Algorithm for gyroscopic precession where precession is inhibited 1

[Intermesher]

I have a situation where the Angular Momentum of a ring is known and I wish to apply a sinusoidal force, parallel to the primary axis of rotation, on this ring. The frequency of this force is constant, however the amplitude may vary. The unusual aspect is that the gyroscopic is not allowed to precess. The gyro is to act as a damper on the oscillating force.

Could someone provide the algorithm or information that is required to calculate the force?


Thanks.

Dave

 

[rb1957]

the gyro precesses (if that's a word) because the spin imparts an angular momentum on the gyro. Iw would be the moment caused, and the moment to be reacted

 

[zekeman]

You will have to explain this better. How is the ring restrained and where is the sinusoidal force applied relative to the axis of the ring? And what is the rotational axis for the existing angular momntum?
Knowing that,, the moment applied to the ring is equal to the rate of change of angular momentum.Or if the angular momentum vector is changed by the motion then the rate of change of that vector is the induced torque from the motion.
So, a rotation at right angles to the spin axis will induce a torque about the axis normal to the spin axis.

 

[Intermesher]

zekeman,

The ring will be turning in the XY-plane. This ring is contained by a 2-axis gimbal. The ring will rotate about the Z-axis. An external oscillating torque will rock the ring about the X-axis, by approximately 30-degrees. However, the ring cannot rock about the Y-axis.

The desire is for the 'frame' to experience, at the Y-axis, the same value of oscillating torque as that which is being applied at X-axis.

I assume (or hope) that a fixed optimal angular momentum of the ring can be calculated and this will allow the 'transfer' of the varying torque and the fixed frequency from about the X-axis to about the non-moving Y-axis. Of course, the amplitude will not be transmitted.

I also hope that this makes sense.

 

[zekeman]

Gyro restrained in the y axis:
From the sinusodial input around x axis, I get
@x=Asin(Wxt)
@x'=AWxcos(Wxt)
@x"=-A(Wx)^2sin(Wxt)
The torque around the x axis
Tx=Ix@x"=-IxA(Wx)^2sin(Wxt)
The torque in the y axis, since motion there is restrained is:
Ty=IzWz@x'=IzWzAWxcos(Wxt)
Wx,Wz =angular velocities x,z axes
Iz,Ix = angular momenta x, z axes
Unfortunately,it looks like the torques are 90 degrees out of phase.

 

[Intermesher]

zekeman

Thank you for your assistance.

I apologize for the belated reply, but I was hoping to slowly work my way through the problem before responding.

Thanks again.

Dave

 

[Geesh]

This thread (I believe is just what I am looking for) is excellent, thanks!

I think I have a similar case: we are trying to determine the amount of torque required to change the thrust vector of a spinning propeller in order steer a scale model airship. In determining this, we can scale the driving hardware (motor, gear reducer, etc.). at true 90deg, this still applies?

thanks again

 

[Intermesher]

A possible problem???

My application is for a Control Moment Gyro with a single gimbal. In this application, the moment of inertia of the 'frame' is approximately 1,000 time greater than the moment of inertia of the rotor (wheel).

I experimented with a toy gyro and discovered the following;

The application of input torque is easily discernable, if there is no resistance to the rotation of the output.

However, the application of input torque is negligible, if the rotation of the output is frozen. In fact, with the output rotation frozen there is no discernable difference between when the rotor (wheel) is turning and when it is stationary.

The question is; is it possible for a Control Moment Gyro to 'control' if there is a large difference between the two moments?

Thanks.

Dave