- #1
jimgram
- 95
- 1
I’ve seen this problem phrased several ways and posted several times – a couple of times by me. But I have not seen an explanation or a solution that can be applied in a real-life situation.
The problem is simple: Given two flywheels coupled together by an infinitely-variable-transmission, with one flywheel at rest and the other at an initial angular velocity, calculate the ending velocities for both wheels when the transmission varies through 0 (geared neutral or infinity) to n in t(time) seconds.
The only known parameters are:
A. Flywheel_1 inertia = 1000*ft2*lb
B. Flywheel_2 inertia = 4000*ft2*lb
C. Initial angular velocity of FW1 = 10,000*rpm
D. Initial angular velocity of FW2 = 0
E. The transmission ratio (n) = 0...0.3 (I.E. 1/n = inf…..3.33)
F. The period change ratio: t = 15 sec
You can set n (ratio) as a function of t (time) this way: n(t)=t*ne/te
Where ne=ending ratio (.3) and te=ending time (15*s)
My problem has been that solving for ending velocities (or velocity[n]) based on the conservation of momentum the subsequent torque calculation will not be correct; when calculating based on the correct torque relationship (which cannot be anything except fw1tor=fw2tor*n ) then momentum is not conserved.
I know that momentum is a vector quantity and that torque is applied to the gear reducer, but even when doing the comparison based on small grounding mass (e.g. a space station) I still cannot make velocity, torque, and momentum to all come out correctly.
I suspect (hope) that I’m missing something relatively simple. Any insight will be greatly appreciated
The problem is simple: Given two flywheels coupled together by an infinitely-variable-transmission, with one flywheel at rest and the other at an initial angular velocity, calculate the ending velocities for both wheels when the transmission varies through 0 (geared neutral or infinity) to n in t(time) seconds.
The only known parameters are:
A. Flywheel_1 inertia = 1000*ft2*lb
B. Flywheel_2 inertia = 4000*ft2*lb
C. Initial angular velocity of FW1 = 10,000*rpm
D. Initial angular velocity of FW2 = 0
E. The transmission ratio (n) = 0...0.3 (I.E. 1/n = inf…..3.33)
F. The period change ratio: t = 15 sec
You can set n (ratio) as a function of t (time) this way: n(t)=t*ne/te
Where ne=ending ratio (.3) and te=ending time (15*s)
My problem has been that solving for ending velocities (or velocity[n]) based on the conservation of momentum the subsequent torque calculation will not be correct; when calculating based on the correct torque relationship (which cannot be anything except fw1tor=fw2tor*n ) then momentum is not conserved.
I know that momentum is a vector quantity and that torque is applied to the gear reducer, but even when doing the comparison based on small grounding mass (e.g. a space station) I still cannot make velocity, torque, and momentum to all come out correctly.
I suspect (hope) that I’m missing something relatively simple. Any insight will be greatly appreciated