Simple Gear Train: Pitch Circle Diameter and Typo in Homework

[EastWindBreaks]

Homework Statement

Homework Equations

The Attempt at a Solution

if you do 38*25/pi , you would get 302.394 for the exact pitch circle diameter, similarly, exact d2 should be 907.183 mm, is it a typo? or did I miss something?

 

[CWatters]

The used a slightly different value for pi. Probably 3.142

 

[EastWindBreaks]

The used a slightly different value for pi. Probably 3.142

the new exact d1 should be T1*Pc/pi, correct? but it has only Pc/T1

 

[CWatters]

Yes their equation appears to be wrong.

https://en.m.wikipedia.org/wiki/List_of_gear_nomenclature#Standard_pitch_diameter

D=pN/pi

= 25*38/3.142
= 302.36

Or if you use pi to more decimal places you get your answer of 302.394

 

[EastWindBreaks]

Yes their equation appears to be wrong.

https://en.m.wikipedia.org/wiki/List_of_gear_nomenclature#Standard_pitch_diameter

D=pN/pi

= 25*38/3.142
= 302.36

Or if you use pi to more decimal places you get your answer of 302.394

thank you, i probably can't trust my professor's lecture notes anymore...

 

[EastWindBreaks]

Yes their equation appears to be wrong.

https://en.m.wikipedia.org/wiki/List_of_gear_nomenclature#Standard_pitch_diameter

D=pN/pi

= 25*38/3.142
= 302.36

Or if you use pi to more decimal places you get your answer of 302.394

gear ratio can not be greater than 10 correct?

 

[CWatters]

You can have a single stage with a bigger ratio but I think there are frequently better options, eg a multi stage might be smaller or have less wear. I am not a mechanical engineer but I think single stage spur gears for power transmission are normally limited to somewhere under 10. Some sites say under 7. The issue is with the small gear, where I think the practical minimum number of teeth is around 20 teeth.

Technically a rack and pinion has an infinite ratio.

Some tower cranes have a small pinion turning a very large ring gear under the cab and I think the ratio there might be more than 20. That's in addition to a sealed gearbox between the electric motor and pinion.