# Coil Winding Mechanics

1. Nov 23, 2005

### cjenrick

Hi folks!
Long time listener-first time caller.
I am building a coil winder for building my own transformers-fun fun!
Anyway, I came across an interesting aspect associated with winding which, if not for anything else, provides an interesting math physycs problem.
I am trying to understand what happens with the magnet wire as it is spooled onto, lets say for simplicity, a square bobbin. The corners of the bobbin will lift the wire up and drag it forward, for a rotional distance of π/2 Radians - 90 degrees. After this, the cycle begins all over again, for another 90 degrees, until after four cycles, the bobbin has completed one turn. So we only need to look at a 90 degree segment, since this pattern repeats itself.
I brute forced this on a piece of polar graph paper to try and jump start my understanding of this winding process. I assumed that the wire comes from a point in space an infinite distance away so I could ignore the effects of the vertical transition as the bobbin rotates.
So, I am looking for the relationship between the angular velocity of the bobbin and the linear speed of the wire as it is spooled on the bobbin.
I am using a constant rotational velocity of the bobbin, which has a distance of 1 from it's center to it's outside edge, 90 degrees up from the center.
I need help deriving the equation for the linear wire speed.
Location would be an extra bonus!

Here is what I came up with so far, I started the math table with the corner at 45 degrees, rotated it in 5 degree increments, and took the difference in distance between the two, to get the horizontal distance traveled by the wire.

cos b - cos a = distance traveled
Thanks!
cj

#### Attached Files:

• ###### wirespeed1.jpg
File size:
39.6 KB
Views:
106
Last edited: Nov 23, 2005