Question

01- (08 Pts) Figure below is a diagram of a DC motor connected in parallel to a current source is the torque and back-EMF constants of the motor are K. K respectively, the motor resistance is R, also modeled as connected in parallel, the motor inertia is I. (not shown), and the motor inductance is negligible. The motor load is an inertia compliance (stiffness) K and viscous friction coefficient b, and it is attached to the motor via a gear pair with gear ratio N/N (N and Nu are the numbers of teeth on gear pair). The system of the inertia. input is the current i, and the output is the rotation angle en is the rotation angle of the motor To is the torque generated by the motor. Vs: back emf. A - The torque is proportional to the armature current, so T. Km 12. The induced voltage vs is directly proportional to the angular velocity d/dt, or v - K, d./dt. Tm=km The equivalent inertia of the gear train referred to shaft inertia is les = J + 22.m Jeg = € Q 1.1- Derive the governing equations for the electrical part (2pts). Q 1.2-Derive the governing equations for the mechanical part (2pts).

Answer 1

Equivalent electric circuit i - R ) bre is R = iz R + Vp G is = iz + Vo 12 = is - Ku 12. 1.2 Mache past 12 = is h do + ko = Tmi + b de hele (1 + (n . Ton + be t ko - Tom 13. But I'm = Keniz = km (is- kv dom na (J + (1 m) do + b det kB = km Nz is - Kmkv dem (Iterations add + (6 + Kim ku det + ko C R at Konku I do tko Rdt 1.(s): (It can In) s*o(s) + (67 Konku ) sovs74 kW) 105) (5+ ( au Tan) s? + (b+ Kinkiv )s+ k Km. N/N (5)