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z`zvmI0)}(@8(=VX@YXWjrUBOea7&JM13NH^>vu{B_XeDr1{lu0R|1UUwhFj>BDn`) zz!(uXS>R#_Y{QWnLtx_PVr<&;Fy2iGg|l-lhYs%6I!BH_?E{8YoExp|0L!h|aQVus z_HcHG3o#B8c&fpT54baik|9k8_6LyRo`flwoWaSMDXB8f3B}@06Z!J`Bdl1>zn&5^M#+lbdsN@sV+1$HifYaMNFUu!^k$x ylrn~=&ImCLrA$Z@TqvBP`u~$Ss=`B0fA#_AT0ggC@*o6M1bNvB6Q*0ukpDkli=Wm2 diff --git a/ENT4_FS.tex b/ENT4_FS.tex index 78d9907..3b2aaeb 100644 --- a/ENT4_FS.tex +++ b/ENT4_FS.tex @@ -56,11 +56,17 @@ pdfpagelabels, % Zur korrekten Erstellung der Bo hypertexnames=false % Zur korrekten Erstellung der Bookmarks ]{hyperref} + +% PDFs einbinden +\newenvironment{Figure} + {\par\medskip\noindent\minipage{\linewidth}} + {\endminipage\par\medskip} + % Header \pagestyle{fancy} \fancyhead{} \fancyfoot{} -\fancyhead[L]{FS ENT4 SoSe2020, Annette Schmidt, \url{https://git.efi.th-nuernberg.de/gitea/schmidtan65529/ENT4_Formelsammlung.git} Fehler bitte sofort melden!} +\fancyhead[L]{FS ENT4 SoSe2020 \url{https://git.efi.th-nuernberg.de/gitea/schmidtan65529/ENT4_Formelsammlung.git} Fehler bitte sofort melden!} \fancyhead[R]{Seite $\thepage$ von $\pageref{LastPage}$} \fancyheadoffset{0cm} @@ -132,15 +138,21 @@ hypertexnames=false % Zur korrekten Erstellung der Bookmarks $f_1~^{2)}$ & Ständerfrequenz [Hz]\\ $f_2$ & Läuferfrequenz [Hz]\\ $\omega_{1/2}$ & Sänder-/Läuferkreisfrequenz [$\frac{1}{s}$]\\ - $n = n_1$ & Läuferdrehzahl [$\frac{1}{min}$]\\ + $n_1$ & Läuferdrehzahl (synchron) [$\frac{1}{min}$]\\ + $n = n_N$ & Ständerdrehzahl (asyncrhon) [$\frac{1}{min}$]\\ $s$ & Schlupf [\%]\\ $p$ & Polpaarzahl\\ $\underline{I}_\mu$ & ?\\ $\underline{I}_1$ & ?\\ $\underline{I}_2$ & ?\\ + $M_A$ & ?\\ + $U_A$ & ?\\ + $I_A$ & ?\\ + $\phi_N$ & ? \\ \end{tabularx} $~^{1)}$ ' heißt die Läufergröße ist auf Ständer umgerechnet\\ $~^{2)}$ Index 1 immer Ständergröße, Index 2 immer Läufergröße\\ + $~^{3)}$ $~^*$ heißt reduziert\\ \subheading{Am Netz} Voraussetzung für ein zeitlich konstantes Drehmoment ist ein mit konstanter Winkelgeschwindgkeit im Luftspalt umlaufendes, räumlich möglichst sinusförmig verteiltes magnetisches Feld. \\ \colorbox{yellow!60}{Grundfeld einer Drehstromwicklung:} @@ -177,21 +189,6 @@ hypertexnames=false % Zur korrekten Erstellung der Bookmarks \underline{I}_\mu = \underline{I}_1 + \underline{I}_2 \end{equation} \textcolor{magenta}{Kanns sein, dass in der Formel die ' nicht passen?} - \colorbox{yellow!60}{Leitwertsortskurve(?????)} - \begin{equation} - s = 0:~~~~~~~~\underline{Y}_0 = \frac{-j}{X_R} - \end{equation} - \begin{equation} - s = \infty:~~~~~~~~\underline{Y}_\infty = \frac{-j}{X_R} - \frac{j}{X_K} - \end{equation} - \colorbox{yellow!60}{Kreismuttelpunkt:} - \begin{equation} - \underline{Y} = \frac{-j}{X_R}- \frac{j}{2X_K} - \end{equation} - \colorbox{yellow!60}{Kreisradius:} - \begin{equation} - r = \frac{1}{2X_K} - \end{equation} im Läufer \colorbox{yellow!60}{umgesetzte Leistung:} (Läuferverlustleistung) \begin{equation} P_\mu = 3\cdot I_2' \cdot \frac{R_2'}{s} = s \cdot P_\mu + (1-s)\cdot P_\mu = P_{Cu2} + P_{mech} @@ -214,13 +211,81 @@ hypertexnames=false % Zur korrekten Erstellung der Bookmarks \eta = \frac{P_{Welle}}{P_{el}} \end{equation} + \subsubheading{Stromortskurve} + \colorbox{yellow!60}{Leitwertstromortskurve(?????)} + \begin{equation} + s = 0:~~~~~~~~\underline{Y}_0 = \frac{-j}{X_R} + \end{equation} + \begin{equation} + s = \infty:~~~~~~~~\underline{Y}_\infty = \frac{-j}{X_R} - \frac{j}{X_K} + \end{equation} + \colorbox{yellow!60}{Kreismittelpunkt:} + \begin{equation} + \underline{Y} = \frac{-j}{X_R}- \frac{j}{2X_K} + \end{equation} + \colorbox{yellow!60}{Kreisradius:} + \begin{equation} + r = \frac{1}{2X_K} + \end{equation} + Leerlaufstrom/Magnestisierungsstrom: $I_0 = I_\mu$ (0|0)-$P_0$\\ + Ständerstrom $I_1$ (0|0) - P\\ + Läuferstrom $I_2'$ P - $P_0$\\ + \begin{equation} + \textcolor{orange}{\overline{P_k C}} \sim (3)^* R_2' I_{2k}' (= 2\pi n_1 M_A) + \end{equation} + $~^* $Faktor 3 nur bei Sternschaltung + \begin{equation} + \textcolor{orange}{\overline{P_0 B}} \sim I_{2}'^2 + \end{equation} + \begin{equation} + \textcolor{red}{\overline{P_0 C}} \sim I_{2k}'^2 + \end{equation} + Läuferstromwärmeverluste: + \begin{equation} + \textcolor{red}{\overline{A B}} = \frac{\overline{P_0 B}}{\overline{P_0 C}}\cdot \overline{P_k C} \sim \frac{I_{2}'^2}{I_{2k}'^2} (3)^* R_2' I_{2k}' = P_{Cu2} + \end{equation} + Luftspaltleistung/elektrisch aufgenommene Leistung: + \begin{equation} + \textcolor{blue}{\overline{P B}} \sim P_{el} = P_\delta + \end{equation} + mechanische Leistung: + \begin{equation} + \textcolor{blue}{\overline{P A}} \sim P_{mech} = P_\delta - P_{Cu2} + \end{equation} + \colorbox{yellow!60}{Y-Schaltung:} $P_{Cu2} = 3 R_2' I_2'^2$\\ + \colorbox{yellow!60}{$\Delta$-Schaltung:} $P_{Cu2} = R_2' I_{2L}'^2$\\ + \colorbox{SpringGreen!40}{Parameterbeiche:}\\ + \colorbox{yellow!60}{motorischer Beiche:} $s \leq s \leq 1$\\ + $s = 0$: Synchronismus, Leerlauf\\ + $s = 1$: Stillstand, Kurzschluss\\ + \colorbox{yellow!60}{generatorischer Bereich:} $s < 0$\\ + Luftspaltleistung wird negativ, Asynchronmaschine geht ohne Schaltungsänderung in Generatorbetrieb\\ + \colorbox{yellow!60}{Gegenstrombremsbereich:} $s > 1$\\ + Drezahl n wird negativ ($n = n_1(1-s)$)\\ + \begin{itemize} + \item Läufer dreht entgegen der Umlaufrichtung des Luftspaltfeldes. + \item In diesem Bereich nimmt die ASM mechanische Leistung über die Welle und elektrische Leistung aus dem Netz auf. + \item Gesamte aufgenommene Leistung wird in Stromwärme umgesetzt. + \end{itemize} + \begin{equation} + M_A = (\frac{U_A}{U_A^*})^2 \cdot M_A^* + \end{equation} + \begin{equation} + I_A = \frac{U_N}{U_N^*} \cdot I_A^* + \end{equation} + + + \colorbox{SpringGreen!40}{Maßstäbe:}\\ + Strom: $m_I$ gewählt (Leiterstrom) Einheit: A/cm\\ + Leistung: $m_P = \sqrt{3} U_N m_I$ Einheit: W/cm\\ + Drehmoment: $m_M = m_P/(2\pi n_1)$ Einheit: Nm/cm\\ + \includegraphics[width= 1.75\columnwidth, angle = 90]{SOK_TEG_FS.pdf} \subheading{Stationär} \end{multicols*} \begin{multicols*}{2} - \includepdf[width = \columnwidth]{Abbildungen/SOK_TEG_FS.pdf} \subheading{Synchronmaschine} \begin{tabularx}{\columnwidth}{p{2cm} X} \textbf{Formelzeichen} & \textbf{Beschreibung} \\