I am trying to construct an equation that describes the output torque as a function of lambda and omega
I have obtained the following bond graph but I am unsure of how to proceed.
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1 Answer
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It might help to organize the equations a little in steps. I think you have all this above:
Output torque of system:
$\tau_F$
Output torque at motor:
$\tau_0 = \tau_F/N$
Motor output speed:
$\omega_a = N\omega_M$
Motor torque speed relationship$^{*}$:
$\displaystyle{\frac{K_m}{R}}V_{in} = \frac{L}{R}\displaystyle{\frac{d\tau_0}{dt}} + \displaystyle{\frac{K_m^2}{R}}\omega_a$
I think it is also correct to state that:
$\lambda = LI_a$
This doesn't quite answer your question, but maybe gives you some new ideas.
$^{*}$ See, e.g., Harry Asada, Introduction to Robotics, Chapter 2
