My simulation is Excel for case 1 of constant torque,
and a toolset I created in F90 many years ago for case 2 of proportional torque. This was due to a need to carry out a convergent iteration for position.
I modelled a point mass in free space with the forces necessary to create the motion described in a rotating frame of reference,
I chose to use centripetal force ~v2,
and normal to that, tangential which depends on the case.
For case 1 it was constant but swapping sign at the top of the circle. (assumption)
For case 2 ~θ similar to SHM. (assumption)
I am aware of no other forces acting on the mass to create the described motion.
The tangential force, created by the torque, causes an increase in angular velocity.
The centripetal force, necessary to maintain circular motion, grows from minimum at the bottom to maximum at the top as the mass reaches its maximum angular velocity, and then reduces back to mimimum at the bottom.
Draw out all the "centrifugal forces" acting on the mass as it travels around its circular path if you wish. Or consider that if the torque magnitude is symmetrical laterally (assumption), then all the centrifugal forces in the bottom half of the circle are always smaller then their mirror in the top half, as the velocity is always greater in the top half of the cricle than the bottom. Due to the reversal of the torque, the tangential force always has a vector horizontal or above.
Graviman, with your engineering experience, can you please point to the incorrect assumption(s) or the ommission(s) in the above analysis that lead to your statement that my analysis is "garbage". I am always willing to learn from my mistakes.
In mechanical implementation. The torque acts at the driveshaft, is transferred via the rotor arm, creating acceleration. The centripetal force is provided by the rotor arm, constraining the motion to a circular path. This force must be reacted at the driveshaft end. The changing centrifugal force (in reality the reaction of the centripetal) doesn't negate anything, but in fact is the mechanism for the linear force creation.
I suggest a turboshaft is a bit of overkill, and not the best way to create varying rotational motion. I imagine that Jiff is thinking some form of electrical motor to create the torque, with polarity changing to produce the reversal. This is all assumed implementation of course.
Jiff, creating the torque is just one (and probably the least) of your problems.
1. How do you react the opposing torque on the engine body, such that it doesn't undergo an equal and opposite motion? If not reacted this would produce an equal and opposite motion. Net change at best is rotation.
2. Instinctively I suspect that the centre of mass of the rotor is towards the lump at the end. The motion would therefore be both mass and drive mechanism rotating about this centre and causing an almost self cancelling effect. How do you intend to "anchor" the driveshaft?
3. When the body starts to translate, the motion is no longer circular, and the torque would have to be varied in order to maintain the same equations of motion, as the start and end point are no longer the same place. How do you intend to calculate and compensate for this effect?