problem calculation foot rays & base toothed wheel

[Sanbimu]

Hello everyone, I ask this question because maybe I did not understand how the dentate wheels work, or simply took a bark or who knows it.
By doing some checks with a wheel produced by the manufacturer, relying on his data on the data sheet, I realized that a basic radius of the foot comes out.
the wheel is a simple toothed wheel with straight teeth of module 1.5 with tooth number z=19 and primitive diameter 28.5.

considering a pressure angle of 20° the basic gage from where the evolving profile starts:

radius_base = radius_primitive*cos(20) = 13.39

while the foot radius considering it placed at a distance of 1.25*m from the primitive comes out:

radius_piede = radius_primitive - 1.25*1.5 = 12.37

Also considering a dedendum of m (and not 1.25*m) I always get a value lower than the base radius. you can not consider a lower dedendum because it must always be greater than the addendum that is equal to m.

how is it possible that the tooth foot is lower than the basic circumference?

I need to reproduce such dense rout but how can I do it? Is everything normal? I was wrong with the calculations, am I wrong with considerations or what?

thank you in advance to those who will be able to explain the matter well.

 

[meccanicamg]

the basic circumference serves to build the evolved and is not a measurable thing. all the rest is,
However, keep in mind that the tool that is used for the creation of the wheel and subsequent grinding still affects slightly the bottom diameter, the one at the base of the tooth or lower diament.

I'd say you better take the formulas on some safe book and put yourself there to build something.
if you want there is kisssoft that allows you to design and build also 2d/3d of gears and a detailed report.

If you don't get something, you'd better resume the topic and do more theoretical checks.

 

[Marpozio]

can well happen, especially for low teeth numbers.
take a look at the figure (I apologize for the fact that the sketched abdendum is bigger than the dedendum, sorry, but for what it serves, the figure is fine the same:tongue.the primitive has radius rp and the radius of the base circle is rb.
to have a base circle below the foot circle you must impose that the dedendum is smaller than the difference of the two rays:
♪<rp-rb=rp*(1-cosø) 1,25m,="" 2*rp="" 5="" a="" avrai="" avrai:="" cioè:="" dedendum="" denti.="" di="" disuguaglianza="" dove="" il="" nella="" numero="" pari="" per="" prima,="" sostituendo="" u="1,25m=5/4m=5/4*(2*rp/z)=5/2*rp/z" un="" z="" z<rp*(1-cosø)="" è="">(5/2)/(1-cosø)
If this was verified, the base circle would be smaller than the foot circle.
as you can see the only parameters that regulate this condition are only the number of teeth and the pressure angle.
in your case (pressure angle of 20°) must be:
> point 1.4.54
...we do 42...
I hope I've been clear:</rp-rb=rp*(1-cosø)>

 

[me-bac]

Hello everyone, I ask this question because maybe I did not understand how the dentate wheels work, or simply took a bark or who knows it.
By doing some checks with a wheel produced by the manufacturer, relying on his data on the data sheet, I realized that a basic radius of the foot comes out.
the wheel is a simple toothed wheel with straight teeth of module 1.5 with tooth number z=19 and primitive diameter 28.5.

considering a pressure angle of 20° the basic gage from where the evolving profile starts:

radius_base = radius_primitive*cos(20) = 13.39

while the foot radius considering it placed at a distance of 1.25*m from the primitive comes out:

radius_piede = radius_primitive - 1.25*1.5 = 12.37

Also considering a dedendum of m (and not 1.25*m) I always get a value lower than the base radius. you can not consider a lower dedendum because it must always be greater than the addendum that is equal to m.

how is it possible that the tooth foot is lower than the basic circumference?

I need to reproduce such dense rout but how can I do it? Is everything normal? I was wrong with the calculations, am I wrong with considerations or what?

thank you in advance to those who will be able to explain the matter well.

on the website www.me-bac.com you can find a tool to generate, calculate and export toothed wheels to straight teeth, as well as a complete nomenclature. I hope you can help.