Cheetos
Mechanical
- Jul 27, 2007
- 56
My original problem is to find the torsional frequency for a rotor cage. I first looked into the torsional frequency for 2 discs (J1, J2) and 1 massless rod in between (standard textbook problem). Using torsional stiffness equation, kT = G*J/L, I was able to find my torsional frequency of the system. For a single rod (with diameter = Do) on top of the rotational axis, J orig = (pi*Do^4/32). I then tried to find an equivalent system with multiple rods (that is made up of multiple N parallel rods (with diameter = Dn) located at R away from center of rotation). I used parallel axis theorem. (pi*Dn^4/32+ R^2*(area))*N = J total. Since rods are parallel, the total k should be the sum of each k.
For an equivalent system, J orig should = J total, I was able to find Dn. The problem is when I tried to verify it using FEA, my natural frequency is way off.
Did I make wrong assumptions somewhere in there?
Given for standard text book calc: J1 = 5.66 kg-m2, J2 = 22.6 kg-m2, G = 7.69e10 kg/m2, L = 0.6m, Do = 0.1m
Standard text book calc: J orig = 9.817e-6 m^4, kT = 1.26e6 Nm/rad and freq ~ 84 Hz
FEA text book calc: freq ~ 82 Hz
For equivalent system, my calc for 4 rods with Dn = 0.0176m, R = 0.1m, same J and kT, freq ~ 84 Hz
FEA for 4 rods: freq ~ 6.2 Hz
For an equivalent system, J orig should = J total, I was able to find Dn. The problem is when I tried to verify it using FEA, my natural frequency is way off.
Did I make wrong assumptions somewhere in there?
Given for standard text book calc: J1 = 5.66 kg-m2, J2 = 22.6 kg-m2, G = 7.69e10 kg/m2, L = 0.6m, Do = 0.1m
Standard text book calc: J orig = 9.817e-6 m^4, kT = 1.26e6 Nm/rad and freq ~ 84 Hz
FEA text book calc: freq ~ 82 Hz
For equivalent system, my calc for 4 rods with Dn = 0.0176m, R = 0.1m, same J and kT, freq ~ 84 Hz
FEA for 4 rods: freq ~ 6.2 Hz
