I'm sorry if this in the wrong section, this is my first post. My problem is that I need to improve the diameter measurement on a paper winding machine.
The paper roll is sitting on top of two drums and there is another roller sitting on top of it to keep it from bouncing away from the machine (rider roll).
The position of the rider roll is measured using a linear position sensor.
At the start a core is inserted into the machine and the paper is taped to it. This is illustrated to the left in the picture below.
The cores can have different diameter, but is always known.
As paper is winded onto the paper roll, its diameter is growing and that pushes the rider roll up. A finished roll can be seen to the right in the picture.
Obviously the distance between the Main Drums and their diameter is known. It seems to me that it would be possible to make a formula that takes these values and the measurement and give you the paper roll diameter, I just can't figure it out.
The measured distance can be calibrated to start or end somewhere else if that makes it easier.
If you are curious here are some measurements:
Main Drum diameter: MDd=790 mm
MainDrum Center distance: MDcc=810 mm
Core diameter: Cd= 70-150 mm
Finshed roll diameter: 1000-1500 mm