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Sorry for the delay in getting this to you but I wanted to do some additional calculations and add more detail along with some commentary which I hope is helpful.
Here are the results for the 3 1/2 – 2 size:
Velocity Factor = .917
Pressure Factor = .0396
@ 57,000 lbs., 30 RPM:
PV = 62,000 PSIFPM
Service life = 1.68 million inches (theo.)
@ 7,000 lbs., 109 RPM
PV = 27,700 PSIFPM
Service Life = 13.7 million inches (theo.)
And, here are results for 3 – 2 size:
Velocity Factor = .787
Pressure Factor = .0643
@57,000 lbs., 30 RPM
PV = 86,500 PSIFPM
Service Life = 1.2 million inches (theo.)
@7,000 lbs., 97 RPM
PV = 34,100 PSIFPM
Service Life = 9.8 million inches (theo.)
The Factors are used as follows:
Multiplying the RPM * Velocity Factor = Surface Velocity, V (FPM)
Multiplying the Load in lbs. * Pressure Factor = Unit Surface Load, P (PSI)
P * V = PV Factor (PSIFPM)
For this bronze material, maximums are: 100 FPM, 8,000 PSI and 125,000 PSIFPM.
The RPMs used in the above results are not what you requested but based upon the above maximum.
As to wear, we use the Archard theory of rubbing surfaces which states that the volumetric loss of material is proportional* to the service time multiplied by the PV, or W =KPVT.
W = Volume of material sacrificed to wear.
K = a fixed wear rate and is a function of mating materials (the slope of the wear versus time plot)
PV = Pressure Velocity Factor of the mating surfaces (see above)
T = time
*(Testing reveals that the actual wear versus time plot is shaped like a toe down hockey stick, a very steep slope at the beginning of testing, indicative of initial wear-in, then mostly proportional on a much softer slope for the long term, steady state wear period. The Archard technique ignores the steep portion and uses the steady state slope for the wear rate. In practice, when life testing, do not extrapolate the wear rate until the rate drops to its long term slope.)
This theory is just that and in practice provides a guideline which can be used as we have used it here, to get reasonable comparatives. The K’s we used were generated in our test lab which has ideal axial loading, a clean environment and excellent lubrication. We monitored torque and heat and restricted these to very safe limits using cooling and frequent relubrication. Wide variance in life tests was still exhibited. Nevertheless, we feel these are the best guesses we can make until a better method is discovered. If you want to get a copy of Archard’s work and slog thru it all, I would recommend a full weekend with a full coffee pot with no breaks for watching football.
One more caveat in addition to those mentioned for wear life, you should use a “safety nut” whereby a steel nut is mounted in tandem with the bronze nut such that if the bronze nut fails, the steel nut will prevent the load from dropping in the event of the bronze internal threads stripping. The wear can be monitored by measuring the distance between the follower safety nut and the load bearing bronze nut. When this exceeds a threshold amount, the system should issue a warning or simply shut off. This is situation was exquisitely demonstrated by the Alaskan Airlines plane that crashed near San Diego some years ago when the elevator nut stripped out. Lack of lubrication and inadequate wear monitoring was the problem as determined from the parts salvaged from the sea bottom. (A contributing factor was the use of an aft elevator pivot such that a leadscrew/nut failure caused the elevator to jam full down or full up rendering the aircraft unflyable. Had the pivot been forward the elevator would have followed benignly in the airstream and the plane could have been flown with aileron control alone. When I proposed this to the Boeing legal defense team my name was quickly removed from the prospective expert witness list.
One more tip from an engineer having practiced the trade for some 40+ years: Build a test unit of the articulating modules of your design as quickly as possible and get some operational and wear life feedback before you start constructing the first unit which you said has to work as built. Your marketing and management team will squeeze you on the budget for this but we see so many applications constructed that have to be redesigned because the most rudimentary testing was not conducted. We have an expression here that says “One test is worth a thousand expert opinions”. That number may be too low. If you want to chew the fat some time, ask me about our experience with springs and SolidWorks simulation. (Steve Lochmoeller)