Helical milling – helix angles etc
Any helix has three main parameters. Since it can only be cut on the surface of a round part – the first parameter is the diameter of the round part. The second parameter is the helix angle – alpha. The third parameter is the lead of the helix.
“Diameter” of the workpiece
If the helix was simply a mark on the surface of the workpiece what the diameter of the workpiece is, is obvious. But if the helix is a cut into the surface of the workpiece then the diameter is different at the top of the cut to the bottom of the cut. In practice, the diameter is the average of both of these.
This is the angle the helix forms on the surface of the workpiece relative to the axis of the workpiece. This is the angle that is seen when looking at a helix. This is the same all the way along the helix.
The lead is the distance the workpiece has to move in order for it to rotate by exactly one revolution.
How these are related
These three are related by the formula:
tan (helix angle) = ( pi * diameter ) / lead
This can, of course, be written in two other ways:
lead = tan (helix angle) / ( pi * diameter )
diameter = tan ( helix angle ) * lead / pi
An example of the first equation can be seen as follows.
In this case we know the diameter and the lead. If we take a piece of paper and cut it so one edge is the diameter and the other is the lead this can be fitted round the workpiece. If the paper is flattened we can draw a line from one corner to the opposite corner. The angle of this line to the edge is the helix angle.