RENSSELAER POLYTECHNIC INSTITUTE
DSES-6070 HV7
STATISTICAL METHODS FOR RELIABILITY ENGINEERING
FALL 2008
PROF. ERNESTO GUTIERREZ-MIRAVETE
FAILURE ANALYSIS OF AIRCRAFT ENGINE BEARING
PROPOSSED BY:
ORLANDO J. RIVERA-ANGLERO
DECEMBER 11, 2008
Introduction
Growth in aircraft manufacturing has been very strong in recent years and
forecasts suggest that this will continue in years to come. Programs include the
development of long-range wide-body aircraft such as the Airbus Industrie’s A340500/600 model (which started service in the new millennium), the Airbus A380 with 550
and 650 seats, and Boeing’s ultra-long-range 777-200/300X derivative. The production of
regional aircraft such as the Boeing 717 and Airbus A319M5 is also increasing.
The propulsion system of these aircraft typically has two or three rotating shafts
in order to meet the aerodynamics requirements of the engine. The bearings that support
these shafts are subject to very demanding operating conditions such as high axial loads.
For application in advanced aircraft gas turbine engines with a wide-chord fan, the mainshaft bearing is expected to have higher load capacity and higher-speed performance due
to the need for a higher thrust-to-weight ratio. Moreover, higher reliability of the mainshaft bearing is required to meet demand for increased engine reliability, particularly as
ETOPS (Extended-Range Twin-Engine Operations) certification becomes more
necessary for increasing the efficiency of aircraft operation.
In the development of the engine, improvement of the main shaft rolling bearing
has been the key to overcoming various hurdles. Presently, important considerations for
the development of bearings for aircraft engines include:
• The increased speed of the main shaft
• Increased engine thrust and the resulting need for higher bearing load capacity
• Dependable performance of bearings in extreme conditions (including oil interruption
resulting from changes in the oil-level in the reservoir caused by an aircraft going into a
nose-dive, and skidding, the excessive sliding of rolling elements on the raceway under
high speed and low load)
• The assessment of bearing fatigue life in terms of L1 life (99% reliable life estimation)
Figure 1 shows a typical aircraft engine with its respective bearings
Figure 1: Advanced turbofan engine (BMW Rolls-Royce Aeroengines)
It is extremely important to have in mind that Gas Turbine main engine bearings
are critical components that affect overall system safety and reliability. It is for this
reason that the primary purpose of a gas turbine main bearing is to provide support and
positioning for the engine rotor shaft. One of the challenges with a bearing is the ability
to detect a failure before an in-flight shut down occurs (IFSD) which could result in
secondary damage to other turbo-machinery components. Currently, preventive
maintenance practices are performed in order to replace a bearing before catastrophic
failure occurs.
The objective of this study is to determine the reliability of an aircraft engine
bearing by using several reliability and statistical techniques. This study outlines the
operating requirements of bearings for advanced aircraft gas turbine engines, and will
discuss technical solutions developed to meet these requirements.
Failure Mechanism
High rotor gas turbine bearings rotate at speeds greater than 2 million DN; where
D is the bearing bore diameter in millimeters and N is the shaft rotation in rpm. At these
high speeds the bearings can be subjected to fatigue spalls that eventually will cause a
bearing ring fracture. A ring fracture can cause serious failures that will lead to an engine
IFSD; for example, it can cause the engine to lose its centerline and potentially jeopardize
the aircraft performance. These types of failures are unacceptable and they have been a
reason for great concern for many years. Bearings typically fail by fatigue that is initiated
at the sub-surface.
Performance Expectations
Characteristics such as, bearing B10 life and outer mean contact stress are usually
calculated in order to predict the bearing performance expectation for the spall
progression test. Ball bearing B10 life is commonly referred as the bearing life associated
with 90% reliability when operating at normal engine conditions. In other words, it can
be expressed as the number of hours that a bearing can operate before any damage starts
from rolling contact fatigue. The bearing total B10 life is the sum of the B10 lives for
each engine mission point, i.e. take off, climb, cruise, idle and descent/landing.
Failure Event
Here’s an example of why the bearings are such an important component of an aircraft
engine:
About 1140 eastern daylight savings time on September 22, 1981, the No. 2
engine, a Rolls-Royce RB-211-22B, failed as Eastern Airlines Flight 935, a Lockheed L1011-385 (N309 EA), was climbing through 10,000 feet after departing Newark
International Airport, Newark, New Jersey, for San Juan, Puerto Rico. The displacement
of the fan module in the course of the engine failure sequence caused loss of hydraulic
systems A, B, and D and jammed the captain's and first officer's rudder pedals in the
neutral position. The flight crew performed the appropriate emergency procedures,
requested an immediate landing at John F. Kennedy International Airport, Jamaica, New
York, and dumped about 48,000 pounds of fuel. The aircraft, with 11 crewmembers and
190 passengers aboard, landed on runway 22L at 1212 e.d.t. without further incident. No
one aboard was injured, and there was no damage to property or injury to persons on the
ground. The aircraft was substantially damaged.
The National Transportation Safety Board determines that the probable cause of
the accident was thermally induced degradation and consequent failure of the No. 2
engine low pressure location bearing because of inadequate lubrication. Oil leaks
between the abutment faces of the intermediate pressure compressor rear stubshaft and
the low pressure location bearing oil weir and between the intermediate pressure location
bearing inner front flange and the intermediate pressure compressor rear stubshaft
reduced the lubricating oil flow to the low pressure location bearing which increased
operational temperatures, reduced bearing assembly clearance, and allowed heat to build
up in the bearing's balls and cage. The bearing failure allowed lubricating oil to spray
forward into the low pressure fan shaft area where it ignited into a steady fire; the fire
overheated the fan shaft and the fan fail-safe shaft both of which failed, allowing the fan
module to move forward and break through the No. 2 engine duct. This caused extensive
damage to the aircraft's structure and flight control systems. The oil leaks were most
likely caused by poor mating of the abutment surfaces.
Methodology
The analysis performed in this study was similar to what has been done in class. I did:
1) Obtain the raw data from the field from 1998 to 2007
2) Calculate all descriptive statistics for the sample
3) Construct a histogram of the raw data
4) Use Minitab to select the best distribution to fit the data
5) Determine the parameters of that distribution
6) Determine the Failure Probability Distribution Function, the Survival Probability
Distribution Function, the Hazard Rate, the MTTF, the MRL and all relevant
quantities using Maple Software
7) Randomly generate some large samples and compare predictions with the raw
data.
Results
Table 1 shows the raw data obtained for bearing failure time in both cycles and hours.
Table 1: Raw data for bearing failure time (cycles and hours)
Based on this data, an analysis was run in Minitab to obtain descriptive statistics results.
The results are shown below.
Descriptive Statistics: Hours, Cycles
Variable
Hours
Cycles
N
19
19
N*
0
0
Variable
Hours
Cycles
Q3
29379
7697
Mean
24198
5661
SE Mean
2742
909
StDev
11953
3963
Variance
142874646
15702822
Minimum
4590
1658
Q1
13466
2462
Median
23989
5306
Maximum
52006
18963
Figures 2 and 3 show histograms for failure time both in hours and cycles, respectively.
By looking at the histograms, it gives you the idea that the data sets tend to follow
different distributions. It can be interpreted that the failure time in hours fits a normal
distribution and the failure time in cycles fits either an exponential distribution or a
Weibull distribution. On the next test it will be demonstrated the opposite.
Histogram of Hours
Histogram of Cycles
4
6
5
Frequency
Frequency
3
2
4
3
2
1
1
0
10000
20000
30000
Hours
40000
50000
Figure 2: Histogram for failure time in hours
0
4000
8000
12000
16000
Cycles
Figure 3: Histogram for failure time in cycles
The next step was to run a Minitab analysis to determine which distribution fits
the data the best. Figure 4 and Figure 5 show the probability plot for both failure times in
hours and cycles, respectively.
Figure 4: Probability plot for failure time in hours
Out of the four distributions available, it can be seen that a Weibull is the best fit
for the failure time in hours with a correlation coefficient of 0.984.
On the other hand, Figure 5 shows that out of the 4 distributions available, a
Lognormal or Loglogistic would be the best fit for the failure time in cycles with a
correlation coefficient of 0.981. However, for simplicity a Weibull distribution will be
used for this data set since all semester we have focused on either Weibull or
Exponential. Besides, a Weibull shows a correlation coefficient of 0.953 which is pretty
good.
Figure 5: Probability plot for failure time in cycles
The parameters were determined in Figure 6 and Figure 7.
Shape = 2.08174 = b
Scale = 27482.1 = a
F = 1-exp(-(t/27482)^2.08)
Figure 6: Distribution Overview plot for failure time in hours
Shape = 1.99466 = b
Scale = 6175.32 = a
F = 1-exp(-(t/6175)^1.99)
Figure 7: Distribution Overview plot for failure time in cycles
Following it will be found the different reliability functions for failure time in hours as
they were calculated by Maple:
>
>
>
>
>
>
>
Then, following it will be found the different reliability functions for failure time in
cycles as they were calculated by Maple:
>
>
>
>
>
>
>
From the results above it can be seen that the MTTF for hours = 24342 and the MTTF for
cycles = 5473. A Monte Carlo simulation was run and the results were similar as it can be
seen in Figures 8 and 9.
Figure 8: MC simulation for failure time in hours Figure 9: MC simulation for failure time in cycles
This indicates that the Monte Carlo simulation will give you a very good estimate of the
actual result for MTTF.
Then, finally Figures 10 and 11 show the plot of F vs R for both failure time in hours and
cycles, respectively.
Figure 10: F vs. R for failure time in hours
Figure 11: F vs. R for failure time in cycles
From the charts above it can be seen that they match the results obtained for the MTTF in
Maple.
Conclusion
This study was able to successfully demonstrate the following:
1) Descriptive statistics were calculated for the sample bearing failure time in both
hours and cycles,
2) A histogram of the raw data was constructed and the one for failure time in hours
was misleading,
3) Minitab was used to select the best distribution to fit both data sets and it gave
good results determining the best fit for both sets was a Weibull distribution,
4) Parameters for both distributions were determined,
5) Failure Probability Distribution Function, the Survival Probability Distribution
Function, the Hazard Rate, the MTTF, the MRL and all relevant quantities using
Maple Software were determined,
6) A Monte Carlo simulation was successfully created and it generated large
samples that accurately compared with the results obtained from Maple.
Appendix: Reliability functions plots
>
>
>
>