Gearbox efficiency while back-driving

I suppose if there's a "sci.engr.mechanical" group I should post it there -- but r.c.m has some smart mechanical types, and s.e.c may still have
some lurkers who might come out of the woodwork for this one.
So here's a question for the mechanical engineers in the group(s).
I was giving a seminar on control systems last week, and had the embarrassment of not only having a huge mathematical error in one of my slides, but had one of the smarter audience members question my underlying assumptions -- and I didn't have answers for either problem while standing there.
The basic problem is this:
If I'm putting a gearbox into a control system, and I have a data sheet (or measurements) for the gearbox that tell me it's efficiency in the designed direction of power transfer (usually when it's gearing down), I would like to know what its efficiency is in the backward direction.
In other words, if I have a gearbox with a gear-down ratio of K:1 and 100% efficiency, then when I drive a torque into the thing I should get K * torque out. But what I really get is K * torque * efficiency.
I know both from experimentation with one sample, and from working out the math, that if I have a single-stage worm gear that I try to back- drive, its efficiency in the backward direction is pretty close to
h_b = h_f / (1 - 2 * h_f), where h_f is the efficiency in the forward direction.
But I don't know if this is general to all gearboxes, or even to all worm gear trains -- it's quite possible that I messed up my calculation and then lucked out on the one sample that I experimented on.
So -- anyone know? Are there any mechanical engineering texts that I should buy to check up on this?
--

Tim Wescott
Wescott Design Services
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I don't know the numbers, Tim, but I know that unless that worm has an awfully steep pitch, it's back-drive efficiency is almost zero. There's probably a critical pitch, combined with lubricant selection and materials selection where the efficiency suddenly and exponentially approaches zero.
Lloyd
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On Tue, 30 Jul 2013 12:09:06 -0500, Lloyd E. Sponenburgh wrote:

That's certainly my experience. I used to work on a product that had a worm drive, and this honkin' big flywheel on the motor that drove it. The worm drive was selected because its compact and because you can't back-drive the thing with power off. The flywheel on the motor was added because with the power on, when you commanded a reduction in speed the gearbox would seize, then the inertia of the driven mechanism would immediately break the output shaft of the gearbox.
I've heard of worm-drive gearboxes being changed from "can't back-drive" to "back-drives just fine" with a lubricant change. This from a fellow engineer that I trust. Apparently the lubricant in question was one of those "more expensive than gold" aerospace things that engineers sometimes use to patch over mistakes in design that aren't discovered until it's too late to fix them in a more reasonable way.
I've actually got a gearmotor in my office that uses a worm drive that can be back-driven. It's about 70% efficient in the forward direction, and about 57% efficient in the reverse direction, which is consistent with the formula that I cooked up. I suspect that it's got a two-, three- or four-lead worm, though.
--

Tim Wescott
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On 30/07/13 18:29, Tim Wescott wrote:

Vibration can also make the difference between a gearbox that won't back drive to one that will so the operating environment can make a difference.
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On Tue, 30 Jul 2013 20:31:39 +0100, David Billington wrote:

I know. It's a complex subject. That's why I was thinking that maybe the "real" answers would be buried in some mechanical engineering text.
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Tim Wescott wrote:

That can't be right. It makes no sense. If h_f was 50% h_b would be infinite. If h_f was between 50% and 100% then H_b would be between minus infinity and -1. for example: If h_f were 80% then h_b would be -133%. What does an efficiency of -133% mean?

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On Tue, 30 Jul 2013 13:40:12 -0500, jim wrote:

AAAAAGH! I got it backwards AGAIN!!!! That's what's on the erroneous slide! Crap! Crap! Crap! Proofreading's a bitch.
It should read
{ (2 * h_f - 1) / h_f if h_f > 1/2 h_b = { { 0 if h_f <= 1/2
where h_b = 0 means that the gear locks when you back-drive it.
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Tim Wescott wrote:

OK that formula produces numbers that are at least possible.
My wild guess is that there is no standard relationship for the efficiency forward and back on a worm gear.
Your formula has another problem. The efficiency in reverse is never really zero. If you get a worm gear that is theoretically not reversible started going in reverse it can usually be driven backwards to keep it going. It is just under static friction that it jams.

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Nooo... that's not even close. Try that with a 100:1 worm drive. You couldn't reverse-drive such a box with all the horsepower and "pre- starting" in the world.
We're not talking about "theoretical mechanical advantage" here. There are niggly little things like _actual_ mechanical friction at work, also.
Lloyd
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Side topic:
I have read that the Wehrmacht's tanks, esp. the later ones that were so large, suffered badly from final drive failures. So much so that a road march of them for any distance would disable say 33%. This helped me better understand Allied anti-railroad tactics...forcing them onto the roads.
[They also lacked tank retrievers of enough strength to salvage them....]
The failures were because of 2 basic reasons: they lacked sufficient chromium to fully harden the gearing, and the second was my question.....
This source (that I now can't find again...) said there was a way to better design/machine the ring gears needed, but Germany lacked the tooling/resources to use that approach, and instead used less strong methods. I inferred the better way needed more time or a better mill but beyond that, I don't know.
I'm curious about what that might have meant, and wonder if anyone can speak to gear design issues...
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On Fri, 2 Aug 2013 15:49:25 +0000 (UTC), David Lesher

Only in fragments. If the issue was an internal-tooth ring gear, as for a planetary gearset, that wasn't a milling issue. That was a gear-shaper issue. They also can be broached, but I don't see that as likely during the war, on big gears. Perhaps that's the tooling that Germany lacked. It requires very big pieces of high-quality tool steel, and chromium shortages would be an issue.
Germany had some very good gearmaking capability but that of the US was better at that time. Gleason was the world leader in making big, strong gears of several types.
BTW, the US had power-transmission issues on some tanks at the time, too. Caterpillar made a big 24-cylinder porcupine diesel engine that was supposed to be the end-all for our largest tanks. But it had so much torque that it twisted off driveshafts like they were swizzle sticks.
--
Ed Huntress

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On Fri, 02 Aug 2013 12:05:18 -0400, Ed Huntress wrote:

Steven Ambrose has some interesting comments in "Citizen Soldier" about the Sherman tank. The allied soldiers in Europe reportedly disliked it because it was so wimpy compared to the big German tanks -- but Eisenhower could get three Shermans for every one big US tank (I can't remember what we had), and a Sherman used less gasoline. The thinking was that as soon as the allies broke out in Normandy and started for Berlin that the mobility of the Sherman tanks would outweigh the size difference.
It's hard to say who was right, but we did win using those little tanks.
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Tim Wescott
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On Fri, 02 Aug 2013 12:09:24 -0500, Tim Wescott

Yeah, I've always wondered how we shot up Tigers with Shermans. Did the Shermans have the high-velocity 90mm guns, our answer to the German 88s?
--
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The Panther and Tiger were susceptible to ambush from the side where the armor was much thinner, though this upgunned British version could penetrate their frontal armor if it managed to shoot first: http://en.wikipedia.org/wiki/Sherman_Firefly
http://www.achtungpanzer.com/michael-wittmann.htm "British Sherman VC "Firefly" armed with 17 pounder gun was capable of penetrating Tiger's armor at range of 800m. "
General Hatcher claimed that our bridging equipment wasn't strong enough for the heavy tank we had designed. The Germans retreated across intact bridges and then demolished them. We chose instead to use a gun too large for a turret in the open-topped Tank Destroyer, which required infantry support and didn't suit Blitzkrieg assaults but fit Eisenhower's slow, steady approach. https://en.wikipedia.org/wiki/Tank_destroyer "The weight saved from the lack of a turret could allow more armour to be fitted, and the lower profile allowed this armour to be concentrated in the hull."
"In part because of the effectiveness of US TD tactics, no German campaign against the US ever achieved its objectives, nor did any TD unit lose more vehicles than its German opponent."
The Bulge area was defended by a thin screen of infantry since we considered it poor tank country. jsw
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On Fri, 2 Aug 2013 13:47:32 -0400, "Jim Wilkins"

Very interesting. Thanks.
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Ed Huntress

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The tank destroyer story I liked {and feared} was when Patton was trying to relieve Bastogne; he sent several M18 Hellcats at top speed to attack the German rear and create confusion.
A Hellcat, powered by a 9 cyc. 450HP radial aircraft engine, could do 60 MPH full out and these did just that. Imagine those 40,000 lbs going 60 mph up a narrow road....
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David Lesher wrote:

The image of a group of angry Tasmanian Devils popped into my head. I loved those stupid cartoons. :)
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This 15,000 lbs at 30-40MPH was about all I could handle on narrow, winding Bavarian back roads, the Ultimate Driving Machine's native habitat:
http://en.wikipedia.org/wiki/File:M-109A2_Shop_Van_pic1.JPG
The Romans built straighter, wider roads for foot and wagon traffic. One road across an open field meandered in sync with a stream a few hundred meters away, as if following an ancient land boundary.
They were fun in a Jeep or my VW, though once a convoy of British APCs forced me to dart into the wood when we met in a corner.
Coming down a twisty mountain road as passenger in a heavily loaded 5-ton I watched the tach hit 5000 RPM, twice the redline. I suppose the engine can survive whatever full scale on the tach is, right? jsw
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Not if it is Cummins NHC-250
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typed in rec.crafts.metalworking the following:

    Depends. One thing if you are using the engine as a large air-compressor "brake, another thing if you are trying to get power out of it at that RPM.     Your Mileage (engine hours) will vary

-- pyotr filipivich "With Age comes Wisdom. Although more often, Age travels alone."
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