Radial distance (eccentric) and Cradle angle calculation for cutting of spiral bevel ZAKgears.

Radial distance is the distance from the center of the cradle (machine center) to the center of the gear cutting tool. Changing the radial distance changes the spiral angle of the finished gear.
Cradle angle is the angular position of the cradle when the cutter is in the middle of the tooth space. Setting a cradle angular rotation is not critical for the finished tooth geometry. Normally an experienced in cutting operator would know at what angles to set the rotation of the cradle.

Input:
Pitch cone distance to the middle of the tooth face:
C

Diameter of the cutting tool at pitch point.
CD
Spiral angle at pitch point in the middle of the tooth. [deg]:
Fi

Output:
Radial distance (R):
R=SQRT(C*C+0.25*CD*CD-C*CD*Cos(90-Fi))

Cradle angle (CA) [Deg]:
CA=arctan(Cos(Fi)/(2*C/CD-sin(Fi))

Other calculators: ZAKGEAR roll and machine angle. ZAKGEAR cutter diameter. Contact pattern. ZAKGEAR TCA

Geometry of ZAKGEAR spiral bevel production method.

Click on image to enlarge:

There is a practical reason for measuring ZAKGEAR cutters on the blade pitch points. Unlike the traditional spiral technology ZAKGEAR method allows calculation of the tooth geometry for the cutters with modified cutting edge including but not limited by Wildhaber-Novikov profile, root and tip relief, and tip and root radius. In general, the geometry of ZAKGEAR spiral bevel cutting blade is given by a list of x,y,z co-ordinates of the cutting edge points. While Direct Digital Simulation method determines the number of points [2n+1, n=1,2,3], x,y,y co-ordinates can be, frankly, any realistic numbers.

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