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ÒÅÎÐÅÒÈ×ÅÑÊÈÅ ÎÑÍÎÂÛ ÝËÅÊÒÐÎÌÅÕÀÍ= ÈÊÈ

 =


ÑÎÄÅÐÆÀÍ= ÈÅ

1.   1.8= . Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 1.

·      =   2.5. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 2.

·      =   3.4. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 3.

·      =   4.3 Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 4.

·      =   5.5. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 5.



1. ÒÅÎÐÅÒÈ×ÅÑÊÈÅ ÎÑÍÎÂÛ ÝËÅÊÒÐÎÌÅÕÀÍÈÊÈ


1.1. Óðàâíåíèÿ äâèæåíèÿ. Ýëåêòðîìåõàíè÷åñêèå àíàëîãèè

Ìåõàíè÷åñêàÿ ñèñòåìà îáëàäàåò ýíåðãèåé. Ñóììàðíàÿ ýíåðãèÿ ìåõàíè÷åñêîé ñèñòåìû ñîñòîèò èç òðåõ ñîñòàâëÿþù= èõ:

·      =   êèíåòè÷åñêîé ýíåðãèè äëÿ ïîñòóïàòåëüíîãî äâèæåíèÿ è äëÿ âðàùàòåëüíîãî äâèæåíèÿ;

·      =   ïîòåíöèàëüíîé ýíåðãèåé Ï= ;

·      =   ìîùíîñòüþ ðàññåÿíèÿ (äèññèïàöèè) D.

Êèíåòè÷åñêàÿ ýíåðãèÿ - ýíåðãèÿ äâèæåíèÿ ñèñòåìû, ïîòåíöèàëüíàÿ - ýíåðãèÿ, çàïàñàåìàÿ óïðóãèìè ýëåìåíòàìè, â ÷àñòíîñòè, ïðóæèíàìè. Åñëè ïðóæèíà ðàáîòàåò íå ðàñòÿæåíèå (ñæàòèå), òî , ãäå C- æåñòêîñòü, à h-= ïåðåìåùåíèå. Åñëè ïðóæèíà ðàáîòàåò íà ñêðó÷èâàíèå, òî , ãäå = s- æåñòêîñòü, à f- óãîë ïîâîðîòà.

Ìîùíîñòü ðàññåÿíèÿ - ýòî îáû÷íî ýíåðãèÿ, çàòðà÷èâàåìàÿ íà ïðåîäîëåíèå âÿçêîãî òðåíèÿ è èëè â çàâèñèìîñòè îò ôîðìû äâèæåíèÿ.

Ïðè äâèæåíèè ñèñòåìû â íåé âîçíèêàþò ñèëû, âûçâàííûå èçìåíåíèåì ýíåðãèè ñèñòåìû ïðè èçìåíåíèè åå îáîáùåííûõ êîîðäèíàò h- ïåðåìåùåíèé èëè óãëîâ ïîâîðîòà åå ýëåìåíòîâ.

Ìåõàíè÷åñêàÿ ñèñòåìà, èìåþùàÿ = S ñòåïåíåé ñâîáîäû, îïèñûâàåòñÿ óðàâíåíèÿìè Ëàãðàíæà âòîðîãî ðîäà:

, .

Çäåñü :

·      =   - Äàëàìáåðîâû ñèëû èíåðöèè,

·      =   -ñèëû òðåíèÿ,

·      =   - ñèëû óïðóãîãî ïðîòèâîäåéñòâèÿ,

·      =   Ps- îáîáùåííûå âíåøíèå ñè= ëû (ìîìåíòû).

Íàïðèìåð, äëÿ ïðîñòåéøåé ñèñòå= ìû, èìåþùåé îäíó ñòåïåíü ñâîáîäû è ñîâåðøàþùåé âðàùàòåëüíîå äâèæåíèå, èìååì

; ;

; ; ;

Ïîëó÷èì îäíî óðàâíåíèå

.

Åñëè ìîìåíò èíåðöèè J íå çàâèñèò îò óãëà = ïîâîðîòà = f, êàê ýòî ÷àñòî áûâàåò, òî è óðàâíåíèå ïðèíèìàåò âèä:

.


1.2. Ýëåêòðîìåõàíè÷åñêèå àíàëîãèè óðàâíåíèÿ Ëàãðàíæà-Ìàêñâåëëà

Ýëåêòðîìåõàíè÷åñêàÿ ñèñòåìà îáëàäàåò íå òîëüêî ìåõàíè÷åñêîé, íî è ýëåêòðè÷åñêîé (ýëåêòðîìàãíèòíîé) ýíåðãèåé, ñîñðåäîòî÷åííîé â ýëåìåíòàõ åå ýëåêòðè÷åñêîé öåïè (èíäóêòèâíîñòÿõ, êîíäåíñàòîðàõ è ðåçèñòîðàõ).

Ïîñêîëüêó ïðîöåññû â ýëåêòðè÷å= ñêèõ öåïÿõ îïèñûâàþòñÿ òàêæå äèôôåðåíöèàëüíûìè óðàâíåíèÿìè, ñóùåñòâóþò îïðåäåëåí= íûå àíàëîãèè ìåæäó ìåõàíè÷åñêèìè è ýëåêòðè÷åñêèìè âåëè÷èíàìè, îïèñûâàþùèìè ïîâåäåíèå ñèñòåìû (ñì. òàáëèöó).

Ìåõàíè÷åñ= êàÿ ñèñòåìà

Ýëåêòðè÷å= ñêàÿ ñèñòåìà

Ïåðâàÿ ñè= ñòåìà àíàëîãèé

Âòîðàÿ ñè= ñòåìà àíàëîãèé

Ïåðåìåùåí= èå

Çàðÿä

Ïîòîêîñöå= ïëåíèå

Ñêîðîñòü = V=3Dh<= /span>`

Òîê I=3Dq`<= /p>

Íàïðÿæåíè= å U=3DΨ`

Ñèëà P

ÝÄÑ e

Òîê i

Ìàññà m

Èíäóêòèâí= îñòü L

Åìêîñòü C=

Ìåõàíè÷åñ= êîå ñîïðîòèâëåíèå r

Ñîïðîòèâë= åíèå R

Ïðîâîäèìî= ñòü G

Æåñòêîñòü C

Èíâåðñíàÿ åìêîñòü

S=3Dc-1

Èíâåðñíàÿ èíäóêòèâíîñòü Ã

Êèíåòè÷åñ= êàÿ ýíåðãèÿ

Ýíåðãèÿ ì= àãíèòíîãî ïîëÿ

Ýíåðãèÿ ýëåêòðè÷åñêîãî ïîëÿ

Ïîòåíöèàë= üíàÿ ýíåðãèÿ

Ýíåðãèÿ ýëåêòðè÷åñêîãî ïîëÿ

Ýíåðãèÿ ì= àãíèòíîãî ïîëÿ

Ìîùíîñòü = ðàññåÿíèÿ

Ìîùíîñòü = ðàññåÿíèÿ

Ìîùíîñòü = ðàññåÿíèÿ

Ïåðâàÿ ñèñòåìà àíàëîãèé ìåæäó ìåõàíè÷åñêèìè è ýëåêòðè÷åñêèìè öåïÿìè áîëåå "ôèçè= ÷íà", ïîýòîìó â îñíîâíîì 6óäåì ïîëüçîâàòüñÿ åþ, õîòÿ â íåêîòîðûõ ñëó÷àÿõ ïðèìåíåí= èå âòîðîé ñèñòåìû äàåò áîëåå ïðîñòûå óðàâíåíèÿ.

Èç ýòîé ñèñòåìû âèäíî, ÷òî ÝÄÑ= â ýëåêòðè÷åñêîé öåïè àíàëîãè÷íà ñèëå, èíäóêòèâíîñòü àíàëîãè÷íà ìàññå è îáëàäà= åò èíåðöèîííîñòüþ, è ýíåðãèÿ, çàïàñàåìàÿ â ìàãíèòíîì ïîëå, ÿâëÿåòñÿ êèíåòè÷åñêîé ýíåðãèåé. Êîíäåíñàòîð, àíàëîãè÷íî ïðóæèíå, çàïàñàåò ýíåðãèþ, êîòîðóþ ëîãè÷íî ñ÷èòàòü ïîòåíöèàëüíîé. Àêòèâíîå ñîïðîòèâëåíèå äåéñòâóåò àíàëîãè÷íî ìåõàíè÷åñêîìó âÿçêîìó ñîïðîòèâëåíèþ, è ýíåðãèÿ, âûäåëÿåìàÿ íà íåì, ðàññåèâàåòñÿ â = âèäå òåïëà.

Òîãäà ïðîñòåéøåé ìåõàíè÷åñêîé öåïè, ñîäåðæàùåé ìàññó, ïðóæèíó è âÿçêîå ñîïðîòèâëåíèå, è îïèñûâàåìîé óðàâíåíèåì âèäà

ìîæíî ïîñòàâèòü â ñîîòâåòñòâèå ïðîñòåéøóþ ýëåêòðè÷åñêóþ öåïü ñ ïîñëåäîâàòåëüíî âêëþ÷åí= íûìè èíäóêòèâíîñòüþ, åìêîñòüþ è ñîïðîòèâëåíèåì, îïèñûâàåìóþ óðàâíåíèåì

ãäå L·q``- ÝÄÑ ñàìîèíäóêöèè, R·q`- ïàäåíèå íàïðÿæåíèÿ íà ñîïðîòèâëåíèè, S·q- íàïðÿæåíèå íà åìêîñòè.

 ýëåêòðîòåõíèêå îáû÷íî ýòî óðàâíåíèå çàïèñûâàåòñÿ â âèäå:

Ýëåêòðîìåõàíè÷åñêóþ ñèñòåìó, èìåþùóþ Sm<= /span> ñòåïåíåé ìåõàíè÷åñêîé ñâîáîäû è S1 íåçàâèñèìûõ ýëåêòðè÷åñêèõ êîíòóðîâ, ó÷èòûâàÿ ýëåêòðîìåõàíè÷åñêèå àíàëîãèè, ìîæíî ïðåäñòàâèòü â âèäå ìåõàíè÷åñêîé ñèñòåìû, èìåþùåé Sm+S1 ñòåïåíåé ñâîáîäû è î= áëàäàþùåé

·      =   ñóììàðíîé ýëåêòðîìåõàíè÷åñêîé êèíåòè÷åñêîé ýíåðãèåé TΣ<= /sub>=3DTM+WM;

·      =   ïîòåíöèàëüíîé ýíåðãèåé Ï= Σ=3DÏ= Ì+WÝ;

·      =   ìîùíîñòüþ ðàññåÿíèÿ DΣ=3DDM+= DÝ.=

Îòñþäà äâèæåíèå â òàêîé ñèñòåìå áóäåò îïèñûâàòüñÿ óðàâíåíèÿìè, àíàëîãè÷íûìè óðàâíåíèÿì Ëàãðàíæà è íàçûâàåìû= ìè óðàâíåíèÿìè Ëàãðàíæà-Ìàêñâåëëà :

,

Ïåðâûå Sm óðàâíåíèé îïèñûâàþò ìåõàíè÷åñêèå äâèæåíèÿ â ñèñòåìå (ìåõàíè÷åñêèå óðàâíåíèÿ), ïîñëåäóþùèå S1 óðàâíåí= èé îïèñûâàþò ïðîöåññû â ýëåêòðè÷åñêèõ öåïÿõ (ýëåêòðè÷åñêèå óðàâíåíèÿ - óðàâíåí= èÿ 2-ãî çàêîíà Êèðõãîôà).


1.3. Ýíåðãèÿ ýëåêòðè÷åñêîãî è ìàãíèòíîãî ïîëåé. Ñèëû è ìîìåíòû, âîçíèêàþùèå ïðè ýëåêòðîìåõàíè÷åñêîì ïðåîáðàçîâàíèè ýíåðãèè

 îáùåì âèäå ýíåðãèÿ ýëåêòðè÷åñêîãî ïîëÿ â îáúåìå V âûðàæàåò= ñÿ èíòåãðàëîì

,

ãäå E- âåêòîð íàïðÿæåííîñòè ýëåêòðè÷åñ= êîãî ïîëÿ, D- âåêòîð ñìåùåíèÿ.

Äëÿ îäíîðîäíîãî ïîëÿ â êîíäåíñàòîðå

Ýíåðãèÿ ìàãíèòíîãî íîëÿ â îáúå= ìå V òàêæå âûðàæàåòñÿ èí= òåãðàëîì

ãäå B- âåêòîð ìàãíèòíîé èíäóêöèè, H- âåêòîð íàïðÿæåííîñ= òè ìàãíèòíîãî ïîëÿ.

Äëÿ îäíîðîäíîãî ìàãíèòíîãî ïîë= ÿ

Äëÿ n ìàãíèòíî ñâÿ= çàííûõ êîíòóðîâ ñ òîêàìè ïîëó÷èì:

,

ãäå Ljk- èíäóêòèâíîñòè è âç= àèìíûå èíäóêòèâíîñòè êîíòóðîâ

Èëè , ãäå = Yj- ïîòîêîñöåïëå= íèå êîíòóðîâ.

Òîãäà äëÿ îäèíî÷íîãî êîíòóðà ñ òîêîì èìååì:

äëÿ äâóõ êîíòóðîâ: ;

äëÿ êîíòóðà ñ òîêîì, ïîìåùåííî= ãî â ìàãíèòíûé ïîòîê Φ: ,

ãäå L- èíäóêòèâíîñòü êîíòóðà, Y- ïîòîêîñöåïëåíèå âíåøíåãî ïîòîêà F ñ êîíòóðîì.

Ðàññìîòðèì ãèïîòåòè÷åñêóþ ýëåêòðîìåõàíè÷åñêóþ ñèñòåìó. â êîòîðîé ìåõàíè÷åñêè ñâÿçàíû êîíòóð ñ òîêîì, ïîìåùåííûé â ìàãíèòíîå ïîëå, è = ðîòîð êîíäåíñàòîðà, ïðè÷åì ïðè ïîâîðîòå ïðîèñõîäèò èçìåíåíèå èíäóêòèâíîñòè êîíòóð= à, ïîòîêîñöåïëåíèÿ ñ êîíòóðîì è åìêîñòè êîíäåíñàòîðà.

Îáùàÿ êèíåòè÷åñêàÿ ýíåðãèÿ òàê= îé ñèñòåìû áóäåò:

;

ïîòåíöèàëüíàÿ

;

ðàññåÿíèÿ

Ïîäñòàâëÿÿ ýòî âûðàæåíèå â óðàâíåíèå Ëàãðàíæà-Ìàêñâåëëà è ïðèíèìàÿ çà îáîáùåííóþ êîîðäèíàòó h- óãîë ïîâîðîòà f, à òàêæå ñ÷èòàÿ, ÷òî âíåøíÿÿ ñèëà îòñóòñòâóåò, ïîëó÷èì = äâà óðàâíåíèÿ - ìåõàíè÷åñêîå è ýëåêòðè÷åñêîå

Èç ïåðâîãî (ìåõàíè÷åñêîãî) óðàâíåíèÿ ïîëó÷àåì ñèëû (â äàííîì ñëó÷àå - ìîìåíòû), âîçíèêàþùèå ïðè ýëåêòðîìåõàíè÷åñêîì ïðåîáðàçîâàíèè ýíåðãèè :

·      =   - ñèëà (ìîìåíò), âûçâàííàÿ èçìåíåíèåì èíäóêòèâíîñòè îò èçìåíåíèÿ êîîðäèíàòû (óãëà ïîâîðîòà) - çëåêòðîìàãíèòíàÿ ñ= èëà,

·      =   - ñèëà (ìîìåíò), äåéñòâóþùàÿ íà ïðîâîäíèê (êîíòóð) ñ òàêîì, ïîìåùåííûé â ìàãíèòíûé ïîòîê,- ìàãíèòîýëåêòðè÷å= ñêèé ìîìåíò,

·      =   - ñèëà (ìîìåíò), âûçâàííàÿ ýëåêòðè÷åñêèì ïîëåì ïðè ìåõàíè÷åñêîì èçìåíåíèè åìêîñòè êîíäåíñàòîðà .

Ðåàëüíî â òåõíèêå ïðèìåíÿþòñÿ ïðåîáðàçîâàòåëè, â êîòîðûõ äåéñòâóåò òîëüêî îäíà èç ïåðå÷èñëåííûõ ñèë - ýëåêòðîìàãíèòíûå, ìàãíèòîýëåêòðè÷åñêèå, ýëåêòðîñòàòè÷åñêèå.

Ñëàãàåìûå âòîðîãî, ýëåêòðè÷åñê= îãî óðàâíåíèÿ ÿâëÿþòñÿ ýëåêòðè÷åñêèìè ðåàêöèÿìè ñèñòåìû:

·      =   - ïðîòèâîÝÄÑ, âûçâàííàÿ èçìåíåíèåì èíäóêòèâíîñòè ïðè ïîâîðîòå êîíòóðà ñ òîêîì (åñëè èíäóêòèâíîñòü èçìåíÿåòñÿ, = ÷òî ïðîèñõîäèò íå âñåãäà);

·      =   - ÝÄÑ èíäóêöèè, âûçâàííàÿ âðàùåíèåì êî= íòóðà â ìàãíèòíîì ïîëå;

·      =   - ÝÄÑ ñàìîèíäóêöèè;

·      =   - íàïðÿæåíèå êîíäåíñàòîðà;

·      =   R·i- ïàäåíèå íàïðÿæåíèÿ= íà ñîïðîòèâëåíèè.

Ýêâèâàëåíòíàÿ ñõåìà ýëåêòðè÷åñ= êîé öåïè òàêîé ñèñòåìû èìååò âèä íà .

Ðèñ. 1-1. Ýêâèâàëåíòíàÿ ñõåìà ãèïîòåòè÷åñêîé ýëåêòðîìåõàíè÷åñêîé ñèñòåìû


1.4. Ýëåêòðîìàãíèòíûå, ýëåêòðîäèíàìè÷åñêèå è ýëåêòðîñòàòè÷åñêèå ïðåîáðàçîâàòåëè.=

·      =   1.4= .1. Ýëåêòðîìàãíèòíûå ïðåîáðàçîâàòåëè.

·      =   1.4= .2. Ýëåêòðîäèíàìè÷åñêèå ïðåîáðàçîâàòåëè.

·      =   1.4= .3. Ýëåêòðîñòàòè÷åñêèå ïðåîáðàçîâàòåëè.


1.4.1. Ýëåêòðîìàãíèòíûå ïðåîáðàçîâàòåëè.

 ýëåêòðîìàãíèòíîì ïðåîáðàçîâà= òåëå óñèëèå ñîçäàåòñÿ çà ñ÷åò èçìåíåíèÿ ìàãíèòíîé ýíåðãèè, çàïàñåííîé â êàòóøêå èíäóêòèâíîñòè L ïðè ïåðåìåùåíèè ñåðäå÷íèêà. Ìàãíèòíàÿ è <= span class=3DGramE>ýíåðãèÿ è ýíåðãèÿ ðàññåÿíèÿ èìåþò ñëåäóþùèé âèä:

,

 ýòèõ ñèñòåìàõ , ïîýòîìó äèôôåðåíöèàëüíûå óðàâíåíèÿ èìåþò âèä (ïðè îòñóòñòâèè âíåøíåé ñèëû):

;

Òèïè÷íûì ïðåîáðàçîâàòåëåì òàêî= ãî òèïà ÿâëÿåòñÿ ýëåêòðîìàãíèòíîå ðåëå, ñõåìà êîòîðîãî ïðèâåäåíà íà .

Ðèñ. 1-2. Ýëåêòðîìàãíèòíîå ðåëå.

Ðåëå ïðåäñòàâëÿåò ñîáîé ýëåêòðîìàãíèò ñ êîíòàêòàìè Ê. Ïðè ïîäà÷å íàïðÿæåíèÿ U íà îáìîòêó ýëåêòðîìàãíèòà, èìåþù= óþ èíäóêòèâíîñòü L= è àêòèâíîå ñîïðîòèâëåíèå R ñîçäàåòñÿ ýëåêòðîìàãíèòíîå òÿãîâîå óñèëèå , êîòîðîå ïðèòÿãèâàåò ÿêîðü Ð, èçìåíÿÿ= åãî ïîëîæåíèå îòíîñèòåëüíî ñåðäå÷íèêà 1 (êîîðäèíàòó hîò 0 äî d), ïðè ýòîì ïðîèñõîäèò ïåðåêëþ÷åíèå êîíòàêòîâ Ê.

Èç àíàëèçà äèôôåðåíöèàëüíûõ óðàâíåíèé èìååì:

·      =   m·h``- ñèëà èíåðöèè,

·      =   r·h`- ñèëà âÿçêîãî ñîïðîòèâëåíèÿ, êîòîðîé â ðåëå ìîæíî ïðåíåáðå÷ü,

·      =   c·h- ñèëà ñîïðîòèâëåíèÿ âîçâðàòíîé ïðóæèíû ÂÏ, èìåþùåé æåñòêîñòü Ñ,

·      =   - òÿãîâîå óñèëèå,

·      =   - ÝÄÑ, âûçâàííàÿ èçìåíåíèåì èíäóêòèâíî= ñòè ïðè ïåðåìåùåíèè ÿêîðÿ,

·      =   - ÝÄÑ, âûçâàííàÿ èçìåíåíèåì òîêà,

·      =   R·i- ïàäåíèå íàïðÿæåíèÿ= íà àêòèâíîì ñîïðîòèâëåíèè îáìîòêè ðåëå.

Èòàê, òÿãîâîå óñèëèå ðåëå îïðåäåëÿåòñÿ èçìåíåíèåì èíäóêòèâíîñòè L ïðè ïåðåìåùåíèè ÿêîðÿ. Ïðè ïîêàçàííîé í= à êîíñòðóêöèè ðåëå (êëàïàííîãî òèïà) è ìàëîì ïåðåìåùåíèè ÿêîðÿ ìîæíî ñ÷èòàòü, ÷òî

.

Òîãäà , îòêóäà , ãäå .

Ïðè âêëþ÷åíèè ðåïå íà ïîñòîÿíí= îå íàïðÿæåíèå, êàê ýòà îáû÷íî áûâàåò, ïðîöåññ îïèñûâàåòñÿ íåëèíåéíûìè äèôôåðåíöèàëüíûìè óðàâíåíèÿìè:

, ãäå

Òîãäà òàê íàçûâàåìûå òÿãîâûå õàðàêòåðèñòèêè ðåëå èìåþò âèä íà .

Ðèñ. 1-3à. Ìåõàíè÷åñêèå õàðàêòåðèñòèêè ýëåêòðîìàãíèòíîãî ðåëå

Õàðàêòåðèñòèêè âõîä-âûõîä èìåþò ñêà÷êîîáðàçíûé õàðàêòåð ( ).

Ðèñ. 1-3á. Õàðàêòåðèñòèêè "âõîä-âûõîä" ýëåêòðîìàãíèòíîãî ðåëå.

Ïåðåõîäíûé ïðîöåññ ïðè âêëþ÷åí= èè ðåëå ïîêàçàí íà .

Ðèñ. 1-4. Ïåðåõîäíûé ïðîöåññ ïðè âêëþ÷åíèè ðåëå.

Ìîäåëü ýëåêòðîìàãíèòíîãî ðåëå ïðèâåäåíà â  .


1.4.2. Ýëåêòðîäèíàìè÷åñ= êèå ïðåîáðàçîâàòåëè.

 ìàãíèòîýëåêòðè÷åñêîé (ýëåêòðîäèíàìè÷åñêîé) ñèñòåìå óñèëèå ñîçäàåòñÿ çà ñ÷åò èçìåíåíèÿ âòîðîé ñîñòàâëÿþùåé ìàãíèòíîé ýíåðãèè Y(h)×i. Òî åñòü óðàâíåíèÿ èìåþò ñëåäóþùèé âèä:

;

Ýëåêòðîäèíàìè÷åñêèé ïðèíöèï ïðåîáðàçîâàíèÿ ýíåðãèè èñïîëüçóåòñÿ â ýëåêòðîèçìåðèòåëüíûõ ïðèáîðàõ, ñîäåðæ= àùèõ ïîñòîÿííûé ìàãíèò, äâèãàòåëÿõ ïîñòîÿííîãî òîêà, òàõîãåíåðàòîðàõ ïîñòîÿííîãî òîêà.  ýòèõ óñòðîéñòâàõ îáîáùåííîé õàðàêòåðèñòèêîé ÿâë= ÿåòñÿ óãîë ïîâîðîòà ðîòîðà f è óðàâíåíèÿ èìåþò âèä:

;

Îáû÷íî îáîçíà÷àþò óãëîâóþ ÷àñò= îòó âðàùåíèÿ , òîãäà

;

Çäåñü

·      =   - ìîìåíò ñîïðîòèâëåíèÿ, âûçâàííûé ìåõàíè÷åñêîé èíåðöèîííîñòüþ ñèñ= òåìû (I - ìîìåíò èíå= ðöèè ñèñòåìû),

·      =   ρ·ω- ì= îìåíò âÿçêîãî ñîïðîòèâëåíèÿ,

·      =   σ·f- ìîìåíò óïðóãîãî ñîïðîòèâëåíèÿ,

·      =   - âðàùàþùèé ìîìåíò,

·      =   Mc- ñòàòè÷åñêèé ìîìåíò ñîïðîòèâëåíèÿ,

·      =   - ÝÄÑ èíäóêöèè (âðàùåíèÿ),

·      =   - ÝÄÑ ñàìîèíäóêöèè,

·      =   R·i- ïàäåíèå íàïðÿæåíèÿ= íà àêòèâíîì ñîïðîòèâëåíèè.

Ïðè ïðèìåíåíèè ïðåîáðàçîâàòåëÿ= êàê èñïîëíèòåëüíîãî óñòðîéñòâà (èçìåðèòåëüíîãî ïðèáîðà) èñïîëüçóåòñÿ ôàêò âîçíèêíîâåíèÿ ìàãíèòîýëåêòðè÷åñêîãî âðàùàþùåãî ìîìåíòà, ïðîïîðöèîíàëüíîãî ò= îêó â öåïè ðîòîðà. Ïðè ïðèìåíåíèè åãî êàê äàò÷èêà ñêîðîñòè èñïîëüçóåòñÿ âîçíèêíîâåíèå â öåïè ÝÄÑ èíäóêöèè, ïðîïîðöèîíàëüíîé ÷àñòîòå âðàùåíèÿ ðîòîðà= .  ýòîì ñëó÷àå ýëåêòðè÷åñêîå óðàâíåíèå ïðåîáðàçîâàòåëÿ èìååò âèä :

È â óñòàíîâèâøåìñÿ ðåæèìå, êîã= äà , èìååì .

 ÷àñòíîñòè, ïðè ïîâîðîòå â ìàãíèòíîì ïîëå ñ èíäóêöèåé B ðàìêè äëèíîé 1 è ðàäèóñîì r èìååì =3Dr·ω·B·1·r·d= f, îòêóäà .

Îñíîâíûì äîñòîèíñòâîì ýëåêòðîäèíàìè÷åñêèõ ñèñòåì ÿâëÿåòñÿ ëèíåéíîñòü èõ õàðàêòåðèñòèê.



1.4.3. Ýëåêòðîñòàòè÷åñêèå ïðåîáðàçîâàòåëè.

 ýëåêòðîñòàòè÷åñêèõ ñèñòåìàõ èñïîëüçóåòñÿ ýíåðãèÿ ýëåêòðè÷åñêîãî ïîëÿ, çàïàñåííàÿ â êîíäåíñàòîðå

;

 ýòîì ñëó÷àå äèôôåðåíöèàëüíûå óðàâíåíèÿ òàêîâû:

;

Çäåñü - òÿãîâîå óñèëèå, S×q- íàïðÿæåíèå íà êîíäåíñàòîðå .

Ýòè óðàâíåíèÿ èìåþò ìåíüøå ñëàãàåìûõ, ÷åì óðàâíåíèÿ èíäóêöèîííûõ ñèñòåì, ïîýòîìó ýëåêòðîñòàòè÷åñêèå ïðåîáðàçîâàòåëè îáëàäàþò ìåíüøèìè âîçìîæíîñòÿìè è ïîëó÷èëè ìåíüøåå ðàñïðîñòðàíåíèå.

Èñïîëíèòåëüíûå óñòðîéñòâà ýëåêòðîñòàòè÷åñêîãî òèïà î÷åíü ìàëîìîùíû, òàê êàê ýëåêòðè÷åñêîå ïîëå â åäèí= èöå îáúåìà ìîæåò ñêîíöåíòðèðîâàòü ãîðàçäî ìåíüøå ýíåðãèè, ÷åì ìàãíèòíîå. Ïîýòîìó òÿãîâîå óñèëèå ñðàâíèòåëüíî íåáîëüøîå. Èñïîëíèòåëüíûå óñòðîéñòâà òàêîãî òèïà ïðèìåíÿþòñÿ â îñíîâíîì êàê èçìåðèòåëüíûå è èíäèêàòîðíûå.

Âîçìîæíîñòè ýëåêòðîñòàòè÷åñêîãî ïðåîáðàçîâàòåëÿ êàê äàò÷èêà, êàê âèäíî èç ýëåêòðè÷åñêîãî óðàâíåíèÿ, òàêæå îãðàíè÷åíû, òàê êàê îí íå ìîæåò èíäóöèðîâàòü ÝÄÑ= è ÿâëÿåòñÿ, ïî ñóùåñòâó, ïàññèâíûì åìêîñòíûì äàò÷èêîì ñ óðàâíåíèåì âèäà:

Îáîçíà÷èâ Uc- íàïðÿæåíèå íà êîíäåíñàòîðå, ïîëó÷èì :

Ïàññèâíûé = åìêîñòíîé ïðåîáðàçîâàòåëü ïåðåìåííîãî òîêà.


1.5. Êëàññèôèêàöèÿ ýëåêòðîìåõàíè÷åñêèõ ïðåîáðàçîâàòåëåé

Ýëåêòðîìåõàíè÷åñêèå ïðåîáðàçîâàòåëè, ïðèìåíÿåìûå â ñèñòåìàõ àâòîìàòèêè è âû÷èñëèòåëüíîé òåõíèêå, ìîæíî êëàññèôèöèðîâàòü ïî íàçíà÷åíèþ, êîíñòðóêòèâíîìó èñïîëíåíèþ è ïðèíöèïó äåéñòâèÿ (ñì. ).

Ðèñ. 1-5. Êëàññèôèêàöèÿ ýëåêòðîìåõàíè÷åñêèõ ïðåîáðàçîâàòåë= åé.


1.6. Ïðåäñòàâëåíèå ýëåêòðîìåõàíè÷åñêèõ ïðåîáðàçîâàòåëåé êàê ïðåîáðàçîâàòåëåé ñèãíàëîâ (èíôîðìàöèè)

Ïðè ïðèìåíåíèè ýëåêòðîìåõàíè÷å= ñêèõ ïðåîáðàçîâàòåëåé â ñèñòåìàõ àâòîìàòè÷åñêîãî óïðàâëåíèÿ îíè ðàññìàòðèâàþòñÿ = íå êàê ýíåðãåòè÷åñêèå óñòðîéñòâà, à êàê èíôîðìàöèîííûå ïðåîáðàçîâàòåëè ñèãíàëîâ ïðè èõ ïðîõîæäåíèè îò âõîäîâ ê âûõîäàì (ñì. ).

<= /span>

Ðèñ. 1-6à. Ôóíêöèîíàëüíàÿ ñõåìà äèíàìè÷åñêîé ñèñòåìû.

Åñëè ýëåêòðîìåõàíè÷åñêèé ïðåîáðàçîâàòåëü îïèñûâàåòñÿ èñõîäíûìè ëèíåéíûìè èëè ëèíåàðèçîâàííûìè äèôôåðåíöèàëüíûìè óðàâíåíèÿìè, òî îò íèõ ìîæíî ïåðåéòè ê äèôôåðåíöèàëüíûì óðàâíåíèÿì "âõîä-âûõîä" âèäà

ãäå y(t) è u(t) - âåêòîðû âûõîäíûõ= è âõîäíûõ êîîðäèíàò

; - ïîëèíîìèàëüíûå ìàòðèöû,

- îïåðàòîð äèôôåðåíöèðîâàíèÿ ïî âðåìåíè.

Ïåðåéòè îò èñõîäíûõ ýíåðãåòè÷å= ñêèõ óðàâíåíèé ê óðàâíåíèÿì "âõîä-âûõîä" óäîáíî, èñïîëüçóÿ ñòðóêòóðíûå ñõåìû è ïåðåäàòî÷íûå ôóíêöèè. Òèïè÷íàÿ ñòðóêòóðíàÿ ñõåìà èìååò âèä, ïðåäñòàâëåííûé íà , ãäå W(p) - ïåðåäàòî÷íûå ôóí= êöèè, à u(p), y(p), i(p) - èçîáðàæåíèÿ âõîäíûõ, âûõîäíûõ= è âíóòðåííèõ ïåðåìåííûõ (p=3Dc+j·= ;ω).

Ðèñ. 1-6á. Ñòðóêòóðíàÿ ñõåìà äèíàìè÷åñêîé ñèñòåìû.

Óðàâíåíèå "âõîä-âûõîä&quo= t; ïîëó÷èì â âèäå:

,

ãäå

Ñòðóêòóðíàÿ ñõåìà òåñíî ñâÿçàí= à ñ ôèçèêîé ðàáîòû ïðåîáðàçîâàòåëÿ è ïîýòîìó ëåãêî ìîæåò áûòü ñîñòàâëåíà ïî èñõîäíûì ýíåðãåòè÷åñêèì óðàâíåíèÿì, à óðàâíåíèÿ "âõîä-âûõîä" ïðåäñòàâëÿþò áîëåå àáñòðàêòíóþ ìîäåëü ñèñòåìû.

Ìîæíî ïåðåéòè ê åùå áîëåå àáñòðàêòíîé ìîäåëè - óðàâíåíèÿì ñîñòîÿíèÿ, êîãäà ñèñòåìà ïðåäñòàâëÿåòñÿ ñòàíäàðòíîé ñòðóêòóðîé â âèäå àâòîìàòà ñ ïàìÿòüþ ( ).

Ðèñ. 1-7à. Ñòðóêòóðíàÿ ñõåìà äèíàìè÷åñêîé ñèñòåìû â âèäå íåïðåðûâíîãî àâòîìàòà.<= /p>

;

,

ãäå x- âåêòîð ñîñòîÿíèÿ, A- ìàòðèöà êîýôôèöèåíòîâ, B- ìàòðèöà óïðàâëåíèÿ= , C- ìàòðèöà âûõîäà, D - ìàòðèöà îáõîäà. <= /p>

 ýòîé ñòðóêòóðå ïåðåìåííûå ñîñòîÿíèÿ ÷àñòî íå ÿâëÿþòñÿ ôèçè÷åñêèìè âåëè÷èíàìè, êîòîðûå ìîãóò áûòü èçìå= ðåíû â ðåàëüíîé ñèñòåìå.

Äëÿ ìîäåëèðîâàíèÿ ýëåêòðîìåõàíè÷åñêîé ñèñòåìû íà ÝÂÌ èëè ïðè óïðàâëåíèè å= þ îò ÝÂÌ óäîáíî ýòó ñèñòåìó ïðåäñòàâèòü êàê äèñêðåòíóþ ïî âðåìåíè (èìïóëüñíóþ), â êîòîðîé åå ïåðåìåííûå íàáëþäàþòñÿ (âû÷èñëÿþòñÿ) ÷åðåç äèñêðåòíûå ïðîìåæóòêè âðåìåíè Ò. Ïðè âûáîðå Ò äîñòàòî÷íî ìàëîì ïî ñðàâíåíèþ ñ èíåðöèîííîñòüþ ñèñò= åìû, äèñêðåòíàÿ ìîäåëü äîñòàòî÷íî òî÷íî îïèñûâàåò íåïðåðûâíóþ ñèñòåìó.

Äëÿ àíàëèçà äèñêðåòíîé ìîäåëè ââîäèòñÿ àïïàðàò äèñêðåòíîãî ïðåîáðàçîâàíèÿ Ëàïëàñà è äèñêðåòíûå ïåðåäàòî÷í= ûå ôóíêöèè D(Z), ãäå Z- îïåðàòîð çàïàçäûâàíèÿ íà èíòåðâ= àë Ò .

Ïðè äîñòàòî÷íî ìàëîì Ò ìîæíî ïðèíÿòü .

Èìåÿ ïåðåäàòî÷íóþ ôóíêöèþ ñèñò= åìû W(P), çàìåíîé ïîëó÷èì D(Z) â âèäå

,

ãäå Z-1- çàïàçäûâàíèå íà îä= èí òàêò (âðåìÿ Ò). Ýòîé ôóíêöèè ñîîòâåòñòâóåò ðàçíîñòíîå óðàâíåíèå "âõîä-âûõîä"

Ýòîé ìîäåëè ñîîòâåòñòâóåò äèñêðåòíûé ðåêóðñèâíûé ôèëüòð âèäà , ãäå À è Â îëèíîìèàëüíûå ìàòðèöû, à Ò - ìàòðèöà çàäåðæåê òàêòîâ.

Ðèñ. 1-7á. Ñòðóêòóðíàÿ ñõåìà äèíàìè÷åñêîé ñèñòåìû â âèäå äèñêðåòíîãî àâòîìàòà.

Ïî ñõåìå ðåêóðñèâíîãî ôèëüòðà ìîæåò áûòü âîññòàíîâëåí àëãîðèòì âû÷èñëåíèÿ âûõîäíîé âåëè÷èíû y(n) â äàííîì òàêòå, çíàÿ y(n-i) â ïðåäûäóùèå òàêòû= , è çíà÷åíèÿ âõîäíîãî âîçäåéñòâèÿ u(n) â äàííûé òàêò è u(n-i) â ïðåäûäóùèå òàêòû - ïðÿìîå ïðîãðàììèðîâàíèå. Ïðèìåíÿþòñÿ òàêæå ïîñëåäîâàòåëüíîå è ïàðàëëåëüíîå ïðîãðàììèðîâàíèå, êîãäà D(Z) ïðåäñòàâëÿåòñÿ â âèäå ïðîèçâåäåíèÿ èëè ñóììû áîëåå ïðîñòûõ ôóíêöèé.

Îò ðàçíîñòíûõ óðàâíåíèé "= âõîä-âûõîä" ìîæíî ïåðåéòè ê óðàâíåíèÿì ïðîñòðàíñòâà ñîñòîÿíèé è ïðåäñòàâèòü ñèñòåìó â â= èäå äèñêðåòíîãî àâòîìàòà ñ ïàìÿòüþ â âèäå .

;

ãäå x[n] - ñîñòîÿíèå â äàííûé òàêò, x<= /span>[n+1] - ñîñòîÿíèå â ñëåäóþùèé òàêò.

Óäîáíîé ìîäåëüþ äëÿ àíàëèçà äèíàìè÷åñêîé ñèñòåìû ÿâëÿåòñÿ ÷àñòîòíàÿ õàðàêòåðèñòèêà

êîòîðàÿ îáû÷íî ïðåäñòàâëÿåòñÿ â âèäå äâóõ õàðàêòåðèñòèê, àìïëèòóäíîé A(ω) è ôàçîâîé = f(= ω).


1.7. Àíàëèç ïðîñòåéøåãî ýëåêòðîìåõàíè÷åñêîãî ïðåîáðàçîâàòåëÿ. =

Ðàññìîòðèì ïðîñòåéøèé ìàãíèòîýëåêòðè÷åñêèé ïðåîáðàçîâàòåëü, èìåþùèé îäíó ñòåïåíü ìåõàíè÷åñêîé í ýëåêòðè÷åñêîé ñâîáîäû, â êà÷åñòâå êîòîðîãî ìîæåò áûòü ïðèâåäåí ëèíåéíûé èñïîëíèòåëüíûé äâèãàòåëü, ïðèìåíÿåìûé â ñèñòå= ìå ïîçèöèîíèðîâàíèÿ â íàêîïèòåëÿõ íà æåñòêèõ äèñêàõ ÑÌ-ÝÂÌ.

Åãî äèíàìèêà îïèñûâàåòñÿ äâóìÿ óðàâíåíèÿìè:

Ìîäåëü òàêîãî ïðåîáðàçîâàòåëÿ ïðèâåäåíà íà  è .

Îáîçíà÷èâ è , ïîëó÷èì ýòè óðàâíåíèÿ â îïåðàòîðíîé ôîðìå:

Ïåðåéäÿ ê èçîáðàæåíèÿì, ïîëó÷èì ñëåäóþùèå óðàâíåíèÿ:

Ïî ýòèì óðàâíåíèÿì ìîæíî ïîëó÷= èòü ñòðóêòóðíóþ ñõåìó ñîãëàñíî , ïî êîòîðîé ìîæíî ïîëó÷èòü ïåðåäàòî÷íóþ ôóíêöèþ

ãäå ; ; =

Ðèñ. 1-8. Ñòðóêòóðíàÿ ñõåìà ýëåêòðîìåõàíè÷åñêîãî ïðåîáðàçîâàòåëÿ.

Ïåðåéäÿ îáðàòíî âî âðåìåííóþ îáëàñòü, ìîæíî ïîëó÷èòü óðàâíåíèå "âõîä-âûõîä"

, ãäå

Äëÿ ïåðåõîäà ê óðàâíåíèÿì ñîñòîÿíèÿ ïðåäñòàâèì óðàâíåíèå âõîä-âûõîä â ñêîáî÷íîé ôîðìå

Ââåäåì íîâûå êîîðäèíàòû, ñîîòâåòñòâóþùèå ïåðåìåùåííûì â êâàäðàòíûõ ñêîáêà= õ è ïîëó÷èì äèôôåðåíöèàëüíî-àëãåáðàè÷åñêóþ ñèñòåìó (ñëåâà) è åå ïðåîáðàçîâàííóþ ôîðìó (ñïðàâà)

Ýòèì óðàâíåíèÿì ñîîòâåòñòâóåò ñòðóêòóðà, ïîêàçàííàÿ íà .

Ðèñ. 1-9. Ñòðóêòóðíàÿ ñõåìà ïðåîáðàçîâàòåëÿ â ïðîñòðàíñòâå ñîñòîÿ= íèÿ.

Ïðè ïåðåõîäå ê óðàâíåíèÿì ñîñòîÿíèÿ ïîëó÷èì x`=3DA·x+B·u; h=3DC·x+u,

ãäå u=3DU; ; ; ; ; D= =3D0.

Ïðè äîñòàòî÷íî ìàëîì ïåðèîäå êâàíòîâàíèÿ Ò ïî ñðàâ= íåíèþ ñ èíåðöèîííîñòüþ ñèñòåìû åå ìîæíî ïðåäñòàâèòü êàê äèñêðåòíóþ (ïî âðåìåíè) ñ äèñêðåòíîé ïåðåäàòî÷íîé ôóíêöèåé

Ïðîèçâåäÿ íåîáõîäèìûå ïðåîáðàçîâàíèÿ, ïîëó÷èì

ãäå ; ; B1=3DB2=3D3·B0; B3=3DB0.

Îáîçíà÷èì h`=3Dh·K0-1.Òîãäà èç âûðàæåíèÿ ïîëó÷èì ðàçíîñòíîå óðàâíåíèå "âõîä-âûõîä":

Ýòîìó óðàâíåíèþ ñîîòâåòñòâóåò ñòðóêòóðà ðåêóðñèâíîãî ôèëüòðà, ïðåäñòàâëåííàÿ íà .

Ðèñ. 1-10à. Ñòðóêòóðíàÿ ñõåìà ïðåîáðàçîâàòåëÿ â âèäå ðåêóðñèâíîãî ôèëüòðà.

Èñïîëüçóÿ, íàïðèìåð, ïðÿìîå ïðîãðàììèðîâàíèå, ìîæíî ìîäåëèðîâàòü ñèñòåìó íà ÝÂÌ, âû÷èñëÿÿ çíà÷åíèÿ âûõî= äíîé âåëè÷èíû h(n) ïî øàãàì. Ñêàæåì, ïåðåõîäíóþ ôóíêöèþ ïðè ñòóïåí÷àòîì âîçäåéñòâèè

U(n)=3DU ïðè n>0 (ñì. )

<= /span>

Ðèñ. 1-10á. Âûõîä ïðåîáðàçîâàòåëÿ ïðè ñòóïåí÷àòîì âîçäåéñòâèè.

è.ò.ä.

Îò ðàçíîñòíîãî óðàâíåíèÿ âõîä-âûõîä ìîæíî ïåðåéòè ê óðàâíåíèÿì ñîñòîÿíèÿ è ïðåäñòàâèòü ñèñòåìó â âèä= å äèñêðåòíîãî àâòîìàòà ñ ïàìÿòüþ

;

·      =   X(n) - âåêòîð ñîñòîÿíèÿ= àâòîìàòà â äàííûé äèñêðåòíûé ìîìåíò âðåìåíè,

·      =   X(n+1) - âåêòîð ñîñòîÿí= èÿ â ñëåäóþùèé íàáëþäàåìûé ìîìåíò ÷åðåç ïðîìåæóòîê âðåìåíè Ò,

·      =   B- ìàòðèöà âõîäíîãî ïðåîáðàçîâàíèÿ,

·      =   A- ìàòðèöà, ðåàëèçóþùàÿ ôóíêöèþ ïåðåõîäîâ,

·      =   C- ìàòðèöà, ñîîòâåòñòâóþùàÿ ôóíêöèè âûõîäîâ.

×àñòîòíàÿ õàðàêòåðèñòèêà ñèñòå= ìû

 ýòîì ñëó÷àå, åñëè õàðàêòåðèñòè÷åñêîå óðàâíåíèå èìååò âåùåñòâåííûå îòðèöàòåëüíûå êîðíè, ïîëó÷è= ì

ãäå T1·T2·T3=3Da0; T1·T2+T1·T3+T2·T3=3Da1; T1+T2+T3=3Da2, à êîðíè α1=3D-T1-1; α2=3D= -T2-1<= /sup>; α3=3D= -T3-1<= /sup>.

Òîãäà àìïëèòóäíàÿ ÷àñòîòíàÿ õàðàêòåðèñòèêà áóäåò (ñì. )

<= /span>

Ðèñ. 1-11. ×àñòîòíàÿ õàðàêòåðèñòèêà ýëåêòðîìåõàíè÷åñêîãî ïðåîáðàçîâàòåëÿ.


1.8. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 1.

1.      Ïåðå÷èñëèòå îñíîâíûå ìåõàíè÷åñêèå àíàëîãèè, äîï= îëíèâ êîëîíêè 1 è 2 òàáëèöû 1-1 ðàçìåðíîñòÿìè ïðåäñòàâëåííûõ â íèõ ôèçè÷åñêèõ âåëè÷èí.

2.      Âûâåäèòå óðàâíåíèÿ äèíàìèêè ïðîñòåéøèõ ìåõàíè÷å= ñêîé è ýëåêòðîìåõàíè÷åñêîé ñèñòåì èç óðàâíåíèé Ëàãðàíæà-Ìàêñâåëëà. Íàðèñóéòå ñõåìû, ñîîòâåòñòâóþùèå ýòèì óðàâíåíèÿì.

3.      Ïåðå÷èñëèòå îñíîâíûå òèïû ýëåêòðîìåõàíè÷åñêèõ ï= ðåîáðàçîâàòåëåé è ïðèâåäèòå ïðèìåðû ýòèõ ïðåîáðàçîâàòåëåé.

4.      Âûâåäèòå ïåðåäàòî÷íóþ ôóíêöèþ è íàðèñóéòå ñòðóê= òóðíóþ ñõåìó ëèíåéíîãî äâèãàòåëÿ áåç ïðóæèíû è áåç òðåíèÿ.

5.      Ïî ïîëó÷åííîé â ï.4 ïåðåäàòî÷íîé ôóíêöèè âûâåäèòå âûðàæåíèå äëÿ ÷àñòîòíîé õàðàêòåðèñòèêè äâèãàò= åëÿ è ïîñòðîéòå åå, çàäàâøèñü ÷èñëåííûìè çíà÷åíèÿìè ïàðàìåòðîâ äâèãàòåëÿ (íàïðè= ìåð, Òý=3D10 ìñ, m=3D50 = ã, Êýì=3D0,05 Âñ).

 

 


ÃËÀÂÀ 2. ÏÐÅÎÁÐÀÇÎÂÀÍÈÅ ÝÍÅÐÃÈÈ Â ÝËÅÊÒÐÈ×ÅÑÊÈÕ ÌÀØÈÍÀÕ


2.1. Ïðèíöèï ýëåêòðîìåõàíè÷åñêîãî ïðåîáðàçîâàíèÿ ýíåðãèè â ýëåêòðè÷åñêîé ìàøèíå

Ýëåêòðîìàãíèòíàÿ ñõåìà ïðîñòå= éøåé ýëåêòðè÷åñêîé ìàøèíû ïîêàçàíà íà .

Ðèñ. 2-1. Ýëåêòðîìàãíèòíàÿ ñõåìà ïðîñòåéøåé ýëåêòðè÷åñêîé ìàøèíû

a) â ðåæèìå ãåíåðàòîðà

b) â ðåæèìå äâèãàòåëÿ

Îíà ñîñòîèò èç äâóõ îñíîâíûõ ýëåìåíòîâ: íåïîäâèæíîãî ñòàòîðà è âðàùàþùåãîñÿ ðîòîðà.  ïàçàõ íà ïîâåðõíîñ= òè ðîòîðà ðàñïîëîæåíà îáìîòêà ñ ÷èñëîì âèòêîâ ω1, à íà ñòàòîðå= - îáìîòêà ω2.

Ýëåêòðîìåõàíè÷åñêîå ïðåîáðàçî= âàíèå ýíåðãèè â ìàøèíå ñâÿçàíî ñ ÝÄÑ, êîòîðûå èíäóêòèðóþòñÿ â îáìîòêàõ âñëåäñòâèå èçìåíåíèÿ èõ âçàèìíîãî ðàñïîëîæåíèÿ â ïðîñòðàíñòâå.

Ïðåäïîëîæèì, ÷òî ìàøèíà ðàáîò= àåò â ðåæèìå ãåíåðàòîðà ( ), òîãäà â îáìîòêå ω2 ïðîòåêàåò ïîñòîÿ= ííûé òîê i2, êîòîðûé ñîçäàåò ïîñòîÿííûé ìàãíèòíûé ïîòîê f. Ïîòîêîñöåïëåíèå ýòîãî ïîòîêà ñ îáìîòêîé ðîòîðà ω1 çàâèñèò îò óãëà γ. Ïðè γ=3D0 ïîòîêîñöåïëåíèå èìååò ìàêñèìàëüíîå ïîëîæèòåëüíîå çíà÷åíèå

Ïðè ïîâîðîòå ðîòîðà ïîòîêîñöå= ïëåíèå ëèíåéíî èçìåíÿåòñÿ â ôóíêöèè óãëà γ, êàê ïîêàçàíî íà .

Ðèñ. 2-2. Èçìåíåíèå ïîòîêîñöåïëåíèÿ è ÝÄÑ â ïðîñòåéøåé ýëåêòðè÷åñ= êîé ìàøèíå.

Àíàëîãè÷íûì îáðàçîì èçìåíÿåòñÿ âçàèìíàÿ èíäóêòèâíîñòü ìåæäó îáìîòêàìè :

Ïðè âðàùåíèè ðîòîðà ñ óãëîâîé ñêîðîñòüþ ω óãîë ^= 7;=3Dω·t ëèíåéíî óâåëè÷èâàåòñÿ, ÷òî ïðèâîäèò ê âîçíèêíîâåíèþ â îáìîòêå ω1<= /sub> òàê íàçûâàåìîé ÝÄÑ âðàùåíèÿ:

Êàê âèäíî èç , â îáìîòêå ðîòîðà ïðîñòåéøåé ìàøèíû èíäóêòèðóåòñÿ ÝÄÑ ïðÿìîóãîëüíîé ôîðìû ñ ïåðèîäîì . ( ìàøèíàõ ñ îäíîïîëþñíîé ñèñòåìîé âçàèìíàÿ èíäóêòèâíîñòü L12 è èíäóêòèðóåìàÿ ÝÄÑ e1 èçìåíÿþòñÿ ïî ãàðìîíè÷åñêîìó çàêîíó, êàê ïîêàçàíî íà ïóíêòèðîì). Ïðè çàìûêàíèè ðîòîðíîé îáìîòêè íà íàãðóçêó= RH â öåïè âîçíèêàåò ïåðåìåííûé òîê , ãäå R1- àêòèâíîå ñîïðîòèâëåíèå îáìîòêè ω1. Ïðè ýòîì â îáìîòêå ω= ;1 áóäåò ãåíåðèðîâàòüñÿ ýëåêòðè÷åñêàÿ ìîùíîñòü

.

 ðåçóëüòàòå âçàèìîäåéñòâèÿ ìàãíèòíîãî ïîëÿ òîêà i2 ñ òîêîì i1 íà poòop áóäåò äåéñòâîâàòü ýëåêòðîìàãíèòíûé ìîìåíò <= span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>M, êîòîðûé óðàâíîâåøè= âàåòñÿ âíåøíèì ìîìåíòîì MB:

Ïðè ýòîì ÷åðåç âàë ê ðîòîðó ä= îëæíà áûòü ïîäâåäåíà ìåõàíè÷åñêàÿ ìîùíîñòü, ïðåîáðàçóåìàÿ â ðàâíóþ åé ýëåêòðè÷åñê= óþ ìîùíîñòü e= 1·i1 ïî

Êàê âèäíî èç , òîê i1 è ïðîèçâîäíàÿ âñåãäà èìåþò ïðîòèâîïîëîæíûå çíàêè, ïîýòîìó ñîãëàñíî ìîùíîñòü âñåãäà ïîëîæèòåëüíà. Ýòî îçíà÷àåò, ÷òî â ýëåêòðè÷åñêîé ìàøèíå îñóùåñòâëÿåòñÿ îäíîíàïðàâëåííîå ýëåêòðîìåõàíè÷åñêîå ïðåîáðàçîâàíèå ýíåðãèè.  äàííîì ñëó÷àå èç ìåõàíè÷åñêîé= â ýëåêòðè÷åñêóþ, òàê êàê ìàøèíà ðàáîòàåò â ðåæèìå ãåíåðàòîðà.

Ïðè ðàáîòå â ðåæèìå äâèãàòåëÿ ñîãëàñíî çàïèøåì óðàâíåíèå ðîòîðíîé öåïè â âèäå:

,

è, óìíîæèâ åãî íà i1, ïîëó÷èì ìîùíîñòü, ïîñòóïàþùóþ èç ñåòè íà îáìîòêó ω1

×àñòü ýòîé ìîùíîñòè R1·i12 âûäåëÿåòñÿ â âèäå òåïëîòû â îáìîòêå, à îñòàëüíàÿ åå ÷àñòü ïðåîáðàçóåòñÿ â ìåõàíè÷åñêóþ ìîùíîñòü

.

Âðàùàþùèé ìîìåíò â ðåæèìå äâè= ãàòåëÿ ïîëîæèòåëåí (M&= gt;0) è íàïðàâëåí â ñòîðîíó âðàùåíèÿ.

Òàêèì îáðàçîì, â ïðîñòåéøåé ýëåêòðè÷åñêîé ìàøèíå âûïîëíÿåòñÿ ïðèíöèï îáðàòèìîñòè, óñòàíîâëåííûé àêàäåìè= êîì Ëåíöåì åùå â 1883 ãîäó.


2.2. Îäíîíàïðàâëåííîå ïðåîáðàçîâàíèå ýíåðãèè â ýëåêòðè÷åñêèõ ìàøèíàõ

Êàê ïîêàçàíî â 2-1, âçàèìíàÿ èíäóêòèâíîñòü L= 12 ìåæäó îáìîòêàìè ñòàòîðà è ðîòîðà â ýëåêòðè÷åñêîé ìàøèíå ÿâëÿåòñÿ ïåðèîäè÷åñ= êîé ôóíêöèåé óãëà ïîâîðîòå ðîòîðà.  îáùåì âèäå ýòó ôóíêöèþ ìîæíî ïðåäñòàâèòü â âèäå:

.

Òîãäà ýëåêòðîìàãíèòíûé ìîìåíò ñîãëàñíî áóäåò ïðåäñòàâëåí â âèäå:

,

ãäå p- ÷èñëî ïàð ïîëþñîâ.

Ïî îáìîòêàì ìàøèíû â îáùåì ñë= ó÷àå ïðîòåêàþò ïåðåìåííûå òîêè:

Ðèñ. 2-3. Óñëîâèÿ ïîëó÷åíèÿ îäíîíàïðàâëåííîãî ìîìåíòà â ýëåêòðè÷åñêîé ìàøèíå.

Íà ïðèíÿòî ω1=3D4·p·ω, ω2=3D3·ω, f1=3D0, f2=3Dπ/2.

Îäíîíàïðàâëåííîå ïðåîáðàçîâàí= èå ýíåðãèè â ýëåêòðè÷åñêîé ìàøèíå áóäåò ïðîèñõîäèòü, åñëè ÷àñòîòû òîêîâ â îáìî= òêàõ áóäóò ñîãëàñîâàíû ñ ïåðèîäè÷íîñòüþ èçìåíåíèÿ èíäóêòèâíîñòè L12, ÷òî ñðåäíåå çíà÷åí= èå ýëåêòðîìàãíèòíîãî ìîìåíòà áóäåò îòëè÷íî îò íóëÿ:

,

ãäå - ïåðèîä èçìåíåíèÿ âçàèìíîé èíäóêòèâíîñòè L12.

Ïîäñòàâëÿÿ â , è ïðåäñòàâèâ ïðîèçâåäåíèå ñèíóñîâ ñóììîé ñèíóñîâ àëãåáðàè÷åñêîé ñóììîé àðãóìåíòîâ, ïîëó÷èì:

Ïîäûíòåãðàëüíîå âûðàæåíèå ñîñ= òîèò èç ÷åòûðåõ ñëàãàåìûõ, èçìåíÿþùèõñÿ ñ ÷àñòîòàìè ω1±ω2-p·ω, ω1±ω<= sub>2+p·ω= , èíòåãðàëû îò êîòîðûõ ðàâíà íóëþ, åñëè ýòè ÷àñòîò= û íå ðàâíû íóëþ.

Òàêèì îáðàçîì, ñðåäíåå çíà÷åí= èå ìîìåíòà M0= íå áóäåò ðàâíûì íóëþ, åñëè îäíà èç ÷àñòîò ðàâíà íóëþ, ò.å. ω1+ω2=3Dp·ω èëè ω1-`= 9;2=3Dp·ω

Ïðè âûïîëíåíèè óñëîâèÿ ïîëó÷èì:

Êàê âèäíî èç , ñðåäíèé ìîìåíò äîñòèãàåò íàèáîëüøåãî çíà÷åíèÿ â äâèãàòåëüíîì ðåæèìå (M= 0>0) ïðè è â ãåíåðàòîðíîì ðåæèìå (M0<0) ïðè .

Ïîëó÷åíèå îäíîíàïðàâëåííîãî ïðåîáðàçîâàíèÿ ýíåðãèè â äâóõîáìîòî÷íîé ìàøèíå ïîêàçàíî íà ïðè ω12=3Dp·ω= è .

Èòàê, äëÿ ïîëó÷åíèÿ îäíîíàïðàâëåííîãî ïðåîáðàçîâàíèÿ ýíåðãèè â ìàøèíå ïåðåìåííîãî .òîêà ñ äâóìÿ îáìîòêàìè íåîáõîäèìî, ÷òîáû ñóììà èëè ðàçíîñòü óãëîâûõ ÷àñòîò òîêîâ â îáìîòêàõ ðàâíÿëàñü óãëîâîé ÷àñòîòå èçìåíåíèÿ âçàèìíîé èíäóêòèâíîñòè ìåæäó îáìîòêàìè p·ω, íàïðàâëåíèå ïðåîáðàçîâàíèÿ ýíåðãèè çàâèñèò îò çíà÷åíèÿ ñóììû èëè ðàçíîñòè ñäâèãà ôàç òî= êîâ ïî îòíîøåíèþ ê âçàèìíîé èíäóêòèâíîñòè: ïðè ýëåêòðè÷åñêàÿ ýíåðãèÿ ïðåîáðàçóåòñÿ â ìåõàíè÷åñêóþ (äâèãàòåëüíûé ðåæèì), ïðè ìåõàíè÷åñêàÿ ýíåðãèÿ ïðåîáðàçóåòñÿ â ýëåêòðè÷= åñêóþ (ãåíåðàòîðíûé ðåæèì).

Ðàçëè÷àþò äâà òèïà ìàøèí ïåðåìåííîãî òîêà: àñèíõðîííûå ìàøèíû è ñèíõðîííûå ìàøèíû.

 ñèíõðîííûõ ìàøèíàõ îáå îáìî= òêè ïèòàþòñÿ òîêàìè ñ æåñòêî çàäàííûìè ÷àñòîòàìè ω1 è ω2. Óãëîâàÿ ñêîðîñòü ðîòîðà ïðè ýòîì îñòàåòñÿ ïîñòîÿííîé íåçàâèñèìî îò ìîìåíòà ïî âàëó. Ïðè èçìåíåíèè ìîìåíòà ìåíÿþòñÿ ëèøü àìïëèòóäû è ôàçû òîêîâ i1 è i2= .

Íàèáîëåå øèðîêîå ïðèìåíåíèå í= àøëè ñèíõðîííûå ìàøèíû ñ òðåõôàçíîé îáìîòêîé íà ñòàòîðå í îäíîôàçíîé îáìîòêîé íà ðîòîðå, ïèòàåìîé ïîñòîÿííûì òîêîì. Â îñíîâíîì ýòî ìî= ùíûå ãåíåðàòîðû. Ó ýòîé ìàøèíû ω2=3D0 è = f2=3D0.

 àñèíõðîííûõ ìàøèíàõ òîëüêî = îäíà èç îáìîòîê - îáû÷íî îáìîòêà ñòàòîðà ïîëó÷àåò ïèòàíèå îò ýëåêòðè÷åñêîé ñåòè, ÷àñòîòà êîòîðîé ω 1- çàäàíà. Âò= îðàÿ îáìîòêà çàìûêàåòñÿ íàêîðîòêî. Òîê i2 â ýòîé îáìîòêå ïîÿâëÿåòñÿ â ðåçóëüòàòå ýëåêòðîìàãíèòíîé èíäóêöèè ñ îáìîòêîé ñòàòîðà. ×àñòîòà ω2 òî= êà i2 ÿâëÿåòñÿ ôóíêöèåé óãëîâîé ñêîðîñòè ðîòîðà ω2=3Dω1-ω è óäîâëåòâîðÿåò óñëîâèþ îäíîíàïðàâëåííîãî ïðåîáðàçîâàíèÿ ýíåðãèè .

Íàèáîëåå ðàñïðîñòðàíåííûìè ÿâ= ëÿþòñÿ àñèíõðîííûå ìàøèíû ñ òðåõôàçíîé îáìîòêîé íà ñòàòîðå è êîðîòêîçàìêíóòûì ðîòî= ðîì, ðàáîòàþùèì â äâèãàòåëüíîì ðåæèìå.

Òðåõôàçíûé àñèíõðîííûé äâèãàò= åëü áûë âïåðâûå ðàçðàáîòàí Ì.Î. Äîëèâî-Äîáðîâîëüñêèì â 1889-90 ã.ã. è ñ òåõ ïîð ïðèíöèïèàëüíî ïî÷òè íå èçìåíèëñÿ.


2.3. Ýëåêòðîìåõàíè÷åñê= îå ïðåîáðàçîâàíèå ýíåðãèè ñ ïîìîùüþ âðàùàþùåãîñÿ ìàãíèòíîãî ïîëÿ. Ïîòåðè ýíåðã= èè. ÊÏÄ .

 ýëåêòðè÷åñêèõ ìàøèíàõ ïåðåì= åííîãî òîêà îáû÷íî ñîçäàåòñÿ âðàùàþùååñÿ ìàãíèòíîå ïîëå ñ ïîìîùüþ ìíîãîôàçíûõ îáìî= òîê ñòàòîðà. Ïðè óãëîâîé ÷àñòîòå òîêà ñòàòîðà ω1 ÷àñòîòà âðàùåí= èÿ ýòîãî ïîëÿ áóäåò . Âåêòîð ýòîãî ïîëÿ f1 ïîêàçàí íà .

Ðèñ. 2-4. Âçàèìíîå ðàñïîëîæåíèå ïîòîêîâ ðîòîðà è ñòàòîðà âî âðàùàþùåìñÿ ìàãíèòíîì ïîëå ìàøèíû.

Òîê ðîòîðà òàêæå ìîæåò èçìåíÿ= òüñÿ ñ ÷àñòîòîé ω2 è ïðè ýòîì ïîëå ðîòîðà âðàùàåòñÿ îòíîñèòåëüíî ðîòîðà ñ ÷àñòîòîé . Íî òàê êàê ñàì ðîòîð âðàùàåòñÿ ñ ÷àñòîòîé = ω îòíîñèòåëüíî ñòàòîðà, ïîëå ðîòîðà âðàùàåòñÿ ñ ÷àñòîòîé . Ó÷èòûâàÿ óñëîâèå îäíîíàïðàâëåííîãî ïðåîáðàçîâàíèÿ ýíåðãèè , ïîëó÷èì:

,

òî åñòü îáà ïîëÿ âðàùàþòñÿ îòíîñèòåëüíî ñòàòîðà ñ îäíîé è òîé æå ñêîðîñòüþ , òîëüêî âåêòîð ïîëÿ ðîòîðà îòñòàåò îò ïîëÿ ñòàòîðà íà óãîë , êàê ïîêàçàíî íà . Òàêèì îáðàçîì, â ðàáî÷åì = çàçîðå ýëåêòðè÷åñêîé ìàøèíû ñóùåñòâóåò åäèíîå âðàùàþùååñÿ ìàãíèòíîå ïîëå, êîòîðîå ìîæíî îõàðàêòåðèçîâàòü ñóììàðíûì âåêòîðîì

.

Ýíåðãèÿ ìàãíèòíîãî ïîëÿ â ðàá= î÷åì çàçîðå ìîæåò áûòü âûðàæåíà ÷åðåç ýòîò âåêòîð:

,

à ýëåêòðîìàãíèòíûé ìîìåíò ìîæ= åò áûòü âûðàæåí ÷åðåç ýíåðãèþ ìàãíèòíîãî ïîëÿ:

.

Ïîäñòàâëÿÿ â , à çàòåì ïðîèçâåäÿ äèôôåðåíöèðîâàíèå ñîãëàñíî , ïîëó÷àåì âûðàæåíèå äëÿ ýëåêòðîìàãíèòíîãî ìîìåíòà:

.

Èç= âèäíî, ÷òî ìîìåíò çàâèñèò î= ò óãëà "ðàññîãëàñîâàíèÿ" ìåæäó âåêòîðàìè ïîòîêîâ ñòàòîðà è ðîòîðà è óâåëè÷èâàåòñÿ ïðè óâåëè÷åíèè ýòîãî óãëà äî îïðåäåëåííûõ ïðåäåëîâ.

Ôèçè÷åñêè íàëè÷èå äâóõ âåêòîð= îâ f1 è = f2 â åäèíîì ìàãíèòíîì ïîëå ìîæíî ïðåäñòàâèòü êàê èñêðèâëåíèå ìàãíèòíûõ ñèëîâûõ ëèíèé â ðàáî÷åì çàçîðå ìàøèíû, ïðè÷åì ýòî èñêðèâëåíèå óâåëè÷èâàåòñÿ ñ óâåëè÷åíèåì íàãðóçêè (ìîìåíòà). Òàêèì îáðàçîì ïå= ðåäà÷ó ýíåðãèè (ìîìåíòà) îò âðàùàþùåãîñÿ ìàãíèòíîãî ïîëÿ ê ðîòîðó ìàøèíû â äâèãàòåëüíîì ðåæèìå èëè íàîáîðîò â ãåíåðàòîðíîì, ìîæíî åùå îáúÿñíèòü íàòÿæå= íèåì ìàãíèòíûõ ñèëîâûõ ëèíèé, ïðè÷åì ïðè óâåëè÷åíèè ýòîé ýíåðãèè ýòî íàïðÿæåíèå = çà ñ÷åò èñêðèâëåíèÿ â ðàáî÷åì çàçîðå óâåëè÷èâàåòñÿ.

Âðàùàþùååñÿ ìàãíèòíîå ïîëå îá= ëàäàåò îïðåäåëåííîé ìîùíîñòüþ Pýì, êîòîðóþ ìî= æíî âûðàçèòü ÷åðåç ýëåêòðîìàãíèòíûé ìîìåíò

.

Òàêèì îáð= àçîì ìîæíî âûðàçèòü ýëåêòðè÷åñêóþ è ìåõàíè÷åñêóþ ìîùíîñòè ðîòîðà

.

Äîìíîæèâ= âûðàæåíèå , ñâÿçûâàþùåå ÷àñòîòû âðàùåíèÿ ïîëåé è ðîòîðà, ïîëó÷èì= , îòêóäà

.

Ýëåêòðîìàãíèòíàÿ ìîùíîñòü P= ýì ïðåäñòàâëÿåò ñîáîé ïîëíóþ ìîùíîñòü, ïåðåäàâàåìóþ âðàùàþùèìñÿ ïîëåì â ðîòîð. ×àñòü ýòîé ìîùíîñòè Pýï âûäåëÿåòñÿ â âèäå òåïëîòû â ýëåêòðè÷åñêîé öåïè ðîòîðà, à îñòàâøàÿñÿ ÷àñòü ïðåîáðàçóåòñÿ â ìåõàíè÷åñêóþ ìîùíîñòü Pìåõ.

ÊÏÄ ýëåêòðè÷åñêîé ìàøèíû íà ý= òàïå ýëåêòðîìàãíèòíîãî ïðåîáðàçîâàíèÿ ýíåðãèè îïðåäåëÿåòñÿ ïîòåðÿìè â ðîòîðå í ìîæåò áûòü ïðåäñòàâëåí â âèäå .

 áîëåå î= áùåì ñëó÷àå ÊÏÄ çàâèñèò îò ñóììàðíûõ óòåðü ìîùíîñòè â ðîòîðå è ñòàòîðå ìàøèíû è ìîæåò áûòü ïðåäñòàâëåí â âèäå

- äëÿ ãåíåðàòîðà

- äëÿ äâèãàòåëÿ.

Êîýôôèöèåíò ïîëåçíîãî äåéñòâèÿ âñåãäà ìåíüøå åäèíèöû, ïðè÷åì ÷åì ìåíüøóþ äîëþ ñîñòàâëÿþò ïîòåðè, òåì áëèæå ÊÏÄ ìàøèíû ê åäèíèöå.


2.4. Êëàññèôèêàöèÿ ýëåêòðè÷åñêèõ ìàøèí

Ýëåêòðè÷åñêèå ìàøèíû ìîæíî êëàññèôèöèðîâàòü ïî ïðèíöèïó äåéñòâèÿ, êîíñòðóêòèâíîìó èñïîëíåíèþ è íàçíà÷å= íèþ .

Ðèñ. 2-5. Êëàññèôèêàöèÿ ýëåêòðè÷åñêèõ ìàøèí.

Ïî ïðèíöèïó äåéñòâèÿ:

Êàê óæå ãîâîðèëîñü âûøå, â ñèíõðîííûõ ìàøèíàõ ÷àñòîòà âðàùåíèÿ ïîëåé ðîòîðà è ñòàòîðà çàäàþòñÿ èçâíå è ïîýòîìó ñîãëàñíî , ÷àñòîòà âðàùåíèÿ ðîòîðà çàâèñèò òîëüêî îò ýòèõ ÷àñòî= ò.  àñèíõðîííûõ ìàøèíàõ èçâíå çàäàåòñÿ òîëüêî ÷àñòîòà âðàùåíèÿ ïîëÿ ñòàòîðà, à ÷àñòîòà âðàùåíèÿ ïîëÿ ðîòîðà çàâèñèò îò ÷àñòîòû âðàùåíèÿ ðîòîðà òàê, ÷òîáû âûïîëíÿëîñü óñëîâèå .  ìàøèíàõ ñ êîììóòàòîðàìè ÷àñòîòà âðàùåíèÿ ïîëÿ(ñòàòîðà èëè ðîòîðà) íå çàäàåòñÿ èçâíå, à ñâÿçûâàåòñÿ= ñ ÷àñòîòîé âðàùåíèÿ ðîòîðà ñ ïîìîùüþ äàò÷èêà ïîëîæåíèÿ è êîììóòàòîðà îáìîòêè = òàê, ÷òîáû âûïîëíÿëîñü óñëîâèå . Ïîýòîìó ñèíõðîííûå è àñèíõðîííûå ìàøèíû èìåþò ÷àñòîò= íîå óïðàâëåíèå, à ìàøèíû ñ êîììóòàòîðàìè - àìïëèòóäíîå. Ïî êîíñòðóêòèâíîé ðåàëèçàöèè ôèçè÷åñêèõ ïðèíöèïîâ íàèáîëåå ðàñïðîñòðàíåíû ñèíõðîííûå ìàøèíû. = Ýòî òðåõôàçíûå ãåíåðàòîðû è ñïåöèàëüíûå äâèãàòåëè. Òðåõôàçíûé ñèíõðîííûé ãåíåðà= òîð ñ âîçáóæäåíèåì îò ýëåêòðîìàãíèòà ïîñòîÿííîãî òîêà ÿâëÿåòñÿ îñíîâíûì òèïîì ãåíåðàòîðà íà ñîâðåìåííûõ ýëåêòðîñòàíöèÿõ. Èç ñïåöèàëüíûõ ñèíõðîííûõ ìàøèí, ïðèìåíÿåìûõ â ñèñòåìàõ àâòîìàòèêè è âû÷èñëèòåëüíîé òåõíèêè, ÿâëÿþòñÿ øàãîâûå èìïóëüñíûå äâèãàòåëè.

Èç àñèíõðîííûõ ìàøèí íàèáîëåå ðàñïðîñòðàíåíû òðåõôàçíûå ïðèâîäíûå äâèãàòåëè ñðåäíåé è áîëüøîé ìîùíîñòè è äâóõôàçíûå áûñòðîäåéñòâóþùèå äâèãàòåëè ñèñòåì àâòîìàòè÷åñêîãî óïðàâëåíèÿ, à òàêæå ñïåöèàëüíûå ìàøèíû, ðàáîòàþùèå â ðåæèìå òðàíñôîðìàòîðà èëè ãåíåðàòîðà= è ïðèìåíÿåìûå â ñèñòåìàõ àâòîìàòè÷åñêîãî óïðàâëåíèÿ â êà÷åñòâå äàò÷èêîâ ïîëîæ= åíèÿ è ñêîðîñòè. Ìàøèíû ñ êîììóòàòîðàìè ìîæíî ðàçäåëèòü íà äâå ãðóïïû - êîëëåêòî= ðíûå ìàøèíû, èìåþùèå ýëåêòðîìåõàíè÷åñêèé êîììóòàòîð -êîëëåêòîð, è âåíòèëüíûå ñ ïîëóïðîâîäíèêîâûìè êîììóòàòîðàìè. Íàèáîëåå ðàñïðîñòðàíåííûìè= èç ýòîãî êëàññà ìàøèí ÿâëÿþòñÿ ìàøèíû ïîñòîÿííîãî òîêà.  àâòîìàòèêå îíè èñïîëüçóþòñÿ â êà÷åñòâå èñïîëíèòåëüíûõ äâèãàòåëåé è òàõîãåíåðàòîðîâ - äàò÷è= êîâ ñêîðîñòè.


2.5. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 2.

  1. Ïîñòðîéòå çàâèñèìîñòü, âûðàæàþùóþ ìîìåíòû ïðîñòåéøåé ýëåêòðè÷åñêîé ìàøèíû (ðèñ. = 2-1) îò âðåìåíè ïðè ïîñëåäîâàòåëüíîì âêëþ÷åíèè åå îáìîòîê â ñåòü 50 Ãö ñ àìïëèòóäîé òîêà Im=3D0,5 A = ïðè dL/dg=3D0,5 Ãí/ðàä. Îïðåäåëèòå ñðåäíåå çíà÷åíèå ìîìåíòà.
  2. Ïîñòðîèòü çàâèñèìîñòü, àíàëîãè÷íóþ ï.1 ïðè L=3DLm cosg. =
  3. Ïîëüçóÿñü ðåçóëüòàòàìè ï.2 ïîñòðîèòü çàâèñèìîñòü Ìñð=3Df(g).
  4. Ó÷èòûâàÿ ñîîòíîøåíèå (2-18) è ðåçóëüòàòû ï. 3, íàðèñîâàòü ñîãëàñíî ðèñ. 2-1 âçàèìíîå ðàñïîëîæåíèå îáìîòîê ðîòîðà è ñòàòîðà ïðè ðàçëè÷íûõ çíà÷åíèÿõ ñðåäíåãî ìîìåíòà.
  5. Ïåðå÷èñëèòå îñíîâíûå òèïû ýëåêòðè÷åñêèõ ìàøèí.


ÃËÀÂÀ 3. ÀÑÈÍÕÐÎÍÍÛÅ Ì= ÀØÈÍÛ


3.1. Îáùèå ñ ñâåäåíèÿ è ýëåêòðîìåõàíè÷åñêîå ïðåîáðàçîâàíèå ýíåðãè= è â àñèíõðîííûõ ìàøèíàõ

Êàê óêàçûâàëîñü âûøå, àñèíõðî= ííîé ìàøèíîé íàçûâàåòñÿ ìàøèíà ïåðåìåííîãî òîêà, ó êîòîðîé òîëüêî ïåðâè÷íàÿ îáìî= òêà ïîëó÷àåò ïèòàíèå îò ýëåêòðè÷åñêîé ñåòè ñ ïîñòîÿííîé ÷àñòîòîé, à âòîðàÿ îáìî= òêà çàìûêàåòñÿ íàêîðîòêî èëè íà ýëåêòðè÷åñêîå ñîïðîòèâëåíèå. Òîêè âî âòîðè÷íîé îáìîòêå ïîÿâëÿþòñÿ â ðåçóëüòàòå ýëåêòðîìàãíèòíîé èíäóêöèè. Èõ ÷àñòîòà ω çàâèñèò îò óãëîâîé ñêîðîñòè âðàùåíèÿ ðîòîðà ω.

Àñèíõðîííûå ìàøèíû èñïîëüçóþò= ñÿ â îñíîâíîì êàê äâèãàòåëè, â êà÷åñòâå ãåíåðàòîðîâ îíè ïðèìåíÿþòñÿ êðàéíå ðåäêî. Íàèáîëüøåå ðàñïðîñòðàíåíèå ïîëó÷èëè òðåõôàçíûå àñèíõðîííûå äâèãàòåëè ñ êîðîòêîçàìêíóòûì ðîòîðîì, èìåþùèå òðåõôàçíóþ îáìîòêó íà ñòàòîðå è ïèòàþùèåñ= ÿ îò òðåõôàçíîé ñåòè. Òðåõôàçíûé àñèíõðîííûé äâèãàòåëü ÿâëÿåòñÿ íàèáîëåå ðàñïðîñ= òðàíåííûì äâèãàòåëåì ïîñòîÿííîãî òîêà.

 ñèñòåìàõ àâòîìàòè÷åñêîãî óïðàâëåíèÿ èñïîëüçóþòñÿ äâóõôàçíûå àñèíõðîííûå äâèãàòåëè ñ êîðîòêîçàìêíóòûì, ÷àùå âñåãî ñ íåìàãíèòíûì ïîëûì ðîòîðîì.

 àñèíõðîííûõ ìàøèíàõ îáìîòêè ñòàòîðà, ïèòàþùèåñÿ ïåðåìåííûì òîêîì ÷àñòîòû , ñîçäàþò ìàãíèòíîå ïîëå, âðàùàþùååñÿ ñ ÷àñòîòîé , ãäå p- êîëè÷åñòâî ïàð ïîëþñîâ íà ñòàòîðå. Ïîä äåéñòâèåì ýëåêã= ðîìàãíèòíîé èíäóêöèè â îáìîòêàõ èëè ýëåìåíòàõ êîðîòêîçàìêíóòîãî ðîòîðà ("áåëè÷üåé êëåòêå")

èíäóêòèðóþòñÿ âòîðè÷íûå ÝÄÑ <= span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>e2 è òîêè = i2 ÷àñòîòû ω2, êîòîðûå âçàèìîäåéñò= âóþò ñ âðàùàþùèìñÿ ìàãíèòíûì ïîëåì, ñîçäàåòñÿ ýëåêòðîìàãíèòíûé ìîìåíò M, ÷òî ïðèâîäèò ê âðà= ùåíèþ ðîòîðà ñ ÷àñòîòîé ω1.

Ñêîðîñòü âðàùåíèÿ ðîòîðà ω íå ìîæåò áûòü ðàâíîé ñêîðîñòè âðàùåíèÿ ïîëÿ, ò= àê êàê ïðè ýòîì íå áóäåò èíäóöèðîâàòüñÿ âòîðè÷íàÿ ÝÄÑ e2, ÷òî ïðèâåäåò ê îòñóòñòâèþ âðàùàþùåãîñÿ ìîìåíòà. Ïîýòîìó ðîòîð â ñâîåì äâèæå= íèè äîëæåí îòñòàâàòü îò ìàãíèòíîãî ïîëÿ - ïðîñêàëüçûâàòü - îòñþäà íàèìåíîâàíèå äâèãàòåëÿ - àñèíõðîííûé, à îäèí èç îñíîâíûõ ïàðàìåòðîâ - ñêîëüæåíèå:

×àñòî ðàññìàòðèâàþò òàê íàçûâ= àåìóþ îäíîïåðèîäíóþ ìîäåëü äâèãàòåëÿ, â êîòîðîé p=3D1, òîãäà

Ñêîëüæåíèå ÿâëÿåòñÿ îòíîñèòåë= üíîé âåëè÷èíîé è â äâèãàòåëüíîì ðåæèìå èçìåíÿåòñÿ â ïðåäåëàõ 0<S≤1, ïðè÷åì S=3D0 ñîîòâåòñòâóåò ñèíõðîííîé ðàá= îòå, à S=3D1- ïóñêó äâèãàòåë= ÿ.

×àñòîòà èíäóöèðóåìûõ âî âòîðè= ÷íîé îáìîòêå (ðîòîðå) ÝÄÑ è òîêîâ çàâèñèò îò ñêîëüæåíèÿ

.

Òîãäà ýêâèâàëåíòíóþ ñõåìó öåïè ðîòîðà ìîæíî ïðåäñòàâèòü ñîãëàñíî .

Ðèñ. 3-2à. Ýêâèâàëåíòíàÿ ñõåìà öåïè ðîòîðà àñèíõðîííîé ìàøèíû.

 íà÷àëüíûé ìîìåíò ïóñêà äâèã= àòåëÿ ðîòîð íåïîäâèæåí S=3D1, ω2=3D ω1, è â ðîòîðå èíäóöèðóåòñÿ ÝÄÑ, ïðîïîðöèîíàëüíàÿ ïåðâè÷íîé ÷àñòîòå

;

;=

 ðàáî÷åì ðåæèìå ω2= 1, òàê êàê S<1<= /p>

Ýêâèâàëåíòíàÿ ñõåìà öåïè ðîòî= ðà â ðàáî÷åì ðåæèìå ïîêàçàíà íà . Îíà ñîäåðæèò èçìåíÿåìûé èñòî÷íèê ÝÄÑ Eðï·S è èçìåíÿåìîå èíäóêò= èâíîå ñîïðîòèâëåíèå x= ð=3Dxðï·S.

Ðèñ. 3-2á. Ýêâèâàëåíòíàÿ ñõåìà öåïè ðîòîðà àñèíõðîííîé ìàøèíû.

Ïîëüçóÿñü ýòîé ñõåìîé ìîæíî âû÷èñëèòü òîê ðîòîðà

Ðàçäåëèâ ýòî âûðàæåíèå íà S, ïîëó÷èì

Ïîëüçóÿñü ôîðìóëîé (3-3) ïîëó= ÷èì ýêâèâàëåíòíóþ ñõåìó öåïè ðîòîðà, ïðèâåäåííóþ ê ïàðàìåòðàì ïóñêîâîãî ðåæèìà,= òî åñòü ïðè íåïîäâèæíîì ðîòîðå ( ).

Ðèñ. 3-2â. Ýêâèâàëåíòíàÿ ñõåìà öåïè ðîòîðà àñèíõðîííîé ìàøèíû.

 ýòîé ñõåìå ÝÄÑ ðîòîðà è åãî èíäóêòèâíîå ñîïðîòèâëåíèå íå èçìåíÿåòñÿ ïðè èçìåíåíèè ñêîëüæåíèÿ (÷àñòîòû âðàùåíèÿ), à èçìåíÿåòñÿ àêòèâíîå ñîïðîòèâëåíèå, õîòÿ ôèçè÷åñêè ïðîèñõîäèò <= span class=3DGramE>âñå íàîáîðîò - ïðè èçìåíåíèè ÷àñòîòû âðàùåíèÿ èçìåíÿåò= ñÿ ÷àñòîòà âòîðè÷íîé ÝÄÑ = f2 è èç-çà ýòîãî ìåíÿåòñÿ åå àìïëèòóäà è èíäóêòèâíîå ñîïðîòèâëåíèå öåïè ðîòîðà= .

Ïðèâåäÿ ðàáî÷èé ðåæèì äâèãàòå= ëÿ ê ðåæèìó íåïîäâèæíîãî ðîòîðà, ìîæåì ðàññìàòðèâàòü àñèíõðîííóþ ìàøèíó êàê îáû÷= íûé òðàíñôîðìàòîð ñ íåïîäâèæíûìè îáìîòêàìè, ñõåìà êîòîðîãî ïîêàçàíà íà , ãäå n- êîýôôèöèåíò òðàíñôîðìàöèè.

Ðèñ. 3-3à. Ýêâèâàëåíòíàÿ ýëåêòðè÷åñêàÿ ñõåìà àñèíõðîííîãî äâèãàòåëÿ.

Ïðèâåäÿ ïàðàìåòðû âòîðè÷íîé ö= åïè è ïåðâè÷íîé, ïîëó÷èì îêîí÷àòåëüíóþ ýêâèâàëåíòíóþ ñõåìó àñèíõðîííîãî äâèãàòåëÿ, ïîêàçàííóþ íà ,

Ðèñ. 3-3á. Ýêâèâàëåíòíàÿ ýëåêòðè÷åñêàÿ ñõåìà àñèíõðîííîãî äâèãàòåëÿ.

ãäå ; - ïðèâåäåííûå ñîïðîòèâëåíèÿ, à r1- àêòèâíîå ñîïðîòèâëåíèå öåïè ðîòîðà.

Íà îñíîâàíèè ýòîé ñõåìû ïîëó÷= èì âûðàæåíèå äëÿ òîêà ðîòîðà

Âûðàæåíèå äëÿ âðàùàþùåãîñÿ ìî= ìåíòà ìîæåì ïîëó÷èòü èç ýíåðãåòè÷åñêîãî óðàâíåíèÿ M·ω= 1=3D M·ω+m1·Ip2·Rp, ãäå m1- êîëè÷å= ñòâî ôàç.

Ëåâàÿ ÷àñòü óðàâíåíèÿ - ýëåêòðîìàãíèòíàÿ ìîùíîñòü, à ïðàâàÿ - ìåõàíè÷åñêàÿ ïëþñ ýëåêòðè÷åñêàÿ ìîùíî= ñòè.

Èç ýòîãî óðàâíåíèÿ ïîëó÷èì:

.

Ïîäñòàâëÿÿ ñþäà âûðàæåíèÿ äëÿ= òîêà ðîòîðà è ó÷èòûâàÿ, ÷òî ,ïîëó÷èì àíàëèòè÷åñêîå âûðàæåíèå äëÿ ýëåêòðîìàãíèòíîãî ìîìåíòà:

Ãðàôèê çàâèñèìîñòè ýëåêòðîìàãíèòíîãî ìîìåíòà îò ñêîëüæåíèÿ ïðåäñòàâëåí íà<= /span> .

Ðèñ. 3-4à. Çàâèñèìîñòü ýëåêòðîìàãíèòíîãî ìîìåíòà îò ñêîëüæåíèÿ.

Ïðàâàÿ ÷àñòü ãðàôèêà îòíîñèòñ= ÿ ê ðåæèìó äâèãàòåëÿ, à ëåâàÿ - ãåíåðàòîðà. Ñêîëüæåíèå, ñîîòâåòñòâóþùåå ìàêñèìàëüíîìó ìîìåíòó, íàçûâàåòñÿ êðèòè÷åñêèì è îáîçíà÷àåòñÿ SK èëè SM. Âûðàæåíèå äëÿ ìîìåí= òà äâèãàòåëÿ ìîæåò áûòü ïðåäñòàâëåíî ÷åðåç ïàðàìåòðû êðèòè÷åñêîé òî÷êè

,

ãäå , à .

Ïðè ïðåíåáðåæåíèè àêòèâíûì ñîïðîòèâëåíèåì ñòàòîðà r1=3D0, ε=3D0, ïîëó÷èì áîëåå ïðîñòîå âûðàæåíèå äëÿ= ìîìåíòà

.

Êðèòè÷åñê= îå ñêîëüæåíèå çà çàâèñèò îò ñîîòíîøåíèå àêòèâíîãî è èíäóêòèâíîãî ñîïðîòèâëåíèé ðîòîðà. Ïðè r1=3D0 . Âèä õàðàêòåðèñòèêè ïðè ðàçíûõ ñîîòíîøåíèÿõ ïîêàçàí íà .

Ðèñ. 3-4á. Çàâèñèìîñòü ýëåêòðîìàãíèòíîãî ìîìåíòà îò ñêîëüæåíèÿ.

Õàðàêòåðèñòèêà 1 ñîîòâåòñòâóåò ñëó÷àþ R`<= span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>p<xðï, à õàðàêòåðèñòèêà 2 - R= `p>xðï, ò.å. â çàâèñèìîñòè îò âåëè÷èíû àêòèâíîãî ñîïðîòèâëåíèÿ ðîòîðà êðèòè÷åñêîå ñêîëüæåíèå ìîæåò áûòü êàê ìåíüøå, òàê è áîëüøå åäèíèöû.  òðåõôàçíûõ äâèãàò= åëÿõ SM&l= t;1, à â äâóõôàçíûõ SM>1.

 ðÿäå ñëó÷àåâ â äâóõôàçíûõ è îäíîôàçíûõ àñèíõðîííûõ äâèãàòåëÿõ ïðîèçâîäèòñÿ ïèòàíèå íåñèììåòðè÷íûì íàïðÿæåíèåì, ÷òî ïðèâîäèò ê ïîÿâëåíèþ ïóëüñèðóþùåãî ìàãíèòíîãî ïîëÿ. Ïî ïðèíöèïó ñóïåðïîçèöèè íåñèììåòðè÷íóþ ñèñòåìó ìîæíî ïðåäñòàâèòü â âèäå äâóõ ñèììåòðè÷íûõ, íî ñîçäàþùèõ ìàãíèòíûå ïîëÿ, âðàùàþùèåñÿ â ïðîòèâîïîëîæíûõ íàïðàâëåíèÿõ, ïðÿìîì è îáðàòíîì. Ñóììàðíûé âðàùàþùèé ìî= ìåíò áóäåò ðàâåí àëãåáðàè÷åñêîé ñóììå äâóõ ìîìåíòîâ - ïðÿìîãî è îáðàòíîãî, âûðàæ= åíèÿ äëÿ êîòîðûõ àíàëîãè÷íû .

Ïðè ïðåíåáðåæåíèè àêòèâíûì ñîïðîòèâëåíèåì ñòàòîðà ýòî âûðàæåíèå áóäåò èìåòü âèä:

Õàðàêòåðèñòèêè ïðè íåñèììåòðè= ÷íîì ïèòàíèè ïîêàçàíû íà = .

Ðèñ. 3-5. Õàðàêòåðèñòèêè àñèíõðîííîãî äâèãàòåëÿ ïðè íåñèììåòðè÷íîì ïèòàíèè.

à) Mmax_= ïð>Mmax_îáð

á) Mmax_= ïð=3DMmax_= îáð

Íà =  Mmax_ïð>Mmax_îáð è ñóùåñòâóåò ïóñêîâîé ìîìåíò Mï, êîòîðûé ìîæíî èçìåíÿòü, ìåíÿÿ íåñèììåòðèþ ïèòàþùèõ íàïðÿæåíèé, êàê ýòî äåëàåòñÿ â óïðàâëÿåìûõ àñèíõðîííûõ äâóõôàçíûõ äâèãàòåëÿõ. Íà =  Mmax_ïð=3DMmax_= îáð è ïóñêîâîé ìîìåíò ðàâåí íóëþ, êàê ýòî áûâàå= ò â îäíîôàçíûõ äâèãàòåëÿõ. Íî åñëè äâóõôàçíûé äâèãàòåëü ñ ïîìîùüþ äîïîëíèòåëüíîé îáìîòêè, êàê ýòî îáû÷íî äåëàåòñÿ, òî ïðè S<1 ïîÿâëÿåòñÿ âðàùàþùèé ìîìåíò è äâèãàòåëü áóäåò âðàùàòüñ= ÿ, íàõîäÿñü â ðàáî÷åé òî÷êå Síîì, M<= /span>íîì.


3.2. Àñèíõðîííûå òðåõô= àçíûå äâèãàòåëè

 àñèíõðîííîì òðåõôàçíîì äâèã= àòåëå âðàùàþùååñÿ ìàãíèòíîå ïîëå ñîçäàåòñÿ òðåìÿ îáìîòêàìè ñòàòîðà, íà êîòîðûå ïîäàåòñÿ òðåõôàçíîå íàïðÿæåíèå ñåòè.

Ñõåìà òðåõôàçíîãî äâèãàòåëÿ è âðåìåííàÿ äèàãðàììà ïèòàþùåãî íàïðÿæåíèÿ ïîêàçàíû íà .

Ðèñ. 3-6à,â. Ñõåìû âêëþ÷åíèÿ àñèíõðîííîãî äâèãàòåëÿ= .

Ðèñ. 3-6ã. Âðåìåííàÿ äèàãðàììà ïèòàþùèõ íàïðÿæåíèé àñèíõðîííîãî äâèãàòåëÿ.

Äëÿ äâèãàòåëåé îñíîâíîé ÿâëÿå= òñÿ ìåõàíè÷åñêàÿ õàðàêòåðèñòèêà ω=3Df(M), òî åñòü çàâèñèìîñòü ÷àñòîòû âðàùåíèÿ îò ìîìåíòà, êîòîðàÿ = äëÿ àñèíõðîííîãî äâèãàòåëÿ ìîæåò áûòü ïîëó÷åíà íà îñíîâàíèè âûðàæåíèÿ èëè ñ ó÷åòîì ñâÿçè ìåæäó ñêîëüæåíèåì S è ÷àñòîòîé âðàùåíèÿ ω. Âèä ìåõàíè÷åñêîé õàðàêòåðèñòèêè ïîêàçàí íà .

<= /span>

Ðèñ. 3-7à. Ìåõàíè÷åñêàÿ õàðàêòåðèñòèêà àñèíõðîííîãî òðåõôàçíîãî äâèãàòåëÿ.

Åå ìîæíî ðàçáèòü íà äâà ó÷àñò= êà - ðàáî÷èé (0-à) ïðè 0<S<SM è ó÷àñòîê ïóñêà (a-b) ïðè SM&l= t;S<1. Îáû÷íî â àñèí= õðîííûõ òðåõôàçíûõ äâèãàòåëÿõ ñ êîðîòêîçàìêíóòûì ðîòîðîì SM=3D0.05..0.15, ò.å. õàðàêòåðèñòèêè äîñòàòî÷íî æåñòêèå è ðàáî÷àÿ ÷àñòîòà âðàùåíèÿ ωí áëèçêà ê ñèíõðîííîé ω0. Äëÿ òàêèõ äâèãàòåëåé íà ðàáî÷åì ó÷àñòêå ò.å. ïðåîáëàäàåò àêòèâíàÿ ñîñòàâëÿþùàÿ ñîïðîòèâëåíèÿ ðîòîðà. Òîãä= à, ïðåíåáðåãàÿ â ôîðìóëå ñîïðîòèâëåíèÿìè x´ðï = è r1 ïî ñðàâ= íåíèþ ñ , ïîëó÷èì óïðîùåííîå âûðàæåíèå äëÿ ðàáî÷åãî ó÷àñòêà ìåõàíè÷åñêîé õàðàêòåðèñòèêè

îòêóäà

,

ãäå `= 9; - ÷àñòîòà âðàùåíèÿ ðîòîðà, ω1- ÷àñòîòà âðàùåíèÿ ïîëÿ, Uc- íàïðÿæ= åíèå ïèòàíèÿ ñåòè, R´p- ïðèâåäåííîå ñîïðîòèâëåíèå ðîòîðà. Êàê âèäíî èç âûðàæ= åíèÿ è , èçìåíåíèå íàïðÿæåíèÿ ïèòàíèÿ ìàëî âëèÿåò íà ÷àñòîòó âðàùåíèÿ ðîòîðà íà ðàáî÷åì ó÷àñòêå è äèàïàçîí óïðàâëåíèÿ íàïðÿæåíèåì âåñüìà îãðàíè÷åí.

Ðèñ. 3-7á. Ìåõàíè÷åñêàÿ õàðàêòåðèñòèêà àñèíõðîííîãî òðåõôàçíîãî äâèãàòåëÿ.

Íåñêîëüêî áîëüøèé äèàïàçîí ìî= æåò áûòü îáåñïå÷åí äâèãàòåëåì ïîâûøåííîãî ñêîëüæåíèÿ (SM≥1). Îäíàêî â ý= òîì ñëó÷àå ìåõàíè÷åñêèå õàðàêòåðèñòèêè èìåþò áîëüøóþ êðóòèçíó ( ) è óñòîé÷èâàÿ ðàáîòà äâèãàòåëÿ ìîæåò áûòü äîñòèãíóòà ëèøü ïðè èñïîëüçîâàíèè çàìêíóòîé ñèñòåìû, îáåñïå÷èâàþùåé ñòàáèëèçàöèþ ñêîðîñòè. Ïðè èçìåíåíèè ñòàòè÷åñêîãî ìîìåíòà ñèñòåìà ðåãóëèðîâ= àíèÿ ïîääåðæèâàåò çàäàííûé óðîâåíü ñêîðîñòè è ïðîèñõîäèò ïåðåõîä ñ îäíîé ìåõàíè÷åñêîé õàðàêòåðèñòèêè íà äðóãóþ, â èòîãå ðàáîòà ïðîòåêàåò íà õàðàêòåðèñòèêàõ, ïîêàçàííûõ íà øòðèõîâûìè ëèíèÿìè.

Ðèñ. 3-7â. Ìåõàíè÷åñêàÿ õàðàêòåðèñòèêà àñèíõðîííîãî òðåõôàçíîãî äâèãàòåëÿ.

Ïëàâíîå ðåãóëèðîâàíèå ñêîðîñò= è â øèðîêèõ ïðåäåëàõ ñ ñîõðàíåíèåì äîñòàòî÷íîé æåñòêîñòè õàðàêòåðèñòèê âîçìîæíî òîëüêî ïðè ÷àñòîòíîì óïðàâëåíèè. Êàê âèäíî èç ôîðìóëû , èçìåíÿÿ ÷àñòîòó âðàùåíèÿ ïîëÿ ω1, ìî= æíî èçìåíÿòü ÷àñòîòó âðàùåíèÿ ðîòîðà ω çà ñ÷åò ïåðâîãî ñëàãàåìîãî ôîðìóëû, ïðè ýòîì æåëàòåëüíî, ÷òîáû âòîðîå ñëàãàåìîå íå ìåíÿëîñü, ò.å. æåñòêîñòü õàðàêòåðèñòèêè ïðè ýòîì íå èçìåíÿëàñü. Äëÿ ýòîãî îäíîâðåìåííî ñ ÷àñòîòîé, èçìåíÿþò íàïðÿæåíèå ïèòàíèÿ Uc òàê, ÷òîáû èõ îòíîøå= íèå îñòàâàëîñü ïîñòîÿííûì .

Òîãäà ðàáî÷èé ó÷àñòîê ìåõàíè÷= åñêîé õàðàêòåðèñòèêè ïðè ÷àñòîòíîì óïðàâëåíèè ìîæíî ïðèáëèæåííî ïðåäñòàâèòü ôîðìó= ëîé:

Òàêîå óïðàâëåíèå íàçûâàåòñÿ ïðîïîðöèîíàëüíûì ÷àñòîòíûì óïðàâëåíèåì.

Âèä ìåõàíè÷åñêèõ õàðàêòåðèñòè= ê ïðè ïðîïîðöèîíàëüíîì óïðàâëåíèè ïîêàçàí íà .

Ðèñ. 3-8à. ×àñòîòíîå óïðàâëåíèå àñèíõðîííûì äâèãàòåëåì.

Ôóíêöèîíà= ëüíàÿ ñõåìà ÷àñòîòíîãî óïðàâëåíèÿ ïðåäñòàâëåíà íà . Îíà ñîñòîèò èç óïðàâëÿåìîãî âûïðÿìèòåëÿ ÓÂ, ïðåîáðàçóþùåãî ñåòåâîå íàïðÿæåíèå ïåðåìåííîãî òîêà ÷àñòîòîé 50 Ãö â íàïðÿæå= íèå ïèòàíèÿ ïîñòîÿííîãî òîêà Uï, âåëè÷èíà êîòîðîãî ìîæåò ðåãóëèðîâàòüñÿ = îò óñòðîéñòâà óïðàâëåíèÿ ÓÓ, è àâòîíîìíîãî èíâåðòîðà ÀÈ, ïðåîáðàçóþùåãî íàïðÿæ= åíèå Uï â òðåõôàçíîå íàïðÿæåíèå èçìåíÿåìîé ÷àñòîòû f1. Óïðàâëÿþùåå óñòðîéñòâî, èçìåíÿÿ ÷àñòîòó= f â çàâè= ñèìîñòè îò çàäàíèÿ ωç, èçìåíÿåò òàêæå è= íàïðÿæåíèå U<= /span>ï òàê, ÷òîáû èõ îòíîøåíèå îñòàâàëîñü ïîñòî= ÿííûì. Ñèñòåìà óïðàâëåíèÿ ìîæåò èìåòü îáðàòíóþ ñâÿçü ïî ñêîðîñòè âðàùåíèÿ ÷åðåç òàõîãåíåðàòîð ÒÃ.

Ðèñ. 3-8á. Ôóíêöèîíàëüíàÿ ñõåìà ÷àñòîòíîãî óïðàâëåíèÿ.

Áîëåå ñîâåðøåííûì, ÷åì ïðîïîðöèîíàëüíîå óïðàâëåíèå, ÿâëÿåòñÿ ÷àñòîòíî-òîêîâîå óïðàâëåíèå, ïðè êîòî= ðîì êîíòðîëèðóåòñÿ, êðîìå ÷àñòîòû âðàùåíèÿ, òîê ÿêîðÿ îò äàò÷èêà òîêà (ÄÒ), êàê ïîêàçàíî íà , ÷òî ïîçâîëÿåò îñòàâëÿòü ïîñòîÿííûì ïîòîê ïðè èçìåíåí= èè ÷àñòîòû f1= è íàãðóçêè.

Êàê äèíàìè÷åñêàÿ ñèñòåìà àñèíõðîííûé òðåõôàçíûé äâèãàòåëü îïèñûâàåòñÿ íåëèíåéíûì äèôôåðåíöèàëüíûì óðàâíåíèåì ïåðâîãî ïîðÿäêà:

,

ãäå J- ìîìåíò èíåðöèè ðîòîðà.

Ó÷èòûâàÿ, ÷òî ω=3Dω0·(1-S) è , è ïðèíèìàÿ ε=3D0, ïîëó÷èì:

Ó÷èòûâàÿ, ÷òî ,ïîëó÷èì:

Ýòîìó óðàâíåíèþ ñîîòâåòñòâóåò ñòðóêòóðíàÿ ñõåìà, ïðåäñòàâëåííàÿ íà .

Ðèñ. 3-9à. Ñòðóêòóðíàÿ ñõåìà àñèíõðîííîãî òðåõôàçíîãî äâèãàòåëÿ.

Èíòåãðèðóÿ óðàâíåíèå ( ) â ïðåäåëàõ îò S1 äî S, ïîëó÷èì

,

ãäå - ýëåêòðîìåõàíè÷åñêàÿ ïîñòîÿííàÿ âðåìå= íè.

Âûðàæåíèå ( ) ïîçâîëÿåò ïîñòðîèò êðèâûå ïåðåõîäíîãî ïðîöåññà S=3Df(t) è ñîîòâåòñòâåííî ω=3Df(t), âû÷èñëÿÿ ðÿä çíà÷åíèé t ïðè íåèçìåííîì S1 è èçìåíÿþùåìñÿ S. Êðèâûå ðàçãîíà äâèãàòåëÿ ïðè ðàçëè÷íûõ SM ïðèâåäå= íû íà . Êàê âèäíî, äëèòåëüíîñòü ïåðåõîäíîãî ïðîöåññà ñóùåñòâ= åííî çàâèñèò îò SM è ïðè íåêîòîðîì çíà÷åíèè SM_îïò ìèíèìàëüíà. Äâèãàòåëè ïîâûøåííîãî ñêîëüæåíèÿ ÿâëÿþòñÿ áîëåå áûñòðîäåéñòâóþù= èìè, òàê êàê SM<= /span>_îïò≈0.4..0.5.

Ïðè ïðîïîðöèîíàëüíîì ÷àñòîòíîì óïðàâëåíèè äëÿ ìàëûõ ïðèðàùåíèé äâèãàòåëü ìîæíî îïèñàòü ëèíåéíûìè óðàâíåíèÿ= ìè (ñì. 3-1)

Ýòèì óðàâíåíèÿì ñîîòâåòñòâóåò ñòðóêòóðíàÿ ñõåìà, ïðåäñòàâëåííàÿ íà .

Ðèñ. 3-9â. Ñòðóêòóðíàÿ ñõåìà àñèíõðîííîãî òðåõôàçíîãî äâèãàòåëÿ.

Íà îñíîâàíèè àíàëèçà ýòîé ñõå= ìû ìîæíî ïîëó÷èòü ïåðåäàòî÷íóþ ôóíêöèþ äâèãàòåëÿ ïðè ÷àñòîòíîì óïðàâëåíèè

,

ãäå K - ýëåêòðîìåõ= àíè÷åñêàÿ ïîñòîÿííàÿ âðåìåíè.


3.3. Àñèíõðîííûå äâóõô= àçíûå óïðàâëÿåìûå äâèãàòåëè

Òðóäíîñòè óïðàâëåíèÿ òðåõôàçí= ûìè äâèãàòåëÿìè ïðèâåëè ê èñïîëüçîâàíèþ â ïðèâîäàõ ìàëîé ìîùíîñòè óïðàâëÿåìûõ äâóõôàçíûõ äâèãàòåëåé, èìåþùèõ äâå îáìîòêè - îáìîòêó âîçáóæäåíèÿ è îáìîòêó óïðàâëåíèÿ, íàïðÿæåíèÿ â êîòîðûõ ñäâèíóòû íà 90o ýëåêòðè÷åñêèõ ãðàäóñîâ, êàê ïîêàçàíî íà è .

Ðèñ. 3-10à. Ñõåìà àñèíõðîííîãî äâóõôàçíîãî äâèãàòåëÿ.

Ðèñ. 3-10á. Âðåìåííûå äèàãðàììû ïèòàíèÿ àñèíõðîííîãî äâóõôàçíîãî äâèãàòåëÿ.

Äëÿ óïðîùåíèÿ óïðàâëåíèÿ îñóùåñòâëÿåòñÿ óïðàâëåíèå âîçäåéñòâèåì òîëüêî íà îäíó îáìîòêó - îáìîòêó óïðàâëåíèÿ ÷åðåç óñèëèòåëüíî ïðåîáðàçóþùåå óñòðîéñòâî - ÓÏÓ. Âòîðàÿ îáìîòêà ÷åðåç êîíäåíñàòîð ïîäêëþ÷àåòñÿ ê ñåòè.

Ïðè ðåãóëèðîâàíèè òîêà â îáìî= òêå óïðàâëåíèÿ ïî âåëè÷èíå è ôàçå âíîñèòñÿ àñèììåòðèÿ â ÌÄÑ îáìîòîê, è âìåñòî êðóãîâîãî ìàãíèòíîãî ïîëÿ â ìàøèíå âîçíèêàåò ýëåêòðè÷åñêîå ïîëå. Ïðè ýòîì íàðÿäó ñ íàïðÿæåíèÿìè è òîêàìè ïðÿìîé ïîñëåäîâàòåëüíîñòè ôàç, ñîçäàþùèìè äâèãàòåëüíûé ðåæèì, âîçíèêàåò íàïðÿæåíèå è òîêè îáðàòíîé ïîñëåäîâàòåëüíîñòè, âûçûâàþùèå òîðìîæåíèå. Òàêèì îáðàçîì, ìåíÿÿ ñòåïåíü àñèììåòðèè, ìîæíî ðåãóëèðîâàòü ñêîðîñòü äâèãàòåëÿ.

 çàâèñèìîñòè îò òîãî, êàê ñîçäàåòñÿ â ìàøèíå àñèììåòðèÿ ìàãíèòíîãî ïîëÿ, ðàçëè÷àþò òðè ñïîñîáà óïðàâëåíèÿ: àìïëèòóäíûé, ôàçîâûé è àìïëèòóäíî-ôàçîâûé.

×àùå âñåãî èñïîëüçóåòñÿ àìïëè= òóäíîå íåñèììåòðè÷íîå óïðàâëåíèå, êîãäà UB=3DUC, à Uγ=3Dα·Uc, ãäå α ìåíÿåòñÿ îò 0 äî 1. Ïîëüçóÿ= ñü ñîîòíîøåíèÿìè è ìîæíî ïîëó÷èòü âûðàæåíèÿ äëÿ âðàùàþùåãî ìîìåíòà ïðè àìïëèòóäíîì óïðàâëåíèè:

Ïðè ñèììåòðèè íàïðÿæåíèé, êîã= äà α=3D1, èç óðàâíå= íèÿ ïîëó÷èì íîðìàëüíîå óðàâíåíèå - âûðàæåíèå äëÿ àñèíõðîíí= îé ìàøèíû .

Òàê êàê â äâóõôàçíûõ äâèãàòåë= ÿõ SM>1, ò= î ïðè α=3D0, ò.å. ïðè = îòêëþ÷åíèè îáìîòêè óïðàâëåíèÿ äâèãàòåëü òîðìîçèòñÿ, òàê êàê âòîðîå ñëàãàåìîå â ñòàíîâèòñÿ áîëüøå ïåðâîãî è îñòàíàâëèâàåòñÿ ïðè S<= /span>=3D1, êîãäà îáà ñëàãàåìûõ ñòàíîâÿòñÿ îäèíàêîâûìè.

Ìåõàíè÷åñêèå õàðàêòåðèñòèêè ï= ðè àìïëèòóäíîì óïðàâëåíèè äëÿ ñëó÷àÿ SM=3D2 è ε=3D3 ïð= èâåäåíû íà ñëåâà.

Ðèñ. 3-10â. Ñòàòè÷åñêèå õàðàêòåðèñòèêè àñèíõðîííîãî äâóõôàçíîãî äâèãàòåëÿ.

Ïóñêîâîé ìîìåíò ìîæíî ïîëó÷èò= ü èç óðàâíåíèÿ , ïîëîæèâ S=3D1.

Íà ñïðàâà ïîêàçàíû ðåãóëèðîâî÷íûå õàðàêòåðèñòèêè, êîòîðûå ìîãóò áûòü ïîëó÷åíû íåïîñðåäñòâåííî èç ìåõàíè÷åñêèõ.

Ýòè õàðàêòåðèñòèêè ìîãóò áûòü ëèíåàðèçîâàíû, è àñèíõðîííûé äâèãàòåëü ïðåäñòàâëåí êàê ëèíåéíàÿ äèíàìè÷åñêàÿ ñèñòåìà, îïèñûâàåìàÿ ñëåäóþùèìè óðàâíåíèÿìè:

,

ãäå KU è Kω- êîýôôèöèåíòû ïåðåäà÷è, ïîëó÷àåìûå ïðè ëèíåàðèçàöèè õàðàêòåðèñòèê, êàê ïîêàçàíî íà .

Ðèñ. 3-11à. Ëèíåàðèçàöèÿ õàðàêòåðèñòèê ÀÄÄ.

;

Óðàâíåíèÿì ñîîòâåòñòâóåò ñòðóêòóðíàÿ ñõåìà ,<= /span> ïðåäñòàâëåííàÿ íà .

Ðèñ. 3-11á. Ñòðóêòóðíàÿ ñõåìà ÀÄÄ.

Ïî ýòîé ñõåìå ìîæíî ïîëó÷èòü ïåðåäàòî÷íóþ ôóíêöèþ ÀÄÄ

,

ãäå - êîýôôèöèåíò ïåðåäà÷è, à - ýëåêòðîìåõàíè÷åñêàÿ ïîñòîÿííàÿ âðåìåíè.


3.4. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 3.

  1. Ïîñòðîèòü â îòíîñèòåëüíûõ åäèíèöàõ çàâèñèìîñòü ìîìåíòà îò ñêîëüæåíèÿ äëÿ òðåõôàç= íîãî àñèíõðîííîãî äâèãàòåëÿ f(s)=3DÌä/Ììàêñ äëÿ ðàçëè÷íûõ (íàïðèìåð, Sì=3D0,1; 0,5; 1; 2).
  2. Ïîëüçóÿñü ðåçóëüòàòàìè ï. 1, ïîñòðîèòü ìåõàíè÷åñêèå õàðàêòåðèñòèêè òðåõôàçíîãî äâèãàòåëÿ â îòíîñèòåëüíûõ åäèíèöàõ f(Ìä/Ììàêñ)=3DW// ïðè òåõ æå çíà= ÷åíèÿõ , ÷òî è â ï. 1.
  3. Ïîëüçóÿñü ôîðìóëîé (3-10), ïîñòðîèòü (â îòíîñèòåëüíûõ åäèíèöàõ) êðèâûå ïåðåõîäíî= ãî ïðîöåññà ïðè ïóñêå äâèãàòåëÿ ïðè ðàçëè÷íûõ çíà÷åíèÿõ Sì, êàê ïîêàçàíî íà ðèñ. 3-9,á.
  4. Ïîëüçóÿñü ôîðìóëîé (3-12), ïîñòðîèòü (â îòíîñèòåëüíûõ åäèíèöàõ) ñòàòè÷åñêèå õàðàêòåðèñòèêè àñèíõðîííîãî äâóõôàçíîãî äâèãàòåëÿ, êàê ïîêàçàíî íà ðèñ. 3-10, â, ïðè çàäàííûõ çíà÷åíèÿõ e<0.3 è >1. (íàïðèìåð, e=3D0, Sì=3D1,5).
  5. Ïîëüçóÿñü ôîðìóëàìè (3-13) è (3-14), ðàññ÷èòàòü ïî ïàñïîðòíûì äàííûì äâèãàòåëÿ êîýôôèöèåíòû Êw, Êv è Êäâ è ïîñòîÿííóþ âðåìåíè Òì= (äëÿ ÀÄÏ-362: Ní=3D1950 îá/ìèí, No=3D2650 îá/ìèí , Ìí=3D9,5= Í ñì, Ìï=3D17 Í ñì, Uóí= =3D 120 Â, J=3D0,4 êã ñì**2). Ïðèìå÷àíèå. Ïåðåä ðàñ÷åòîì âñå âåëè÷èíû äîë æíû= áûòü ïðèâåäåíû ê ñèñòåìå åäèíèö ÑÈ.


ÃËÀÂÀ 4. ÑÈÍÕÐÎÍÍÛÅ ÌÀ= ØÈÍÛ


4.1. Ýëåêòðîìåõàíè÷åñê= îå ïðåîáðàçîâàíèå ýíåðãèè â ñèíõðîííûõ ìàøèíàõ

Ñèíõðîííîé ìàøèíîé íàçûâàåòñÿ= äâóõîáìîòî÷íàÿ ýëåêòðè÷åñêàÿ ìàøèíà ïåðåìåííîãî òîêà,= îäíà èç îáìîòîê êîòîðîé âîçáóæäàåòñÿ ñ ÷àñòîòîé ω1, à âòîðàÿ - ïîñòîÿííûì òîêîì.

Íàèáîëüøåå ðàñïðîñòðàíåíèå ïî= ëó÷èëè òðåõôàçíûå ñèíõðîííûå ãåíåðàòîðû áîëüøîé ìîùíîñòè.

 ñèíõðîííûõ ìèêðîìàøèíàõ äëÿ îáðàçîâàíèÿ ïîëÿ âîçáóæäåíèÿ ÷àñòî èñïîëüçóþòñÿ ïîñòîÿííûå ìàãíèòû.

 çàâèñèìîñòè îò ôîðìû ìàãíèò= íîé ñèñòåìû ðîòîðà ñèíõðîííûå ìàøèíû áûâàþò ÿâíîïîëþñíûìè<= /span> è íåÿâíîïîëþñíûìè.

Ðàññìîòðèì ýëåêòðîìåõàíè÷åñêîå ïðåîáðàçîâàíèå ýíåðãèè â ñèíõðîííîé ìàøèíå íà ïðèìåðå îäíîïåðèîäíîé ìîäåëè = ÿâíîïîëþñíîãî ñèíõðîííîãî ãåíåðàòîðà, ñõåìà êîòîðîãî ïîêàçàíà íà .

Ðèñ. 4-1à. Ñõåìà ÿâíîïîëþñíîãî= ñèíõðîííîãî ãåíåðàòîðà.

Òàêàÿ ìàøèíà èìååò òðåõôàçíóþ îáìîòêó íà ñòàòîðå è äâóõïîëþñíûé ðîòîð, íà êîòîðîì íàõîäèòñÿ îáìîòêà âîçáóæäåíèÿ. Ïðîòåêàþùèé ïî ýòîé îáìîòêå òîê âîçáóæäåíèÿ ñîçäàåò ÌÄÑ F0, íàïðàâ= ëåííóþ ïî ïðåäåëüíîé îñè ðîòîðà d è ñîîòâåòñòâåííî ïîòîê âîçáóæäåíèÿ Ô0= (ñì. ). Ïðè âðàùåíèè ðîòîðà â îáìîòêàõ ñòàòîðà âîçíèêàåò ïåðåìåííàÿ ÝÄÑ ñèíóñîèäàëüíîé ôîðìû è ÷àñòîòû ω1=3Dω. Ýòó ÝÄÑ ìîæíî ïðåäñòàâèòü â âèäå âåêòîðà E`0, âðàùà= þùåãîñÿ ñ ÷àñòîòîé ω è íàïðàâëåííîãî ïåðïåíäèêóëÿð= íî âåêòîðó ïîòîêà âîçáóæäåíèÿ Ô`0.

Îäíîïåðèîäíàÿ ìîäåëü ìàøèíû ó= äîáíà òåì, ÷òî â íåé âðåìåííûå è ïðîñòðàíñòâåííûå óãëû ìåæäó âåêòîðàìè ñîâïàäàþò,= ÷òî äàåò âîçìîæíîñòü íàëîæèòü âðåìåííóþ âåêòîðíóþ äèàãðàììó òîêîâ è íàïðÿæåíèé = íà ïðîñòðàíñòâåííóþ êàðòèíó ïîëåé â ìàøèíå, êàê ýòî ñäåëàíî íà .

Ïðè ïîäêëþ÷åíèè îáìîòîê ÿêîðÿ (ñòàòîðà) ê íàãðóçêå â íèõ ïîä äåéñòâèåì ÝÄÑ E0 âîçíèêàåò ïåðåìåííûé òîê ÿêîðÿ Ia, êîòîðûé ñîçäàåò ïåðåìåííûé ìàãíèòíûé ïîòîê ðåàêöèè ÿêîðÿ Ôa, êàê ï= îêàçàíî íà . Ïîëå ðåàêöèè ÿêîðÿ íàêëàäûâàåòñÿ íà ïîëå âîçáóæäåíèÿ, èñêàæàÿ åãî è èçìåíÿÿ, òàêèì îáðàçîì, âåêòîð E`0 êàê ïî âåëè÷èíå, òàê è ïî íàïðàâëåíèþ.  íàãðóæåííîé ìàøèíå âîçíèêàåò ñëîæíàÿ êàðòèíà âðàùàþùåãîñÿ ìàãíèòíîãî ïîëÿ, âñëåäñòâèå ÷åãî àíàëèç ïðîöåññîâ âåñüìà çàòðóäíèòåëåí.

Äëÿ íåíàñûùåííîé ìàøèíû ñïðàâ= åäëèâû ëèíåéíûå çàâèñèìîñòè ìåæäó ÌÄÑ, ïîòîêîì è ÝÄÑ, ïîýòîìó ïðèìåíèì ïðèíöèï ñóïåðïîçèöèè, ò.å. ìîæíî ðàññìàòðèâàòü îòäåëüíî ïîëå âîçáóæäåíèÿ è âîçíèêàþ= ùèå ïðè ýòîì ÝÄÑ è ïîëå ðåàêöèè ÿêîðÿ è ÝÄÑ, âîçíèêàþùèå îò åãî âðàùåíèÿ, à çàò= åì ïðîèçâîäèòü âåêòîðíîå ñëîæåíèå ÝÄÑ.

Áóäåì ñ÷èòàòü, ÷òî ãåíåðàòîð íàãðóæåí íà àêòèâíî-èíäóêòèâíóþ íàãðóçêó (êàê ýòî îáû÷íî áûâàåò). Òîãäà òîê ÿêîðÿ Ia îòñòàåò ïî ôàçå îò îñíîâíîé ÝÄÑ E0 íà óãîë Ψ, êàê ïîêàçàíî íà . Ýòîò òîê ñîçäàåò â ìàãíèòíîé ñèñòåìå ìàøèíû ÌÄÑ Fa, âåêòîð= êîòîðîé ïîêàçàí íà . Äëÿ òîãî, ÷òîáû îöåíèòü âëèÿíèå ÌÄÑ ðåàêöèè ÿêîðÿ Fa íà îñíîâíóþ ÝÄÑ E0, ïðîèçâîäÿò ðàçëîæåíèå âåêòîðà íà äâå ñîñòàâëÿþ= ùèõ, íàïðàâëåííûõ âäîëü ïðîäîëüíîé è ïîïåðå÷íîé îñåé ðîòîðà:

,    

Ýòèì ÌÄÑ ñîîòâåòñòâóþò òîêè <= span lang=3DEN-US style=3D'mso-ansi-language:EN-US'>Id è Iq, äëÿ êî= òîðûõ ñïðàâåäëèâû àíàëîãè÷íûå ôîðìóëû:

.

Ýòè òîêè = ñîçäàþò ÝÄÑ ïðîäîëüíîé è ïîïåðå÷íîé ðåàêöèè ÿêîðÿ, êîòîðûå îòñòàþò îò ñâîèõ ÌÄÑ íà = óãîë 90 ãðàäóñîâ, è, òàêèì îáðàçîì, ÝÄÑ ïðîäîëüíîé ðåàêöèè ÿêîðÿ íàïðàâëåíà âäîëü ïîïåðå÷íîé îñè, à ÝÄÑ ïîïåðå÷íîé ðåàêöèè, íàîáîðîò, âäîëü ïðîäîëüíîé îñè ðîòîðà, êàê ïîêàçàíî íà . Ýòè ñîñòàâëÿþùèå ÝÄÑ ðåàêöèè ÿêîðÿ ìîæíî âûðàçèòü ÷å= ðåç òîê ÿêîðÿ Ia:

ãäå xd è xq íàçûâàþ= òñÿ ñèíõðîííûìè èíäóêòèâíûìè ñîïðîòèâëåíèÿìè ìàøèíû ïî ïðîäîëüíîé è ïîïåðå÷íîé îñÿì.

Åñëè ïðåíåáðå÷ü èíäóêòèâíîñòüþ ðàññåÿíèÿ è àêòèâíûì ñîïðîòèâëåíèåì îáìîòîê ÿêîðÿ, ïîëó÷èì óïðîùåííóþ ýêâèâàëåíòíóþ ñõåìó öåïè ÿêîðÿ ( ). Âðåìåííàÿ âåêòîðíàÿ äèàãðàììà ÿêîðíîé öåïè äëÿ ýòîãî ñëó÷àÿ ïðèâåäåíà íà .

<= /span>

Ðèñ. 4-2à. Óïðîùåííàÿ ýêâèâàëåíòíàÿ ñõåìà ÿêîðíîé öåïè ñèíõðîííîé ìàøèíû.

Ðèñ. 4-2á. Âðåìåííàÿ äèàãðàììà ÿêîðíîé öåïè ñèíõðîííîé ìàøèíû.

Ýëåêòðîìàãíèòíàÿ ìîùíîñòü ñèíõðîííîé ìàøèíû ìîæåò áûòü çàïèñàíà êàê

ãäå U è I- ôàçíîå íàïðÿæåíèå è ôàçíûé òîê ìàøèíû, m- ÷èñëî ôàç.

Ñîãëàñíî óïðîùåííîé âåêòîðíîé äèàãðàììå ìàøèíû ( )

.

Ïîäñòàâëÿÿ â âûðàæåíèå ( ) ïîëó÷èì

Îäíàêî èç äèàãðàììû ñëåäóåò <= /p>

Îòñþäà

Ïîäñòàâëÿÿ ýòè âûðàæåíèÿ â ( ), ïîëó÷èì

Ýëåêòðîìàãíèòíàÿ ýíåðãèÿ ñîñò= îèò èç äâóõ ñîñòàâëÿþùèõ: ïåðâàÿ ÿâëÿåòñÿ ýíåðãèåé âðàùàþùåãîñÿ ìàãíèòíîãî ïîëÿ, ñîçäàâàåìîãî îáìîòêîé âîçáóæäåíèÿ ñ ó÷åòîì åãî èñêàæåíèÿ ðåàêöèåé ÿêîðÿ, à âòîðàÿ - ýíåðãèåé íåñèììåòðèè âðàùàþùèõñÿ ïîëåé ïðîäîëüíîé è ïîïåðå÷íîé ðåàêöèé ÿêîðÿ.

 èäåàëüíîé ìîäåëè ýëåêòðîìàã= íèòíàÿ ýíåðãèÿ ïðåâðàùàåòñÿ â ìåõàíè÷åñêóþ (èëè íàîáîðî= ò), ò.å.

Îòñþäà ìîæåò áûòü ïîëó÷åíî âûðàæåíèå äëÿ ýëåêòðîìàãíèòíîãî ìîìåíòà, òàêæå êàê ñóììû äâóõ ñîñòàâëÿþùèõ =

Ïåðâàÿ ñîñòàâëÿþùàÿ ìîìåíòà -= ýòî ìàãíèòîýëåêòðè÷åñêèé ìîìåíò, âûçâàííûé âîçäåéñòâèåì ïîëÿ âîçáóæäåíèÿ ñ âðàùàþùèìñÿ ìàãíèòíûì ïîëåì, âòîðàÿ ñîñòàâëÿþùàÿ - òàê íàçûâàåìûé ðåàêòèâíûé ìîìåíò, êîòîðûé ñîçäàåòñÿ à ñ÷åò èçìåíåíèÿ èíäóêòèâíîñòè ñèñòåìû ïðè ïîâîðîòå ðîòîðà, ò.å. íåðàâåíñòâà ìàãíèòíûõ ñîïðîòèâëåíèé ïî îñÿì = d è q.

Ñóùåñòâóþò ìàøèíû, â êîòîðûõ èñïîëüçóåòñÿ òîëüêî ïåðâàÿ ñîñòàâëÿþùàÿ ìîìåíòà - ìàãíèòîýëåêòðè÷åñêèå ìàøè= íû, ëèáî òîëüêî âòîðàÿ ñîñòàâëÿþùàÿ - ðåàêòèâíûå ìàøèíû.


4.2. Ñïåöèàëüíûå ñèíõð= îííûå äâèãàòåëè

Ñèíõðîííûå äâèãàòåëè íåáîëüøîé ìîùíîñòè ïðèìåíÿþòñÿ â ñèñòåìàõ àâòîìàòèêè. Ïîñêîëüêó â ñèíõðîííûõ äâèãàòåë= ÿõ ÷àñòîòà âðàùåíèÿ æåñòêî ñâÿçàíà ñ ÷àñòîòîé ïèòàíèÿ, òàêèå äâèãàòåëè ïðèìåíÿ= þòñÿ ëèáî â ñèñòåìàõ, òðåáóþùèõ ñòðîãî ïîñòîÿííîé ÷àñòîòû âðàùåíèÿ, ëèáî ïðè ÷àñòîòíîì óïðàâëåíèè ñêîðîñòüþ.

Ê ãðóïïå ñèíõðîííûõ äâèãàòåëåé ìîæíî îòíåñòè òàêæå äâèãàòåëè, ÷àñòîòà ïèòàíèÿ êîòîðûõ çàâèñèò îò ÷àñòîòû âðàùåíèÿ - ýòî òàê íàçûâàåìûå âåíòèëüíûå äâèãàòåëè. Íî ïîñêîëüêó îíè èìåþò êîììóòàòîð è èõ õàðàêòåðèñòèêè ïîõîæè íà õàðàêòåðèñòèêè äâèãàòåëåé ïîñòîÿíí= îãî òîêà, îíè áóäóò ðàññìîòðåíû â ãëàâå 5.

 öèôðîâûõ ñèñòåìàõ àâòîìàòèêè íàõîäÿò øèðîêîå ïðèìåíåíèå øàãîâûå äâèãàòåëè, â îáìîòêè ñòàòîðà êîòîðûõ ïîñòóïàþò èìïóëüñû òîêà è ïðè ïîñòóïëåíèè êàæäîãî èìïóëüñîâ ïðîèñõîäèò ïîâî= ðîò ðîòîðà íà îïðåäåëåííûé óãîë - äâèãàòåëü ñîâåðøàåò øàã.  çàâèñèìîñòè îò îñîáåííîñòåé âîçáóæäåíèÿ øàãîâûå äâèãàòåëè, êàê è äðóãèå òèïû ñèíõðîííûõ äâèãàòåëåé, äåëÿòñÿ íà äâèãàòåëè ñ àêòèâíûì ðîòîðîì, ïðåäñòàâëÿþùèì ñîáîé <= span class=3DSpellE>ÿâíîïîëþñíûé ðîòîð èç ïîñòîÿííîãî ìàãíèòà, è ñ ðåàêòè= âíûì ðîòîðîì, ïðåäñòàâëÿþùèì ñîáîé ÿâíîïîëþñíûé èëè çóá÷àòûé ðîòîð èç ìàãíèòîìÿãêîãî ìàòåðèàëà.

Ðàññìîòðèì áîëåå ïîäðîáíî ïðè= íöèï äåéñòâèÿ è õàðàêòåðèñòèêè øàãîâûõ äâèãàòåëåé.

Ñòàòîð øàãîâûõ äâèãàòåëåé â î= òëè÷èå îò ñèíõðîííûõ ìèêðîäâèãàòåëåé íåïðåðûâíîãî âðàùåíèÿ èìååò ÿâíîâûðàæåííûå ïîëþñû, íà êîòîðûõ ðàñïîëàãàþòñÿ îáìîòêè óïðàâëåíèÿ. ×èñëî ïàð ïîëþñîâ êàæä= îé èç îáìîòîê óïðàâëåíèÿ p ðàâíî ÷èñëó ïàð ïîëþñîâ ðîòîðà.

Íàèáîëüøåå ðàçâèòèå ïîëó÷èëè = ØÄ àêòèâíîãî òèïà - ñ ðîòîðîì, ñîäåðæàùèì ìíîãîïîëþñíûé ïîñòîÿííûé ìàãíèò.

Ïðèíöèï äåéñòâèÿ òàêîãî ØÄ ðàññìîòðèì íà ïðèìåðå äâóõôàçíîé äâóõïîëþñíîé êîíñòðóêöèè ( ).

Ðèñ. 4-3à. Ñõåìà øàãîâîãî äâèãàòåëÿ.

Ýòîò äâèãàòåëü èìååò äâå âçàè= ìíî ïåðïåíäèêóëÿðíûå îáìîòêè À è Â, â êîòîðûå ìîãóò ïîäàâàòüñÿ èìïóëüñû òîêà ðàçíîé ïîëÿðíîñòè, êàê ïîêàçàíî íà .

Ðèñ. 4-4. Âðåìåííàÿ äèàãðàììà ðàáîòû ØÄ.

Íàëè÷èå òîêà â îáìîòêå ñîçäàåò ìàãíèòíûé ïîòîê ñòàòîðà Ô0, êîòîðûé ïîâîðà÷èâàåòñÿ ïðè ïåðåêëþ÷åíèè îáìîòîê íà óãîë α= . Âñëåä çà ïîòîêîì ïîâîðà÷èâàåòñÿ è àêòèâíûé ðîòîð, ò.å. ïðè êàæäîì ïåðåêëþ÷å= íèè äâèãàòåëü äåëàåò øàã. Ïîëíûé îáîðîò ïîòîêà ñîâåðøàåòñÿ çà m-òàêòíûé (â äàíí= îì ñëó÷àå ÷åòûðåõòàêòíûé) öèêë.

 îáùåì ñëó÷àå äëÿ äâèãàòåëÿ ñ àêòèâíûì ðîòîðîì øàã äâèãàòåëÿ

ãäå p- ÷èñëî ïàð ïîëþñîâ, m- ÷èñëî òàêòîâ óïðàâëåíèÿ.

Ïîâîðîò ðîòîðà ñîâåðøàåòñÿ ïîä äåéñòâèåì òàê íàçûâàåìîãî ñèíõðîíèçèðóþùåãî ìîìåíòà, êîòîðûé âîçíèêàåò ïðè îòêëîíåíèè ðîòîðà îò íàïðàâëåíèÿ ïîòîêà íà óãîë γ= , êàê ïîêàçàíî íà .

×àñòî ââîäÿò ïîíÿòèå ýëåêòðè÷= åñêèõ óãëîâ, ïðè êîòîðûõ ìíîãîïîëþñíûõ äâèãàòåëü ñâîäèòñÿ ê äâóõïîëþñíîé (îäíîïåðèîäíîé) ìîäåëè. Äëÿ äâèãàòåëåé ñ àêòèâíûì ðîòîðîì

; .

Ýëåêòðè÷åñêèé óãîë γý ýêâèâàëåíòåí âíóòðåííåìó óãëó ñèíõ= ðîííîé ìàøèíû Θ â ôîðìóëå . Òîãäà ñîãëàñíî â ØÄ ñ àêòèâíûì ðîòîðîì, ãäå ïðåîáëàäàåò ìàãíèòîýëåêòðè÷åñêèé ìîìåíò

,

ãäå Mc_max- ìàêñèìàëüí= ûé ñèíõðîíèçèðóþùèé ìîìåíò, fñý è fðý- ýëåêòðè÷åñêèå óãëû ïîâîðîòà ÌÄÑ ñòàòîðà è îñè ðîòîðà.

Ïðè ïåðåêëþ÷åíèè ôàçû ïðîèñõî= äèò ñäâèã ñòàòè÷åñêîé õàðàêòåðèñòèêè íà óãîë αý<= /sub>, êàê ïîêàçàíî íà .

Ðèñ. 4-3â. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà øàãîâîãî äâèãàòåëÿ.

Âîçíèêàåò ïóñòîé ìîìåíò M= ï, ïîä äåéñòâèåì êîòîðîãî ïðîèñõîäèò ïîâîð= îò ðîòîðà â ñîãëàñîâàííîå ñ ìàãíèòíûì ïîòîêîì ïîëîæåíèå. Åñëè äâèãàòåëü íàãðóæ= åí âíåøíèì ìàãíèòîì MB, òî ðîòîð ïåðåõîäèò èç òî÷êè 1 â òî÷êó 3 ïî òðàåêòîðèè 1-2-3. Äëÿ òîãî, ÷òîáû ïðè ïåðåêëþ÷åíèè îáìîòêè ïðîèñõîäèë ïîâîðîò ðîòîðà, íåîáõîäèìî âûïîëíåíèå óñëîâèÿ MÏMB. Îò= ñþäà ñóùåñòâóåò äîïóñòèìûé âíåøíèé ìîìåíò Mäîï è ñîîòâåòñòâóþùèé= åìó äîïóñòèìûé óãîë îòêëîíåíèÿ îñè ðîòîðà îò íàïðàâëåíèÿ ïîòîêà γý_äîï, ïðè êîòîðûõ ÌÏ=3DÌÂ=3DÌÄÎÏ. ×åì áîëüøå ØÄ èìååò ôàçíûõ îáìîòîê è ñîîòâåòñòâåííî òàêòîâ ïåðåêëþ÷åíèÿ, òåì ìåíüøå ó íåãî øàã γý è ñîîòâåòñ= òâåííî áîëüøå ÌÄÎÏ. Ïîýòîìó îáû÷íî ØÄ ÿâëÿþòñÿ ìíîãîôàçíûìè (îò 3-õ äî = 6-òè ôàç). Ïî ýòîé ïðè÷èíå, êàê âèäíî èç , äâóõôàçíûé ØÄ ñ ïàññèâíûì ðîòîðîì âîîáùå íå ðàáîòîñïîñîáåí.

Ðèñ. 4-3ã. Ñõåìà øàãîâîãî äâèãàòåëÿ.

Ðèñ. 4-3ä. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà øàãîâîãî äâèãàòåëÿ.

Ðèñ. 4-3å. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà øàãîâîãî äâèãàòåëÿ.

Òàê, ó íåãî ñîãëàñíî âðàùàþùèé ìîìåíò îïðåäåëÿåòñÿ ðåàêòèâíîé ñîñòàâëÿþùåé =

è ñòàòè÷åñêàÿ õàðàêòåðèñòèêà = èìååò âèä, ïîêàçàííûé íà .

Îòñþäà ñîîòíîøåíèÿ äëÿ ýëåêòðè÷åñêèõ è ãåîìåòðè÷åñêèõ óãëîâ ïîâîðîòà ðîòîðà áóäóò

; ,

ò.å. äëÿ = äâóõôàçíîãî ØÄ p=3D1,α= =3D90·ãðàä, à αý=3D180·ãðàä, ñäâèã õàðàêòåð= èñòèêè ïðè ïåðåêëþ÷åíèè ôàçû ïðîèñõîäèò íà 180 ãðàäóñîâ, êàê ïîêàçàíî íà è ðîòîð íå ïîâîðà÷èâàåòñÿ, òàê êàê ïóñêîâîé ìîìåíò ðàâ= åí íóëþ.

Ôèçè÷åñêè ýòî ìîæíî îáúÿñíèòü= òåì îáñòîÿòåëüñòâîì, ÷òî ïðè ïàññèâíîì ðîòîðå íàïðàâëåíèå ñèíõðîíèçèðóþùåãî ìîì= åíòà íå çàâèñèò îò íàïðàâëåíèÿ ïîòîêà. Ìîìåíò ðàâåí íóëþ è â òîì ñëó÷àå, êîãäà ï= îòîê íàïðàâëåí âäîëü ïîëþñîâ è êîãäà ïîïåðåê ïîëþñîâ, è äîñòèãàåò ìàêñèìóìà, êîã= äà îñü ðîòîðà ðàñïîëàãàåòñÿ ìåæäó ïîëþñàìè ñòàòîðà, â îòëè÷èå îò àêòèâíîãî ðîò= îðà, â êîòîðîì ìîìåíò ìàêñèìàëåí, åñëè ïîòîê íàïðàâëåí ïîïåðåê ðîòîðà. Ïîýòîìó ðåàêòèâíûå ØÄ äîëæíû èìåòü êàê ìèíèìóì òðè îáìîòêè è ò= ðåõòàêòíóþ ñèñòåìó êîììóòàöèè.

Ñóùåñòâóþò ðàçëè÷íûå ðåæèìû ð= àáîòû ØÄ:

Ñòàòè÷åñêèé ðåæèì ñîîòâåòñòâó= åò ïðîõîæäåíèþ ïîñòîÿííîãî òîêà ïî îáìîòêàì óïðàâëåíèÿ, ñîçäàâàÿ íåïîäâèæíîå ìàãíèòíîå ïîëå. Îñíîâíîé õàðàêòåðèñòèêîé ýòîãî ðåæèìà ÿâëÿåòñÿ ñòàòè÷åñêàÿ õàðàêòåðèñòèêà MC= =3Df(γý), ðàññìîòðåííàÿ ðàíåå ( ).

Ðåæèì îòðàáîòêè åäèíè÷íûõ øàã= îâ ñîîòâåòñòâóåò ÷àñòîòå óïðàâëÿþùèõ èìïóëüñîâ, ïðè êîòîðîé ïåðåõîäíûé ïðîöåññ, ÷àùå âñåãî êîëåáàòåëüíûé, íà êàæäîì øàãå çàêàí÷èâàåòñÿ ê íà÷àëó ñëåäóþùåãî øàãà, ò.å. óãëîâàÿ ñêîðîñòü ðîòîðà f`ð â íà÷àëå êàæäîãî øàãà ðàâíà íóëþ (ñì. ).

<= /span>

Ðèñ. 4-5. Îòðàáîòêà åäèíè÷íûõ øàãîâ.

Îñíîâíûìè ïîêàçàòåëÿìè ýòîãî = ðåæèìà ÿâëÿþòñÿ: ïåðåðåãóëèðîâàíèå Δfï, ìàêñèìàëüíîå çíà÷åíèå ìãíîâåííîé óãëîâîé ñêîðîñòè f`p_max, âðåìÿ çàòóõàíèÿ ñâîáîäí= ûõ êîëåáàíèé ðîòîðà tçàò.

Åñëè âðåìÿ ýëåêòðîìàãíèòíûõ ïåðåõîäíûõ ïðîöåññîâ çíà÷èòåëüíî ìåíüøå, ÷åì ìåõàíè÷åñêèõ, äâèæåíèå ðîòîðà íåíàãðóæåííîãî ØÄ ìîæíî îïèñàòü ñëåäóþùèì óðàâíåíèåì

,

ãäå Mäèí- äèíàìè÷åñêèé ìîìåíò= , Ìäåì- äåìïôèðóþùèé ýëåêòðîìàãíèòíûé ìîìåíò= .

Äèíàìè÷åñêèé ìîìåíò îïðåäåëÿå= òñÿ ìîìåíòîì èíåðöèè ðîòîðà è óñêîðåíèåì:

Âíóòðåííåå ýëåêòðîìàãíèòíîå äåìïôèðîâàíèå êîëåáàíèé ðîòîðà ïðîèñõîäèò çà ñ÷åò ïîâåäåíèÿ ÝÄÑ âðàùåíèÿ â îáìîòêàõ óïðàâëåíèÿ. Çíà÷åíèå äåìïôèðóþùåãî ìîìåíòà ïðîïîðöèîíàëüíî óãëîâîé ñêîðîñòè ðîòîðà:

,

ãäå D- êîýôôèöèåíò äåìïôèðîâàíèÿ.

Åñëè ðàññìàòðèâàòü ðàáîòó ØÄ ïðè ìàëûõ óãëàõ ðàññîãëàñîâàíèÿ îñåé ðîòîðà è ÌÄÑ ñòàòîðà (sin(γ)≈ γ), ò= î, ïîäñòàâèâ , è â , ïîëó÷èì äèôôåðåíöèàëüíîå óðàâíåíèÿ äâèæåíèÿ ðîòîðà: =

 ýòîì âûðàæåíèè êîýôôèöèåíò = ïðè fðý åñòü êâàäðàò óãëîâîé ÷àñòîòû ñîáñòâåííûõ êîëåáàíèé ðîòîðà

,

à êîýôôèöèåíò ïðè f`ðý õàðàêòåðèçóåò îòíîñèòåëüíûé êîýôôèöèåíò çàòóõàíèÿ êîëåáàíèé λ:

.

Óñòàíîâèâøèéñÿ ðåæèì ðàáîòû ØÄ ñîîòâåòñòâóåò ïîñòîÿííîé ÷àñòîòå óïðàâëÿþùèõ èìïóëüñîâ f, ïðè÷åì .  óñòàíîâèâøåìñÿ ðåæèìå âðàùåíèå ðîòîðà ñ íåêîòîðîé ñðåäíåé óãë= îâîé ñêîðîñòüþ ω ñîïðîâîæäàåòñÿ âûíóæäåííûìè êîëåáàíèÿìè.

Àìïëèòóäà êîëåáàíèé äîñòèãàåò íàèáîëüøåãî çíà÷åíèÿ ïðè ÷àñòîòå óïðàâëÿþùèõ èìïóëüñîâ, ñîâïàäàþùåé ñ ðåçîí= àíñíîé - ñîáñòâåííîé ÷àñòîòîé ðîòîðà:

Âàæíîé õàðàêòåðèñòèêîé óñòàíîâèâøåãîñÿ ðåæèìà ÿâëÿåòñÿ ïðåäåëüíàÿ ìåõàíè÷åñêàÿ õàðàêòåðèñòèêà, ïðåäñòàâëÿþùàÿ ñîáîé çàâèñèìîñòü äîïóñòèìîãî ìîìåíòà ñîïðîòèâëåíèÿ îò ÷àñòî= òû óïðàâëÿþùèõ èìïóëüñîâ. Ïðåäåëüíóþ ìåõàíè÷åñêóþ õàðàêòåðèñòèêó ðàññìàòðèâàþò îáû÷íî ïðè f>= ;f0 ( ).

Ðèñ. 4-6à. Ïðåäåëüíûå ìåõàíè÷åñêèå õàðàêòåðèñòèêè ØÄ.

Ñíèæåíèå = MÄÎÏ ïðè óâåëè÷åíèè f îáúÿñíÿåòñÿ â îñíîâíîì íàëè÷èåì ýëåêòðîìàãíèòíîé ïîñòîÿííîé âðåìåíè Tó îáìîòîê óïðàâëåíèÿ

,

ãäå Ró è Ló-= àêòèâíîå ñîïðîòèâëåíèå è èíäóêòèâíîñòü îáìîòîê óïðàâëåíèÿ. Ïîñëåäíåå îáúÿñíÿåòñÿ òåì, ÷òî ÷åì áîëüøå Tó, òåì ìåíüøå çà âðåìÿ èìïóëüñà íàðàñòàåò òîê, ÷òî ñíèæàåò ñèíõðîíèçèðóþùèé ìîìåíò. Ñíèæåíèå íàïðÿæåíèÿ ïèòàíèÿ òàêæå óìåíüøàåò MÄÎÏ.

Ïåðåõîäíûå ïðîöåññû - ïóñê, òîðìîæåíèå, ðåâåðñ, ïåðåõîä ñ îäíîé ÷àñòîòû íà äðóãóþ - ñîïðîâîæäàþòñÿ ïåðåõîäíûìè ïðîöåññàìè â ØÄ.

Âàæíûì ïîêàçàòåëåì ïåðåõîäíîãî ðåæèìà ÿâëÿåòñÿ ïðèçåìèñòîñòü ØÄ - íàèáîëüøàÿ ÷àñòîòà óïðàâëÿþùèõ èìïóëüñîâ, îòðàáàòûâàåìàÿ ØÄ äëÿ ïîòåðè øàãà - ÷àñòîòà ïðèåìèñòîñòè fïð= .

Ïðèåìèñòîñòü ðàñòåò ñ óâåëè÷å= íèåì ñèíõðîíèçèðóþùåãî ìîìåíòà, à òàêæå ñ óìåíüøåíèåì øàãà, ìîìåíòà èíåðöèè è ñòàòè÷åñêîãî ìîìåíòà ñîïðîòèâëåíèÿ (ñì. , ãäå ÌÂ- âíåøíèé ìîìåíò ñîïðîòèâëåíèÿ òèïà òðåíèÿ).

Ðèñ. 4-6á. Ïðåäåëüíûå äèíàìè÷åñêèå õàðàêòåðèñòèêè ØÄ.


4.3. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 4.

  1. Àíàëîãè÷íî ðèñ. 4-3, à è á ïîñòðîèòü êàðòèíó ìàãíèòíîãî ïîëÿ è óñòàíîâèâøåãîñÿ ïîëîæåíèÿ ðîòîðà ØÄ ïðè îäíîâðåìåííîé çàïèòêå äâóõ îáìîòîê ñòàòîðà.
  2. Àíàëîãè÷íî ðèñ. 4-3, â ïîñòðîèòü ñòàòè÷åñêèå õàðàêòåðè= ñòèêè ØÄ äëÿ ðåæèìà ïîñëåäîâàòåëüíîãî âêëþ÷åíèÿ îäíîé îáìîòêè è ïàðû îáìîòîê. Îïðåäåëèòü äëÿ ýòîãî ðåæèìà Ìäîï è = g= ýäîï .
  3. Äëÿ ÷åòûðåõôàçíîãî ØÄ òèïà ÄØ78-0,16-1 îïðåäåëèòü ñîáñòâåííóþ ÷àñòîòó êîëåáàíèé fî. <= span class=3DGramE>(Ïàðàìåòðû äâèãàòåëÿ: Ìñìàêñ=3D0,56 Íì; J=3D= 0.00001 êã ì**2; a=3D1 ãðàä.).


ÃËÀÂÀ 5. ÝËÅÊÒÐÈ×ÅÑÊÈÅ ÌÀØÈÍÛ ÏÎÑÒÎßÍÍÎÃÎ ÒÎÊÀ


5.1. Ïðèíöèï äåéñòâèÿ è ïðåîáðàçîâàíèå ýíåðãèè â ìàøèíàõ ïîñòîÿííîãî òîêà

Ïðèíöèï äåéñòâèÿ ýëåêòðè÷åñêîé ìàøèíû ïîñòîÿííîãî òîêà ìîæåò áûòü ðàññìîòðåí íà ïðèìåðå ïðîñòåéøåãî ãåíåðà= òîðà ïîñòîÿííîãî òîêà, ôóíêöèîíàëüíàÿ ñõåìà êîòîðîãî ïîêàçàíà íà .

Ðèñ. 5-1à. Ïðîñòåéøàÿ ìàøèíà ïîñòîÿííîãî òîêà.

Îíà ïðåäñòàâëÿåò ñîáîé ðàìêó, ñîäåðæàùóþ îäèí èëè w<= /span> âèòêîâ, è âðàùàþùóþñÿ ñ ÷àñòîòîé ω â ïîñòî= ÿííîì ìàãíèòíîì ïîëå, ñîçäàâàåìîì ïîñòîÿííûì ìàãíèòîì èëè ýëåêòðîìàãíèòîì.

Ïî çàêîíó ýëåêòðîìàãíèòíîé èí= äóêöèè ïðè èçìåíåíèè ïîòîêîñöåïëåíèÿ â ïðîâîäíèêàõ âîçíèêàåò = ÝÄÑ

,

ãäå ]= 6;- ïîòîêîñöåïëåíèå, w- ÷èñëî âèòêîâ, B- ìàãíèòíàÿ èíäóêöèÿ, S<= /span>- ñå÷åíèå, ÷åðåç êîòîðîå ïðîõîäèò ïîòîê ïðè âçàèìîäåéñòâèè ñ îáìîòêîé. ÝÄÑ âîçíèêàåò, åñëè ìåíÿåòñÿ âî âðåìåíè õîòÿ áû îäíà = èç âåëè÷èí, ñòîÿùèõ â ÷èñëèòåëå ôîðìóëû .  òðàíñôîðìàòîðàõ è ìàøèíàõ ïåðåìåííîãî òîêà èçìåíÿå= òñÿ ìàãíèòíàÿ èíäóêöèÿ, à â ìàøèíàõ ïîñòîÿííîãî òîêà èíäóêöèÿ ïîñòîÿííà, à èçìåíÿåòñÿ ïëîùàäü ñöåïëåíèÿ îáìîòîê ÿêîðÿ ñ ïîëåì âîçáóæäåíèÿ èç-çà âðàùåí= èÿ ðîòîðà.

Åñëè ïðîâîäíèê ïåðåìåùàåòñÿ â ìàãíèòíîì ïîëå â ïëîñêîñòè, ïåðïåíäèêóëÿðíîé ñèëîâûì ëèíèÿì, êàê ýòî áûâàåò= â ëèíåéíûõ äâèãàòåëÿõ, òî

,

ãäå l- äëèíà ïðîâîäíèêà â ïîëå, v- ëèíåéíàÿ ñêîðîñòü ïåðåìåùåíèÿ ïðîâîäíèêà.

Òîãäà ñîãëàñíî

.

Ïðè âðàùåíèè ñ ÷àñòîòîé ω

,

ãäå D- äèàìåòð ðîòîðà, êàê ïîêàçàíî íà .

Ðèñ. 5-1á. ÝÄÑ, âîçíèêàþùàÿ ïðè âðàùåíèè ÿêîðÿ ìàøèíû ïîñòîÿííîãî òîêà= .

 ýòîì ñëó÷àå ñîãëàñíî ïîëó÷èì

,

ò.å. â îáìîòêå ÿêîðÿ èíäóöèðó= åòñÿ ÝÄÑ, èçìåíÿþùàÿñÿ ïî ïåðèîäè÷åñêîìó çàêîíó ñ ÷àñòîòîé (ñì. ).

Ðèñ. 5-1â. ÝÄÑ, âîçíèêàþùàÿ ïðè âðàùåíèè ÿêîðÿ ìàøèíû ïîñòîÿííîãî òîêà= .

×òîáû âî âíåøíåé öåïè òîê ïðî= òåêàë â îäíîì íàïðàâëåíèè, îí äîëæåí áûòü âûïðÿìëåí. Äëÿ ýòîãî ñëóæèò ñïåöèàëüíûé ýëåêòðîìåõàíè÷åñêèé âûïðÿìèòåëü - êîëëåêòîð (Ê), ðàñïîëîæåííûé íà âàëó ìàøè= íû.  ïðîñòåéøåì ñëó÷àå, êàê íà , èñïîëüçóþòñÿ äâå ïëàñòèíû ñ íàëîæåííûìè íà íèõ ùåòêà= ìè. Ïîñëåäíèå òàê äîëæíû áûòü ðàñïîëîæåíû â ïðîñòðàíñòâå, ÷òîáû êîììóòàöèÿ ïðîèñõîäèëà â ìîìåíòû ïåðèîäà ÝÄÑ ÷åðåç íîëü. Ï= ðè ýòîì ÝÄÑ, ñíèìàåìàÿ ñî ùåòîê, áóäåò èìåòü âèä, ïîêàçàííûé íà ñïëîøíîé ëèíèåé, ïóëüñèðóþùàÿ ÝÄÑ= . Ñ óâåëè÷åíèåì êîëè÷åñòâà ðàìîê (ñåêöèé) è ñîîòâåòñòâåííî ïëàñòèí êîëëåêòîðà ïóëüñàöèè óìåíüøàþòñÿ. Òàê, íà , ïóíêòèðíîé ëèíèåé ïîêàçàíà ÝÄÑ<= /span> ïðè ÷åòûðåõ êîëëåêòîðíûõ ïëàñòèíàõ, à ïðè âîñüìè êîëëåêòîðíûõ ïëàñòèíàõ ïóëüñàöèÿ íàïðÿæåíèÿ íà ùåòêàõ íå ïðåâûøàåò 1% îò ñðåäíåãî, ïîýòîìó òîê, ïðîòåêàþùèé âî âíåøíåé öåïè, ìîæíî ñ÷èòàòü ïðàêòè÷åñêè ïîñòîÿííûì. <= /p>

Ðèñ. 5-1ã. Âîçíèêàþùàÿ ÝÄÑ.

Ìàãíèòíîå= ïîëå, ñîçäàâàåìîå â ìàøèíå ïîñòîÿííîãî òîêà, ñîñòîèò èç äâóõ ñîñòàâëÿþùèõ - ïîëÿ âîçáóæäåíèÿ, ñîçäàâàåìîãî ïîñòîÿííûì ìàãíèòîì èëè ýëåêòðîìàãíèòîì (ñì. ) è ïîëÿ ÿêîðÿ (ðåàêöèè) ÿêîðÿ, ñîçäàâàåìîãî òîêîì ÿêî= ðÿ, ïðîòåêàþùèì â îáìîòêàõ ÿêîðÿ, ðàñïîëîæåííûõ íà ðîòîðå (ñì. ).

à)

á)

Ðèñ. 5-2à. Êàðòèíà ìàãí= èòíîãî ïîëÿ â ìàøèíå ïîñòîÿííîãî òîêà.

Ïîëå âîçáóæäåíèÿ íåïîäâèæíî î= òíîñèòåëüíî ñòàòîðà, à ïîëå ðåàêöèè ÿêîðÿ èç-çà ñèíõðîííîé êîììóòàöèè îáìîòîê ÿêîðÿ âðàùàåòñÿ îòíîñèòåëüíî ðîòîðà ñ òîé æå ÷àñòîòîé ω= , ñ êàêîé âðàùàåòñÿ ñàì ðîòîð, íî â îáðàòíóþ ñòîðîíó, è òàêèì îáðàçîì òàêæå íåïîäâèæíî îòíîñèòåëüíî ñòàòîðà.

Íàïðàâëåíèå ïîòîêà ðåàêöèè ÿê= îðÿ ñîâïàäàåò ñ ëèíèåé, íà êîòîðîé ðàçìåùåíû ùåòêè ì= àøèíû. Ïðè ýòîì ðåçóëüòèðóþùàÿ êàðòèíà ìàãíèòíîãî ïîëÿ ìàøèíû ïðèîáðåòàåò âèä, ïðåäñòàâëåííûé íà .

Ðèñ. 5-2â. Êàðòèíà ìàãíèòíîãî ïîëÿ â ìàøèíå ïîñòîÿíí= îãî òîêà.

Ïðîèñõîäèò èñêàæåíèå ïîëÿ âîçáóæäåíèÿ è îòêëîíåíèÿ òàê íàçûâàåìîé ôèçè÷åñêîé íåé= òðàëè îò ãåîìåòðè÷åñêîé íåéòðàëè íà óãîë α. ×åì áîëüøå íàãðóæåíà ìàøèíà, òåì áîëüøå òîê ÿ= êîðÿ, ïðîèñõîäèò áîëüøåå èñêàæåíèå ïîëÿ, íàòÿæåíèå ìàãíèòíûõ ñèëîâûõ ëèíèé è óâåëè÷åíèå óãëà α.

Òàêèì îáð= àçîì, ïî ïðèíöèïó äåéñòâèÿ ìàøèíà ïîñòîÿííîãî òîêà ÿâëÿåòñÿ îáðàùåííîé ñèíõðîííîé ìàøèíîé ñ ñèíõðîííûì êîììóòàòîðîì, â êîòîðîé ñîçäàåòñÿ âðàùàþùååñÿ ìàãíèòíîå ïîëå íå îòíîñèòåëüíî ñòàòîðà, à îòíîñèòåëüíî ðîòîðà, ïðè÷åì áëàãîäàðÿ íàëè÷= èþ êîëëåêòîðà (ñèíõðîííîãî êîììóòàòîðà) ýòî ïîëå âðàùàåòñÿ ñèíõðîííî ñ ðîòîðîì= , íî â îáðàòíóþ ñòîðîíó, à ïðè óâåëè÷åíèè íàãðóçêè ïðîèñõîäèò ôàçîâûé ðàçâîðîò ý= òîãî ïîëÿ îòíîñèòåëüíî ïîëÿ ñòàòîðà íà óãîë α. =

Âåñüìà âàæåí â ìàøèíå ïîñòîÿí= íîãî òîêà ïðîöåññ êîììóòàöèè. Ïðè êîììóòàöèè òîê â êîììóòèðó= åìîé ñåêöèè îáìîòêè ÿêîðÿ i= k ìåíÿåò íàïðàâëåíèå íà îáðàòíîå (ñì. ).

à)

á)

â)

Ðèñ. 5-3à. Êîììóòàöèÿ= ñåêöèé îáìîòêè ÿêîðÿ.

Ïðè îòñóòñòâèè ÝÄÑ â êîììóòèðóåìîé ñåêöèè èçìåíåíèå òîêà ik ïðîèñõîäèò ïî ëèíåéíîìó çàêîíó - ëèíèÿ 1 íà  (ëèíåéíàÿ êîììóòàöèÿ). Ýêâèâàëåíòíàÿ ñõåìà ëèíåéíîé êîììóòàöèè ïîêàçàíà íà , ãäå rc- ñîïðîòèâëåíèå ñåêöèè, à r1 è r2- ñîïðîòèâëåíèÿ ùåòî÷íûõ êîíòàêòîâ, êîòîðûå îáðàòíî ïðîïîðöèîíàëüíû ïëîùàäè ùåòî÷íîãî êîíòàêòà è ìåíÿþòñÿ ïðè ïîâîðîòå êîëëåêòîðà òàê, ÷òî òîêè i1 è i2 èçìåíÿþ= òñÿ ëèíåéíî çà âðåìÿ êîììóòàöèè, êîòîðîå îáû÷íî ñîñòàâëÿåò åäèíèöû ìèëëèñåêóíä.=

 ðåàëüíûõ óñëîâèÿõ â êîðîòêîçàìêóíîòîé ñåêöèè ñóùåñòâóåò ÝÄÑ âðàùåíèÿ, âûçâàííàÿ ðåàêöèåé ÿêîðÿ, è ÝÄÑ ñàìîèíäóêöèè, êîòîðûå ïðèâîäÿò ê çàäåðæêå ñïàäà òîêà ik- çàìåäëåííàÿ êîììóòà= öèÿ (êðèâàÿ 2 íà ).

Ýòî ïðèâîäèò ê óñèëåíèþ èñêðå= íèÿ íà ñáåãàþùåì êðàå ùåòî÷íîãî êîíòàêòà, êîòîðîå ìîæåò îêàçàòüñÿ îïàñíûì äëÿ ìàøè= íû. Äëÿ óëó÷øåíèÿ óñëîâèé êîììóòàöèè â áîëüøèõ ìàøèíàõ ñîçäàþòñÿ äîïîëíèòåëüíûå ïîëþñà, êîìïåíñèðóþùàÿ ÝÄÑ<= /span> ñàìîèíäóêöèè è êîìïåíñàöèîííûå îáìîòêè, íåéòðàëèçóþùèå ðåàêöèþ ÿêîðÿ.  íåðåâåðñèâíûõ ìàøèíàõ ìàëîé ìîùíîñòè ïðîèçâîäèòñÿ ñìåùåíèå ùåòîê íà ôèçè÷åñ= êóþ íåéòðàëü.

×ðåçìåðíî áîëüøîé ïîòîê äîáàâ= î÷íûõ ïîëþñîâ òàêæå íåæåëàòåëåí. Ïðè ïðåêîìïåíñàöèè âîçíèêàåò òàê íàçûâàåìàÿ óñêîðåííàÿ êîììóòàöèÿ, (êðèâàÿ 3 íà ), ïðè êîòîðîé ïîÿâëÿåòñÿ èñêðåíèå ïîä íàáåãàþùèì êðàåì ùåòêè.

Ðàññìîòðèì ýëåêòðîìåõàíè÷åñêîå ïðåîáðàçîâàíèå ýíåðãèè â ìàøèíå ïîñòîÿííîãî òîêà íà ïðèìåðå äâèãàòåëÿ ñ âîçáóæäåíèåì îò ïîñòîÿííîãî ìàãíèòà, ñõåìà êîòîðîãî ïðèâåäåíà íà .

Ðèñ. 5-4à. Äâèãàòåëü ïîñòîÿííîãî òîêà.

Ýêâèâàëåíòíàÿ ñõåìà ÿêîðíîé ö= åïè ïîêàçàíà íà , ãäå Rß- àêòèâíîå ñîïðîòèâëåíèå îáìîòîê ÿêîðÿ, Lß- èíäóêòèâíîñòü îáìîòîê, Eß- ñðåäíåå çíà÷åíèå ÝÄÑ âðàùåíèÿ.

Ðèñ. 5-4á. Ýêâèâàëåíòíàÿ ñõåìà äâèãàòåëÿ ïîñòîÿííîãî= òîêà.

Ïðè äîñòàòî÷íî áîëüøîì êîëè÷å= ñòâå ñåêöèé îáìîòîê ÿêîðÿ è ñîîòâåòñòâóþùåì åìó êîëè÷åñòâå ïëàñòèí êîëëåêòîðà ÝÄÑ âðàùåíèÿ Eß ïðàêòè÷åñêè íå = èìååò ïóëüñàöèé è íå çàâèñèò îò ïîëîæåíèÿ ðîòîðà, à òîëüêî îò ñêîðîñòè åãî âðàùåíèÿ. Ïîýòîìó åå ìîæíî âû÷èñëÿòü íå ïî , à ïî , ïðèíÿâ ; , ãäå N- îáùåå ÷èñëî ïðîâîäíèêîâ ÿêîðÿ, 2·a- ÷èñëî ïàðàëëåëüíûõ âåòâåé îáìîòêè, D- äèàìåòð ÿêîðÿ.

Ìàãíèòíóþ èíäóêöèþ B ìîæíî âûðàçèòü ÷åðå= ç ïîòîê âîçáóæäåíèÿ ÔÂ:

,

ãäå S- ïëîùàäü ïîëþñíîãî íàêîíå÷íèêà.<= /p>

,

ãäå p- ÷èñëî ïàð ïîëþñîâ ìàøèíû.

Ïîäñòàâëÿÿ âñå ýòè âûðàæåíèÿ â ôîðìóëó , ïîëó÷èì

,

ò.å. ÝÄÑ= âðàùåíèÿ çàâèñèò îò êîíñòðóêòèâíûõ ïàðàìåòðîâ, ïîòîêà âîçáóæäåíèÿ è ÷àñòîòû âðàùåíèÿ. Îáîçíà÷èâ ñîâîêóïíîñòü êîíñòðóêòèâíûõ ïàðàìåòðîâ â ÷åðåç êîýôôèöèåíò K= ÝÌ, ïîëó÷èì âûðàæåíèå äëÿ ÝÄÑ âðàùåíèÿ â ñëåäóþùåì = âèäå:

.

Ïðè íåèçìåííîì ïîòîêå âîçáóæä= åíèÿ, êàê ýòî ïðèíÿòî â äàííîì ñëó÷àå ïðè âîçáóæäåíèè îò ïîñòîÿííîãî ìàãíèòà, ââî= äÿò ïîíÿòèå ýëåêòðîìàãíèòíîãî êîýôôèöèåíòà

,

êîòîðûé ìîæåò áûòü îïðåäåëåí ïî íîìèíàëüíûì äàííûì ýëåêòðè÷åñêîé ìàøèíû. Òîãäà ôîðì= óëà áóäåò èìåòü âèä:

.

Ïîëüçóÿñü ýêâèâàëåíòíîé ñõåìî= é , ìîæíî ïîñòðîèòü ýíåðãåòè÷åñêóþ äèàãðàììó äâèãàòåëÿ.  óñòàíîâèâøåìñÿ ðåæèìå äëÿ ýêâèâàëåíòíîé ñõåìû èìååì ýëåêòðè÷åñêèå óðàâíåíèÿ=

ãäå P1= =3DU·Iß-= ìîùíîñòü ïîòðåáëÿåìàÿ èç ñåòè, PÝÏ=3DIß2·Rß- ýëåêòð= è÷åñêèå ïîòåðè â îáìîòêå ÿêîðÿ,PÝÌ=3DEß·Iß - ýëåêòðîìàãíèòíàÿ ìîùíîñòü, ñîäåðæàùàÿñÿ â ìàãíèòíîì ïîëå.

Ýëåêòðîìàãíèòíóþ ìîùíîñòü, èñ= õîäÿ èç çàêîíà ñîõðàíåíèÿ ýíåðãèè, ìîæíî ïðåäñòàâèòü ÷åðåç ýëåêòðîìàãíèòíûé ìîìå= íò M:

.

Îòêóäà, ó÷èòûâàÿ âûðàæåíèÿ

.

Ñîãëàñíî äèàãðàììå íà ìîùíîñòü, ïîñòóïàþùàÿ íà âàë P2, áóäåò ìåíüøå ýëåêòðîìàãíèòíîé ìîùíîñòè íà âåëè÷èíó ïîòåðü â ñ= òàëè PMAT è ìåõàíè÷åñêèõ ïîòåðü P<= sub>MEX. Âðàùàþùèé ìîìåíò (ìîìåíò íà âàëó) áóäåò ñîîòâåòñòâåííî ìåíüøå ýëåêòðîìàãíèò= íîãî ìîìåíòà

Ðèñ. 5-4â. Ýíåðãåòè÷åñêàÿ äèàãðàììà äâèãàòåëÿ ïîñòîÿ= ííîãî òîêà.

èç-çà ýòèõ ïîòåðü, òàê êàê

,

îòêóäà

.


5.2. Äâèãàòåëè ïîñòîÿí= íîãî òîêà

Äâèãàòåëè ïîñòîÿííîãî òîêà ðàçëè÷àþòñÿ ïî õàðàêòåðó âîçáóæäåíèÿ. Äâèãàòåëè ìîãóò áûòü íåçàâèñèìîãî, ïàðàëëåëüíîãî, ïîñëåäîâàòåëüíîãî è ñìåøàííîãî âîçáóæäåíèÿ (ñì. ). Ñâîéñòâà äâèãàòåëåé â çíà÷èòåëüíîé ìåðå îïðåäåëÿþòñ= ÿ èõ ñèñòåìîé âîçáóæäåíèÿ.

Ðèñ. 5-5à,â,ã. Âîçáóæäå= íèå ÄÏÒ.

Ïîñêîëüêó â àâòîìàòèêå ïðèìåí= ÿþòñÿ â îñíîâíîì äâèãàòåëè íåçàâèñèìîãî âîçáóæäåíèÿ, áóäåì â äàëüíåéøåì ðàññìàòðè= âàòü äâèãàòåëè ýòîãî òèïà ( ).

Ðàçëè÷àþò ñòàòè÷åñêèå è äèíàìè÷åñêèå ðåæèìû ðàáîòû äâèãàòåëåé.  ñòàòè÷åñêîì ðåæèìå ω=3Dconst; Iß=3Dconst; UÄÂ=3Dconst è îí îïèñûâàåòñÿ òàê íàçûâàåìûìè ìåõàíè÷åñêèìè õàðàêòåðèñòèêàìè

.

 ñòàòè÷åñêîì ðåæèìå äâèãàòåëü íåçàâèñèìîãî âîçáóæäåíèÿ îïèñûâàåòñÿ ñëåäóþùåé ñèñòåìîé óðàâíåíèé:

ãäå ïåðâîå óðàâíåíèå - óðàâíå= íèå ÿêîðíîé öåïè, âòîðîå è òðåòüå - è , ÷åòâåðòîå - ìåõàíè÷åñêîå óðàâíåíèå, ïÿòîå - óðàâíåíèå öåïè âîçáóæäåíèÿ.

Èç ïåðâûõ ÷åòûðåõ óðàâíåíèé ïîëó÷èì óðàâíåíèå ìåõàíè÷åñêîé õàðàêòåðèñòèêè:

Ïîñêîëüêó ïðèìåíÿåìûå â ñèñòå= ìàõ àâòîìàòè÷åñêîãî óïðàâëåíèÿ äâèãàòåëè ÿâëÿþòñÿ óïðàâëÿåìûìè, ðàçëè÷àþò äâà ò= èïà óïðàâëåíèÿ äâèãàòåëÿìè ïîñòîÿííîãî òîêà - ÿêîðíîå óïðàâëåíèå è ïîëþñíîå óïðàâëåíèå.

Ïðè ÿêîðíîì óïðàâëåíèè ïðîèçâ= îäèòñÿ èçìåíåíèå íàïðÿæåíèÿ, ïîäàâàåìîãî â ÿêîðíóþ öåïü áåç èçìåíåíèÿ âîçáóæäåíèÿ.= Ïðè ïîëþñíîì óïðàâëåíèè, íàîáîðîò, ìåíÿåòñÿ ïîëå âîçáóæäåíèÿ ïóòåì èçìåíåíèÿ òî= êà â îáìîòêàõ ãëàâíûõ ïîëþñîâ iB. Äëÿ ðàñøèðåíèÿ äèàïàçîíà óïðàâëåíèÿ ïðèìåíÿþò òàêæå êîìáèíèðîâàííîå óïðàâëå= íèå.

Ïðè ïîëþñíîì óïðàâëåíèè ÔB=3Dconst, ïîýòîìó óðàâíå= íèå ìåõàíè÷åñêîé õàðàêòåðèñòèêè ñîãëàñíî áóäåò èìåòü âèä:

Ãðàôè÷åñêè ýòà õàðàêòåðèñòèêà= ïðè ôèêñèðîâàííîì íàïðÿæåíèè íà äâèãàòåëå ïðåäñòàâëÿåò ñîáîé ïðÿìóþ, ïåðåñåêàþù= óþ êîîðäèíàòíûå îñè â òî÷êàõ ω0 è = M= Ê.Ç.  (ñì. ), ãäå ω0- ÷àñòîòà âðàùåíèÿ õîëîñòîãî õîäà, à MÊ.Ç.- ìîìåíò êîðîòêîãî çàìûêàíèÿ, êîãäà ðîòîð äâèãàòåëÿ íåïîäâèæåí.

Ðèñ. 5-6à. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ÄÏÒ.

Ýëåêòðè÷åñêàÿ ìàøèíà ðàáîòàåò= â ðåæèìå äâèãàòåëÿ ïðè 0<M<M= Ê.Ç., ïðè M>MÊ.Ç. ïðîè= ñõîäèò âðàùåíèå äâèãàòåëÿ â ïðîòèâîïîëîæíóþ ñòîðîíó ïîä äåéñòâèåì âíåøíåãî ìîìåíòà= - ìàøèíà ðàáîòàåò â ðåæèìå òîðìîçà (ðåæèì ïðîòèâîâêëþ÷åí= èÿ), ïðè ω>ω0= ìàøèíà ðàáîòàåò â ðåæèìå ãåíåðàòîðà íà ñåòü, èìåþùóþ íàïðÿæåíèå UH.

Ðèñ. 5-6á. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ÄÏÒ.

Ìåõàíè÷åñ= êèå õàðàêòåðèñòèêè ïðè ðàçëè÷íûõ íàïðÿæåíèÿõ ïèòàíèÿ äâèãàòåëÿ âûãëÿäÿò, êàê ñåìåéñòâî ïðÿìûõ, ïîêàçàííûõ íà . ×àñòî èõ ñòðîÿò â ôóíêöèè òîêà ÿêîðÿ Iß, òîãäà àíàëèòè÷åñêîå âûðàæåíèå äëÿ ìåõàíè÷åñêèõ õàðàêòåðèñòèê ïðèìåò âèä:

,

îòêóäà âèäíî, ÷òî ïàäåíèå ñêî= ðîñòè ïðè íàãðóçêå äâèãàòåëÿ çàâèñèò èñêëþ÷èòåëüíî îò ñîïðîòèâëåíèÿ ÿêîðíîé öåïè = R= ß.

Êðîìå ìåõ= àíè÷åñêèõ, ñóùåñòâóþò ðåãóëèðîâî÷íûå õàðàêòåðèñòèêè. Äëÿ ÿêîðíîãî óïðàâëåíèÿ ýòî çàâèñèìîñòü ÷àñòîòû âðàùåíèÿ îò íàïðÿæåíèÿ ïèòàíèÿ UÄÂ. Âèä ýòèõ õàðàêòåðèñòèê ïîêàçàí íà , ãäå UÒÐ- íàïðÿæåíèå òðîãàíèÿ äâèãàòåëÿ.

Ðåãóëèðîâî÷íàÿ õàðàêòåðèñòèêà= äëÿ ïîëþñíîãî óïðàâëåíèÿ ìîæåò áûòü ïîëó÷åíà èç ïðè UÄÂ=3Dconst.

Ðèñ. 5-6â. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ÄÏÒ.

Âèä ýòèõ õàðàêòåðèñòèê ïðè ðàçëè÷íûõ íàãðóçêàõ ïîêàçàí íà .

Ðèñ. 5-6ã. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ÄÏÒ.

Äëÿ õîëîñòîãî õîäà, êîãäà M=3D0, ýòà õàðàêòåðèñ= òèêà èìååò âèä ãèïåðáîëû

Äâèãàòåëü ïîñòîÿííîãî òîêà êàê äèíàìè÷åñêàÿ ñèñòåìà îïèñûâàåòñÿ ñëåäóþùèìè óðàâíåíèÿìè â îïåðàòîðíîé ôîðìå= :

Íà îñíîâàíèè ýòèõ óðàâíåíèé ì= îæåò áûòü ïîñòðîåíà ñòðóêòóðíàÿ ñõåìà äâèãàòåëÿ êàê äèíàìè÷åñêîé ñèñòåìû ( ).

Ðèñ. 5-7à. Ñòðóêòóðíàÿ ñõåìà ÄÏ= Ò.

Èç ñòðóêò= óðíîé ñõåìó ïîëó÷èì ïåðåäàòî÷íûå ôóíêöèè äâèãàòåëÿ:

ãäå - êîýôôèöèåíò ïåðåäà÷è, - ïîñòîÿííàÿ âðåìåíè ÿêîðÿ, - ýëåêòðîìåõàíè÷åñêàÿ ïîñòîÿííàÿ âðåìåíè.

Ïîëüçóÿñü ôîðìóëîé Õåâèñàéäà, ïî ïåðåäàòî÷íûì ôóíêöèÿì ìîæíî ïîñòðîèòü ïåðåõîäíûå ïðîöåññû, íàïðèìåð ïðè ïóñêå äâèãàòåëÿ, êàê ýòî ïîêàçàíî íà .

Ðèñ. 5-7á. Ïåðåõîäíûé ïðîöåññ ïðè ïóñêå ÄÏÒ.

Ïðè TM»= Tß,= êàê ýòî îáû÷íî áûâàåò, ïîëó÷èì âûðàæåíèÿ äëÿ òîêà è ñêîðîñòè ïðè ïóñêå:

Äëÿ àíàëèçà äèíàìèêè äâèãàòåëÿ ïîñòîÿííîãî òîêà ïðè ïîëþñíîì óïðàâëåíèè ðàññìàòðèâàþò óðàâíåíèÿ, àíàëîãè÷í= ûå óðàâíåíèÿì â îòêëîíåíèÿõ, òàê êàê ðåãóëèðîâî÷íàÿ õàðàêòåðèñòèêà ï= ðè ïîëþñíîì óïðàâëåíèè ÿâëÿåòñÿ íåëèíåéíîé.

Ïðîèçâîäÿò ëèíåàðèçàöèþ ñèñòå= ìû äëÿ ìàëûõ îòêëîíåíèé îòíîñèòåëüíî êàêèõ-òî íóëåâûõ çíà÷åíèé, ïðåäñòàâèâ ïåðåìåí= íûå â ñëåäóþùåì âèäå:

; ; ; ;

Òîãäà íà îñíîâàíèè óðàâíåíèé = ìîæíî íàïèñàòü óðàâíåíèÿ â îòêëîíåíèÿõ (ïðè T= ß=3D0).

Íà îñíîâàíèè ýòèõ óðàâíåíèé ì= îæåò áûòü ïîñòðîåíà ñòðóêòóðíàÿ ñõåìà äâèãàòåëÿ êàê äèíàìè÷åñêîé ñèñòåìû ïðè ïîëþñíîì óïðàâëåíèè ( ).

Ðèñ. 5-8à. Ñòðóêòóðíàÿ ñõåìà ÄÏ= Ò ïðè ïîëþñíîì óïðàâëåíèè.

Ñ ïîìîùüþ ýòîé ñõåìû ïîëó÷èì ïåðåäàòî÷íóþ ôóíêöèþ äëÿ ÄÏÒ ïðè ïîëþñíîì óïðàâ= ëåíèè

Ïî ýòîé ïåðåäàòî÷íîé ôóíêöèè, ïîëüçóÿñü ôîðìóëîé Õåâèñàéäà, ìîæíî ïîëó÷èòü êð= èâûå ïåðåõîäíîãî ïðîöåññà â äâèãàòåëå ïðè ñòóïåí÷àòîì èçìåíåíèè íàïðÿæåíèÿ âîçáóæäåíèÿ, ïîêàçàííûå íà .

Ðèñ. 5-8á. Ïåðåõîäíûé ïðîöåññ ïðè ïóñêå ÄÏÒ ïðè ïîëþñíîì óïðàâëåíèè.


5.3. Ãåíåðàòîðû ïîñòîÿ= ííîãî òîêà

Ãåíåðàòîðû ïîñòîÿííîãî òîêà, = òàêæå êàê è äâèãàòåëè, ðàçëè÷àþò ïî õàðàêòåðó èõ âîçáóæäåíèÿ.  çàâèñèìîñòè îò ýòîãî = èõ ïîäðàçäåëÿþò íà ãåíåðàòîðû íåçàâèñèìîãî âîçáóæäåíèÿ è ñàìîâîçáóæäåíèåì.  ãåíåðàòîðàõ íåçàâèñèìîãî âîçáóæäåíèÿ ïîòîê âîçáóæäåíèÿ ìîæåò ñîçäàâàòüñÿ îáìîòêîé âîçáóæäåíèÿ (ýëåêòðîìàãíèòíîå âîçáóæäåíèå) èëè ñ ïîìîùüþ ïîñòîÿííî= ãî ìàãíèòà (ìàãíèòîýëåêòðè÷åñêîå âîçáóæäåíèå). Ãåíåðàòîðû ñ ñàìîâîçáóæäåíèåì áûâàþò ïàðàëëåëüíîãî è ñìåøàííîãî âîçáóæäåíèÿ(ñì= . ).

Ðèñ. 5-9à. Ñõåìà ãåíåðàòîðà ïîñòîÿííîãî òîêà.

Î ñâîéñòâàõ ãåíåðàòîðà ñóäÿò = ïî åãî îñíîâíûì õàðàêòåðèñòèêàì, ê êîòîðûì îòíîñÿò õàðàêòåðèñòèêó õîëîñòîãî õîäà, à òàêæå íàãðóçî÷íóþ, âíåøíþþ è ðåãóëèðîâî÷íóþ.

Ïîä õàðàêòåðèñòèêîé õîëîñòîãî= õîäà ïîíèìàþò çàâèñèìîñòü U=3Df(I= B) ïðè Iß=3D0 è ω= =3Dconst (êðèâàÿ 1 íà ). Ýòà çàâèñèìîñòü õàðàêòåðèçóåò ñâîéñòâà ìàãíèòíîé öå= ïè ìàøèíû, è ïî íåé ìîæíî îïðåäåëèòü óñëîâèå ñàìîâîçáóæäåíèÿ ãåíåðàòîðà ñ ïàðàëëåëüíûì âîçáóæäåíèåì, ýòî âîçìîæíî, åñëè ñîïðîòèâëåíèå îáìîòîê âîçáóæä= åíèÿ ìåíüøå êðèòè÷åñêîãî RÂÕ. Ïðè âûïîëí= åíèè ýòîãî óñëîâèÿ óñòàíîâèâøååñÿ çíà÷åíèå íàïðÿæåíèÿ íà âûõîäå ãåíåðàòîðà áóäåò ñîîòâåòñòâîâàòü òî÷êå ïåðåñå÷åíèÿ õàðàêòåðèñòèêè õîëîñòîãî õîäà è ïðÿìîé IB·RB (ñì. ).

Ðèñ. 5-9á. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ãåíåðàòîðà ïîñòîÿííîãî òîêà.

Âíåøíÿÿ õàðàêòåðèñòèêà ( ) ïðåäñòàâëÿåò ñîáîé çàâèñèìîñòü U=3Df(Iß) ïðè ω=3Dconst.

Ðèñ. 5-9â. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ãåíåðàòîðà ïîñòîÿííîãî òîêà.

Êðèâàÿ 1 ñîîòâåòñòâóåò ãåíåðà= òîðó ñ íåçàâèñèìûì âîçáóæäåíèåì ïðè IB=3Dconst.Ñ óâåëè÷åíèåì ò= îêà ÿêîðÿ (íàãðóçêè) íàïðÿæåíèå íà çàæèìàõ ãåíåðàòîðà óìåíüøàåòñÿ èç-çà ïàäåíèÿ íàïðÿæåíèÿ íà ñîïðîòèâëåíèè ÿêîðÿ Rß è ðåàêöèè ÿêî= ðÿ.  ãåíåðàòîðå ñ ïàðàëëåëüíûì âîçáóæäåíèåì ýòî óìåíüøåíèå ïðîèñõîäèò áîëåå èíòåíñèâíî (êðèâàÿ 2), òàê êàê îíî óñóãóáëÿåòñÿ óìåíüøåíèåì òîêà âîçáóæäåíè= ÿ. Äëÿ êîìïåíñàöèè óìåíüøåíèÿ íàïðÿæåíèÿ ïðè óâåëè÷åíèè íàãðóçêè ïðèìåíÿåòñÿ êîìáèíèðîâàííîå âîçáóæäåíèå (êðèâàÿ 3).

Íàãðóçî÷íàÿ õàðàêòåðèñòèêà - = ýòî çàâèñèìîñòü U= =3Df(IB) ïðè Iß= =3Dconst (êðèâàÿ 2 íà ). Îíà ïðîõîäèò íèæå õàðàêòåðèñòèêè õîëîñòîãî õîäà 1 âñëåäñòâèå ïàäåíèÿ íàïðÿæåíèÿ â ÿêîðíîé öåïè è ðåàêöèè ÿêîðÿ. ×åì áîëüøå òîê ÿêîðÿ, òåì íèæå õàðàêòåðèñòèêà 2 ïðîõîäèò ïî îòíîøåíèþ ê õàðàêòåðèñòèêå 1. =

Ðåãóëèðîâî÷íàÿ õàðàêòåðèñòèêà= - ýòî çàâèñèìîñòü IB=3Df(Iß) ïðè U=3Dconst ( ). ×òîáû ïîääåðæàòü íàïðÿæåíèå ïîñ= òîÿííûì, íåîáõîäèìî ïðè óâåëè÷åíèè òîêà Iß óâåëè÷èâàòü òîê âîçáóæäåíèÿ.

Ðèñ. 5-9ã. Ñòàòè÷åñêàÿ õàðàêòåðèñòèêà ãåíåðàòîðà ïîñòîÿííîãî òîêà.

 ñèñòåìàõ àâòîìàòè÷åñêîãî óïðàâëåíèÿ øèðîêîå ïðèìåíåíèå èìåþò òàõîãåíåðàòîðû ïîñòîÿííîãî òîêà. Òàõîãåíåðàòîðû ïðåäñòàâëÿþò ñîáîé ãåíåðàòîðû íåáîëüøîé ìîùíîñòè, ñëóæàùèå ä= ëÿ ïðåîáðàçîâàíèÿ ÷àñòîòû âðàùåíèÿ â ýëåêòðè÷åñêèé ñèãíàë. Êàê ïðàâèëî, òàõîãåíåðàòîðû âûïîëíÿþò ñ íåçàâèñèìûì ýëåêòðîìàãíèòíûì èëè ìàãíèòîýëåêòðè÷åñêèì âîçáóæäåíèåì ( ).

Ðèñ. 5-10à. Ñõåìà òàõîãåíåðàòîðà.

Âûõîäíàÿ õàðàêòåðèñòèêà òàõîãåíåðàòîðà - ýòî çàâèñèìîñòü UÒÃ=3Df(ω). Îíà ìîæåò áûòü ïîëó÷åíà èç àíàëèçà ýêâèâàëåíòíîé ñõåìû ÿêîðíîé öåïè, ïðåäñòàâëå= ííîé íà . Îòêóäà â óñòàíîâèâøåìñÿ ðåæèìå ïîëó÷èì:

Èç ýòèõ óðàâíåíèé ïîëó÷èì âûð= àæåíèå äëÿ âûõîäíîé õàðàêòåðèñòèêè:

,

ãäå KÒÃ- êîýôôèöèåíò ïåðåäà÷è òàõîãåíåðàòîðà, êîòîðûé îïðåäåëÿåò êðóòèçíó âûõîäíîé õàðàêòåðèñòèêè òàõîãåíåðàòîðà (ñì. ). ×åì áîëüøå ÊÝÌ=3DÊ= `ÝÌ·ÔB = è áîëüøå RH ïî ñðàâíåíèþ ñ Rß òåì áîëüøå êðóòèçíà õàðàêòåðèñòèêè.

Ðèñ. 5-10â. Õàðàêòåðèñòèêè òàõîãåíåðàòîðà.

Èç= ñëåäóåò, ÷òî âûõîäíîå íàïðÿ= æåíèå UÒà è ïðè íàãðóçêå ÿâëÿåòñÿ ëèíåéíîé ôóíêöèåé ÷àñòîòû âðàùåíèÿ. Îäíàêî ïðàêòè÷åñêè âûõîäíàÿ õàðàêòåðèñòèêà îòêëîíÿåòñÿ îò ëèíåéíîé ( ) èç-çà ðåàêöèè ÿêîðÿ, îñëàáëÿþùåé ïîòîê âîçáóæäåíèÿ <= span class=3DSpellE>ÔÂ. Îòêëîíåíèå îò ëèíåéíîñòè îïðåäå= ëÿåò îäíó èç îñíîâíûõ ïîãðåøíîñòåé òàõîãåíåðàòîðà. Äëÿ óìåíüøåíèÿ åå ñëåäóåò íàãðóæàòü òàõîãåíåðàòîð íà îòíîñèòåëüíî áîëüøîå ñîïðîòèâëåíèå íàãðóçêè RH è èñïîëüçîâàòü íåáîëüøîé äèàïàçîí ÷àñòîò âðàùåíèÿ.

Òàõîãåíåðàòîð êàê äèíàìè÷åñêàÿ ñèñòåìà îïèñûâàåòñÿ óðàâíåíèÿìè, àíàëîãè÷íûìè óðàâíåíèÿì :

Îòêóäà ìîæåò áûòü ïîëó÷åíà ïåðåäàòî÷íàÿ ôóíêöèÿ òàõîãåíåðàòîðà

,

ãäå - ïîñòîÿííàÿ âðåìåíè òàõîãåíåðàòîðà.


5.4. Âåíòèëüíûå äâèãàò= åëè

Ìàøèíû ïîñòîÿííîãî òîêà èìåþò= áîëåå âûñîêèå òåõíè÷åñêèå ïîêàçàòåëè (ëèíåéíîñòü õàðàêòåðèñòèêè, âûñîêèé ÊÏÄ, ìàë= ûå ãàáàðèòû), ÷åì ìàøèíû ïåðåìåííîãî òîêà. Ñóùåñòâåííûé íåäîñòàòîê - íàëè÷èå ýëåêòðîìåõàíè÷åñêîãî êîëëåêòîðà, êîòîðûé ñíèæàåò íàäåæíîñòü, ñîçäàåò ðàäèîïîìåõè, âçðûâîîïàñíîñòü è ò.ä.

Ýòèõ íåäîñòàòêîâ ëèøåí áåñêîíòàêòíûé äâèãàòåëü ïîñòîÿííîãî òîêà, íàçûâàåìûé âåíòèëüíûì äâèãàòåëåì.=  ýòîì äâèãàòåëå ùåòî÷íûé àïïàðàò çàìåíåí ïîëóïðîâîäíèêîâûì êîììóòàòîðîì, ÿêî= ðü íàõîäèòñÿ íà ñòàòîðå, à ðîòîð ïðåäñòàâëÿåò ñîáîé äâóõïîëþñíûé (ðåæå ÷åòûðåõïîëþñíûé) ïîñòîÿííûé ìàãíèò. Äëÿ óïðîùåíèÿ êîììóòàòîðà ÷èñëî ñåêöèè îáìîòêè ÿêîðÿ âûáèðàåòñÿ ìàëûì= - òðè, ÷åòûðå.

Ðèñ. 5-11à. Òðåõôàçíûé âåíòèëüíûé äâèãàòåëü.

Ñõåìà òðåõôàçíîãî âåíòèëüíîãî äâèãàòåëÿ ñ äâóõïîëþñíûì ðîòîðîì ïðåäñòàâëåíà íà= . Ñóùåñòâåííûì ýëåìåíòîì äâèãàòåëÿ ÿâëÿåòñÿ äàò÷èê ïîëîæåíèÿ - ÄÏÐ. Îí ìîæåò îñíîâàí íà ðàçíûõ ïðèíöèïàõ - ôîòîýëåêòðè÷åñêèå, èíäóêòèâíûå, åìêîñòíûå, íà ýôôåêòå Õîëëà, è ò.ä.  ðàññìàòðèâàåìîì äâèãàòåëå ïðèìåíÿåòñÿ ôîòîýëåêòðè÷å= ñêèé äàò÷èê, ñîäåðæàùèé òðè íåïîäâèæíûõ ôîòîïðèåìíèêà mlk, êîòîðûå çàêðûâàþòñÿ ïîî÷åðåäíî âðàùàþùåéñÿ øòîðêîé. Äâîè÷íûé êîä, ïîëó÷àåìûé ñ ÄÏÐ, ôèêñèðóåò øåñòü ðàçëè÷= íûõ ïîëîæåíèé ðîòîðà (øåñòü ôàç), ýòî ñîîòâåòñòâèå êîäîâ è ôàç ïðèâåäåíî â âåðõ= íåé ÷àñòè .

Ôàçà

1

2

3

4

5

6

K

1

0

0

0

1

1

L

1

1

0

0

0

1

M

1

1

1

0

0

0

U1

1

0

0

0

0

1

U2

0

1

1

0

0

0

U3

0

0

0

1

1

0

U4

0

0

1

1

0

0

U5

0

0

0

0

1

1

U6

1

1

0

0

0

0

 ýòîé òàáëèöå åäèíèöå ñîîòâåòñòâóåò íàëè÷èå ñèãíàëà íà âûõîäå äàò÷èêà, ò.å. êîãäà ôîòîïðèåìíèê îòêðûò, à íóëþ - îòñóòñòâèå ñèãíàëà, êîãäà ñîîòâåòñòâóþùèé ôîòîýëåìåíò çàêð= ûò øòîðêîé.

Ðèñ. 5-11á. Òðåõôàçíûé âåíòèëüíûé äâèãàòåëü.

Ñèãíàëû äàò÷èêîâ ïðåîáðàçóþòñÿ óïðàâëÿþùèì óñòðîéñòâîì ÓÓ ( ) â êîìáèíàöèþ óïðàâëÿþùèõ íàïðÿæåíèé U1-U6, êîòîðûå óïðàâëÿþò òðàíçèñòîðíûìè êëþ÷àìè K1-K6 ñîãëàñíî íèæíåé ÷àñòè , òàê, ÷òî â êàæäûé òàêò (ôàçó) ðàáîòû äâèãàòåëÿ âêëþ÷åíû äâà êëþ÷à - âåðõíèé è íèæíèé è ê ñåòè ïîäêëþ÷åíû ïîñëåäîâàòåëüíî äâå èç òðåõ îáìîòîê ÿêîðÿ. Îáìîòêè ÿêîðÿ a,b,c ðàñïîëîæåíû íà ñòàòîðå ñî ñäâèãîì íà 120·ãðàä (ñì. ) è èõ íà÷àëà è êîíöû ñîåäèíåíû òàê, ÷òî ïðè ïåðåêëþ÷å= íèè êëþ÷åé ñîçäàåòñÿ âðàùàþùååñÿ ìàãíèòíîå ïîëå. Îäíîìó öèêëó ðàáîòû êîììóòàòîðà ñîîòâåòñòâóåò îäèí îáîðîò ðîòîðà. Öèêë äåëèòñÿ íà øåñòü òàêòîâ (âðåìåííûõ ô= àç), êîòîðûì ñîîòâåòñòâóåò ïðîñòðàíñòâåííûé óãîë α=3D60·ãðàä. Êîììóòàöèÿ ïðîèçâîäèòñÿ òàê, ÷òî ïîòîê âîçáóæäåíèÿ Ô0 îòñòàåò íà óãîë α îò ïîòîêà ÿêîðÿ. Íà òîêè â îáìîòêàõ è ïîëîæåíèå ðîòîðà ïîêàçàíû äëÿ ôàçû 1= .  ðåçóëüòàòå âçàèìîäåéñòâèÿ ïîòîêà ÿêîðÿ è âîçáóæäåíèÿ ñîçäàåòñÿ âðàùàþùèé ìî= ìåíò M, êîòîðûé ñòðå= ìèòñÿ ðàçâåðíóòü ðîòîð òàê, ÷òîáû ïîòîêè ÿêîðÿ è âîçáóæäåíèÿ ñîâïàëè, íî ïðè ïîâî= ðîòå ðîòîðà ïîä äåéñòâèåì ÄÏÐ ïðîèñõîäèò ïåðåêëþ÷åíèå îáìîòîê è ïîòîê ÿêîðÿ ïîâîðà÷èâàåòñÿ íà ñëåäóþùèé øàã.

Ðèñ. 5-12á. Âðåìåííàÿ äèàãðàììà òðåõôàçíîãî âåíòèëüí= îãî äâèãàòåëÿ.

Âðåìåííàÿ äèàãðàììà ðàáîòû âåíòèëüíîãî äâèãàòåëÿ ïðèâåäåíà íà . Êàê âèäíî èç äèàãðàììû, âåíòèëüíûé äâèãàòåëü ðàáîòàåò êàê â äàííîì ñëó÷àå òðåõôàçíûé ñèíõðîííûé äâèãàòåëü, ÷àñòîòà âðàùåíèÿ åãî ðîòîðà ïðîïîðöèîíàëüíà ÷àñòîòå âðàùåíèÿ ïîë= ÿ. Îñíîâíûì îòëè÷èåì îò ñèíõðîííîãî ÿâëÿåòñÿ åãî ñàìîñèíõðîíèçàö= èÿ ñ ïîìîùüþ ÄÏÐ, â ðåçóëüòàòå ÷åãî ó ýòîãî äâèãàòåëÿ, íàîáîðîò, ÷àñòîòà âðàùåíèÿ ïîëÿ ïðîïîðöèîíàëüíà (â äàííîì ñëó÷àå ïðè äâóõïîëþñíîì ÿêîðå ðàâíà) ÷àñòîòå âðàùåíèÿ ðîòîðà, à ÷àñòîòà âðàùåíèÿ ðîòîðà çàâèñèò îò íàïðÿæåíèÿ ïèòàíèÿ, ò= .å. äâèãàòåëü ðàáîòàåò êàê äâèãàòåëü ïîñòîÿííîãî òîêà.

 îòëè÷èå îò äâèãàòåëÿ ïîñòîÿ= ííîãî òîêà, òàê êàê âåíòèëüíûé äâèãàòåëü èìååò ìàëî ñåêöèé â îáìîòêå ÿêîðÿ, ìîìåíò èìååò ïóëüñàöèè, è ñðåäíåå çíà÷åíèå ìîìåíòà çàâèñèò îò ïåðèîäà âêëþ÷åíèÿ êë= þ÷à β, ïîêàçàííîãî íà .

 = ïîëó÷åíà ôîðìóëà äëÿ ñðåäíåãî çíà÷åíèÿ ýëåêòðîìàãíèòíî= ãî ìîìåíòà âåíòèëüíîãî äâèãàòåëÿ

ãäå M*è ω*- îòíîñèòåëüíûå ìîìåíò è ÷àñòîòà âðàùåíèÿ ïî îòíîøåíèþ ê = áàçîâûì:

; ; ; ,

ãäå m- ÷èñëî îáìîòîê (ñåêöèé), R- ñîïðîòèâëåíèå ñåêö= èè.

Ó÷èòûâàÿ ýòè ñîîòíîøåíèÿ, èç ìîæíî ïîëó÷èòü âûðàæåíèå äëÿ ìåõàíè÷åñêîé õàðàêòåðèñòèêè âåíòèëüíîãî äâèãàòåëÿ

,

ãäå A è B- êîýôôèöèåíòû, çàâè= ñÿùèå îò β.

;

Ýòè êîýôôèöèåíòû çàâèñÿò îò ñ= ïîñîáà êîììóòàöèè îáìîòîê è ïðèâåäåíû â .

Ñïîñîá êîììóòàöèè

β

A

B

m

Ïàðíàÿ

Π

1.27

4

4

Ïîî÷åðåäíàÿ(ïîëóøàãè)

1.24

4.1

4

Òðåõôàçíàÿ

 

1.17

4.17

3

Îäèíàðíàÿ

 

1.02

8.4

4

 ðàññìàòðèâàåìîì ïðèìåðå ïðè= ìåíåíà òðåõôàçíàÿ êîììóòàöèÿ, äðóãèå ïåðå÷èñëåííûå â ñïîñîáû êîììóòàöèè ñîîòâåòñòâóþò êîììóòàöèè îáìîòîê â øàãîâûõ äâèãàòåëÿõ, òàê êàê âåíòèëüíûé äâèãàòåëü ìîæíî ÷åðåç äàò÷èê ïîëîæåí= èÿ ðîòîðà. Ìåõàíè÷åñêèå õàðàêòåðèñòèêè ïîêàçàíû íà = .

Ðèñ. 5-13à. Ìåõàíè÷åñêèå õàðàêòåðèñòèêè âåíòèëüíîãî äâèãàòåëÿ.

Ïðè ðàññìîòðåíèè äèíàìèêè âåíòèëüíîãî äâèãàòåëÿ íàäî äîïîëíèòü óðàâíåíèå óðàâíåíèåì äâèæåíèÿ âèäà

Ðèñ. 5-13á. Ñòðóêòóðíàÿ ñõåìà âåíòèëüíîãî äâèãàòåëÿ.=

Íà îñíîâàíèè è ìîæåò áûòü ïîñòðîåíà ñòðóêòóðíàÿ ñõåìà ( ), ïî êîòîðîé ïîëó÷åíà ïåðåäàòî÷íàÿ ôóíêöèÿ

,

ãäå - êîýôôèöèåíò ïåðåäà÷è äâèãàòåëÿ, - ýëåêòðîìåõàíè÷åñêàÿ ïîñòîÿííàÿ âðåìåíè.

Òàêèì îáðàçîì, âåíòèëüíûé äâè= ãàòåëü ïî ñâîèì ñòàòè÷åñêèì è äèíàìè÷åñêèì õàðàêòåðèñòèêàì ïîäîáåí äâèãàòåëþ ïîñòîÿííîãî òîêà.


5.5. Óïðàæíåíèÿ è êîíòðîëüíûå âîïðîñû ê ãëàâå 5.

  1. Ïîëüçóÿñü ôîðìóëàìè (5-10) è (5-13) âû÷èñëèòü ïî ïàñïîðòíûì äàííûì äâèãàòåëÿ ïîñòîÿííîãî òîêà åãî îñíîâíûå ñòàòè÷åñêèå è äèíàìè÷åñêèå ïàðàìåòðû: Êýì, Êäâ, Òì, Òÿ. Ïàñïîðòíûå ä= àííûå äëÿ äâèãàòåëÿ òèïà ÑË-369: Uí=3D110 Â; Rÿ=3D15 Îì; Lÿ=3D100 ìÃí; Ií=3D0,9 À; Ní=3D3800 îá/ìèí; J=3D1,5 êã ñì**2).
  2. Ïîñòðîèòü ìåõàíè÷åñêèå è ðåãóëèðîâî÷íûå õàðàêòåðèñòèêè äâèãàòåëÿ ÑË-369 ïðè ðàçëè÷íûõ äîáàâî÷íûõ ñîïðîòèâëåíèÿõ â öåïè ÿêîðÿ: Räîá=3D0...50 Îì.
  3. Íàïèñàòü ïåðåäàòî÷íûå ôóíêöèè äëÿ äâèãàòåëÿ ÑË-369.
  4. Ïîñòðîèòü ïåðåõîäíûå ïðîöåññû Iÿ= (t) è W(t) ïðè ïóñêå äâèãàòåëÿ ÑË-369 ïðè õîëîñòîì õîäå è ðàçëè÷íûõ íàïðÿæåíèÿõ ïèòàíèÿ Uäâ=3D(0,2...0,8) .
  5. Ïîñòðîèòü ñòàòè÷åñêèå õàðàêòåðèñòèêè è íàïèñàòü âûðàæåíèå äëÿ ïåðåäàòî÷íîé ôóíêö= èè äëÿ ÑË-369, ðàáîòàþùåãî â ðåæèìå ãåíåðàòîðà íà ðàçëè÷íûå íàãðóçêè Rí=3D100...500 Îì.

 

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