessdate = 2016-02-22| archive-date = 2019-09-07| archive-url = https://web.archive.org/web/20190907213106/http://iitd.vlab.co.in/?sub=67&brch=185&sim=470&cnt=1| dead-url = no}} {{Wayback|url=http://iitd.vlab.co.in/?sub=67&brch=185&sim=470&cnt=1 |date=20190907213106 }}</ref>：

:<math>E_b = K_\omega\phi\omega</math>
:其他<math>E_b</math>為反電動勢，<math>K_\omega</math>為常數，<math>\phi</math>為磁通 ，而<math>\omega</math>為角速度。

<!--An inverse measure is also sometimes used, which may be referred to as the speed constant.<ref name="kk"/>
-->
依[[楞次定律]]，運轉中馬達的反電動勢和其轉速成正比。若馬達的反電動勢達到供電電池的電壓（直流鏈電壓），馬達的速度即為其最大轉速。

== 馬達轉矩常數 ==
''K<sub>T</sub>''是單位電樞電流可以產生的力矩<ref>{{citation| url = http://electronics.stackexchange.com/questions/33315/understanding-motor-constants-kt-and-kemf-for-comparing-brushless-dc-motors| title = Understanding motor constants Kt and Kemf for comparing brushless DC motors| accessdate = 2016-02-22| archive-date = 2021-05-06| archive-url = https://web.archive.org/web/20210506203901/https://electronics.stackexchange.com/questions/33315/understanding-motor-constants-kt-and-kemf-for-comparing-brushless-dc-motors| dead-url = no}} {{Wayback|url=http://electronics.stackexchange.com/questions/33315/understanding-motor-constants-kt-and-kemf-for-comparing-brushless-dc-motors |date=20210506203901 }}</ref>，可以由馬達的速度常數K<sub>v</sub>計算。

:<math>
K_\mathrm{T} =\frac{\tau}{I_A} =\frac{60}{2\pi\cdot K_V} 
</math>

其中
:<math>I_A</math>為機器的[[電樞]]電流，單位[[安培|A]]。''K<sub>T</sub>''主要可用來計算在某給定轉矩需求下，需要的電樞電流： 
:<math>
{I_A} = \frac{\tau}{K_\mathrm{T}}
</math>

==參考資料==
{{reflist}}

==外部連結==
*[http://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee3/bdeee3_5.aspx DC Motors] {{Wayback|url=http://www.electricmotors.machinedesign.com/guiEdits/Content/bdeee3/bdeee3_5.aspx |date=20130518083300 }}, 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| deadurl = yes| archiveurl = https://web.archive.org/web/20100604201111/http://biosystems.okstate.edu/Home/mstone/4353/downloads/Developement%20of%20Electromotive%20Force.pdf| archivedate = 2010-06-04}} {{Wayback|url=http://biosystems.okstate.edu/home/mstone/4353/downloads/Developement%20of%20Electromotive%20Force.pdf |date=20100604201111 }}

[[Category:電動機]]