Reliability Engineering Snapshot TM

Illustrated Case Studies in the Maintenance Reliability Engineering World of Failure Analysis, Predictive Maintenance, and Non Destructive Evaluation

Material Properties - Case Study No. 128: Mine Hoist Shaft Flange Failure at Sharp Radius Stress Concentration

	Even seemingly large oversized shafts can fail in fatigue, and they can fail by way of the most seemingly trivial detail. The fractured shaft illustrated to the left was 22" in diameter. The flange was 42" in diameter. The shaft use to continue to the left of the flange. The failure was located exactly at the section transition between the shaft and the flange. The transition was accomplished by a 1/8" radius. The first thing that was apparent was the uniformly dished and smooth look of the fracture surface. The only rough area was located exactly in the center of where the shaft use to be.
Figure 1
	Looking at Figure 2, the crack initiated on the flange at the beginning of the 1/8" radius. Following the white line, it progressed perpendicular to the flange surface (parallel to the shaft axis). It then began to change direction until it was parallel with the flange surface (perpendicular to the shaft axis). Figure 3 emphasizes the location of the 1/8" radius. Notice how in this picture the flange face is in focus and everything to the right of the radius location is out of focus. This is because the crack progressed immediately perpendicular to the flange face. It didn't begin tapering at a 45° angle at the location of the 1/8"radius. The significance of this observation is when one considers the orientation of the stress flow lines. The beginner technical books can over simplify the significance of a change in section size. When there is a change in section size the stress flow lines will move up into the larger section size before they move back down into the original section size. The greater the change in section size, the more the stress flow lines will move up into the larger section. However, at some point the change is just too great and the smooth stress flow lines will break up and concentrate around the location where the section size changes. The dished region illustrates the orientation of the stress flow lines that moved up into the larger section and how the crack traveled normal to these lines. There has been tremendous research done around the adverse affects created by section changes in shafting. The literature is out there and the authors are abundant. Roark and Young have compiled one such collection of data. Ironically, it is buried under the title "Miscellaneous Tables." The gist of the data essentially says that all of the equations formulated to calculate the stress concentration at a section change require that the ratio of the height of the section change with respect to the radius at the section change should be less than 20. This told me that anything over 20 was in "no-man's land" that one should clearly avoid at all cost. In the case of this section change, the ratio was 79.5. To put this ratio in perspective, Spotts has a design graph that shows the smallest ratio of the radius to the shaft diameter as 0.02, below which the stress concentration factor sky rockets off the graph. The ratio for this shaft was 0.006. In other words, this shaft design was doomed from the first day. However, before we badmouth the design lets set the record straight. This shaft ran 24/7 for 30 years. Obviously, the designers DID know what they were doing, and considered this problem to be minor. I am not in a position to ridicule a design that lasted 30 years. I hate Sunday armchair quarterbacks, and will not start now. Let's say it again, this design ran 24/7 for 30 years WITH this design flaw.
Figure 2		Figure 3

	Knowing how a shaft failed helps in determining the fix. Figures 4 and 5 show changes in the topography of the fracture surface. A change in topography means that there was a change in the direction and type of stress that predominated at a particular point in time. Remember that as the crack progresses it changes how the shaft is loaded. One thing is obvious, the stress condition was uniform in the circumferential direction. The ridges that are visible in Figure 4 were evident around the shaft's outer circumference, so unidirectional bending and reversed bending could be ruled out. Therefore, a bent or misaligned shaft were not a factor. However, the pattern resembles what one would expect for rotational bending. This is an important observation from the viewpoint that the failure appeared to be normal as opposed to a one time overload event or from an abusive series of events. The drum was loaded with ropes that would create a rotational load under normal conditions. Figure 5 shows a roughened region in the center of the shaft that was the final fracture region (circled). It is quite small and is centered. This would support a failure mode of rotational bending with a high stress concentration. It is important to understand the loading of the shaft. The shaft that was still attached to the flange was the drive side. The shaft section that was missing was essentially a support mechanism for the drum that was bolted to the flange. That section of missing shaft was supported by a large bearing. The flange was 6" in width and had a healthy radius on the drive side. The ratio of the shaft diameter to that other radius was considerably better than the ratio for the 1/8" radius, by many orders. The drive side of this flange did all of the work. If the drive side had been on the side with the 1/8" radius, this shaft probably wouldn't have lasted as long.
Figure 4		Figure 5

	Figures 6 and 7 show the section of shaft that broke away from the flange. Note the mating ridges in Figure 6 and their stepped circumferential orientation. They were not tear marks or grooves that were the aftermath of the failure. Tear marks are shown circled in both figures. The tear pattern was the result of a "weld-and-tear" action between the mating parts. Figure 7 shows the region underneath the drum where a spacer bushing was located. It was quite evident that the bushing came loose and started to rotate with respect to the shaft. The fracture was hidden underneath the drum, but the OEM knew immediately what had happened when they were told that the shaft broke. They didn't even need to see the shaft. I had the chance to work with them on the redesign which is showcased in the article "Machine Design - Case Study No. 127: Undercutting Sharp Flange Corners to Relieve Stress Concentration."
Figure 6		Figure 7

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