Calculating moment of inertia (MoI) using period of oscillation obtained from Simscape leads to inaccurate values

I am meant to design a test rig that can calculate the MoI of a vehicle. The concept that i have generated consist of a platform connected to a spherical air bearing on its center with a spring attached to each end of the platform. Below is the schematic of the Simscape model that I have developed and I have attached the file into the question;

Using free vibration theory the equation i came up with looks like this;

So how im trying to do this is by adding an initial displacement of 5 degrees and allowing free oscillation. The period of oscillation and Moi is then found using this code;

k1 = 1000 ;
k2 = 1000 ;
l = 3 ; 

ytheta = angle(:,3);

coloumns = linspace (1,201,201);

[peaks,coor] = findpeaks(ytheta,coloumns);

interval = tout(coor);

period = interval(2)-interval(1)

MoIx = ((period^2)*((k1+k2)*l^2))/(4*pi^2)

But doing this leads to extremely erroneous answers. I am unsure whether there is something wrong with my simulation or with the equations i am using. Here are some notes;

• I have checked whether the period obtained using the code was accurate and it seemed to do the job.
• I specified the initial angular displacement of 5 degrees using state target in the spherical air bearing, but noticed in the data the displacement was only 2.5 degrees, i cant seem to figure out why
• When trying to do torque sensing using the spherical bearing the data said that there was no torque present
• I am getting a MoI of 3834.5kgm2 when i specified the MoI to be 1000 kgm2
• I made sure that the center of mass of the platform is in line with the pivot axis
• I have tried using alternative methods of calculation such as; calculating (potential and kinetic) energy and using Torque = MoI * AngularAcceleration. But both technique also lead to erroneous values leading me to believe that the simulation is the problem.

Answer 1

[Steve Miller]

Interesting application! As I am sure you know from your studies, the frequency of a rotational harmonic oscillator is sqrt(rotational stiffness/rotational inertia). With a few adjustments to your model, you will get a period of ~4.9 seconds. With the stiffnesses(2 x 1000 N/m) and length of your brick(3), the equation will yield 4500*4.9^2/(4*pi^2) which is 2736, pretty close to the inertia about the y-axis (2761.09).

The equation you are using assumes the spring is at its neutral length at time=0. The way your frames are attached to the platforms, they are slightly compressed at the start of the simulation. The free length is 0.5m, the centers of the platforms are separated by 0.5 m, but the springs are attached to the closest surfaces of the platforms. Change where the springs are attached and you will get results that match theory.

--Steve