From cf5fa644837a5dba11a93c724eb24ffd6363ec0c Mon Sep 17 00:00:00 2001 From: Arne van Iterson Date: Wed, 27 Mar 2024 14:37:57 +0100 Subject: [PATCH] fuck_math.exe --- doc/main.tex | 95 +++++++++++++++++++++++++--------------------- doc/res/rover.png | Bin 0 -> 471783 bytes 2 files changed, 52 insertions(+), 43 deletions(-) create mode 100644 doc/res/rover.png diff --git a/doc/main.tex b/doc/main.tex index 15b0d57..6caeb42 100644 --- a/doc/main.tex +++ b/doc/main.tex @@ -29,7 +29,7 @@ \maketitle \begin{abstract} - Onderzoeksverlag naar een passende motor en tandwieloverbrenging voor de Euro Rover. In dit document wordt onderzocht of de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover. + In dit document wordt onderzocht of de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover. \end{abstract} \noindent\makebox[\linewidth]{\rule{\linewidth}{0.4pt}} @@ -38,11 +38,15 @@ \begin{multicols}{2} \section{Inleiding} - \colorbox{red}{TODO} - De Hogeschool Utrecht werkt samen met andere hogescholen voor het ontwikkelen van een Euro Moon Rover. + De Iris was de eerste onbemande maanrover ontwikkeld door NASA. De Hogeschool Utrecht werkt samen met andere hogescholen voor het ontwikkelen van een Europese versie van de Iris; De Euro Moon Rover. + + \begin{figure}[H] + \includegraphics[width=\linewidth]{./res/rover.png} + \caption{Euro Moon Rover} + \label{fig:rover} + \end{figure} \section{Onderzoek} - \colorbox{red}{TODO} Voor de Eurorover is een set van motor en tandwieloverbrenging voorgesteld, het gaat om de RE25 1187xx motor en de Planetary Gearhead GP xx xx van de firma Maxon. In dit document wordt onderzocht of dat de voorgestelde motor en tandwieloverbrenging voldoet aan de eisen van de rover. @@ -63,6 +67,7 @@ C_r &= 0,1 & [-] \end{align*} + \subsection{Eisen} Met de aandrijving moeten de volgende eisen worden voldaan: \begin{align*} v_{max} &= 2.1 & [m/s] \\ @@ -71,8 +76,8 @@ \end{align*} - \section{Lasteisen/-wensen} - Om te bepalen wat de maximale lasteisen/-wensen van de motor zijn, worden de eisen van de rover onder verschillende scenario's verdeeld. De rover moet in staat zijn om te versnellen, constant te rijden en te vertragen op: + \section{Lasteisen of -wensen} + Om te bepalen wat de maximale lasteisen of -wensen van de motor zijn, worden de eisen van de rover onder verschillende scenario's verdeeld. De rover moet in staat zijn om te versnellen, constant te rijden en te vertragen op: \begin{itemize} \item een vlakke ondergrond \end{itemize} @@ -82,6 +87,8 @@ \item een opgaande helling van 20 graden \item een neergaande helling van 20 graden \end{itemize} + + De rover heeft de mogelijkheid om grotere hellingen, tot 30 graden, te beklimmen; Maar dit hoeft niet met de gegeven eisen voor versnelling en vertraging. De rover is in staat om, op elk gegeven oppervlak, het gewicht eerlijk over de wielen te verdelen; Dit maakt het mogelijk om de lasten voor slechts één wiel te berekenen. In het volgende hoofdstuk worden deze scenario's verder uitgewerkt. Het zwaarste resultaat bepaalt het type motor dat gebruikt zal worden. Omdat het gewicht van de rover wordt verdeeld over de wielen, zal het volgende gewicht worden gebruikt in de berekeningen \begin{align*} @@ -111,19 +118,20 @@ De rolweerstand is afhankelijk van de normaalkracht $F_N$, $F_N$ is in dit geval gelijk aan de zwaartekracht $F_z$ dus: \begin{align*} F_N &= F_z \\ + g_{maan} &= 1.625 & [m/s^2] \\ F_z &= m \cdot g \\ - &= 1.5 \cdot 9.81 \\ - &= 14.715 & [N]\\ + &= 1.5 \cdot 1.625 \\ + &= 2.4375 & [N]\\ \\ F_{rol} &= C_r \cdot F_N\\ - &= 0.1 \cdot 14.715 \\ - &= 1.4715 & [N]\\ + &= 0.1 \cdot 2.4375 \\ + &= 0.24375 & [N]\\ \\ F_{aand} &= F_{rol} \\ \\ - T_{as} &= F_{aand} \cdot r \cdot \frac{1}{4} \\ - &=F_{rol} \cdot r \cdot \frac{1}{4} \\ - &=27.590625 & [mNm] + T_{as} &= F_{aand} \cdot r\\ + &=F_{rol} \cdot r\\ + &=18.28125 & [mNm] \end{align*} \subsubsection{Versnellen} @@ -133,12 +141,12 @@ &= 1.05 & [N] \\ \\ F_{aand} &= F_{eff} + F_{rol} \\ - &= 1.05 + 1.4715 \\ - &= 2.5215 & [N] + &= 1.05 + 0.24375 \\ + &= 1.29375 & [N] \\ - T_{as} &= F_{aand} \cdot r \cdot \frac{1}{4} \\ - &=(F_{eff}+F_{rol}) \cdot r \cdot \frac{1}{4} \\ - &=47.278125 & [mNm] + T_{as} &= F_{aand} \cdot r \\ + &=(F_{eff}+F_{rol}) \cdot r \\ + &=97.03125 & [mNm] \end{align*} \subsubsection{Vertragen} @@ -148,12 +156,12 @@ &= 0.75 & [N] \\ \\ F_{aand} &= F_{rol} - F_{eff} \\ - &= 1.4715 - 0.75 \\ - &= 0.7215 & [N] + &= 0.24375 - 0.75 \\ + &= -0.50625 & [N] \\ - T_{as} &= F_{aand} \cdot r \cdot \frac{1}{4} \\ - &=(F_{eff}-F_{rol}) \cdot r \cdot \frac{1}{4} \\ - &=13.528125 & [mNm] + T_{as} &= F_{aand} \cdot r \\ + &=(F_{eff}-F_{rol}) \cdot r \\ + &=-37.96875 & [mNm] \end{align*} \subsection{Dalende ondergrond} @@ -166,37 +174,38 @@ In dit geval is de zwaartekracht niet haaks aan de ondergrond, de zwaartekracht verdeelt zich in een component loodrecht op de ondergrond een een component parallel aan de ondergrond. De component loodrecht op de ondergrond is gelijk aan de normaalkracht $F_N$. \begin{align*} + g_{maan} &= 1.625 & [m/s^2] \\ F_{z} &= m \cdot g \\ - &= 1.5 \cdot 9.81 \\ - &= 14.715 & [N] \\ + &= 1.5 \cdot 1.625 \\ + &= 2.4375 & [N] \\ \\ \alpha &= 20 & [deg] \\ \\ F_N &= F_{z1} \\ F_{z1} &= \cos{\alpha}\cdot F_{z}\\ - &= \cos{20}\cdot 14.715 \\ - &= 13.743 & [N] \\ + &= \cos{20}\cdot 2.4375 \\ + &= 2.2905 & [N] \\ F_{z2} &= \sin{\alpha}\cdot F_{z}\\ - &= \sin{20}\cdot 14.715 \\ - &= 5.03 & [N] \\ + &= \sin{20}\cdot 2.4375 \\ + &= 0.834 & [N] \\ \end{align*} De rolweerstand in dit geval is: \begin{align*} F_{rol} &= C_r \cdot F_N\\ - &= 0.1 \cdot 13.743 \\ - &= 1.3743 & [N] + &= 0.1 \cdot 2.2905 \\ + &= 0.22905 & [N] \end{align*} Voor een constante snelheid dient $F_{eff}$ nul te zijn dus: \begin{align*} F_{eff} &= F_{aand} + F_{z2} - F_{rol} = 0\\ - &= F_{aand} + 5.03 - 1.3743 = 0\\ - F_{aand} &= 1.3743 - 5.03\\ - &= -3.6557 & [N] + &= F_{aand} + 0.834 - 0.22905 = 0\\ + F_{aand} &= 0.22905 - 0.834\\ + &= -0.60495 & [N] \\ - T_{as} &= F_{aand} \cdot r \cdot \frac{1}{4} \\ - &=-68.544375 & [mNm] + T_{as} &= F_{aand} \cdot r \\ + &=-45.37125 & [mNm] \end{align*} De motor moet in dit geval dus tegenkracht leveren om de kar op en constante snelheid te houden. @@ -212,20 +221,20 @@ \begin{align*} F_{eff} &= F_{aand} - F_{z2} - F_{rol} = 0\\ F_{aand} &= F_{z2} + F_{rol}\\ - &= 5.03 + 1.3743\\ - &= 6.4043 & [N] + &= 0.834 + 0.22905\\ + &= 1.06305 & [N] \\ - T_{as} &= F_{aand} \cdot r \cdot \frac{1}{4} \\ - &=(F_{z2}+F_{rol}) \cdot r \cdot \frac{1}{4} \\ - &=120.080625 & [mNm] + T_{as} &= F_{aand} \cdot r \\ + &=(F_{z2}+F_{rol}) \cdot r \\ + &= 79.72875 & [mNm] \end{align*} \subsection{Slip} In de eigenschappen van de wielen is de statische wrijvingscoëfficiënt $\mu_s$ gegeven. $F_{eff}$ mag niet groter zijn dan de maximale statische wrijvingskracht $F_{s,max}$. De maximale statische wrijvingskracht in dit geval is: \begin{align*} F_{s,max} &= \mu_s \cdot F_N \\ - &= 0.9 \cdot 14.715 \\ - &= 13.2435 & [N] + &= 0.9 \cdot 2.4375 \\ + &= 2.19375 & [N] \end{align*} Als $F_{eff}$ groter is dan $F_{s,max}$ zal er slip optreden. 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