Help with bevel gear calculations

[ZanParticipant @zan]

I am struggling with bevel gear calculations for the od of the pinion ( and wheel). It’s the first gears I have cut for over 50 years and to coin an expression. “ it’s doing my ed in”. Perhaps those with superior knowledge can help here   I’m showing the calcs for the pinion, when the problem is found here all should be easy to follow up for the wheel the cutters are made to clicksring’s “tools glorious tools” utube   A long but interesting task!

It’s for a governor  of 32 dp  with 16 and 32 teeth.

Inner pitch dia. = n/dp = 16/ 32 = 0.5

Slope  angles are  ( pinion ) 26.34. And  (wheel) 64.26 degrees

For reference I am using Lammas data from ME Oct 1991 p 447 and Laws book p 106

Using each of these I get an od for the pinion of. 0.696  (Law)  0.756  (Lammas). Which is correct!

Law is not fully clear about his calculations for the large end dia., it took a while for me to realise the last number in his calculations is in fact the difference between the PCD and the od  of the small end. That is the addendum x 2 and that he uses the cone length in the first expression.

Addendum is thus 1/dp x sin26.34 x 2.  Or .0.0312 x0.4436 x2.  = 0.0137 (on single tooth),  0.027 on diameter

Inner cone length is the same to both authors at 0.563 and face length of 1/3 = .0.75 total

This gives me

(Law)…..[(cone length)x sin26.34×2 ] + addendum. = (.75 x .4436 x 2)+ .027 = 0.696

 

Lammas does it differently using outer pitch dia.  ( 1.4 x ipd ) = 0.7.     So

Od= opd + (2 x cos 63.24 / dp) =  0.7 + (2x .896 / 32)  = 0.756

Now that’s a big difference for such a small gear.  Both should be the same     Help would be appreciated

[Les RileyParticipant @lesriley75593]

If you message me an email address I can send you a spreadsheet that does it all for you.

It is based on Ivan Law’s book method and saves all the confusion and head-scratching.

You can play about with different DP s and tooth numbers until you get the blank sizes you need to fit into your job.

Les.

[Zan]

On 31 October 2024 at 14:55 Zan Said:

Slope  angles are  ( pinion ) 26.34. And  (wheel) 64.26 degrees

 

Od= opd + (2 x cos 63.24 / dp) =  0.7 + (2x .896 / 32)  = 0.756

What is the total angle of the gears? 64.26 + 26.34 does not add up to 90.0 (that is not necessarily a mistake, but is unusual).

Where does 63.24 come from?

Are both of these simply typos. in your post or something more serious?

I was under the impression that the slope angles of a 1:2 pair at 90 degrees would be arctan(0.5)=26.56 and arctan(2.0)=63.43 but this may be irrelevant to your own construction.

[Author]

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