Drive line Critical speed

[Dennis Reinhart]

What it is –
Every rotating object has a “critical” speed or resonant speed, which is a function of its design, mass and stiffness. This is when the driveshaft is whipping in the middle, rather than spinning on a true centerline. For a driveshaft, this is also called “first bending mode”, indicating the shaft actually bows out into a boomerang shape (on a micro-scale). This first mode bending speed is usually referred to in a driveshaft frequency.

What it does –
The energy stored and released through the deflection of the driveshaft through the resonance creates lateral and vertical accelerations of >10g at the problem frequency, which results in broken transmission extension housings, cases and causes moderate to severe vibration at highway speeds (> 70 mph), particularly with axle ratios numerically higher than 3.27:1. This energy release, when compounded by excessive driveshaft imbalance (some is good, too much or too little is not), companion flange run out/imbalance and excessive driveline angles provides the driver with excessive vibration and boom and tortures the driver and driveline components in general.

Because of this, most vehicles have a speed limiter to prevent from entering this mode and causing damage to the driveline.

Some detail –
As mentioned above, the driveshaft rotates at a certain speed based on rear axle ratio; tire size and road speed, but is independent of engine speed (unless you have a vehicle such as a Porsche 944 or C5 Corvette which utilize torque tubes and transaxles, in which case the driveshaft turns at engine speed).

The factors governing driveshaft critical speed include its material properties (i.e., Bulk Modulus of Elasticity which is roughly analogous to material stiffness), diameter, and length and to a lesser degree, wall thickness.

The only factor you can really modify to affect critical speed is material choice. Length is package-dictated, and diameter is usually constrained by driveline tunnel space as well. The answer then becomes a bit simpler – replace your steel shaft with an aluminum or MMC (metal matrix composite) shaft. Both offer reduced weight, which is key in this frequency range. MMC offers the additional bonus of additional damping and stiffness over a typical aluminum alloy.

As mentioned above, at the frequencies in question, a change in rotational mass has a greater impact on resonant frequency than a change in stiffness does, partly since it is easier to reduce mass than increase stiffness (adding stiffness almost invariably means adding mass -- a vicious circle), but particularly since resonant frequency is equal to the sqrt (k/m), where m is mass and k is stiffness. Here m is a stronger function being the in the denominator of a square root. So you can see that as “m” gets smaller, the resonant frequency “f” gets much bigger.

The use of an aluminum shaft provides a dual purpose – increasing critical speed out of the operating range AND directly reduces the rotational forces since those rotational forces are governed by:

F = mr w**2
Where w is rotation speed, m is the mass and r is the radius at which it is spinning.

This means that a 50% reduction in rotational mass results in 50% less rotational force. So, when a driveshaft rotates out of true, due to run out of the shaft itself or due to trans output shaft or axle companion flange run out, the reduced mass * the radius of gyration (i.e., run out) product is smaller than for the same conditions with a steel shaft.

This becomes important not only at critical speed, but at more normal operational speeds where the effects of run out and mass imbalance are more evident than those of resonance:

For a typical Fox or SN95 Mustang, driveline critical speed is around 95-100 Hz. Using stock tires we have the following:

225-60R15, 225-55R16, 245-45R17 all rotate at 812-820 revs/mile at 60 mph.

This give is 13.5 Hz wheel frequency at 60 mph, and assuming a 3.27 axle, we then have:

812/60*3.27 or 44.25 Hz , driveline frequency.

So, 100/44.25*60 yields a driveline critical VEHICLE speed of 135 mph. A good rule of thumb states that the objectionable driveline forces will start becoming significant at 70% of resonant frequency, so for the case of the 3.27 axle, the boom and vibration may be felt beginning at 95 mph.

Typically, 3.27 axles don’t provide the driver with much to complain about; it is 3.73 and above which create the concerns. Using a 3.73, we find that

13.53*3.73 gives 50.5 Hz wheel frequency at 60 mph (substantially higher than the 3.27)

And the critical VEHICLE speed then becomes

100/50.5*60 or 119 mph.

Taking 70% of 119 mph equals 83 mph, certainly a speed at which some Mustang drivers experience occasionally.

For a 4.10 axle, the “70% speed” is 76 mph!

Compounding this problem are factors like transmission output shaft run out, imbalances and run outs from components such as the reverse sun gear, driveshaft, companion flange and pinion pitch line run out (a torque induced run out created when the pinion tries to crawl up the face of the ring gear involutes).

Combine these factors and the already marginal NVH resulting from proximity to 1st bending (critical speed) and the NVH becomes absolutely agricultural.

The aluminum shaft minimizes the contribution from companion flange run out and the driveshaft’s own run out, directly due the lower mass. The pinion is free to pitch +/- 20 degrees and adding in any run outs of the companion flange or driveshaft at the pinion end results in the driveshaft mass having a large eccentric path to wobble about. It is this path times the mass of the driveshaft, which gives the characteristic boom and vibration at highway speeds.

Thus, as Newton predicted, as mass decreases so will the forces. That is why an aluminum shaft is your friend when coupled to 3.73s.

One side note: that great big mass on your pinion nose, fondly named by driveline engineers after the appendage on a male moose, is tuned to 45 Hz, the frequency at which the 2nd order forces created by u-joints as they rotate, force the pinion to bounce or pitch up and down and shake you by the seat of your pants and create an uncomfortable boom in the car. Once again run outs and imbalances will modulate this 2nd order driveline phenomenon to make it worse, so the moral is, LEAVE THE MOOSEB-, uh, DAMPER ON the pinion nose!

Another item: you CAN expect more axle noise when using an aluminum shaft however, which does not necessarily mean the pinion depth or side shims are incorrect, or that the gear cutting process is flawed. It just means that the aluminum shaft is more willing to “bend” circumferentially, torsionally and in a double hump (2nd bending) much more easily than a steel shaft.

Recall my prior statements at the very beginning about aluminum stiffness vs. steel? Picture a piece of sheet metal ducting. Bend it and it makes a WA-WA sound. That is pretty much what a driveshaft does, but at a much higher frequency – higher than even the dreaded “critical speed” of 100 Hz.

Axle noise will occur from about 350 Hz all the way through 500 Hz, sometimes even higher than that. The energy comes from the teeth meshing at the pinion/ring gear interface. This energy is transmitted to the driveshaft (and suspension components) and makes them deflect in the same sense as a piece of sheet metal goes WA-WA. Aluminum is less stiff than steel and takes less energy to deflect it, so it is far more inclined to make your axle go WOOOOO as you drive down the road at 45-70 mph.

Assuming again a 3.73 axle ratio, which has 11 teeth on the pinion and 41 on the ring gear, the axle noise frequency is calculated as (at 45-70 mph):

815/60*3.73*11 or 557 Hz at 60 mph.

This means the WOOO you hear at 45 mph is about 418 Hz and the WEEEEEE you hear at 70 mph is way up there at 650 Hz. You can’t SEE the driveshaft is bending and breathing and twisting, but it is telling you that precisely that is occurring.

So, now armed with this information, you now understand the basics of your vehicle’s driveline.

Information provided by JW

[Marauder57]

Well that was pretty darn informative! Bottom line...new driveshaft for my MM.

[vaderv]

Damn brother,Newtonian theory! I am impressed.

[BigMerc]

I'm sorry I was on the phone, can you repeat that please?

[Billatpro]

OK, now I fully understand the "Dynamics" here! I am glad I read this post in the morning rather then last night or I would have only understood 3% of what you said rather then the 9% I understand now!

[TripleTransAm]

Wow. Killer description. Thanks for posting this!

[jgc61sr2002]

Dennis - You are the MAN.

[MapleLeafMerc]

Originally posted by Dennis Reinhart
What it is –

The energy stored and released through the deflection of the driveshaft through the resonance creates lateral and vertical accelerations of >10g at the problem frequency, which results in broken transmission extension housings, cases and causes moderate to severe vibration at highway speeds (> 70 mph), particularly with axle ratios numerically higher than 3.27:1.

Information provided by JW

Does this mean I shouldn't put 4.10 gears in without upgrading the driveshaft?

Larry

[Dennis Reinhart]

It means its a very good Idea, this whole thread got started by the simple question why is the Marauder speed limited to 123MPH

[MapleLeafMerc]

Thanks Dennis-

After a month at MM.net, I'm an example of the saying "a little knowledge is a dangerous thing"

Larry

[FordNut]

Dennis,
This is very informative, but one statement does bring a question to mind.

You say leave the damper on the yoke. The MMX shaft you got the dynotech folks to craft up for us has the yoke without a damper. Care to explain the reasoning behind this? Maybe it has less flex and is much better balanced and therefore doesn't need it?

Thanks.

[Dennis Reinhart]

The Yoke on the MMDS is directly from Ford thats why the cost is a littile higher, we first tried a after market yoke and it was longer than the OEM and had to be shortened, so I had Dynoteck just use the new updated yoke. the whole assembly is ballanced

[Smokie]

So a stock Marauder with rear tires rotating at 724 revs/mile has 100% critical resonant speed of 140 MPH and at 70% a speed of 98 MPH.

[mroder]

My MM 300A came with a factory aluminum drive shaft . I assume that all MM came with these but I met a several MM owners that had no clue if theirs had one or not.


Do all MMs have this???

[Dennis Reinhart]

THE DRIVE SHAFT IS SPEED LIMITED TO 123mph the OEM shaft is not a MMDS