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Follwoing the ssumptions above we are able to model the force transmission process in a fashion of rotational mass-damper-spring as shwon below. We can assume the shaft 1 is massless. J is the mass moment of inertia for the set of motor, shaft 2 and driving gear and J2 for the driven gear, shaft 3 and prop eller. Assume the mechanical system is initially at rest a Governing Equations With the prescribed applied torque by the motor T(t), set up the necessary free-body diagrams to derive the equations governing the angular displacements (t), θ2(t) and the tangential contact force between the two gears p(t) b Transfer Functions Find the transfer functions, Tr(s) where T(s), Θι (s), Θ2(s), P(s) and F(s) are respectively the Laplace transform of the engine torque T(t), the engine (and shaft 2 and driving gear) angular displacement θ1(t), the driven gear (and the propeller) angular displacement and the output torque or the torque carried by the propeller in the fluid medium Tr(t) 1(t) T(t) .J2 θ2(t)

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