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Tempering and Gear Cutting

Pressure Angle

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Peter Howell 124/07/2020 08:11:18
21 forum posts
4 photos

Reading, with interest, the series Tempering and Gear Cutting.

What I've never really understood is why have the different gear pressure angles?

I understand their effect on tooth shape, but why have the different angles in the first place.

Martin Connelly24/07/2020 09:14:21
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1602 forum posts
175 photos

It is a compromise between strength of tooth and the pressure on the teeth forcing the gears apart under load. Different angles suit different applications.

Martin C

Andrew Johnston24/07/2020 09:29:32
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5824 forum posts
662 photos

I expect 14.5° PA was originally chosen for convenience as sin(14.5) is 0.2504, which makes life easier when you don't have a calculator.

As Martin says there is a compromise between root thickness of the tooth and radial loads as the PA varies; think about the force vector.

However, there are also practical reasons. Larger values of PA reduce undercutting when hobbing gears. Undercutting further weakens the tooth. As an example multistart worms for power transmission may use a PA as high as 60° to avoid undercutting of the mating worm wheel.

Andrew

Peter Howell 124/07/2020 09:47:37
21 forum posts
4 photos

Right.

So if I'm going to make a gear how to I know what pressure angle to use for the job in hand?

Is it all down to experience or are there some specified design criteria ?

Andrew Johnston24/07/2020 09:55:08
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5824 forum posts
662 photos

Depends on what sort of gear and the application, manufacturing method and whether commercial or home made cutters will be used. There's no magic flowchart that can be followed to give an answer - engineering doesn't work like that. smile

Andrew

Steamer191524/07/2020 10:07:11
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166 forum posts
41 photos
Posted by Peter Howell 1 on 24/07/2020 09:47:37:

Right.

So if I'm going to make a gear how to I know what pressure angle to use for the job in hand?

Is it all down to experience or are there some specified design criteria ?

LINK was an interesting post about a month ago.

Best regards,

Steve.

SillyOldDuffer24/07/2020 11:53:12
Moderator
6655 forum posts
1499 photos
Posted by Andrew Johnston on 24/07/2020 09:29:32:

I expect 14.5° PA was originally chosen for convenience as sin(14.5) is 0.2504, which makes life easier when you don't have a calculator.

As Martin says there is a compromise between root thickness of the tooth and radial loads as the PA varies; think about the force vector.

However, there are also practical reasons. Larger values of PA reduce undercutting when hobbing gears. Undercutting further weakens the tooth. As an example multistart worms for power transmission may use a PA as high as 60° to avoid undercutting of the mating worm wheel.

Andrew

Building on Andrew's comments, a picture always helps!

pressureangles.jpg

Comparing the 10° and 35° gears, left and right, the 10° teeth are distinctly notchy whereas 35° teeth are obviously broad, and consequently much stronger, but difficult to mesh. Notchy gears transfer power more efficiently and put less force on bearings, but are weaker. The weakness of low pressure angle gears gets much worse as the number of teeth are reduced because the tooth has to be undercut to avoid interference.

pafewteeth.jpg

Gear design is a compromise between power transmission efficiency, bearing force, strength, interference and manufacturing convenience. I find the geometry and maths challenging!

"The Theory of Machines, Bevan, London, 1950" says the 14.5° angle was decided in the USA by the Brown and Sharpe Manufacturing Company. It's a compromise. Not explained why B&S chose 14.5° rather than some other nearby angle, but it might be to do with the geometry of the underlying rack. The manufacturing accuracy of involute gears depends on the accuracy of the generating rack, so it may be to do with making accurate racks. However, B&S got it wrong! Although 14.5° is a good choice for many Victorian purposes, it's weak compared with 20° teeth, which replaced it at the time for stub teeth, and has been the preferred standard for many decades.

14.5 and 20° teeth are off the shelf gears. Other pressure angles available. A major advantage of Involute Gears is they aren't fussy about centres,. As nothing is ever easy, the pressure angles of involute gears must match. Although eye-ball similar, 14.5° and 20° gears can't be mixed - they interfere and grind.

Which to choose? In a new design, 20° every time. Building to a old plan calling for 14.5° gears, following the plan is likely to be less bother - apart from old gears gradually increasing in price why mess retrofitting a slightly different gear set? Replacing gears in old equipment, always use the right gear.

Dave

Peter Howell 124/07/2020 12:11:44
21 forum posts
4 photos

Thanks that helps.

Up to now I've only cut cycloid clock wheels using commercial cutters. But my interests have moved on from clocks and most other mechanisms use involute, so I thought I'd have a go at making my own cutter. I have Ivan Law's book and had started making the Eureka tool, so I'm interested to read what Martin Gearing has to say.

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