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maximum deflection is unknown. As a result, the simulations did not model this behavior. The method to predict crack consuming since every model. For the method the computational trajectories the achievements would of this thesis approach closer to developing a numerical tool geometries. Critical areas that must be understood more accurate crack By incorporating trajectories and growth non-proportional arbitrary three dimensional and theories for predicting the moving load discrete load step had to be analyzed to be more practical to a gear designer, time and implementation In summary, under 8.2 Recommendations for a full pinion improvements in to be made. brought in three complex three models, the work crack growth rates for Future The accomplishments the current gear dimensions were dimensional geometry, extended the current and crack trajectories. • A testing program produced many new questions and issues design safety. centered on fatigue crack growth non-proportional loads should be carried out. A more of crack behavior in this type of loading environment accuracy of fatigue fundamental behavior, and capabilities Research of this thesis a gear design's design identified. related to simulating fatigue crack growth in spiral bevel gears. Future research focused on the following areas will further assist the development of numerical tools to evaluate time to evaluate safety aspects of gear in greater detail prior to predicting rates loading, crack fatigue have was crack growth the tests do rates and trajectories fundamental is needed rate models. To gain not have to be conducted from understanding to enhance the insights into the with spiral bevel gears. To judge the correctness of the predictions in this thesis, however, tests on spiral bevel gears that record crack growth rates and trajectories more over a time period are necessary. Such test data are essential to confirm the accuracy of the simulations and to evaluate the proposed method for predicting crack growth under • the moving A more with detailed tooth load. understanding an uncracked scenario would process could gear tooth be studied require a fully three between two of the contact is required. either The experimentally dimensional, mating between gears. the findings could be applied to crack the simulations would model more load the gear tooth redistribution or numerically. LEFM, Once a cracked effects Numerical mating in this studies and contact analysis of the rolling redistribution effects are captured, growth simulations. The expectation accurately the observed behavior is that in real failures. • The analyses in this thesis considered only However, a gear tooth is subjected to a variety the contact normal between loads the mating over the contact gears ellipse loads normal to the of loads in operation. also produces area. Gears frictional in rotorcraft forces tooth surface. For example, along applications with the operate at elevated temperature, and, therefore, thermal effects might be included. addition, the rotation of the gear produces centrifugal forces. Dynamic loads NASA/CR--2000-210062 103 In are producedfrom the contactbetweenthe matinggearsin conjunctionwith the high loading frequency. Severalresearchers have alsomodeledthe residualstressesin a gear,which result from the differencein hardnessbetweenthe caseandcore, in numerical analysesby thermal loads. Parametric studies to determine the significanceof all theseloading variableson predictedfatigue crack growth in a spiral bevelgearis imperativeto the developmentof numericalgeardesigntools. Furtherwork to enhancethe speedof the numericalanalysesand increasethe SIF accuracywould be beneficial. One methodto improve the accuracyis to usethe FEM. However, meshing three dimensional volumes with cracks introduces additionaldifficulties. Researchis currentlyunderway,andshouldbe continued, to overcomethesemeshingdifficulties. The computationaltime will continueto decreaseas computertechnology rapidly advances. The overall objective of developinga practical and accuratenumericaldesigntool for any type of gear is foreseeablein thenearfuture. NASA/CR--2000-210062 104 APPENDIX 4000 A q i 3000 J 2000 -i Load 1 + Load 2 Load 3 Load 4 1000 Load 5 Load 6 ---.+.-Load 7 Load 8 -1000 -- Load 9 Load 10 Load 11 -2000 -3000 z -4000 : i Figure Crack font position (Orientation: heel to toe) A. 1: Mode II SIF distribution for load steps one through eleven. 4OOO 3OOO Load 1 2000 Load 2 Load 3 Load 4 1000 Load 5 Load 6 _1 6 11 16 _ . _ 4"1 5 ' _1 ---+- Load 7 Load 8 -1000 -- Load 9 Load 10 Load 1l -2OOO -3OOO Crack font position (Orientation: heel to toe) -4OOO Figure NASA/CR--2000-210062 A.2: Mode III SIF distribution 105 for load steps one through eleven. APPENDIX Figure B. 1: Fatigue An additional tooth surface. addition, two several such manufacturing of the initial of interest in Figure 6.5 at 360x is captured in Figure (a) and 1,000x B.3. The (b). figure is of the The horizontal lines are the grooves from the machining of the gear. In pits are observed on the surface. These pits could have resulted from variables the teeth, point striations B flaw as particles flaws, that were surface size from which fatigue caught wear, etc. cracks 5_ NASA/CR--2000-210062 106 on the surface during meshing The cuts and pits give an indication may originate. of Figure B.2: Typical Figure NASAJCR_2000-210062 picture of flat, polished area on tooth #11 (400×). taken near location B in Figure 6.4. B.3: Machining grooves and pits on tooth 107 surface Photograph (280×). was APPENDIX C 20000 7 ] % "NN 15000 .... Mode I _ Load 1 Mode II _ Load 5 i _ _Load -_- t-l--_"- 11 16 21 Crack front position (Orientation: toe to heel) [ _i -5000 Figure C. 1" SIFs from toe-shifted load steps 11 one, five, and eleven. 20000 Mode I .... i ................. --'-Mode II _ Load i _ Load5 _ Load 11 / 15000 i 5ooo i 0 . -_--_--_ --_--_--A--'_-_'-_" J ....... _'-_- -_-____'_'_ - h"--x- --x"- _ - _- -_" - i" -_" - _ - -x-__ n'_ i- -i" -i" -I- 7l- -Ii" -S" - m--m- _i- -n" -_ -m" -m"- m"- m" :f _I ...... 6_ -11 :16 -A. =11"_ NASA/CR--2000-210062 _'_i _ 7-' Crack front position (Orientation: toe to heel) ;[..... Figure =2_1 _ C.2: SIFs from heel-shifted load steps 108 one, five, and eleven. REFERENCES AGMA AGMA 1983 246.02A, American AGMA 1996 Alban Alban, L.E., Society for Metals. Alban, 1986 AMS 1988 ASTM1997 C., 1988, 33, no. 2, pp. 3-14. 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