Bevel gears cut on a milling machine are always a compromise. Only a bevel gear cutting machine can cut the proper tooth profile on a bevel gear. That said it is possible to cut a decent working bevel gear on a milling machine. Milling machine made bevel gears are not suitable for high speed use, they are noisy.
The bevel gears you can buy are tapered tooth depth and require a different cutter than for spur gears. These cutters are similar to normal spur gear cutters but make a thinner cut. There is also a parallel tooth depth method of making bevel gears that use a standard spur gear cutter and this type of bevel gear is what "Shopcalc" will calculate. These bevel gears will not mesh with "normal" bevel gears.
While it is normal for the shafts of bevel gears to intersect at 90 degrees the intersection angle can be smaller or larger. As the shaft intersection angle gets past 90 degrees and influenced by the pinion to gear teeth ratio there is a tendency for the teeth on the gear to be internal. Trying to cut an internal gear with a milling cutter is not a a good idea.
The calculated face width is a guide and calculated exactly so will give funny sizes. Round the value to a convenient size and enter that in the input box so that OD can be calculated.
Here is the caveat, The number of holes to index to each tooth must be divisible by 4 so not every tooth count is possible. Before doing the bevel gear calculations go to "Dividing head" and select your particular dividing head as the tooth count will be based on your dividing heads hole (index) plates.
The minimum number of teeth on this type of bevel gear is 12 teeth.
The formulas for the calculations are from the "Machinery's Handbook" and "Gear Design Simplified".
Face Width
The face width is obtained by:
- for Diametrical Pitch = 8 / Diametrical Pitch = face width (in inches).
- for Metric Module = 8 x Metric Module = face width (in millimeters).
These formulas result in a face width that is a little over 2.5 times the circular pitch. The face width is not a mandatory value, it can be anything reasonable and it is adjustable from 2 to 3 times the circular pitch. The face width influences the outside diameter so it may prove useful where the gear must fit through a given sized opening.
Cutter selection
The cutter is selected based on the pitch diameter of an imaginary gear or rather how many teeth could be cut on the pitch diameter of the imaginary gear. Our imaginary gear has a diameter that is twice the angular pitch radius.
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The pitch radius is measured from the pitch line to
to the center line on the back angle (90 degrees to the face angle). Obviously the pitch diameter of the imaginary gear is some what larger than the regular pitch diameter. The number of teeth for Diametrical Pitch is Diametrical Pitch x Pitch Diameter (in inches) For metric module the formula is Pitch Diameter (in millimeters) / Metric Module The result will often have a decimal value, just round to the nearest whole number and use that number of teeth for the cutter selection |
1) |
Angle the dividing head on the milling table to the face angle of the
bevel gear you will be cutting. |
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2) |
Center the gear tooth cutter to a center in the dividing head spindle,
by eye if your eyes and judgment are good. |
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3) |
Adjust you milling table so the cutter just touches the face and zero
the dial. Now set your depth of cut to the tooth whole depth by moving the
table. |
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4) |
Some people like to now cut the teeth without any offset as it
supposedly gives a better overall finish, skip this step if you want. |
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5) |
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Offsetting for the first finishing cut. Raise the mill spindle b by 1/4 of the circular pitch. If you have roughed the teeth in step 4 you must also rotate the dividing head a by 1/4 of the holes per index so that the lower side of the roughed tooth rotates toward the cutter. Now cut every tooth, indexing between teeth using the normal number of holes for each index. |
6) |
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Offsetting for the first second finishing cut. Lower the mill spindle d by 1/2 of circular pitch and rotate the dividing head c by 1/2 of the holes per index so that the upper side of the tooth rotates toward the cutter. Now cut every tooth, indexing between teeth using the normal number of holes for each index. |
When raising or lowering the mill spindle or making the offsets on the dividing head, watch out for backlash to ruin your bevel gear.