# motion equation of rotor and stator

I have the situation from the following drawing:

It represents a model for measuring the torque of a generator. There is an arm connected to stator and, the other end of the arm to a bending type load cell. I want to model this system and have as an input the torque of the generator rotor and as output the torque that reaches the load cell. I want to model somehow how is the transfer of energy from the rotor to the load cell. The load cell type is Hottinger Z6FC3. The system is connected like in the figure below.

I am new at this and don't know much mechanics. I don't know how to write the motion equations for the two bodies and connect them.

• This may not be a homework problem, but it is a "homework problem", where you are presenting us with a problem and asking us to solve it. In order for such questions to be valid on this site, you must show whatever work you've already done and describe what specific problem you are having solving it. – Wasabi Mar 30 '16 at 14:32
• I don't know how to write the motion equations for the two bodies and connect them. I need at least just a hint on it. – Razvan Mar 30 '16 at 14:37
• I don't see a way that anything could work out like you want. Your springs and dampers act linearly. The torque does not. – hazzey Mar 30 '16 at 15:00
• Why is not the torque acting linearly? I forgot to mention that is a DC generator – Razvan Mar 30 '16 at 15:05
• For a hint on modeling the system, take a look at this: engineering.stackexchange.com/questions/8190/… – willpower2727 Mar 30 '16 at 15:23

You need to apply Newton's second law that states:

Second law: The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object: F = ma.

In your case, you need to replace force by torque, mass by inertia and acceleration by angular acceleration. Given that the torque provided by the rotational springs is the spring stiffness x the relative angle and that the torque provided by the rotational dampers is (in the first instance) the damping coefficient x the relative angular velocity, you get:

$T = (J_s + J_a) \ddot{\theta_r} + C_m (\dot{\theta_r} - \dot{\theta_s}) + K_m (\theta_r - \theta_s)$

$J_{Gs} \ddot{\theta_s} + C_{Gs} \dot{\theta_s} + K_{Gs} \theta_s = C_m (\dot{\theta_r} - \dot{\theta_s}) + K_m (\theta_r - \theta_s)$

where $\theta_r$ and $\theta_s$ are the rotational displacements of the rotor and the stator, respectively.

• And using this equations how do I obtain the torque at the end of the arm? – Razvan Mar 30 '16 at 15:32
• Not sure what you mean. The only torque here is the torque input from the generator rotor, which is known. – am304 Mar 30 '16 at 16:02
• I got it now. I was thinking at my system. The output is displacement, theta_s. The load cell will transform the displacement into a force. Right? – Razvan Mar 30 '16 at 16:06
• Yes, I assume so. I guess it depends on the load cell, how it's mounted and where. – am304 Mar 30 '16 at 16:28
• I made some modifications and explained better the problem. – Razvan Mar 31 '16 at 6:44