Part
2  Driveshaft Geometry
Proper driveshaft geometry
is critical to getting the most from your driveshafts. Improper
geometry will cause vibration, excessive wear, and premature failure.
Even the best driveshaft in the world will suck if it is not installed
with proper geometry. We also need to know about proper geometry
in order to select the best type of shaft for our application.
Before we discuss geometry,
a couple more definitions of some terms are in order. For the purposes
of this article:
Terms 

Angle:
An angle is the measurement
of angularity, in degrees, between any two planes. Where those 2
planes meet, they form an angle. In other words, where two lines
intersect, providing they are not parallel, there is an angle. In
the case of driveshaft tech, where something rotates through that
angle, we call it an "operating angle"
Slope
Slope. A slope is a special
kind of angle. It is the angle formed between the horizontal surface
of the earth (one plane), and the object in question (e.g. driveshaft)
(second plane). 
When talking
about driveshafts, we say that a slope is down if, when viewed from
the side of the vehicle, it is higher at the transfer case and lower
at the axle (i.e. it descends from the center to the rear of the
vehicle for a rear driveshaft or descends from the center to the
front of the vehicle for a front driveshaft). The slope is up if,
when viewed from the side of the vehicle, it is lower at the transfer
case and higher at the axle (i.e. it rises from the center to the
rear of the vehicle for a rear driveshaft or rises from the center
to the front of the vehicle for a front driveshaft).
Phase:
We say that 2 ujoints
are inphase if they are fitted to yokes that are fixed on the same
shaft, such that the 2 opposing bearing caps in the ujoint that
are held captive by the yoke on the shaft (the inboard yoke's ujoint
caps) are both in the same orientation. 

A pic is worth a thousand
words. Look at the pic to the left. In the top shaft, the 2 joints
indicated by the green arrows (ignore the fact that the rightmost
is part of a double cardan CV assembly) are inphase because in
both joints, the bearing caps held captive in the shaft are both
vertical, while the bearing caps that are free (not held captive
in the shaft) are both horizontal. If you then look at the bottom
shaft, you will notice that this is not the case with the joints
indicated by the blue arrows. The left has captive bearing caps
vertically oriented, while the right most joint has it's captive
bearing caps oriented horizontally. The joints are therefore 90°
out of phase. 
Note that this means
that they would be in phase if you rotated one or the other 90°
(by cutting and rewelding the shaft). Note also that 90° is
the most they can ever be out of phase, for as you pass through
90° difference between the two joints orientation, you begin
to come back into phase.
Ujoint
life span.


One geometry factor
that is common to all shafts, regardless of type, is the decrease
in ujoint life span that is experienced with an increase in the
operating angle of that ujoint.
No matter what the shaft
style, the greater the angle a ujoint operates at, the shorter
it's life span will be. The graph at the left comes directly from
Spicer, and shows the range from 100% expected life span at 0°
up to just over 15% expected life span at 20°. 
As we learned in part
1, there are 2 types of driveshaft that interest us, each with their
own separate geometry requirements.
SingleCardanstyle
universal joint driveshaft geometry 

The singlecardan style
driveshaft, also called a "standard" driveshaft, consists
of a tubular shaft with 2 tube yokes, one at each end, that each
utilize a single cardan ujoint. Recall how, when we have a single
ujoint operating at an angle (as will certainly be the case in
any 4x4 because the transfer case output will be above the pinion)
it causes the driveshaft to speed up twice and slow down twice each
revolution. Uncorrected, this change in angular velocity will cause
annoying vibration, wear out ujoints, and cause undue stress and
strain on the driveshaft itself, transfer case output, and axle
pinion. 

The solution is simple
and elegant. If we ensure that the ujoints at each end of the shaft
are both "in phase" and operating through exactly the
same angle, the pinion end of the driveshaft will speedup and slow
down opposite to the transfer case end, and therefore the different
angular velocities cancel one another out, the pinion is driven
at a steady rate, and vibration is minimal (if I did a decent job
of describing why the elliptical paths happen in the first place
 you should be able to prove this to yourself). This works fairly
well up to angles approaching the maximum operating angles of the
ujoints in question. As the angles grow, so do the magnitude of
the accelerations and decelerations, and the less effective the
matched angle are at eliminating vibration. 
In other words, eventually,
you may have a driveshaft operating at such an angle that, even
though the input (transfer case) and output (pinion) operating angles
match exactly, the shaft will still vibrate. At this point, it's
time for a double cardan CV driveshaft!


Note that in the standard
singlecardan shaft "match the angles" geometry the angles
do not have to be the same "sign". THIS IS A COMMON MISCONCEPTION.
Certainly, the most common method of achieving proper singlecardan
shaft geometry is to set the transfer case output and pinion shaft
centerlines parallel, thus achieving equal angles between each end
of the driveshaft (pic at left). 
Normally, this is done
by rotating the axle housing (with shims in a leafspring suspension,
or with relative lengths of upper and lower control arms with a
link suspension). This is because the transfer case output is usually
considered pretty fixed  the only way to adjust it is to either
lower the transfer case (an all around bad idea and bad deal  I
speak from experience) or to tilt the engine up (raise the engine
mounts) again  not a good idea).


However  this is not
the only acceptable method of achieving the proper matchedangle
geometry. The angle between the driveshaft and pinion can be opposite
to the angle between the transfer case and driveshaft  as long
as they are equal. Note that they must still be in phase. This unusual
configuration is called "Broken back" or "W"
geometry (see pic at left ), and is common on agricultural equipment,
marine drives, some tractortrailers that use stubshafts between
front and rear of a tandem assembly, and most often on powertakeoffs
like hydraulic pumps and PTO shafts. 
Most of the equipment
that uses driven shafts in a brokenback configuration though, are
fairly low RPM (but not all). The reason is, due to the nature (geometry)
of the configuration (again, have a look at the picture above) with
this setup, there's a lot more inherent strain on the slip member
as it rotates. because of the opposite angles, the shaft "wobbles"
the slip member back and forth as it rotates  like a skipping rope
being swung. At high rpm, with anything but the tightest slipjoint
assembly, this would cause a horrible vibration  that's why Spicer
light duty driveshafts do not normally come factory in this arrangement.
Note however, that some Land Rovers do have stock driveshafts in
the broken back configuration, so it can work! I don't have any
experience with these Rover's, but I imagine that the angles in
the stock configuration are pretty darned small. As with the more
standard singlecardan setup  start increasing the operating angles
of the ujoints and the elliptical paths get more and more elliptical,
the angular velocities (amount the shaft speeds up and slows down
each revolution) get greater, and when you spin that shaft at 1000rpm,
the more likely it is that the shaft will be noisy, harsh, and vibrate
 EVEN IF the angles are matched. Again...time for the double cardan
CV shaft!
Double
cardan (near) constant velocity driveshaft (commonly known as a
CV driveshaft) geometry.


Proper CV driveshaft geometry
is actually a lot more simple to understand than singlecardan driveshaft
geometry. Pictured at left, proper CV shaft geometry is achieved when
the operating angle of the CV joint (head assembly) is less than the
maximum (and there is some room for increase in operating angle under
suspension droop), and the operating angle between driveshaft and
pinion is 0 under cruise throttle. 

This is because of
the clever design of the CV joint, or head assembly. If you refer
back to the picture of the CV shaft components in pat one, you will
see that the CV head assembly (double cardan joint) contains two
cardan style universal joints and a centering yoke assembly. This
clever arrangement serves to neutralize the effects of the increasing
and decreasing angular velocities, right at the head assembly. This
relieves us of having to arrange the pinion yoke operating angle
to be equal to the transfer case operating angle. Instead, the pinion
is arranged so that the operating angle between it and the driveshaft
is zero degrees (0°). 
Measuring
and calculating universal joint and driveshaft operating angles
So, we know what the
geometry is supposed to be  how do we find out what ours actually
is, and what do we do about it? This section discusses measuring
your geometry, calculating the results, interpreting the results,
and making necessary adjustments.
The first 2 steps, measuring
slopes of components, and calculating operating angles are the same,
regardless of whether you have a standard singlecardan shaft or
a doublecardan CV shaft. The third step, interpreting the results,
will differ, depending on the style of driveshaft.
Before attempting to
measure angles ensure that tire air pressure is correct, that the
vehicle is at the correct trim (chassis) height (i.e. suspension
loaded, operating weight in/on the vehicle, etc.) and the ground
surface is perfectly level. The driveshaft also needs to be installed
and torqued to spec.
Step
1  Find the slopes of the components involved.
Recall that the slope
is the angle formed between the component in question, and the horizontal.
To find these slopes, we measure them with a protractor as follows:


Transfer case
Measure the slope of
the transfer case output yoke by placing the protractor or angle
finder (inclinometer) on the bottom of the bearing cup, (see pic
at left). Position the angle finder on the clean flat surface of
the bearing cup, level the bubble (if equipped) and note the reading. 
If your transfer case
has an output flange, the best way to measure the slope is to temporarily
remove the shaft from the flange,place the angle finder against
the flat machined surface of the flange, then add or subtract 90°
from the reading taken. Remember to reattach the driveshaft so
that you can correctly measure its slope.
Remember that the slope
is "down" if it is higher at the t case than at the axle.


Driveshaft
Measure the drive shaft
slope, as shown, by placing the angle finder directly against the
tube. level the bubble (if equipped) and note the reading.
Remember that the slope
is "down" if it is higher at the t case end than at the
axle end. 

Axle Pinion
Measure the slope of
the pinion yoke by placing the protractor or angle finder (inclinometer)
on the bottom of the bearing cup, (see pic at left). Position the
angle finder on the clean flat surface of the bearing cup, level
the bubble (if equipped) and note the reading. Alternatively, the
angle finder can be placed against a flat machined surface that
lies 90° to the pinion shaft centerline, the reading taken,
and then 90° added to or subtracted from the result. 
Remember
that the slope is "down" if it is higher towards the center
of the vehicle, and lower at the end of the vehicle.
Step
2  Find each operating angle between each pair of slopes as follows: 

If both slopes are
in the same direction (up or down), subtract the lesser number from
the greater to obtain the operating angle.
If both slopes are in
different directions (one up and one down), add the lesser number
to the greater to obtain the operating angle. 
In the special case of
calculating the operating angle at the pinion in a CV shaft application,
assign the pinion slope a (+) sign if it is DOWN and a () sign
if it is UP, then always subtract the pinion slope from the driveshaft
slope, regardless of their relative sizes, and make note of the
resulting sign (+ or ), as this will help in deciding any possible
corrective action.
Step
3  Interpret the results
Assuming a fairly standard
4x4 setup with no pillow blocks or intermediate shafts, once you
have measured all the slopes of the components, and calculated all
the operating angles, you should have a piece of paper that has
3 slopes and 2 operating angles written on it. It helps to have
a sketch too, like those shown below on the left.
Standard (single
cardan) Shaft:
The first operating angle
must be less than the maximum operating angle of the series of ujoint
used, and preferably less than half the maximum (remember  you
need to allow for increase in operating angles while off road due
to suspension movement, and also how the higher the operating angles,
the more likely vibration, even if geometry is correct). If it is
not, you have only 2 choices: lower the suspension or drop the drivetrain
(lower tcase); or switch to a CV style shaft.
The second operating
angle should be within 0.5° (1/2)° of the first AT CRUISE
THROTTLE. This is a critical point. virtually every axle (to a greater
or lesser degree, depending on power and suspension) will experience
some "axle wrap" or pinion rotation ( pinion rotates up
in rear axle, and down in front axle) depending on acceleration
and to some extent braking torque. This will of course alter the
geometry of the pinion, and therefore the whole driveshaft! Since
the driveshaft will presumably spend most of it's time (and therefore
the effects of it's vibrations will be most annoying and damaging)
in a cruise throttle condition, it is standard practice to set driveshaft
geometry for this state (If you have a highly specialized vehicle,
like a drag car, this may not apply  and you will want to discuss
your needs with an expert like Jess
at High Angle Driveline). Generally, for most truck rear axles,
at cruise, the pinion will rotate up 12° from its static position.
As such, it is common practice to shim the axle or adjust the links,
rotating the pinion and changing the pinion slope at rests, such
that the pinion slope is 2° lower than that required to achieve
equal operating angles at rest. Read that bit again, carefully!
It's a bit of a juggle, because as you adjust the pinion slope itself,
so you also actually alter the driveshafts slope, and therefore
the transfer case operating angle as well. Once you get close though,
you will easily end up at the correct balance point. the point I'm
making is, don't just make a whopping 20° change to the pinion
angle, then weld those spring perches on and call it done. That
big of a change will have effected things, so you'd have to measure
and recalc all the slopes and operating angles again, as you hone
in on the final setting.


Example:
Looking at the sample
worksheet to the left, and assuming it is for a rear driveshaft 
We can see that the front
operating angle is 12°. Assuming we are using a 1350 series
ujoint, and the vehicle is not a frequent, longrange freeway cruiser,
nor does it have a superflexy suspension with monstrous travel,
we decide that this is satisfactory. The axle joint operating angle
is 11°. Because it is a rear driveshaft, the rear pinion will
rotate up, let's say 2° under cruise throttle. Since our measurements
and calculations were done at static, this means that in reality,
under cruise throttle, the pinion slope would change from 6°
down to 8° down (even though the pinion wraps "up"
 remember we describe slopes as up or down depending on orientation
between tcase and axle). This would make the axle joint operating
angle actually 17°  8° = 9° at cruise. Since we need
it to equal 12° at cruise, we need to rotate/shim the pinion
at rest down 3°. This will result in a static pinion slope of
3°. the would net a cruise throttle pinion slope of 3° +
2° = 5°. That would make our axle joint operating angle
now 17°  5° = 12°  A perfect match for the front!
Of course
 we would need to make this adjustment (rotate pinion down 3°
at rest) and then remeasure and recalc everything to get it perfect,
as the change may effect driveshaft slope and therefore tcase joint
angle too. However, this is unlikely with the magnitude of the changes
in this example.
Double cardan
CV shaft
The first operating angle,
the CV joint op angle, must be less than the maximum operating angle
of CV joint used. Remember  you need to allow for increase in operating
angles while off road due to suspension movement. How much you must
allow will depend entirely on your suspension design and the terrain
driven. If it is not, you have only 2 choices: lower the suspension
or drop the drivetrain (lower tcase); or switch to a higher angle
capable CV joint shaft.
The second operating
angle, the pinion op angle, should be within 0.5° (1/2)°
of zero (0°) AT CRUISE THROTTLE. This is a critical point. virtually
every axle (to a greater or lesser degree, depending on power and
suspension) will experience some "axle wrap" or pinion
rotation ( pinion rotates up in rear axle, and down in front axle)
depending on acceleration and to some extent braking torque. This
will of course alter the geometry of the pinion, and therefore the
whole driveshaft! Since the driveshaft will presumably spend most
of it's time (and therefore the effects of it's vibrations will
be most annoying and damaging) in a cruise throttle condition, it
is standard practice to set driveshaft geometry for this state Generally,
for most cars and trucks rear axles, at cruise, the pinion will
rotate up 12° from its static position. As such, it is common
practice to shim the axle or adjust the links, rotating the pinion
and changing the pinion slope at rests, such that the pinion slope
is 2° lower than that required to achieve an operating angles
of zero at rest. Read that bit again, carefully! It's a bit of a
juggle, because as you adjust the pinion slope itself, so you also
actually alter the driveshafts slope, which directly affects what
your pinion angle must be, in a feedback type loop. Once you get
close though, you will easily end up at the correct balance point.
The point I'm making is, don't just make a whopping 20° change
to the pinion angle, then weld those spring perches on and call
it done. That big of a change will have effected things, so you'd
have to measure and recalc all the slopes and op angles again,
as you hone in on the final setting.


Example:
Looking at the sample
worksheet to the left, and assuming it is for a rear driveshaft 
We can see that the front
CV operating angle is 22°. Assuming we are using a High Angle
1350 series CV shaft, we are comfortably within the proper operating
spectrum here. The axle pinion joint operating angle is 1°.
Because it is a rear driveshaft, the rear pinion will rotate up,
let's say 2° under cruise throttle. Since our measurements and
calculations were done at static, this means that in reality, under
cruise throttle, the pinion slope would change from 28° down
to 30° down (even though the pinion wraps "up"  remember
we describe slopes as up or down depending on orientation between
tcase and axle). This would make the axle joint operating angle
actually 27°  30° = 3° at cruise. Since we need it
to equal 0° at cruise, we need to rotate/shim the pinion at
rest down 3°. This will result in a static pinion slope of 25°.
This would net a cruise throttle pinion slope of 25° + 2°
= 27*. That would make our cruise throttle axle joint operating
angle now 27°  27° = 0°  A perfect setup for a CV
shaft!
Note that, in the case
of a CV shaft, since we always calculate the angle the same way
driveshaft slope minus pinion slope, the sign of the result tells
allows us to write an equation, the result of which tells us whether
we need to rotate the pinion at rest down or up.
The equation is RR=DSPSWA.
Where RR = rotation required (of the pinion at rest), DS  driveshaft
slope, PS = pinion slope, and WA is the estimated pinion wrap angle.
If the result is (), we must rotate the pinion down at rest that
many degrees, if the result is (+) we must rotate the pinion up
that many degrees.
Of course
 we would need to make this adjustment (rotate pinion down 3°
at rest) and then remeasure and recalc everything to get to perfect,
as the change may effect driveshaft slope. However, this is unlikely
with the magnitude of the changes in this example. 
How
to chose a Driveshaft for your Rig.
This is actually a fairly
easy one to answer.
First  buy the absolute
best you can possibly afford. Why? It is almost impossible to overstate
the massive annoyance of a bad driveshaft. Driveshaft vibration
is horrendously annoying  street queen or trailonly rig. Believe
me, I know. My current buggy, the Wolf, is always trailered, and
spends 90% of it's time below 10mph  occasionally it may get to
40mph. I had NO IDEA how bad my cobbledtogether shaft was until
I replaced it with a High Angle driveshaft. Even at slow speeds,
a crappy driveshaft will EASILY suck the fun out of driving your
rig. I figured  it's trail buggy  it's loose and noisy anyway
 who cares. Well, I learned....it is Sooooooooo much nicer with
a decent balanced shaft, operating within it's angle capabilities
 and of course  the peace of mind for the components that actually
put the power to the axles is priceless.
Do you need a a CV shaft,
or will a standard singlecardan style do? Well, in my opinion,
unless your rig is only an inch or 2 over stock suspension height,
with minimal wheel travel / flex, the answer is definitely YES!
The CV driveshaft offers
several HUGE advantages to the offroad vehicle.
First, the pinion and
pinion yoke can be rotated up out of harms way, where it will be
less susceptible to damage from rocks and other obstacles.
Secondly, the only limit
to our operating angle at the CV joint (and thus how much suspension
height we can run) is the limit of the doublecardan joint itself.
A stock Spicer double cardan CV joint can run successfully at about
22°, and a High
Angle Driveline doublecardan CV joint can be run successfully
at as much as 32° !!! This allows for successful driveshaft
installations in vehicles with much more suspension height than
a simple singlecardan shaft can accommodate. Even if you matched
the angles on a single cardan shaft exactly, you could never run
it safely and vibration free at 30°!
Thirdly, the doublecardan
CV joint assembly is simply better and more efficient at reducing
or eliminating driveshaft vibration. Even at smaller angles, and
even with correct matchedangle geometry, the singlecardan shaft
is still susceptible to vibration. The CV shaft will always run
smoother, quieter, and with less stress on the ujoints, and transfer
case and pinion shafts, bearings, and seals.
The only advantage the
singlecardan shaft has is that it is cheaper to manufacture / buy,
and you don't have to buy a centering yoke or a third ujoint when
rebuilding it. As always  the best costs a little more! 
