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RMP calculation
For a better understanding, I am working with an overhead coiling door where the door curtain coils around a pipe. I am trying to determine the angular velocity (RPM) of the door opening. I understand this is a dynamic situation, but I would first like to look at it as a static situation. The door has a counterbalance torsion spring inside the pipe that provides a torque to open the door once the motor brake is released. The variables listed below are for when the door is closed. They are technically variable (dynamic), but for initial simplicity, if possible, we will look at it statically with the values provided.
F1 = curtain hanging weight = 451.33 lb (will decrease as door opens)
T1 = torque produced by counter balance springs inside pipe = 2630.91 lbin (will decrease as door opens)
R1 = radius of pipe = 4.75 in (will increase as door opens)
M1 = mass of coil = 1824 F1 = 1372.67 LB (will increase as door opens)
Looking at the picture provided, the pipe is supported through the center by a 2 solid shaft. I have a spreadsheet will the varying values as the door opens, but I thought analyzing the problem statically at the initial condition of the door (when the door is closed) would be best to do first.
I got as far as finding the resultant force from the T1 F1, which I call F3. T1 produces a force F2 which is equal to T1/R1 = 553.87 LB. F3 = F2 F1 = 553.87 LB 451.33 LB = 102.55 LB.
I know the problem consists of angular motion and did some research on equations, but I cant put anything together.

The rotational acceleration and the final assembly rpm is what you need to be most concerned with.
Even though your spring loading is going to decrease during the lift, as long as your spring load is greater than the curtain hanging load (which is necessary to fully lift the curtain and keep it open) your assembly is rpm is going to accelerate throughout the entire lifting cycle and at the end it is going to have the rotational inertial of the full mass of your assembly, including the total curtain mass (1824+451=2275Lbs), spinning at the accumulated rpm that then must be stopped.

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I believe that complicates things, but yes the pipe will accelerate at a varying rate because their is not a linear relationship between spring torque and hanging weight.
See the attached table for more information.
F1 = "hang weight" column
F1 x R = "hang weight" column x "R" column
T1 = "Spg Torque" column
The torque imbalance column is the Spring torque (T1)  the Curtain torque (F1 x R). The torque to back drive through the motor once the brake is released is about 50 lbin. With that being said, as long as the torque imbalance is greater then 50 than the door will continue to open. Due to the torque imbalance decreasing until the door is about half open and then increasing after that, I think whether the door is accelerating or decelerating is not exactly clear.