# Hollow shaft fatigue?

I have some calculations I would like to make, though I am having trouble finding information. I have a circular hollow shaft made of steel. I would like to calculate the breaking point of said shaft at 1000 cycles and 1000000 cycles. What kind of information/properties of the metal needs to be known. Is there a formula for this kind of calculation, or is this something that may come from a table of data after performing fatigue tests. I am kind of new to this, sorry if my questions are a little vague.

Chris Hillman
So, you want to estimate the dimensions of a steel shaft rotating at 1000 cycles which is nearing the yield point? How about: which has reached a bifurcation from stable to marginally stable static equilbrium (wrt centrifugal force)? That is, would predictions from linear elastostatics satisfy you? Oddly enough, I just did the computation for a hollow rigidly rotating cylinder over in the Relativity forum. I obtained the textbook result, so its probably trustworthy!

FredGarvin
Start with an S-N curve for the material you are considering. Depending on your expected loading conditions, you may be able to find a curve with comperable alternating stress levels.

Is the fatigue in bending or torsion?

Well here's what I'm trying to accomplish. I have a piece of software that calculates some information for a strain gaged torque shaft. The software takes the Outer Diameter, and Inner Diameter, and some other parameters strain gage specific. It then calculates various numbers. At the end it estimates the breaking points at 1000 cycles, and 1000000 cycles for hardned an unhardened steel. I'm trying to figure out how it works, so I can write a newer version of the software. I have found that the numbers it comes up with rely on only the Diameter variables.

Here is some of the software's output:

Input:
WHAT IS THE SHAFT OD IN INCHES ? 3.755
WHAT IS THE SHAFT ID IN INCHES ? 0.0
WHAT IS THE GAGE FACTOR ? 2.065
WHAT IS THE GAGE RESISTANCE ? 350
WHAT IS THE TOTAL BRIDGE RESISTANCE INCLUDING LEADS ? 350
WHAT TORQUE WILL THE SHAFT SEE IN NM ? 34000
ZERO OUTPUT IN uE ? –225

Output:
CALIBRATIONS
25K = 45634.85 NM
50K = 22817.43 NM
100K = 11408.71 NM
200K = 5704.356 NM
400K = 2852.178 NM

TOTAL BRIDGE OUTPUT AT 34000 NM = 5197.133 MICRO STRAIN
ACTUAL STRAIN IN SHAFT AT 34000 NM = 1258.386 MICRO STRAIN

DATA FOR TYPICAL 1E509 STEEL TORQUE SHAFT IN FULL REVERSAL CYCLES

FOR UNHARDENED STEEL

BREAKING POINT AT 1000 CYCLES = 72172.97 NM
BREAKING POINT AT 1,000,000 CYCLES = 21780.29 NM
CONSERVATIVE RUNNING TORQUE IS .5 TIMES BREAKING POINT

FOR HARDENED STEEL

BREAKING POINT AT 1000 CYCLES = 168682.4 NM
BREAKING POINT AT 1,000,000 CYCLES = 42311.95 NM
CONSERVATIVE RUNNING TORQUE IS .5 TIMES BREAKING POINT

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FredGarvin
Assuming that the bending moment is negligible, the dimensional quantities required for a shaft in shear will be the polar moment of inertia, J. For a hollow shaft:

$$J = \frac{\pi (D^4-d^4)}{32}$$

The material quantity required will be the modulus of rigidity, G. The modulus of rigidity is the torsional analog to the normal stress elastic modulus.

$$G = \frac{\tau}{\gamma} = const.$$

Now looking at your added program output, there is, as you mentioned, a good amount of strain gauge specific input (you'll need to read up on strain gauge theory). The rest is material constants input which is probably in a lookup table database that the program uses. It also looks like the alternating stresses are around a zero offset.

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