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A REALISTIC METHOD TO ESTABLISH THE REQUIRED GEARBOX
RATING FOR A GAS TURBINE APPUCAT1ON
A. K. Rakhit
Solar Turbines Inc.
San Diego, California
III 111111111111111 111111
ABSTRACT
A reliable gearbox rating is essential for successful operation of
high speed gas turbines. Presently, there is no dependable method to
establish such a rating based on actual gas turbine performance under
operating conditions. A great majority of manufacturers of this equipment use gas turbine output power at inlet air temperature of -20°F as
the basis for this rating, while others assume an arbitrary inlet air
temperature profile for turbine operation and use turbine output powers
at various tanperatures of the profile to derive an avenge rating for the
gearbox. The major drawbacks of these methods are that they do not
consider the effects of turbine performance characteristics and also do
not inchsk temperature profiles of actual installation sites. Thus, a vast
majority of gear transmission equipment used in today's high speed
turbomachinery applications are either under- or over-rated. The procedure, as outlined in this paper, provides a reliable method to rate
gearboxes for gas turbine driven equipment.
INTRODUCTION
Gearbox rating defines the power (HP or KW) at which the gears
have a minimum service life under normal operating conditions. For
gears used in turbomachinery, the minimum service life is taken to be
100,000 hours of trouble-free operation. On the other hand,
components like rolling element bearings are designed for a minimum
810 life of 50,000 hours and fluid film bearings for more than 100,000
hours of service life. Since bearings are regarded as replaceable items
during scheduled overhauls of turbogenerator sets, the life of the gears
is considered to be the service life of a gearbox in these applications.
Presently, the gear industry uses different major international
standards (1,21to rate gears. These standards present general formulae
for calculating pitting resistance and bending strength of gear teeth for
uniform load. Unfortunately, gears used in gas turbine driven
equipment experience a great deal of fluctuating load due to the
performance variation of a gas turbine. Thus, the major problem in
rating turbomachinay gears lies in the selection of a representative load.
The output power of a gas turbine varies with inlet air temperature.
water/steam injection, elevation of an installation rite, performance
degradation with operation, etc. It is thus practical and economical to
include the effects of all of these variables in selecting a weighted
average power for rating these gems. Furthermore it is also intended to
rate the gearbox in tenns of ISO power of a gas turbine. ISO power
generally designates the rating of a turbine.
In this paper, a realistic methodology is proposed to establish the
rating of gearboxes for gas turbine applications. Finally, an empirical
relationship is established between the ISO power of a gas turbine and
the required rating of a gearbox.
THE APPROACH
For 100,000 hours of minimum service life, the design of a high
speed turbomachinery gearbox is primarily limited by the durability of
the gears and cumulative fatigue damage characteristics of gear
materials. To determine the load experienced by the gears used in these
gearboxes, the output power characteristics of the turbine connected to
a gearbox as well as the stress vs. cycles relationship (S-N curve) of gear
materials needs to be properly evaluated.
The output power of a gas turbine is dependent on a number of
factors. These include:
• Turbine performance variation from ISO conditions - power
goes up with decreasing inlet air temperature and down with
increasing temperature. Figure 1 13) illustrates the
performance variation of a typical gas turbine with inlet air
temperature.
Additional power due to water/steam injection
Inlet, exhaust, and auxiliary power losses
Reduced power due to increasing altitude of an installation
site from sea level
Performance degradation with operation
Presented at the International Gas Turbine and Aeroengine Congress and Exposition
Houston, Texas - June 5. 13, 1995
-
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from actual turbine installation sites. Arbitrary temperature profiles used
to define turbine power are not very realistic and very often lead to
Sin over or under rating of a gearbox. A rational approach is to select
profiles from representative installation sites, determine turbine power,
establish the gear rating for each site and then take the average of all of
these ratings. Re this, the geographic distribution of all gas turbines on
a worldwide basis is considered. The worldwide geographic
classification is further rearranged into three district climatic regions:
Arctic, moderate, and -The distribution of stationary industrial gas turbine installations
around the world for one typical manufacturer is illustrated in Sgure 2.
Considering that are Mae major climatic zones, the chart shows a vast
majority of these installations is located in the moderate and tropical
regions. Azure 3 shows the distribution of these installations by
country. In terms of percentage, this amounts to 56% being located in
the moderate climate, 42% in tropical, and just 2% in the Arctic zone.
With such a distribution it allows the gearbox rating to be established
from tubule performance characteristics in the moderate climate
because this not only meets the service life of moderate climate
installations but also those in tropical region where turbine output power
is relatively lower due to higher temperature of inlet air to the turbine.
In Arctic applications (only about 2%) where gear life may be an issue,
limitations can be overcome by offering reduced life with the same
gearbox rating or a reduction in service factor may be justifiable to
achieve the full service life. The minor drawback of gearbox rating
established with temperature profiles from moderate climate alone can
be compensated by including a few Arctic temperature profiles in the
analysis. These will also offset the effects of occasional low
temperatures in moderate climatic zone that would otherwise require a
higher gearbox rating.
ems
FIGURE 1. PERFORMANCE CHARACTERISTICS OF A
TYPICAL. GAS TURBINE
The significance of each of these factors in influencing the gearbox
rating needs to be evaluated separately. Of all these, the inlet air
temperature variation affects gas turbine performance the most. Thus,
the selection of representative temperature profiles is of utmost
importance in rating high speed turbomachinery gears for optimum
performance.
TEMPERATURE PROFILE
A temperature profile depicts the mean ambient temperatures as a
function of time. The selection of such a profile can be made either by
assuming arbitrary temperatures and times or temperatures and time
FIGURE 2. WORLDWIDE DISTRIBUTION OF GAS TURBINE INSTALLATIONS
2
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0.11)
the effect of occasional low temperatures in the moderate climatic
a
To carat= temperature profiles, a year is divided into twelve
intervals. For each of these intervals a mean ambient temperature is
calculated from the tempera= records. It is assumed that a gearbox
in anbomachiray applications will operate at each of these intervals
for 1/12th of its total service life of 100,000 hours. The temperature
profiles of the four cities developed and considered in this procedure
are shown in Tables 1 through 4.
1
rl in"1111/JACK
TURBINE POWER
For a given temperature profile turbine power at each mean
ambient temperature is obtained from its power vs. inlet air
temperature characteristics. Since some turbines may have
water/steam injxtion capability, additional power due to water/steam
injectice is catsidera in rating these gears. In general, this amounts
to about 6% more power at any inlet air temperature. Again, to
compute net turbine power it is necessary to include also the losses.
These are taken to be:
;rat lfsr
"'I
FIGURE 3. GEOGRAPHIC DISTRIBUTION OF GAS
TURBINES BY HORSEPOWER
In this procedure three installation sites are selected from the
moderate climate zone. The sites are Caribou (Maine), International
Falls (Minnesota), and Glasgow (Montana). The question may arise
on the validity of these cities located in the United States to represent
the entire moderate climatic zone of the world. A research of
daily/monthly temperature records of cities around the world
available form various meteorological offices shows that these three
cities of the United States are quite representative of the entire
moderate climate of the world. Further, the reason for selecting only
three cities is that they represent three distinct areas of moderate
climate in the United States. It is also found that increasing the
number of sites in the analysis does not have any significant influence
on better representation of this climatic zone because the average
datlyhnonthly tonperatures of this region are distributed within a very
narrow temperature band. For the three sites selected from the
moderate climate zone, one site from the Arctic region (Barrow.
Alaska) is included inthe analysis which will favorably compensate
Inlet, exhaust and auxiliary losses: 1% of power
Performance degradation with operation loss: I% of power
The loss due to elevation is not considered for the temperature
profiles selected because it is assumed that an actual installation site
with a similar temperature profile may be located at the sea level.
Hence, the net result is that an additional power of 4% should be
included in determining net turbine power for the gear rating.
-
GEARBOX RATING
With the knowledge of actual turbine power at each temperature
of a profile and its time duration, the gearbox rating required for a
profile may now be calculated from gear durability curve (stress vs.
cycles) and Miner's rule for cumulative contact fatigue damage of
Table 1. Caribou, Maine
Mean Ambient
Temp. (E)
Gearbox Operating
Hours
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
11
13
24
37
50
60
65
63
54
43
31
16
8333
8.333
8,333
8,333
8.333
8,333
8.333
8.333
8,333
8,333
8.333
8,333
Table 2. International Falls, Minnesota
Mean Ambient
Temp. (' F)
Gearbox Operating
Hours
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
0
7
21
38
51
61
66
63
53
43
25
8
8.333
8,333
8,333
8,333
8.333
8.333
8333
8.333
8.333
8,333
8333
8,333
3
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Table 3. Glasgow, Montana
-
—
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
8
16
26
43
55
63
70
69
57
46
29
17
8,333
8,333
8,333
8333
8,333
8,333
8,333
8,333
8,333
8,333
8.333
8,333
Mean Ambient
Temp. (°F)
Gearbox operating
Hours
Table 4. Barrow Alaska
r
Jan
Feb
Mar
Apr
May
Jim
Jul
Aug
Sep
Oct
Nov
Dec
-21
-26
-22
-9
14
29
33
34
27
10
4
- 19
8.333
8.333
8,333
8 333
8,333
8.333
8.333
8,333
8,333
8.333
8.333
8,333
Mean Ambient
Temp. (°F)
Gearbox Operating
Hours
_.
gear materials, the primary cause of high speed turbomachinery gear
failure. From the durability curve the life of a gear at a power HP,
can be written as:
Li
= io 7 (
where
1-ff= Total accumulated life
Life at HP,
a, - Fraction of life at HP, and a, + a 2 +
+ a, = 1.00
(1)
S
From equations (3) and (4), the following equation is developed for
the required gear rating(HP„,) as
ca
sc
HP ,
HP
r
• 5 HP 264
• ..... •
a. HI
r
(5)
where
=
Sc. =
Sc =
=
Life cycles at Sc,
Allowable Hertz stress for the material
Hertz stress at the power HP,
Slope of S-N curve for gear durability
Equation (5) can also be written in the form
HP!'
o fat
42R2.14 •
a. R.64
For gears,
Sc, a HP, u2
where
or Sc, = C H17,u2
(2)
HP !: o
Substituting equation (2) in (1)
io 7
HP
(3)
; HP1s0 is the turbine horsepower at ISO
conditions
Using equation (6), the gear rating for each of the temperature
profiles is calculated from which the rating for moderate climate
zone is established. Finally, the avenge of this rating and the rating
required under offsetting Arctic climate is taken to be the gearbox
rating for the gas turbine application.
Now, Miner's rule for cumulative fatigue damage can be written as:
(4)
RESULTS
Using the medtodology outlined, and assuming an applicaiton
factor of 1.0, gearbox ratings for different gas turbines (single and
two-shaft) are computed. A single shaft turbine produces more
output power than a two-shaft design. For this reason, gearbox rating
4
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fluctuating loads. Gearboxes so rated are in use for various single
and two-shaft turbines manufactured by the company with which the
author is currently employed. Some of the gearboxes are inspected
after 50,000 to 70,000 hours of duty cycle without showing any
distress.
for a single shaft turbine is usually higher. Analyzing the gearbox
ratings for several single and two-shaft turbines it is concluded that
for all gas turbine applications:
Gearbox Rating = 1.15 x ISO rating for Single Shaft Turbine
= 1.13 x ISO rating for Two-Shaft Turbine
REFERENCES
A sample calculation for gearbox rating for a two-shaft turbine
is shown in the appendix.
I. AGMA Standard 2001-B88, Fundamental Rating Factors and
Calculating., Methods for Involute Spur and Helical Gear Teeth.
September 1988.
CONCLUSIONS
This rating method for a gearbox works well for high geed
gears (PIN > 10,000ft/min) where the primary mode of gear failure
is detemined by contact fatigue and when the gears are subjected to
2.
ISO/TC60A9G6, Basic Principles for the Calculation of Load
Capacity of Spur and Helical Gears, Parts 1-4, 199E, 200E,
201E, 202E, November 1977.
3.
Gas Turbine Generator Set Manuals, Solar Turbines Inc.
APPENDIX
CALCULATION OF GEARBOX RATING FOR A TWO-SHAFT GAS TURBINE WITH PERFORMANCE
REPRESENTED BY FIGURE 1.
Tables A-1 through A-4 show power levels of this turbine that
include 4% additional power at various temperatures oldie profiles
considered in this procedure.
Table A-1. Turbine Power Level - Temperature Profile of Caribou, Maine
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
11
13
24
37
50
60
65
63
54
43
31
16
Power (lfP)
17.450
17,376
16,976
16,507
16.019
15.587
15,343
15.441
15.862
16.283
16,731
17.264
Gearbox
°Pealing
Noun
8.333
8.333
8.333
8.333
8.333
8.333
8.333
8.333
8,333
8.333
8.333
8.333
Temp
en
Table A-2. Turbine Power - Temperature Profile of International Falls, Minnesota
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Temp CP)
0
7
21
38
51
61
66
63
53
43
25
8
Ponw 0.1P)
17,862
17,599
17,083
16,471
15,979
15.538
15,295
15,441
15.902
16.283
16,943
17561
Gearbox
8,333
8,333
8,333
8 333
8,333
8.333
8,333
8,333
8,333
8,333
8,333
8.333
°Paving
Noun
5
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Table A-3. Turbine Power - Temperature Profile of Glasgow, Montana
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Tarp ('F)
g
16
26
43
55
63
70
69
57
46
29
17
Power OM
17.561
17,264
16,906
16,283
15,823
15,441
15,102
15,149
15,734
16.174
16.802
17.228
Gearbox
OP:talleg
Hours
8,333
8,333
8,333
8,333
8,333
8,333
8,333
8,333
8,333
8,333
8.333
8.333
Table A-4. Turbine Power - Temperature Profile of Barrow, Alaska
Jan
Feb
Mar
Apr
May
Jon
Jul
Aug
Sep
Oct
Nov
Dec
Term CF)
-21
-26
-22
-9
14
29
33
34
27
10
-7
-19
Power ({P)
18,594
18,757
18,627
18202
17,339
16,802
16,658
16,619
16,872
17.487
18.125
18.531
Gearbox
Operating
Wort
8.333
8,333
8,333
8,333
8,333
8,333
8,333
8.333
8,333
8,333
8,333
8,333
Similar calculations for temperature profiles of International Falls,
Glasgow, and Barrow yield the following gearbox ratings:
GEAR BOX RATING
With turbine output powers known at different air inlet
temperatures, the gearbox rating for each temperature profile is
computed using equation (6). Typical calculations for the temperature
profile of Caribou, Maine are shown below:
International Falls, Minnesota :
:
Glasgow, Montana
:
Barrow, Alaska
16,287 HP
16,091 HP
17,538 HP
HP, = HP, fa 1 R 1 11 + a2111'n + + aNRan t.
From the gearbox ratings of Caribou, International Falls, and
Glasgow, the weighted average gearbox rating for moderate climate may
now be computed using either root-mean-square (RMS) method or just
taking the average of the three ratinp. Since these individual ratings are
not widely separated, a sitnpk average yields the same value as obtained
by the RMS method. This is calculated to be:
In the case of this turbine
HP
15,000
a (the slope ofthe S-N curve) = -17.62 (from experimental
data by Dade Dudley and later confirmed by AGMA
Standard 2001-888)
(16,248 + 16,287 + 16,091)/3 = 16,208 HP
Now an average of the gearbox rating for moderate climate and
a,...a„ = 0.0833
Arctic climate (Barrow. Alaska) is taken to be the gearbox rating for this
22
11
iiP1
0
17,450
15,000
turbine.
1.1633
This is:
(16,208 + 17,538)/2 = 16,873 HP
1.125 x 15,000 HP
Thus, the rating of a gearbox for a 2-shaft gas turbine drives can
be written as:
R, = 1.1584
R, = 1.0391
RH, = 1.0855
R 3 = 1.1317
R,= 1.0229
R„ = 11154
R, = 1.1005
R, = 1.0294
R,, = 1.1509
HP, = 1.13 x ISO rating of Turbine
K, = 1.0679
R4 = 1.0575
Substituting these values in the equation:
HPG = 15000 [0.0219 + 0.0228 + 0.0280 + 0.0358 + 0.0467
+ 0.0594 + 0.0682 + 0.0645 + 0.0509 + 0.0404
+ 0.0318 + 0.0241 -"' = 16,248
6
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