23 Mar '16 12:55

I'm looking for some layman explanation on how transfer functions work within the framework of classical mechanics. If it could be related specifically to the example below that would be even better.

A system consists of a gasoline engine (prime mover) with a Torque vs Speed curve: T(w), and Gearbox and a Drum (load) that is to be rotated.

The engine is initially in operation at a fixed speed uncoupled from the load. At time "t" equal to zero the load is engaged (via clutch). If the load has a high mass inertia the engine responds to the step change in load by decreasing it speed abruptly; followed by in increase in speed; followed by an overshoot and sinusoidal ring out to steady state. Typical of the 2nd Order ODE transfer function.

Assuming no system losses, the mechanics of the system would typically be modeled as:

T(w) = I_drum*(GR)*d(w)/dt

I suppose I have to solve the these two ODE's simultaneously to find w(t)?

A system consists of a gasoline engine (prime mover) with a Torque vs Speed curve: T(w), and Gearbox and a Drum (load) that is to be rotated.

The engine is initially in operation at a fixed speed uncoupled from the load. At time "t" equal to zero the load is engaged (via clutch). If the load has a high mass inertia the engine responds to the step change in load by decreasing it speed abruptly; followed by in increase in speed; followed by an overshoot and sinusoidal ring out to steady state. Typical of the 2nd Order ODE transfer function.

Assuming no system losses, the mechanics of the system would typically be modeled as:

T(w) = I_drum*(GR)*d(w)/dt

I suppose I have to solve the these two ODE's simultaneously to find w(t)?