We have all used averages to determine average stresses, forces, torques, service life and other quantities. But care must be taken when using averages. What if a shaft failed with an average torque meter value of 360 ft-lb. Spot values show torques of:
(300 + 800 + 200 + 400 + 100) / 5 = 360 ft-lb
Obviously, it was the 800 ft-lb torque that probably caused the failure, but if the torque meter took hourly averages, it would miss the peaks.
Here is an actual case involving the wear of a gas-engine compressors power cylinder.1 Excessive warping of a lined cylinder can result in expensive downtimes and piston wear, such as shown in Fig. 1. This was occurring on cylinders that had been relined at a high-quality shop for many years. It was suspected that the cylinders were defective and distorting. When the engine manufacturer was contacted, the reply was that they recommend only new cylinders be used at overhaul time and they don't recommend other shops relining them.
| Fig. 1. Galled piston due to |
Existing data was collected on the new and relined cylinders. A new analysis on the averages was presented to the engineering department. The new solid cylinder service life until galling (months) is:
16, 12, 7, 48, 14, 48, 24, 2, 24
Average service life = 21.7 months
Data on the relined cylinder service life until galling (months) is:
8, 4, 4, 5, 48, 12, 12
Average service life = 13.3 months
With only the average values used, it is clear to see how the manufacturer's advice shouldnt be ignored. The solid cylinders seem to last almost twice as long as the relined units.
In contrast, engineering calculated these statistics;
Average service life solid = 21.7 months
Standard deviation solid = 16.5 months
Number of solid = 9
Average service life relined = 13.3 months
Standard deviation relined = 15.7 months
Number of relined = 7.
The tip off that the data was the problem is demonstrated by the large standard deviation values. These should usually be much smaller than the average value.
A test was done on the data, called a Student t test. It indicated that the average of the solid cylinders over the relined could only expect to be larger in 5 times out of 100 times. This said that there was hardly enough data to make an informed decision and that more data was required.
This is important since relined cylinders cost $7,500/unit and new solid cylinders are $15,000/unit. There are eight cylinders per engine and the cylinders are replaced every four years during overhaul. A wrong decision could cost $60,000 every four years. In addition, numerous engines of this design are used within the company.
The decision was to continue testing until an adequate statistical basis could be reached. The final outcome was to tighten up the reline procedure with detailed specifications as to the fit, materials and assembly procedure and inspection with the supplier. With these refined procedures and additional test data, it was determined that the service life of relined cylinders was the same as new solid cylinders. This was only so with proper maintenance of the engine and purchasing relined cylinders from a high-quality repair facility.
Maintenance was a key point addressed from this study since even new cylinders were galling. Better maintenance and eliminating detonation during load changes should address these concerns. HP
1 Sofronas, A., Analytical Troubleshooting of Process Machinery and Pressure Vessels: Including Real-World Case Studies, John Wiley & Sons, p. 222.
|The author |
Dr. Tony Sofronas, P.E., was a worldwide lead mechanical engineer for ExxonMobil before his retirement. Information on his books, seminars and consulting, as well as comments to this article, are available at http://mechanicalengineeringhelp.com.