# drive shaft dynamics

Discussion in 'GS Boxers' started by johnjen, Feb 15, 2004.

1. ### johnjenI've Been Resigned

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I'm posting an article that Rod Neff wrote (with his permission) and just posted on the big GS list.. Its an excellent look into the dynamics of a drive shaft and what happens as the shaft angle changes at the U joints. Enjoy JJ

I'm sure that there are a few among us who can add a bit more to the discussion...

Basically, the shaft being driven through a u-joint or shaft "B"(drive shaft in our case) speeds up and slows down TWICE per revolution at any angle greater than 0 degrees, the more the angle in relation to the constant speed driver shaft, or shaft "A"(transmission output shaft in out case) the greater the speed up/slow down per revolution.

Max speed of shaft B is determined by shaft A rpm times Secant of the shafts angle, minimum speed of shaft B is determined by shaft A rpm times Cosine of the shafts angle.

(Gleaned the above, and some of the below from my Machinist Handbook)

I put the oilhead GS on the center stand and to get full extension of the rear, using a bevel square I determined max downward angle of the swing arm/drive shaft to be 15 degrees from the transmission out put shaft.

So, 15 degree secant=1.0353, 15 degree cosine=0.96592. Plug in 1000 rpm as the multiplier and shaft B has about a 7% speed swing, roughly 3.5% slower, then 3.5% faster than constant speed driver shaft A at 15 degrees or full extension of the rear shock in my case.

Adding shaft C into the mix, (on paralever bikes this would be the shaft the rear drive pinion gear rotates on) which is being driven by variable speed shaft B, it is possible to deliver the constant A shaft velocity to shaft C.

How? The angle of shafts A & B must be the same as the angle of shafts B & C. And the orientation of the u-joints relative to each other must be 90 degrees out of phase.

Its not easily apparent, but if the yolks attached to both ends of the drive shaft are aligned, the u-joints are 90 degrees out of phase. I want to attach the usual disclaimers to this last statement. I am pretty sure it is correct, but please feel free to correct me if I am wrong. Basically, when the drive shaft B is in its fast quadrant, pinion shaft C is in its slow quadrant of the arc, canceling the B driveshaft speed variation, delivering constant A shaft velocity to the pinion shaft C.

Now, understanding all of the above, instead of canceling the shaft B speed variations as outlined, it is also possible to double this twice per revolution speed up/slow down event, if in our case the u-joint alignment is exactly where it should NOT be. I haven't had a paralever apart yet myself, but from looking at the manual, it does look possible to put shafts B and C in identical speed quadrants(not possible on the F-150). Shaft B speeds up/slows down, shaft C speeds up/slows down that much more in addition to the already faster/slower velocity of shaft B.

Which leads me to a post I read on this list several months ago. Someone cross posted some info from the adv rider list about another person who was disassembling, then reassembling his drive line at various u-joint alignment profiles to minimize vibration. If I remember right this person also stated he had taken several un-molested from the factory drive lines apart and there was no rhyme or reason to the u-joint alignment. I found this last statement hard to believe. I have known about this phenomenon for some time, but only recently done this more in-depth research. Do German automotive engineers and QC really allow random u-joint alignment on their motorcycles?

Yes, they sure do.

I ran all this by a local mechanic who I have known for about 20 years, he verified that factory u-joint alignment is random. He is aware of u-joint alignment, BMW teaches it in their mechanics classes. He didn't have an answer as to why they don't do it right at the factory. Says when he has one apart he puts it together correctly.

This may explain at least some of the drive line failures people have experienced. Also would be interested to know if these aftermarket shortened paralever link arms are associated with drive line problems.

Why am I bothering with this? Recently installed an aftermarket rear shock on the 98 which raised the rear end up about 5 degrees at its lowest setting, giving me long term reliability concerns. Also, I have never been into the paralever drive line yet, but am about to find out what it is all about. I have to replace the clutch slave cylinder on the 00.

Going back to at least /2, and most likely before that, BMW compensated for drive line shock by using a cam coupling/ spring dampener affair on the transmission input shaft, this same concept is still used today. Starting with the /7 they added this cam dampener on the drive shaft as well. And sometime in the 80âs at least some of the drive shafts started being built with a rubberized dampener. K bikes for instance. Not sure just exactly how this rubber dampening works, if any one has a cut away view, please let me know.

My little write up here is dry and probably doesnât make much sense just reading through it. But with some time to think about it, and a few pictures this concept should become clear.

The first diagram here will help you quickly understand the concept, the key phrase here is "more/less distance must be traveled in a fixed period of time" . In a nutshell, at an angle, one side of the u-joint travels in a circle, the other side travels in an elliptical path. The second diagram is how the drive shaft yolk orientation should be.
http://www.4xshaft.com/driveline101.html

http://www.drivelinespecialist.com/tech/Driveline101.html

couldn't find the mention of Secant trig function in any of the above links, only my Machinist Handbook mention this, \$10 at used book store, a wealth of information.

Trig table
http://www.industrialpress.com/Trig.htm

Rod Neff
Santa Monica
98 & 00 GS's
Poolside likes this.
2. ### AndrewOptimus PrimerSuper Moderator

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we went round and round on this last year, I can't find the thread as the search tools aren't working yet on the new site.

I am almost positive we agreed the "ears" on the joints need to be as close together as possible for the shaft to be in phase. Not 90 degrees from that, as suggested in Neff's article.

Also, in that thread, I believe we noted that the new driveshafts are coming with non-symetrical teeth, to ensure that joints fit in onle the right phase.
3. ### TimberwoofLong timer

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Nice write-up, Johnjen. I know what you are talking about. :) I suppose one could measure the actual phase-oscillation of the driveshaft in a shaftie like this:

Put the bike up on its centerstand and shift it into top gear. Remove the front cover off the engine. Paint or Sharpie a mark on the crankshaft pulley. With a piece of tape, mark a spot on the rear wheel hub. Figure out a way to hold a protractor in front of the wheel and another in front of the crankshaft pulley. With a wrench, rotate the crankshaft, oh, five or ten degrees at a time. Measure the rotation of the rear wheel.

According to my BMW brochure, for the GS, 5th gear is 1.45:1. Since the final drive ratio is 3:1, that means the engine is making 4.35 rotations for one wheel rotation.

(Sanity check: 150/70ZR17 wheel is 79" or 6.6 ft in circumference. 60 mph = 5280 ft/min. That means 818 RPM at the wheel or 3600 RPM at the engine.)

So rotate the crankshaft through five rotations, stopping at every 10 degrees. At each stop, measure the rotation at the rear wheel. Write these numbers down. Fire up Excel on the PC and make a spreadsheet: Column A gets engine angle. Column B gets A/4.35 , the expected wheel angle. Column D gets the measured wheel angle. Column C gets D-B . Now make a graph out of columns B and C. We hope to see this line as flat as possible. Excel will, of course, scale the graph to make it look scary. Read the numbers. At any given angle, it should not be more than 2 degrees off, though it could be as far as 6 degrees high or low. If it's in the realm of, oh, four degrees off or more, think about getting the shop to change it. If you're in warranty, see if you can get them to fix it as a defect in workmanship.
4. ### PoolsideSyndicated

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Great post JJ! You always get me thinking and in this case, rethinking.

So here is what I concluded concerning the 'in phase', 'out of phase', 90Â°, 180Â°, lined up, offset, crosslinked, backwards, oscillation overthruster.

We have a driveshaft with two u-joints. this means there are technically THREE 'driveshaft' sections, separated by the two u-joints.

The three 'driveshafts' are, the transmission output shaft, the driveshaft in the swingarm, and the final drive input shaft. And these three driveshaft pieces are separated by the two u-joints.

OK, now grab the transmission output shaft and turn it AT A CONSTANT RATE. This constant rate rotation becomes an oscillating rotation on the other side of the FIRST u-joint. So the transmission output shaft is turning at a constant rate, and the driveshaft in the swingarm is turning at an oscillating rate.

This oscillating rotation is then fed through ANOTHER u-joint. This second u-joint 'oscillates' the oscillation. And the end result is a constant rate rotation.

Constant x Oscillating = Oscillating
Oscillating x Oscillating = Constant

It is a case of two negatives becoming a positive.

The 'middle' driveshaft, the one in the swingarm, is turning at an oscillating rate. While the transmission output, and the final drive input, turn at the same rate.

The oscillation is 'added', and then it is 'added again', which effectively removes it.

Thanks again JJ

- Jim

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Now here is another reason that I ride a BMW. What other brand would have a board with secant, cosine, etc.? We be thinkers Another brand might use geometry to triangulate an intercept on the tavern to tavern run; we use it to hone our craft and understanding. This could become important on the side of the road allowing us to diagnose and repair, eg. jumping debris into your fuel pump on your GS!

It seems like I remember from shop and experience that if the driveline assembly is in perfect alignment, no offset, the needle bearings in the u-joints tend to set in one location and will wear quickly. If there is some offset/angle to the driveline, the needles will rotate and allow each one to bear some load and some lubrication. Thoughts? Pure bunk? Gospel?
6. ### TimberwoofLong timer

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... if the two U-joints are correctly aligned, one 90 degrees from the other. OTOH, and this is the second important point, if they are incorrectly aligned, the oscillations are added instead of subtracted, and get worse.
7. ### TimberwoofLong timer

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It makes sense. If you have to stationary machines and you managed to install them with perfect alignment, then conceivably the needle bearings in the U-joints might flatten. But it won't exactly matter, will it?

In most automotive/motorcycle applications, the driveline gets out of alignment every time you flex the suspension. In many designs, the input and output shaft are not coaxial but merely parallel with one another, so the U-joints get flexed with every rotation. In our beasties, you can tell by looking at them, that the transmission and final drive are not aligned. And that is part of the problem.

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Andrew is right. We did decide a year or so ago that the proper alignment is as shown in the 4x diagram that JJ references:

Poolside is counting three shafts and two U-joints. That is just like the above diagram. So, I still don't understand why a 90 degree offset is required in this application. What about our bikes is different than the diagram? I don't mind the math, but don't understand the geometry.

BTW, Timberwolf left out the primary ratio in his calculation, which seems a little irrelevant except to understand the frequency of occilation.

R-dubb

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In rereading the Rod Neff article, I'm beginning to think we have a problem with words. It comes back to understanding terminology.

Rod says:
What does he mean when he says aligned? Does he mean, like the diagram, which is in symetrical alignment? Or does he mean the reverse of that, which would be in linear alignment. If they are out-of-phase, this would presumebly mean that he is talking about linear alignment. We had the same war of words a year ago, and I attached the very same diagram we see above to my R&R article. Final Drive R&R Procedure

I do believe we are back at that same place now. The conclussion Rod has come to is identicle to what was recomended in R&R. Only the words are different. FOLLOW THE DIAGRAM. Follow the math if you wish. Screw the words. 90 degrees from what? It's very easy to be tricked by words like that.

R-dubb
10. ### PoolsideSyndicated

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Geometric Tavern Run

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Yupp,

We agree....it's all a matter of perspective!

Linear makes sense. It's just important too understand the point of reference. The visual for me that is easiest to remember is keeping the pivot pins in the same orientation (not offset 90 degrees).

The conclusion has not changed from a year ago. We're just revisiting,
courtesy of J.J.

R-dubb
12. ### johnjenI've Been Resigned

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Yes, yes, this all very interesting but now, VE HALF XE PRUF... ZE ANCKLES UNT ZE TABELS UND ZE NUMBAHZ... NOW ITZ ALL VELY ZIENTIFIK MIT DER ZIRKLES UNT ARROS... WE HALF ZE PRUF...

JJ
13. ### TimberwoofLong timer

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Rats! Serves me right for just using the numbers in the BMW brochure. So how come my estimate for road RPM came out right? What is the primary ratio?

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The primary ratio is 1:1.889. Stock final drive ratio is 1:2.818

Here are the transmission gear ratios for a standard 1150 GS;

1st 2.05
2nd 1.60
3rd 1.27
4th 1.038
5th 0.90
6th 0.70

Your numbers are close because the gear ratios you referenced appear to include primary reduction. My bad.

Attached is a nice graph someone posted a while back.

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15. ### kevboRubbery-Lip Flappin' PHI

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The pictures above show correct driveline phasing. From the thread a year and a half ago, the shaft should look like this:

=o}========{o=

or this (rotated 90 degrees)

={o========o}=

NOT like this:

=o}======o}=

Looking at the pictures, it would seem there should be two correct ways to mate the splines. (180 degrees apart) Not so on the oilhead. Because the spline count is an odd number, One of the options will be close, but half a spline off. Also, it is MUCH easier to get it right on a car. It is somewhat difficult to determine the position of the front joint when peering up the interior of the swing-arm...And then there is the difficulty of mating the splines at all. Still, getting it right adds only perhaps 10 minutes to the job.

So why are they random from the factory? My guess is that since it is buried inside the swingarm, there is no way for anyone who knows better to realize that Helga missed class on the day Herr Instruktor covered driveshaft phasing. Somebody does know better, as it is mentioned (albeit somewhat crypticly) in the service manual:

[!] CAUTION The universal joints for universal shaft and rear wheel drive must be installed in the same direction.
ref. 1150GS shop manual, p. 33.17

Could it contribute to final drive failure? Possibly. added vibration certainly doesn't serve to reduce stress on any part of the driveline.