Re: U-joint/drive shaft alignment and trig functions

[Bob Hadden <kbhadden@xxxxxxxxxxx>]

Just reread this post going through my inbox.  In doing my spline lube 
last week, I checked for proper u-joint alignment on assembly.  But, I 
forgot to check it on taking apart.  My drive line was smooth, so I 
doubt I had a problem.

On assembly, however, the splines are not set up to force proper 
alignment of the u-joints.  So if you don't think to look for this, you 
could do it wrong.  I wonder if people complaining of high vibration  
might actually just need to properly assemble the shaft.

Bob Hadden '98RS
On Feb 15, 2004, at 2:13 AM, Rod Neff wrote:

>     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, again, which 
> occurs
> twice per revolution, 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 shaft speed variation, delivering
> constant 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. 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 the GS list several months ago 
> which was
> about 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 bit of 
> 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 didnt have an
> answer as to why they dont 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 80s  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 doesnt 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, 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
>
> More info
> http://www.novak-adapt.com/knowledge/driveshafts.htm
> 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

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