Meshing gears badly with either different PA or with different DP

If one has 2 change gears with adjustable positions on a banjo, an 80T driving a 75T, which would be a WORSE mesh: 1.25 MOD PA14.5 driving 1.25 MOD PA20, or 1.25 MOD PA14.5 driving 1.27 MOD PA14.5? Obviously both will not mesh very well, but interested to know out of 2 bad choices which is the worst?

I would imagine that PA 20 driving PA 14.5 would be much worse

... but I don’t really want to think about it !!

MichaelG.

Thanks Michael for your quick and succinct reply as always - it is of course theoretical only!

. . . . so is your theoretical mesh better than Michaels imaginary mesh then ?

:O)

Martin

Well, my empirical evidence does support the expert's theoretical view, that is that rolling by hand a Myford gear around a 1.25 MOD PA14.5 gear feels smoother than rolling by hand a 1.25 MOD PA14.5 gear around a 1.25 MOD PA20 gear.

Rolling the gears by hand only tests at one centre to centre distance, which may not be the optimal distance. So the jury is still out! In neither case are the involutes conjugate so there will never be a mainly rolling action, ie, there must be some sliding as well.

Andrew

Have a look at the animation posted by Rauhul_Varma, here: **LINK**

https://www.chiefdelphi.com/t/turning-down-the-od-of-a-gear/137417/20

It doesn’t include 14.5° but you should get an idea of the likely graunching that will occur with mis-matched PAs

MichaelG.

As Andrew says, not a real world test though as you are jamming the gears together as you go. Set them up on your change gear quadrant with a good amount of clearance -- maybe two sheets of paper instead of the usual one -- and they will most likely work just fine.

Sure there will be some sliding rather than rolling, but big deal. You are not transmitting 500 horsepower from a Chevvy V8 through them at 5,000rpm, only a very small fraction of one horsepower at a couple hundred rpm to drive a leadscrew that can be turned manually with a couple of fingers on the handwheel. Almost no load at all relatively speaking.

The change gears on my ancient Drummond that mass-produced aircraft parts during WW2 are so worn they don't resemble any kind of involute curve or even a definite pressure angle  that I can see and yet they work perfectly and without noise, even when meshing with newly purchased relatively unworn gears. So I don't think its as critical in practice as theory might suggest.

Only one way to find out for sure though...

Edited By Hopper on 21/02/2021 23:43:16

Michael thanks that animation is very good and certainly conveys the difference in tooth shape between different PA's

For lathe change gears that you can adjust the centres on I doubt it matters much at all if you're in a pinch. Having seen all manner of worn, knackered, chipped, chunked and even running-out change gears runing perfectly harmlessly on lathes I think that if you have matching tooth sizes and enough clearance so they don't rumble then you're good enough. For fixed centres or long duty that's a whole different matter.

Remember, many gear pairs are profile-shifted one up, the other down which changes the effective pressure angle, and they work just fine.

I am surprised

Adam offered us a simple binary choice :
Of two bad meshing arrangements ... which one is worse ?

So far; it appears that I am the only one prepared to make the call.

MichaelG.

Surely one first needs to define what is meant by worse, otherwise there is no criteria to judge against?

Andrew

Well aren't you wonderful.

.

No ... not wonderful; just surprised

MichaelG.

.

The level of cyclic changes in velocity ratio was my starting point for a reasonable ‘definition’ of worse

... but it was just ‘visualisation’ as I don’t have the mathematical ability to analyse it fully.

MichaelG.

How about:

• Power loss due to friction (more sliding than rolling)
• Rapid wear
• Noise
• Jambs if the mismatched gears have to be mounted a fixed distance apart.

Isn't this a classic case of balancing practical vs theory. As Adam's mismatched gears will be mounted in a banjo, they can be adjusted to give reasonable clearance, so it works. The gear-train is imperfect in that the gears are wearing, grinding and wasting energy, but it probably doesn't matter because lathe change gears are slow turning and don't transfer massive power. A lathe banjo is a crude device, and the bodge is reasonable as a practical way forward when a matching gear can't be found.

The practical approach is likely to end in tears when gears are mixed in well-made gearbox. These are required to efficiently transfer significant power quietly without overheating and with minimum maintenance. Finding metal filings in gearbox oil is bad. In this example, it's important to fit the correct gears because the centres aren't adjustable : theory wins.

As a general rule, practical approaches are OK in low tech situations, but not for anything demanding. There's plenty of opportunity to commit two opposite sins! I'm not sure which is worse - applying high-tech rules to ordinary problems, or ignorance is bliss guesswork in aerospace! The modern home workshop is an interesting mix: hacksaws are obvious but require skill and practice to use properly, whilst it's easy to operating a DAB radio. It'e easy to use, despite it's internal workings being off-the-scale complicated, perhaps beyond the ability of any individual to understand the whole thing in depth!

Dave

Time to dig out the gear depthing test tool:-

Rescued from a skip!

Used for checking Rolls Royce Merlin supercharger gear engagement against a master gear and giving a hard copy of gear 'run out'.

Remember the Antikythera Mechanism basically used square-shaped teeth and worked

What you can get away with is down to loadings and whether you are gearing up or down and the benefit of a bit of extra clearance.

Neil

I have changed the leadscrew gears on the Smart & Brown model A to metric which were easy to buy and also because I chanced upon a 125/127 mod 1 gear on ebay. The seller told what diameter the gear was, so I was able to check it against the diameter of the 120 idler on the lathe. The teeth pitch and form were similar enough to have mixed and matched because the power through the train was not high,but I chickened out and the 3 original gears are in storage. The S & B gears are 24DP  20PA.

Edited By old mart on 22/02/2021 20:35:13

I would say that cyclic changes in velocity ratio were of the first importance (as Michael says above) as the use is to drive the lead screw and the only operation that requires a defined gear ratio is screw cutting. So I guess the test is what arrangement generates the best approximation to a good thread.

regards