Dear Slanted Sages,

I am measuring driveshaft/U-joint angles on a couple of my cars and wondering if you all have practical experience or advice.

Is it OK to have an operating angle of 4-5 degrees as long as you cancel the U-joint angles down to 1 degree? I see some places say 3 deg operating angle is the max, but I wonder if this is just to be "perfect" and more should not be damaging.

I would like to have minimal vibration, although a little is fine. I can deal with some additional wear compared to stock...

Thanks for your input!

Lou

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Home of Slant6-powered fun machines since 1988

Is this concern coming from lowering the car and changing the angles? If so, on my old Nova Hobby Stock car I ran as much as a 2-1/2 inch lowering block and while I never measured the angle, I never experienced any problems.

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“Buy the ticket, take the ride.”
― Hunter S. Thompson

Yeah, basically playing with lowering blocks and leaf spring mounting points. Also, I have custom OD transmissions (T5, 200-4R) in a coupla cars...

Just looking for practical experience. I drive these on road courses, and on roads, and sometimes go pretty fast...

Lou

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Home of Slant6-powered fun machines since 1988

My only experience with a driveline vibration was a result of swapping a manual transmission where an auto had been. The resulting vibration only occurred under power in high gear. I suspect it was a driveshaft issue rather than a U joint issue, but I just tolerated. It was not awful, but it was less than satisfying. Most passengers probably did not notice it, but it got to be the defining characteristic for me. I put about 40-50K on it, and towards the end a bearing in the transmission started getting noisy and would have failed if the car had not rotted out.

In your instance, is the u-joint angle that is getting out of whack at the rear axle? Would imagine both are changing as a result of lowering..

There is no set-in-stone number, but usually 2-3 degrees is what you want....and closer to 2.

The old Mopar manual that says '5-7 degrees nose down' might be good for a drag-only car but it leads to a lot of cars having driveline vibrations.

I've also read you don't want '0' degrees, either, as the u-joints need to work a little.

But just look at all the Billy-Bob truck that are lifted up, running 20 or 30 degrees....I'm sure they're smooth as glass, lol

Using the above mentioned 5 - 7*, I set up a axle at 6* down. This vibrated and I adjust the angle with a 2* spring wedge. They are used with "traction" bars to adjust pinion angle.

Thanks for the input, guys. With the HP/torque levels in these cars, I cannot see running so much down angle. I just measured the 62 Valiant (from Seymour) and it has 2.8 deg down angle of the diff relative to the trans. This even seems too much for me, so I might play with it. I have wedges in all of my leaf spring cars to adjust angles.

Experiment, experiment, experiment...

Lou

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Home of Slant6-powered fun machines since 1988

The last paragragh is the main point:

"Equation of motion

Diagram of variables for the universal joint. Axle 1 is perpendicular to the red plane and axle 2 is perpendicular to the blue plane at all times. These planes are at an angle β with respect to each other. The angular displacement (rotational position) of each axle is given by {\displaystyle \gamma _{1}}\gamma _{1} and {\displaystyle \gamma _{2}}\gamma _{2} respectively, which are the angles of the unit vectors {\displaystyle {\hat {x}}_{1}}{\hat {x}}_{1} and {\displaystyle {\hat {x}}_{2}}{\hat {x}}_{2} with respect to their initial positions along the x and y axis. The {\displaystyle {\hat {x}}_{1}}{\hat {x}}_{1} and {\displaystyle {\hat {x}}_{2}}{\hat {x}}_{2} vectors are fixed by the gimbal connecting the two axles and so are constrained to remain perpendicular to each other at all times.

Angular (rotational) output shaft speed {\displaystyle \omega _{2}\,}\omega _{2}\, versus rotation angle {\displaystyle \gamma _{1}\,}\gamma _{1}\, for different bend angles {\displaystyle \beta \,}\beta \, of the joint

Output shaft rotation angle, {\displaystyle \gamma _{2}\,}\gamma _{2}\,, versus input shaft rotation angle, {\displaystyle \gamma _{1}\,}\gamma _{1}\,, for different bend angles, {\displaystyle \beta \,}\beta \,, of the joint
The Cardan joint suffers from one major problem: even when the input drive shaft axle rotates at a constant speed, the output drive shaft axle rotates at a variable speed, thus causing vibration and wear. The variation in the speed of the driven shaft depends on the configuration of the joint, which is specified by three variables:

{\displaystyle \gamma _{1}}\gamma _{1} the angle of rotation for axle 1
{\displaystyle \gamma _{2}}\gamma _{2} the angle of rotation for axle 2
{\displaystyle \beta }\beta the bend angle of the joint, or angle of the axles with respect to each other, with zero being parallel or straight through.
These variables are illustrated in the diagram on the right. Also shown are a set of fixed coordinate axes with unit vectors {\displaystyle {\hat {\mathbf {x} }}}{\hat {\mathbf {x} }} and {\displaystyle {\hat {\mathbf {y} }}}{\hat {\mathbf {y} }} and the planes of rotation of each axle. These planes of rotation are perpendicular to the axes of rotation and do not move as the axles rotate. The two axles are joined by a gimbal which is not shown. However, axle 1 attaches to the gimbal at the red points on the red plane of rotation in the diagram, and axle 2 attaches at the blue points on the blue plane. Coordinate systems fixed with respect to the rotating axles are defined as having their x-axis unit vectors ({\displaystyle {\hat {\mathbf {x} }}_{1}}{\hat {\mathbf {x} }}_{1} and {\displaystyle {\hat {\mathbf {x} }}_{2}}{\hat {\mathbf {x} }}_{2}) pointing from the origin towards one of the connection points. As shown in the diagram, {\displaystyle {\hat {\mathbf {x} }}_{1}}{\hat {\mathbf {x} }}_{1} is at angle {\displaystyle \gamma _{1}}\gamma _{1} with respect to its beginning position along the x axis and {\displaystyle {\hat {\mathbf {x} }}_{2}}{\hat {\mathbf {x} }}_{2} is at angle {\displaystyle \gamma _{2}}\gamma _{2} with respect to its beginning position along the y axis.

{\displaystyle {\hat {\mathbf {x} }}_{1}}{\hat {\mathbf {x} }}_{1} is confined to the "red plane" in the diagram and is related to {\displaystyle \gamma _{1}}\gamma _{1} by:

{\displaystyle {\hat {\mathbf {x} }}_{1}=\left[\cos \gamma _{1}\,,\,\sin \gamma _{1}\,,\,0\right]}{\displaystyle {\hat {\mathbf {x} }}_{1}=\left[\cos \gamma _{1}\,,\,\sin \gamma _{1}\,,\,0\right]}
{\displaystyle {\hat {\mathbf {x} }}_{2}}{\hat {\mathbf {x} }}_{2} is confined to the "blue plane" in the diagram and is the result of the unit vector on the x axis {\displaystyle {\hat {x}}=[1,0,0]}{\displaystyle {\hat {x}}=[1,0,0]} being rotated through Euler angles {\displaystyle [\pi \!/2\,,\,\beta \,,\,0}{\displaystyle [\pi \!/2\,,\,\beta \,,\,0}]:

{\displaystyle {\hat {\mathbf {x} }}_{2}=[-\cos \beta \sin \gamma _{2}\,,\,\cos \gamma _{2}\,,\,\sin \beta \sin \gamma _{2}]}{\displaystyle {\hat {\mathbf {x} }}_{2}=[-\cos \beta \sin \gamma _{2}\,,\,\cos \gamma _{2}\,,\,\sin \beta \sin \gamma _{2}]}
A constraint on the {\displaystyle {\hat {\mathbf {x} }}_{1}}{\hat {\mathbf {x} }}_{1} and {\displaystyle {\hat {\mathbf {x} }}_{2}}{\hat {\mathbf {x} }}_{2} vectors is that since they are fixed in the gimbal, they must remain at right angles to each other. This is so when their dot product equals zero:

{\displaystyle {\hat {\mathbf {x} }}_{1}\cdot {\hat {\mathbf {x} }}_{2}=0}{\hat {\mathbf {x} }}_{1}\cdot {\hat {\mathbf {x} }}_{2}=0
Thus the equation of motion relating the two angular positions is given by:

{\displaystyle \tan \gamma _{1}=\cos \beta \tan \gamma _{2}\,}{\displaystyle \tan \gamma _{1}=\cos \beta \tan \gamma _{2}\,}
with a formal solution for {\displaystyle \gamma _{2}}\gamma _{2}:

{\displaystyle \gamma _{2}=\tan ^{-1}\left[{\frac {\tan \gamma _{1}}{\cos \beta }}\right]\,}{\displaystyle \gamma _{2}=\tan ^{-1}\left[{\frac {\tan \gamma _{1}}{\cos \beta }}\right]\,}
The solution for {\displaystyle \gamma _{2}}\gamma _{2} is not unique since the arctangent function is multivalued, however it is required that the solution for {\displaystyle \gamma _{2}}\gamma _{2} be continuous over the angles of interest. For example, the following explicit solution using the atan2(y, x) function will be valid for {\displaystyle -\pi <\gamma _{1}<\pi }-\pi <\gamma _{1}<\pi :

{\displaystyle \gamma _{2}=\operatorname {atan2} (\sin \gamma _{1},\cos \beta \,\cos \gamma _{1})}{\displaystyle \gamma _{2}=\operatorname {atan2} (\sin \gamma _{1},\cos \beta \,\cos \gamma _{1})}
The angles {\displaystyle \gamma _{1}}\gamma _{1} and {\displaystyle \gamma _{2}}\gamma _{2} in a rotating joint will be functions of time. Differentiating the equation of motion with respect to time and using the equation of motion itself to eliminate a variable yields the relationship between the angular velocities {\displaystyle \omega _{1}=d\gamma _{1}/dt}{\displaystyle \omega _{1}=d\gamma _{1}/dt} and {\displaystyle \omega _{2}=d\gamma _{2}/dt}{\displaystyle \omega _{2}=d\gamma _{2}/dt}:

{\displaystyle \omega _{2}={\frac {\omega _{1}\cos \beta }{1-\sin ^{2}\beta \cos ^{2}\gamma _{1}}}}{\displaystyle \omega _{2}={\frac {\omega _{1}\cos \beta }{1-\sin ^{2}\beta \cos ^{2}\gamma _{1}}}}
As shown in the plots, the angular velocities are not linearly related, but rather are periodic with a period half that of the rotating shafts. The angular velocity equation can again be differentiated to get the relation between the angular accelerations {\displaystyle a_{1}}a_{1} and {\displaystyle a_{2}}a_{2}:

{\displaystyle a_{2}={\frac {a_{1}\cos \beta }{1-\sin ^{2}\beta \,\cos ^{2}\gamma _{1}}}-{\frac {\omega _{1}^{2}\cos \beta \sin ^{2}\beta \sin 2\gamma _{1}}{\left(1-\sin ^{2}\beta \cos ^{2}\gamma _{1}\right)^{2}}}}{\displaystyle a_{2}={\frac {a_{1}\cos \beta }{1-\sin ^{2}\beta \,\cos ^{2}\gamma _{1}}}-{\frac {\omega _{1}^{2}\cos \beta \sin ^{2}\beta \sin 2\gamma _{1}}{\left(1-\sin ^{2}\beta \cos ^{2}\gamma _{1}\right)^{2}}}}
Double Cardan shaft

Universal joints in a driveshaft
A configuration known as a double Cardan joint drive shaft partially overcomes the problem of jerky rotation. This configuration uses two U-joints joined by an intermediate shaft, with the second U-joint phased in relation to the first U-joint to cancel the changing angular velocity. In this configuration, the angular velocity of the driven shaft will match that of the driving shaft, provided that both the driving shaft and the driven shaft are at equal angles with respect to the intermediate shaft (but not necessarily in the same plane) and that the two universal joints are 90 degrees out of phase."

https://en.wikipedia.org/wiki/Universal_joint

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Ed
64 Valiant 225 / 904 / 42:1 manual steering / 9" drum brakes

I just tested my 66 Valiant at about 5600 driveshaft RPM with 4 degrees of total angle built in (difference in rear pinion angle and trans output angle) and there was a little but really not much vibration. Nothing below 4500-5000. I will try removing the 2 deg down angle shims in the leafs and see if it changes.

Lou

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Home of Slant6-powered fun machines since 1988

5-7 was for high horsepower stick cars that would try to rip the rear out of the car when you dumped the clutch at 7000. It was not unusual to see leaf springs "S" shaped after that kind of abuse.

2-3 down is pretty standard. Shocks and springs have gotten a lot better in the last 40 years.

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Official Cookie and Mater Tormentor.

Agreed!

Lou

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Home of Slant6-powered fun machines since 1988

I've had issues with vibration before when I have added leafs on a couple of vehicles..
On my 75 Cordoba that I had the springs rebuilt on I went back and asked what I could do to help with the new vibration that wasn't there before, they handed me a couple of angled shims and said "here put these in"
On that one it needed it because when I got it, the back end sagged like it had a 1/2 dozen bags of sakrete in the trunk when it was actually empty. On one of my Dakotas (2wd) I got a "new" slight vibration just in about a 8 mph range that I just lived with.
On my current 96 (4wd) club cab Dakota I built a "bastard pack" on the back of it, using the 2nd leaf from a 80s 3/4 ton and absolutely no problems so far