Just a status report..
Ive learned quite a bit about the math of making a bevel with involute shaving, but still havent managed to complete the algorithm
s to cut them. I can see trouble though..
When we create a helical or spur on the 4th axis, we do it by tangental shaving. This means we take a point on the involute curve of the tooth, and rotate it till its tangent to the Z axis ( the tool). Since its tangent to the tool we're OK to make a pass which will shave only points above that involute tangent point..
( Hard to visualize I know..).
Our problem with bevels is that tilted gears do not change tangent at the same rate as a spur.They rotate their tangent at a ratio of 180 - 2*PitchCone angle / 180 . This means some bevels never hit a tangent point
during their rotation, others have to be rotated to a involute angle times the ratio above.
What this all means is the amount of involute angle for a tooth is limited by the above ratio ,
so as the gear increases its pitchcone angle, the amount of rotation of the toolpath necessary
to get to a shaving point increases
. When it hits 90 degrees your ususally hosed.
The best way to picture this is to picture a 90 degree bevel pitchcone gear.
This is a gear laying totally flat. It has no angle. Its teeth go straight in to center. Obviously,
there is no rotationa
l position that will make those teeth go tangent to the Z axis. The involute tangents
point the same direction in any rotationa
l angle of the gear. The other extreme
is the 0 degree bevel, ( a normal spur gear ), where we'd have no trouble as the tangent rotationa
l angle is equal to the
involute angle for the point in question. Since the involute angle on a gear never goes as high as 90, the rotation that
has to be done is always less than 90 degrees. But in a 20 degree pitchcone angle, for example, you need to rotate the gear almost 180 degrees. ( cutting the gear on its back face).
The numbers tell me that 90 degree pitchcone angles are impossibl
e, while 0 degrees are easily done. Basically
all bevels fall within the two extremes. Whether a bevel is possible or impossibl
e then, falls to a certain amount
of variables that affect the end max involute angle.. Tooth count is important as the lower the tooth count the
higher the involute angles are, thus limiting the amount of pitchcone that can be cut. The higher the tooth count the
more easily it CAN be cut, but the larger the gear. ( A limitatio
n for most of us based on rotary table size. )
John Stevenson, who is annoying correct almost always, was also correct in his assumptio
n that tilting to the pitchcone
angle ( thus making the tooth pitchline flat at the top of the table ), would make the calculati
ons easier. In fact tilting to
an arbitrary degree such as 45 degree's, makes the calculati
ons near impossibl
e. By tilting to a straight pitchline Ive managed to
create several routines that check the numbers for me that prove out the above statement
s on limitatio
n of tangental angles
based on toothcoun
t , gear diameter, and pitchcone angle.
Sooo.. Im starting a third iteration of the code. ( Not unusual for me to go through several iteration
s on complex algorithm
s as each
try teaches a valuable lesson in getting your mind in the right frame of 3d referance
Im still convinced its possible, but with limitatio
as to what gears can and cannot be cut. Ill need to implement some calculato
r to auto figure out if we can cut this on a 4th axis or not.
If nothing else it explains to me why no-one else does this in the context of a 4 axis mill. ( That 5th axis would certainly come in handy here.
Just a status update as to why Ive been pretty quiet.