In order to visualize a finished tooth shape, or to calculate strength factors etc. it can be done on a simple CAD program as long as the facilities are there of layering, moving , rotating and mirroring. Layering may not be needed depending on the CAD program. The following is based on a rack type cutter

Fig.1

Start by calculating the ref diameter required. If tooth strength is required then it needs to be in the normal plane, for a helical gear this will be on the virtual ref dia. Dv=D/cos²(HA), where D is the diameter and HA is the Helix Angle.

Next calculate the co-ordinates ( X,Y in fig.1) on the involute from this circle stepping round it from 0 to say 30° in 2° steps - see Fig 1 - The angle stepped through will be smaller for a greater number of teeth. You can always add more layers if you need to. Note, no involute functions are involved, the angle is from the centre line outwards

Next draw the cutter shape. Fig.2 depicts a cutter in the normal plane, you will need to ensure that this is a true representation of the cutter or the tooth shape will be completely false. For an uncorrected gear the drawing is centralised about a cutter tooth space, with the centerline and the pitch line co-inciding with position 0,0 on the drawing sheet,. If the gear is "corrected" then still use the virtual ref dia to roll the cutter around but displace the cutter by the displacement ( addendum mod X module)

Fig.2 ( for negative correction the point 0,0 will be above the original pitch line )

The next step is the hardest, longest and most boring - be warned, go and get a cup of coffee.

Copy the cutter profile to the number of layers that you think you will need, probably at least 10.

Each layer is going to represent the cutter position for each angle you stepped through for the calculations X & Y.

Leave the first layer or standard layer as fig.2 that’s where the cutter is starting from. On layer 2, ROTATE the image of the cutter through the first angle selected

( say 2°) about the origin 0,0. Next MOVE the image from 0,0 to the X,Y co-ordinates for that angle. see Fig.3

fig.3

On layer 3, ROTATE to next angle (4° ?) about 0,0 and MOVE to new X,Y co-ordinates.

Repeat for all the layers, and when finished merge all layers and you should have a picture like Fig.4

Fig.4

As long as the cutter has now cleared the blank it is finished, if not you will need to add more angles/layers. Only the top LH and bottom RH parts of the picture are correct so this is where the MIRROR command comes in. Mirror both sides about the vertical centre line and with any luck you will be left with a tooth as fig 5.

Fig.5

Outside diameter, root dia. LPC dia. etc. can now also be added.

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