diff --git a/doc/main.tex b/doc/main.tex index 6caeb42..3d43545 100644 --- a/doc/main.tex +++ b/doc/main.tex @@ -56,15 +56,16 @@ m_{rover} &= 6 & [kg] \\ w &= 400 & [mm] \\ l &= 250 & [mm] \\ - \alpha_{typ} &= 20 & [deg] \\ - \alpha_{max} &= 30 & [deg] + \theta_{typ} &= 20 & [deg] \\ + \theta_{max} &= 30 & [deg] \end{align*} De wielen hebben de volgende eigenschappen: \begin{align*} r &= 0.075 & [m] \\ \mu_s &= 0,9 & [-] \\ - C_r &= 0,1 & [-] + C_r &= 0,1 & [-] \\ + J &= 2.1 \cdot 10^{-3} & [kg\cdot m^2] \end{align*} \subsection{Eisen} @@ -72,7 +73,9 @@ \begin{align*} v_{max} &= 2.1 & [m/s] \\ a_{acc} &= 0.7 & [m/s^2] \\ - a_{dec} &= 0.5 & [m/s^2] + a_{dec} &= 0.5 & [m/s^2] \\ + \alpha_{acc} &= \frac{a_{acc}}{r} = 9.33 & [rad/s^2]\\ + \alpha_{dec} &= \frac{a_{dec}}{r} = 6.66 & [rad/s^2]\\ \end{align*} @@ -139,14 +142,15 @@ F_{eff} &= m \cdot a \\ &= 1.5 \cdot 0.7 \\ &= 1.05 & [N] \\ - \\ F_{aand} &= F_{eff} + F_{rol} \\ &= 1.05 + 0.24375 \\ - &= 1.29375 & [N] - \\ - T_{as} &= F_{aand} \cdot r \\ - &=(F_{eff}+F_{rol}) \cdot r \\ - &=97.03125 & [mNm] + &= 1.29375 & [N] \\ + T_{traag} &= J \cdot \alpha_{acc} \\ + &= 2.1\cdot10^{-3}\cdot 9.33 \\ + T_{as} &= F_{aand} \cdot r +T_{traag}\\ + &=(F_{eff}+F_{rol}) \cdot r +T_{traag}\\ + &= 97.03125 + 19.593 \\ + &= 116.62425 & [mNm] \end{align*} \subsubsection{Vertragen} @@ -154,14 +158,15 @@ F_{eff} &= m \cdot a \\ &= 1.5 \cdot 0.5 \\ &= 0.75 & [N] \\ - \\ - F_{aand} &= F_{rol} - F_{eff} \\ - &= 0.24375 - 0.75 \\ - &= -0.50625 & [N] - \\ - T_{as} &= F_{aand} \cdot r \\ - &=(F_{eff}-F_{rol}) \cdot r \\ - &=-37.96875 & [mNm] + F_{aand} &= F_{eff} - F_{rol} \\ + &= 0.75 - 0.24375\\ + &= 0.50625 & [N] \\ + T_{traag} &= J \cdot \alpha_{dec} \\ + &= 2.1\cdot10^{-3}\cdot 6.66 \\ + T_{as} &= F_{aand} \cdot r + T_{traag}\\ + &=(F_{eff}-F_{rol}) \cdot r + T_{traag}\\ + &= 37.96875 + 13.986 \\ + &= 51.95475 & [mNm] \end{align*} \subsection{Dalende ondergrond} @@ -179,13 +184,13 @@ &= 1.5 \cdot 1.625 \\ &= 2.4375 & [N] \\ \\ - \alpha &= 20 & [deg] \\ + \theta &= 20 & [deg] \\ \\ F_N &= F_{z1} \\ - F_{z1} &= \cos{\alpha}\cdot F_{z}\\ + F_{z1} &= \cos{\theta}\cdot F_{z}\\ &= \cos{20}\cdot 2.4375 \\ &= 2.2905 & [N] \\ - F_{z2} &= \sin{\alpha}\cdot F_{z}\\ + F_{z2} &= \sin{\theta}\cdot F_{z}\\ &= \sin{20}\cdot 2.4375 \\ &= 0.834 & [N] \\ \end{align*}