Why Base dia is > minor dia in Gears? 1

[bpr18]

hi friends,

in general, the gear specifications i find, the base dia is greater than minor dia. As per definition of involute curve, it is the profile generated when a rolling tangent rolls around the base circle without slipping.If minor circle is less than base circle dia it leads to undercut. Now, my question is why the base dia can't be < minor dia as in splines and avoid undercuts?

 

[diamondjim]

What you really need to address is the SAP diameter
which is the lowest point of mesh where the two
parts are in contact. Below this point is simply
clearance for the mating part to sweep through.
If the SAP diameter is greater than the base diameter,
you will not have undercutting. An approach similar
to what you were suggesting is the stubbed tooth form
rather than the full depth form. Splines are interlocking
part and do not really mesh like gears. Still a good
question.

 

[julio]

OK with diamondjin about SAP. Anyway, involved in design gear calculations for automotive equipment (starter pinions)one of the first concern is to make smaller everytime !
So when I design a new set of gears I try to have a minimum root diameter : I need to check by calculation there is no root interference i.e. contact between pinion trochoïd and gear tip edge.
This depend on root fillet radius of pinion (depending of cutting tool tooth tip radius), tooth tip radius of mating gear and center distance.
As frequently you want a root fillet radius rather high on pinion to get a good bending resistance you need to lower root diameter to avoid root interference.
May be you would say it is possible to increase center distance to obtain same result : it is correct but you will have a poor contact ratio (specially with spur gears) and perhaps noise problems or drop of allowable power capacity.
Design a root diameter bigger than base diameter is not a cost effective solution.

 

[gearguru]

To answer the question:
Why the base dia can't be < minor dia ? It can be. And on good gears it is.
With splines it is always so. They have different addendum/pitch and dedendum/pitch ratio than gears. Standard tooth addendum on a spline is 50% of the standard tooth addendum of the gear with the same dia. pitch (or module). Similar is valid for dedendum. This alone &quot;lifts&quot; the root diameter higher, allways above the base circle. Do not forget, that the pressure angle in splines is larger than in gears - 30 degree is standard, 45 is regularly used on rolled splines. Compare it to to 20 or 14.5 degrees on standard gear. Large pressure angle &quot;pushes&quot; the base circle lower! (base dia = pitch dia*cos(press. angle)).
One note about the undercut: it can be eliminated (sometimes) or at least minimized by using the profile modification which is a good way to design stronger teeth on the smaller of the meshing gears.
Ask here if more info is needed.
gearguru

 

[FrenchCAD]

May I have yer e-mail gearguru? FrenchCAD
Université Joseph FOURIER
Département Génie Mécanique
Grenoble
France
cyril.guichard@wanadoo.fr