Gelöste Aufgaben/JUMP/E-Motor and Drive-Train - Versionsgeschichte

Mechaniker: /* Parameter */

2021-03-24T15:54:49Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 15:54 Uhr
Zeile 260:		Zeile 260:
	::<math>M_M=\frac{{U_M}\, {k_T}-{k_T}\, {k_e} \tilde{\omega}_M }{{R_M}}</math>.		::<math>M_M=\frac{{U_M}\, {k_T}-{k_T}\, {k_e} \tilde{\omega}_M }{{R_M}}</math>.

	~~Since~~		For our application, it will be easier to replace ''k<sub>e</sub>'', ''k<sub>R</sub>'' and ''R'' by mechanical properties as

	::<~~math~~>~~k_e = k_T~~</~~math~~>

	~~we see that~~

	<ol>		<ol>
	<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have		<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have

	::<math> ~~k_T~~= \frac{U_M}{\tilde{\omega}_{NL}}</math></li>		::<math>k_e= \frac{U_M}{\tilde{\omega}_{NL}}</math></li>
	<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have		<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have

	::<math>R = \frac{\displaystyle ~~U_M~~}{\displaystyle I_{St}}</math> ~~where~~ <math>~~I_{St}~~ = \frac{\displaystyle ~~M_{St}~~}{\displaystyle ~~k_T~~}</math>.</li>		::<math>k_T = \frac{\displaystyle M_{St}}{\displaystyle I_{St}}</math> and <math>R = \frac{\displaystyle U_M}{\displaystyle I_{St}}</math>.</li>
	</ol>		</ol>

			Thus for ''U<sub>M</sub> = 12 V'' we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'' and ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>
	~~and -~~ for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>/ k<sub>e~~</sub>'', ''I<sub>St~~</sub>'' and ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>		''I<sub>St</sub>'' and ''M<sub>St</sub>''.
	and ''M<sub>St</sub>''~~, which make the system parameters to be selected more descriptive~~.

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Mechaniker: /* Parameter */

2021-03-24T13:55:56Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 13:55 Uhr
Zeile 272:		Zeile 272:
	<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have		<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have

	::<math>R = \frac{\displaystyle U_M}{\displaystyle I_{St}}</math> where <math>I_{St} = \frac{\displaystyle ~~\tilde{\omega}_{NL} \cdot~~ M_{St}}{\displaystyle ~~U_{M}~~}</math>.</li>		::<math>R = \frac{\displaystyle U_M}{\displaystyle I_{St}}</math> where <math>I_{St} = \frac{\displaystyle M_{St}}{\displaystyle k_T}</math>.</li>
	</ol>		</ol>

Mechaniker: /* Parameter */

2021-03-24T13:46:32Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 13:46 Uhr
Zeile 277:		Zeile 277:

	and - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>/ k<sub>e</sub>'', ''I<sub>St</sub>'' and ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>		and - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>/ k<sub>e</sub>'', ''I<sub>St</sub>'' and ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>
	and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.		and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.

	{\| class="wikitable" style="border-collapse: collapse;"		{\| class="wikitable" style="border-collapse: collapse;"

Mechaniker: /* Parameter */

2021-03-24T13:45:37Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 13:45 Uhr
Zeile 269:		Zeile 269:
	<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have		<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have

	::<math>\tilde{\omega}_{NL} ~~= \frac{U_M}{k_T~~}</math></li>		::<math> k_T= \frac{U_M}{\tilde{\omega}_{NL}}</math></li>
	<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have		<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have

Mechaniker: /* Parameter */

2021-03-24T13:44:45Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 13:44 Uhr
Zeile 258:		Zeile 258:
	System parameters for the motor are ''k<sub>T</sub>, k<sub>e</sub>'' and ''R<sub>M</sub>'' . For the stationary (<math>\frac{\displaystyle d \; I_M}{\displaystyle dt} = 0</math>) - condition, we derive		System parameters for the motor are ''k<sub>T</sub>, k<sub>e</sub>'' and ''R<sub>M</sub>'' . For the stationary (<math>\frac{\displaystyle d \; I_M}{\displaystyle dt} = 0</math>) - condition, we derive

	::<math>M_M=\frac{{U_M}\, {k_T}-{k_T}\, {k_e} \tilde{\omega}_M }{{R_M}}</math>,		::<math>M_M=\frac{{U_M}\, {k_T}-{k_T}\, {k_e} \tilde{\omega}_M }{{R_M}}</math>.

	~~so that~~ we see:		Since

			::<math>k_e = k_T</math>

			we see that

	<ol>		<ol>
	<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have		<li>under a "no-load"-condition ''M<sub>M</sub>=0'', we have

	::<math>\tilde{\omega}_{NL} = \frac{U_M}{~~k_e~~}</math></li>		::<math>\tilde{\omega}_{NL} = \frac{U_M}{k_T}</math></li>
	<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have		<li>under the "stalled motor"-condition <math>\tilde{\omega}_{St}=0</math>, we have

	::<math>M_{St} ~~= k_T~~ \~~cdot~~ I_{St}</math> ~~and~~ <math>R = \frac{\displaystyle ~~U_M~~}{\displaystyle I_{St}}</math>.</li>		::<math>R = \frac{\displaystyle U_M}{\displaystyle I_{St}}</math> where <math>I_{St} = \frac{\displaystyle \tilde{\omega}_{NL} \cdot M_{St}}{\displaystyle U_{M}}</math>.</li>
	</ol>		</ol>

	~~Since~~
	~~::<math>k_e = k_T</math>~~

	and - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'', ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>~~, ''I<sub>St</sub>''~~ and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.		and - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>/ k<sub>e</sub>'', ''I<sub>St</sub>'' and ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>
			and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.

	{\| class="wikitable" style="border-collapse: collapse;"		{\| class="wikitable" style="border-collapse: collapse;"

Mechaniker: /* Parameter */

2021-03-24T13:22:10Z

Parameter

← Nächstältere Version		Version vom 24. März 2021, 13:22 Uhr
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	\|stall-current		\|stall-current
	\|''I<sub>St</sub>''		\|''I<sub>St</sub>''
	\|0.25		\|8.6
	\|A		\|A
	\|-		\|-

Mechaniker: /* Parameter */

2021-03-19T13:18:15Z

Parameter

← Nächstältere Version		Version vom 19. März 2021, 13:18 Uhr
Zeile 271:		Zeile 271:
	</ol>		</ol>

	~~Thus~~ - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'', ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>, ''I<sub>St</sub>'' and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.		Since
			::<math>k_e = k_T</math>

			and - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'', ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>, ''I<sub>St</sub>'' and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.

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Mechaniker: /* Parameter */

2021-03-18T07:17:43Z

Parameter

← Nächstältere Version		Version vom 18. März 2021, 07:17 Uhr
Zeile 309:		Zeile 309:
	\|1		\|1
	\|}		\|}
	~~[[Datei:Codepage.png\|mini\|code]]~~
	[[Gelöste Aufgaben/JUMP\|Back to Start →]]		[[Gelöste Aufgaben/JUMP\|Back to Start →]]

Mechaniker: /* Parameter */

2021-03-18T07:17:22Z

Parameter

← Nächstältere Version		Version vom 18. März 2021, 07:17 Uhr
Zeile 309:		Zeile 309:
	\|1		\|1
	\|}		\|}
			[[Datei:Codepage.png\|mini\|code]]
	[[Gelöste Aufgaben/JUMP\|Back to Start →]]		[[Gelöste Aufgaben/JUMP\|Back to Start →]]

Mechaniker: /* Parameter */

2021-03-18T06:48:48Z

Parameter

← Nächstältere Version		Version vom 18. März 2021, 06:48 Uhr
Zeile 272:		Zeile 272:

	Thus - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'', ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>, ''I<sub>St</sub>'' and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.		Thus - for ''U<sub>M</sub> = 12 V'' - we can import measured performance parameters and then replace ''k<sub>T</sub>, k<sub>e</sub>'', ''R<sub>M</sub>'' by <math>\tilde{\omega}_{NL}</math>, ''I<sub>St</sub>'' and ''M<sub>St</sub>'', which make the system parameters to be selected more descriptive.


	~~<table style="border-collapse: collapse; border: 1px solid gray;">~~
	<tr style="border: none; background-color:lightgray"><th style="border-right: solid 1px gray; border-left: solid 1px gray;">name</th><th style="border-right: solid 1px gray; border-left: solid 1px gray;>symbol</th></tr>
	<tr style="border: none; "><td style="border-right: solid 1px gray; border-left: solid 1px gray;">name</td><td style="border-right: solid 1px gray; border-left: solid 1px gray;">symbol</td></tr>
	~~<tr style="border: none; border-right: solid 1px gray; border-left: solid 1px gray;"><td>name</td><td>symbol</td></tr>~~
	~~</table>~~





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