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You can find the full set of equations for the subsurface stresses in Boresi: 'Advances mechanics of materials', chapter 17 Contact mechanics. This source is also shown here : http://www.mesys.ch/?page_id=17&lang=en Only the approach for line contact is calculated according to Lundberg, since...

If number of teeth for sun and ring are fixed, I see the main reason in changing the number of teeth for the planet to influence the sum of profile shifts for both pairs. Changing the center distance you get the same sum of profile shifts for both pairs (with opposite sign). For example if you...

If all numbers of teeth are a multiple of the number of planets there are the same contact conditions on each planet. Therefore the variation of stiffness is larger as for shifted positions. For the purpose of reducing noise and vibration it could be better to avoid this. The variation of...

I can only tell, that the formulas in ISO 6336-3 are different for internal and external gears. For internal gears a rim thickness larger 3.5 times module is required to avoid loss of strength, for external gears it would be a rim thickness of 1.2 times whole depth. The formulas are YB = 1.6 *...

For example 14/30/-73 for the number of teeth would give an output speed of 230rpm. The center distance would be 0.44" with Diametral pitch of 50. You would need some profile shift on the sun to avoid undercut.

You would have to increase the lead angle, but is is better to avoid the hard limit.

It is common for small number of teeth, that the base diameter is larger than the root diameter. For a spur gear the base diameter is db=d*cos(alpha), the root diameter is df = d - 2*mn*hfP + 2*mn*x With alpha=20° the base diameter is larger than the root diameter if z < 33 * (hfP - x) For...

Sometimes the calculation of worm gears is done as crossed helical gears, where worm gears are a special case. For crossed helical gears a profile shift can be applied for both gears, which can be useful to have a thinner metal worm and a wider plastic worm gear. If the sum of profile shift...