1、STDeAGMA 95FTHA-ENGL 1995 Ob87575 OOOq739 5bb = 95FTMS I Miners Rule - A More Definitive Approach by: Al Meyer, Allied Signal Engines American Gear Manufacturers TECHNICAL PAPER STD.AGMA 75FTM8-ENGL 1995 Ob87575 0004740 288 Miners Rule - A More Definitive Approach Al Meyer, Allied Signal Engines The
2、 statements and opinions contained herein are those of the author and should not be construed as an officiai action or opinion of the American Gear Manufacturers Association. Abstract ANSVAGMA 2001-B88, Appendix B presents the fundamental method for evaluating Miners Rule. To analyze the load spectr
3、um, stress values are caicuiated for a given loadand then modified using K“ or “C factors. When computing the suesses fur other points, the mess values are usually simply deed rather than recomputing the stresses using new “K“ and “C” for each point. In this paper, the effect of using a dynamic and
4、load distribution factor for each load point is evaluated and compared with the simple ratioing approach. Comparisons are made for anumber of aircraft his tograms as shown in AGMA 911494 along with a cornmerciai ornurid appiication. Copyright O 1995 American Gear Manufacturen Association 1500 King S
5、treet, Suite 201 Aiexandria, Virginia, 223 14 October, 1995 ISBN: 1-55589457-X STD.AGMA 75FTM8-ENGL 2995 Ob87575 0004742 214 MINERS RULE, A MORE DEFINIT= APPROACH by Alvin G. Meyer Alliedsignal Engines Reduction gearbox designs for aerospace applications are based on a design life that is usually es
6、tablished by the application. This requirement has increased from 6,000 hours for a military application . thirty years ago to 50,000 hours for comercial I applications of today. In the sixties, S/N curves had definitive endurance limits and it was not uncommon to design below the knee of the curve
7、at the take-off or military power rating. In this manner, any mission profile (load schedule) would be satisfied for all but the emergency power or transient conditions of operation. Since these conditions were expected to occur infrequently, the effect on design life would have been minimal. One mi
8、ght think that this procedure would lead to a relatively conservative design. But, in the case of gas turbine engine reduction gears, quite the opposite was true. In a typical turboshaft engine helicopter application the planetary reduction gear syctem, see Figure 1, is driven by a sun gear at 20,00
9、0 rpm. With three planets being driven, 10 cycles are reached in less than 3,000 hours. The tank engine is also a turboshaft type and the reduction gear system is shown in Figure 2 and again the sun gear drives three planet gears which see alternating bending in this star type system. The input desi
10、gn speed is 22,000 rpm so that lo1 cycles are reached in an even shorter time than in the first example. With the advent of finite life S/N curves and new design life requirements having escalated to 50,000 hours, the load schedule or duty cycle life, as it is known for commercial applications, has
11、become of prime importance in the continuing effort to achieve the lightest weight overall system design. Usually 100% power, 100% speed Miners Rule was developed to evaluate the effect of varying loads on the life of the material. If a material is operated at a given stress level with an allowable
12、fatigue life of lo6 for a period of 5x105 ., cycles, then one half of the life at that stress level has been used up. If it is then operated at a , different stress level with an allowable fatigue life of lo4 cycles for 5x103 cycles, then one half of the life at that stress level has been used up. W
13、hen the sum of these fractional lives equals one, then the e. total life is used up. If the duty cycle or mission profile life is less than the design life requirement, then the gears require redesign. For gearing there are two failure modes, bending and compression, that relate to fatigue; Each one
14、 has to be evaluated in a full Miners Rule analysis. Figure 1. Turboshaft Engine Reduction Gearbox AGMA 2001-B88, September 1988 Appendix B contains the procedure for using Miners Rule. Part of the discussion states that “The stress used in reducing the data for gear teeth is not measured stress, bu
15、t a calculated stress number, using the calculation methods of AGMA 2001.“ This implies that the stress levels at each duty cycle point should be determined from the stress equations given. 1 STD=AGMA 95FTMB-ENGL 1995 Engine Type Turbochaf t Turboshaft Turboprop Figure 2 Tank Engine Reduction Gearbo
16、x Vehicle Military Helicopter Land Vehicle, M1 Tank /” Fixed Wing Aircraft . Commercial ;: 1.71E22 2.3i18 99. 2.35E58 1 22. = 69,926 hrs (Constant) It ?ar comp. Life (hrs 8.77Ell 1.24309 1.67304 8.33E03 3.89304 1.28E05 2.53308 1.94301 6.69318 1 E07 1 Eo6 1 EO5 e a 1EO4 1 E03 I I I 100 _. I I 10 1 I,
17、/ 1300 1400 1500 1600 1700 1800 1900 Horsepower Figure 3. TURBOSHAFT ENGINE (Gear Design Life) Y I I l l i 1200 (Km)(Kd) - NORMALIZED Figure 4. Dynamic I 1.39305 161. 3.53303 167. I 1.77103 153. 8.20303 41.8 2.40306 I 145. 8.56306 2.32E18 144. 94. 108. 24. 2.90304 5.36307 4. 07306 1.41318 29.2 33.6
18、5.8 3.05E14 3.16354 Mission Profile Life = 34,722 hrs (Variable) = 39,576 hrs (Constant), 12 % difference The next case is for another turboshaft engine that is used in the Armys main battle tank designated the M1. The reduction gear design point is 1,500 hp at 3,000 rpm output speed. The output fee
19、ds into the tank transmission and shifting becomes very much a part of the Mission Profile whose results are shown in Table 2. The table has been condensed especially in the low horsepower area. Multiple values are shown for horsepower and each value in a group has a different output speed associate
20、d with it. The bending stress is low, column 3, which reflects the relatively coarse pitch of 9.5 that was chosen to address the high shock loads that are experienced from driving over rough terrain. The bending stress was also a maximum for the planet-ring mesh because of the design philosophy wher
21、e a tooth is dropped from the planet gear for an improved sun-planet mesh. The compressive life is again the limiting mode for the design because of the early detection warning aspect. The output speeds are not given but, they range from 900 to 2,700 rpm. The gear design point is 1,500 hp at 3,000 r
22、pm output speed. Since the design point is not part of this mission profile, the comparison as made in the previous example would be the column entitled, “Constant 3,000 rpm versus the column entitled, Variable. This provides some interesting Table 2 - Mission Profile For The Tank Engine Reduction G
23、earbox Design Life = 10,000 hrs Input Sun k Planet Gears Variable Km The bending life for the input gear, which is splined to the power turbine, is the next critical mode and both are shown in the table. The duty cycle life is 41,494 hours with variable factors and 79,963 hours with constant factors
24、. The difference in this case is 48 %. Table 3B is a summary of the life results for the agricultural application. The first point is a combination of taxi, idle and landing since they each require the same amount of power. The next two points represent take-off, spray and cruise and the last point
25、represents approach and descent. The power levels are approximately the same for both applications while the duration of each flight and the time at take-off power is different. Again the compressive life of the sun gear is the critical mode followed by the bending life of the input gear. The duty c
26、ycle life is 50,000 hours with variable factors and 92,398 hours with constant factors. The difference in this case is 46 %. A comparison of the two applications reveals the following in terms of % time at power: Twin Asricultural - Take-Of f High Power Low Power 3 94 6 12 51 49 Mission Profile Life
27、 = 41,494 hrs (Variable) = 79,963 hrs (Constant) 48 B difference 5 - STD-AGMA 95FTMB-ENGL 1795 D Ob87575 OOUi79b 7Tb W E Legend: 4 Design - Variable (Krn)(Kd) The Miners Rule analysis for the turboprop engine reduction gear system is a suitable example for evaluating the main theme of this paper. Th
28、e sun gear life, the critical mode, is shown in Figure 6 as a function of horsepower. The dark bars represent design life and the allowable life at each power point is shown as gray for the variable factors and clear for the constant factors. Note that the allowable lives are the same at the maximum
29、 operating load and, as the load decreases, the difference between variable and constant Km) Kd) lives increases. This is explained by the fact that a higher load utilizes a greater portion of the face width as well widening the profile contact footprint. verall the variable method gives more conser
30、vative clear for the constant factors. Note that the allowable lives are the same at the maximum operating load and, as the load decreases, the difference between variable and constant (Km)(Kd) lives increases. This is explained by the fact that a higher load utilizes a greater portion of the face w
31、idth as well widening the profile contact footprint. Overall the variable method gives more conservative and more realistic results. 1+8 L Variable Km & Kd Constant Km & Kd Hrs-Tot Horse- (Des. input Gear Sun Input Gear Sun power Life) PosM 1 GW Pos.Ml Gear Bend. Bend. Comp. Comp. Bend. Bend. Comp.
32、Comp. Stress Life Stress Life Stress Life stress Life - *i) (W (ksi) (h) (ksi) (W (ksi) (kS) 1 E+7 1 E+6 122. 3.30E05 142. 2.09E04 137. 4.09E04 6395 134. 6.08E04 43.6 1.09Ea6 35.7 5.04EO8 - Z = 25OOO 22.5 7.90E14 101. 1 .Om7 45.1 3.78E05 142. 2.WN 131. 8.92E4 38.3 5.80EO7 33.8 2.79EW 123. 2.73E05 1
33、E4 1 E+3 1 E+2 and more realistic results. Since the basic premise of this paper is that more realistic results can be achieved using the applicable K and C factors for each load point, it is worthwhile to note that the dynamic and alignment factors are not the only ones that might vary at each poin
34、t. In some instances, the operating temperature may exceed the allowable for the material in which case the temperature factor must be changed accordingly for that point. The major points discussed in this paper are as follows : Miners Rule is tedious to set up, but with the computing power availabl
35、e today, the calculating time is minimal. Knowledge of the mission profile/duty cycle during the design stage is required for proper gear sizing. It is realized, however, that multiple missions or applications often lead to the choice of a conservative design point. Using the correct values for all
36、factors at each load point will result in more realistic results. Proper evaluation will be greatly enhanced if these factors which vary with load and speed are incorporated into the computer program that is used to perform the design geometry, calculate stresses, and complete a Miners Rule analysis
37、 for overall life. Miners Rule may be further enhanced during the design phase by carefully analyzing each variable in both the bending and compressive stress equations to ensure that they are. properly accounted for in each load point calculation. For example, the operating temperature of the geari
38、ng may exceed the _ material allowable so that the proper temperature factor should be used for that point. 620 589 527 465 310 Horsepower Figure 6. Turboprop Reduction Gear Life Comparison Table 3B - Mission Profile For The Turboprop Gearbox, Agricultural Application Design Life = 25,000 hrs hDUt & Sun Gear Mission Profile Life = 50,000 lus (Variable) = 92,398 brs (Constant) 46 % difference 6
