1、97FTMlO UltraSafe Gear Systems for Critical Applications-Initial Development by: Raymond J. Drago, Ashok D. Sane, Frederick W. Brown, Boeing Defense Note that all major gear, shaft, and rim dimensions of the modified configuration are the same as those of the existing gear except for the rim width w
2、hich is increased to accommodate the groove width. Gear face width and ail other gear parameters are however identical. The width and the depth of the groove (below the root of the tooth) can be altered to evaluate several geometries under this modifications. During initial planning, a constant groo
3、ve width of .25 inch and four groove depths of .07, .14, .21 and .27 inch were considered for analytical evaluation. Accordingly, the existing gear ( Gear 1) and the gear with .27 inch depth (Gear 5) were first analyzed. These analyses indicated that a deeper and wider groove may develop a needed st
4、ress pattern for cracks to propagate in a desired direction for failsafe operation. Therefore, it was decided to drop cases with smaller groove depths (Gears 2, 3 both are .25 inch wide. Figure 5-IC Gear 1 FEM for Tooth 1 Backup U Figure 5-1D Gear FEM for Tooth 1 Final Geometry Page 8 of 22 COPYRIGH
5、T American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 77FTMLO-ENGL 1777 Figure 5-2A Gear 1 Fine Mesh FEM of First Tooth Figure 5-2B Gear 1 Transition Mesh FEM of Tooth Figure 5-2C Gear Tooth 1 Coarse Mesh FEM of Tooth 6 Two bearings supporting the shaft are
6、 simulated by two multi point constraints each consisting of NASTRAN 14 RBE2 elements extending from the center of bearing on the axis of rotation to the nodes on the inner surface of the shaft as illustrated in Figure 5-6. The nodes at the center of both bearings are constrained in the global trans
7、lational DOF (degree of freedom) UY Gear 5 and 6 being identical in applied loading. The loads applied on all gears are listed in Table 5-2 (node points are shown in Figure 5-7). Figure 5-6 Typical Bearing Simulation With Rigid Elements Figure 5-7 Applied Load Line, Gear 1, Tooth 1 Page 10 of 22 COP
8、YRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 97FTML-ENGL 1997 Figure 5-8 Applied Load Line, Gears 5 the rim area adjacent to groove and the tooth root are the two critical regions of concern. The tabulated stresses also include alternating maj
9、or principal stresses. These are calculated by finding the maximum and minimum values of major principal stresses on a given tooth. The maximum stresses occur on Tooth 1 on which the load is applied. Fringe plots are therefore included to show stress distribution on both tension (load side) as well
10、as compression side of Tooth 1. Assuming that the gear is rotating slowly, the major principal stress at desired locations of all teeth were extracted to determine the maximum and minimum values at those locations cf any given tooth during one rotation cycle. The alternating major principal stresses
11、 were then computed from these maximum and minimum values. To extract stress on all teeth we examined fringe plots at the inner surface of the two halves obtained by cutting the gear through the center of its tooth face width. These two half parts are identified as Sections 1 and 2 in Figure 6-1 whi
12、ch shows isometric views of the two parts. Figure 6-2 shows zoomed side views of partial Section 1 and 2. For clarity, Sections 1 and 2 are also depicted in Figures 6-3 and 6-4, respectively showing isometric views of partial sections. The maximum and minimum stress values can be easily be obtained
13、by examination of fringe plots. The major principal stress fringe plot for Tooth 1 of Gear 1 are shown in Figure 6-5 and 6-6; Figure 6-5 shows the tension or load side while Figure 6-6 shows the compression side. The maximum major principal stress at root of Tooth 1 and in the rim near the center ac
14、ross face width is 43517 and 6228 psi, respectively. For consistency, we will use the upper end of the stress fringe plot bands for the maximum stress values and the average of the band for the minimum values while discussing or comparing results. As expected, the stresses on the inner face of Secti
15、on 1 and Section 2 (created by cutting through center of tooth face width) are about the same. Therefore, stresses are presented and discussed only for Section 1 in this report. The maximum stress at the tooth root and in the rim center based on Section 1 stress plots shown in Figures 6-7 and 6-8 is
16、 43517 and 6231 psi, respectively. The minimum major principal stress at these locations was determined by examining the stress plots of Tooth 14 (180 degree from the loaded Tooth 1) and Tooth 28 Cjust behind the loaded Tooth 1) and the inner surface of Section 1. The Stress plots of Tooth 14 and 28
17、 are not included in this report but the values are listed in Table 6-1 for all gears. The minimum major principal stress at the tooth root and near the rim center for Gear 1 is -290 and -170 psi, respectively. The alternating stresses at these two locations of Gear 1 based on the maximum and minimu
18、m values of the major principal stress are 21904 and 3200 psi. Similar stress plots were also generated for Gear 5 and 6; Figures 6-9 through 6-12 show Gear 5 stresses while Figure 6-1 3 through 6-16 present stresses predicted for Gear 6. The maximum, minimum and alternating major principal stresses
19、 at the tooth root and adjacent to the rim groove were extracted for Gear 5 and 6 from these plots using the same process as that for Gear 1 above. These stress values are summarized in Table 6-1. As seen from this table, stresses in the tooth root of all gears are about the same, grooved Gears 5 an
20、d 6 showing slightly higher values of the maximum and alternating major principal stress. However, as expected, introducing a groove in the rim shows a pronounced increase in the rim stress level in the rim adjacent to groove. The rim maximum stress in Gear 5 and 6 is about 2.4 times that in ungroov
21、ed Gear 1 at the same rim location. The grooved gears (Gear 5 and 6) indicate the maximum major principal stress in the rim of about 15ooO psi compared to 6228 psi in ungooved Gear 1. The alternating stress in the rim with groove is about 7400 psi compared to 3200 psi in the ungrooved gear. Table 6-
22、1 also shows that the stresses in Gear 5 and 6 are nearly same, indicating that increasing the groove depth by .10 inch (Gear 6) over .27 inch depth below the root of Gear 5 while keeping the groove width constant at .25 inch resulted in negligible changes in predicted stresses. This suggests the ge
23、ar configuration with one more increased groove depth may be needed to evaluate the effect of depth. Additionally, one or two cases with increased groove width would be required to evaluate the effect of groove width on stresses. The stress plots presented for Gears 5 and 6 show high stresses in the
24、 grooved region of the rim compared to the ungrooved gear but the stress results available so far are insufficient to indicate a possible direction of propagation of a crack initiating at the critical tooth root region. After evaluation of a few more gear configurations, a follow up crack growth ana
25、lysis would be required to confirm if a crack initiating at the tooth root would indeed follow a preferred path through the rim (Figure 2-1) keeping one half of the gear width intact for failsafe operation. This analysis is currently underway and will be supported by single tooth fatigue testing as
26、well. Since Tooth 1 has the highest stresses of all gear configurations, displacements would be high as well on the same tooth. All components of displacements and total displacement fringe plots for Tooth 1 were therefore plotted and evaluated for all gears to ensure that high unacceptable displace
27、ments are not caused by the groove. Figure 6-17, 6-18, 6-19 and 6-20 show the radial, tangential, axial and the total displacement on Tooth 1 of Gear 1. Figures 6-21 through 6-28 show the same plots for Gear 5 and 6. An examination of these plots shows that displacement pattern on ungrooved and groo
28、ved gears is similar and displacement magnitude is about the same. Page 11 of 22 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 77FTMLO-ENGL 1997 m 0b7575 000515b 047 Model 3ear 1 TABLE 5-2 APPLIED GEAR TOOTH CONTACT LOADS Nodes Force (lbs) R
29、adial Tangential Axial 2019 135.52 247.95 0.0 3ear5 ifjTs, 2 7.1 73. 23273. 1 YC73. ;,4,77- i cxi73. cr174. 3274. -1 926. -61 26. -1 0326. * Di 3. -1 4526. Figure 6-13 Gear 6, Tooth 1, Tension Side Major Principal Stress (PSI) b87575 0005Lb 578 E Figure 6-14 Gear 6, Tooth 1, Compression Side Major P
30、rincipal Stress (PSI) 50073. ;3 5Ei 73. 3 1 CTA. 27474. 23274. 19075. I 0675. G47. 22?8. -1 9L?:3. -61 23. -10323. -14523. i 4az. Figure 6-15 Gear 6, Section 1 Major Principal Stress (PSI) at Inner Surface (Lkg +X) -14522. Figure 6-16 Gear 6 Zoomed Section 1, Major Principal Stress (PSI) at Inner Su
31、rface (Lkg +X) Page 16 of 22 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services STD-AGHA 77FTMLU-ENGL L777 Ob87575 0005LbL i-IOLI Figure 6-17 Gear 1, Tooth 1, Radial Displacement (UX, Inch) Figure 6- 18 Gear 1, Tooth 1 , Tangential Displacement (UY, Inch
32、) Figure 6-19 Gear 1, Tooth 1, Axial Displacement (UZ, Inch) Figure 6-20 Gear 1, Tooth 1, Total Displacement, Inch Figure 6-2 1 Gear 5, Tooth 1 , Radial Displacement (UX, Inch) -.NI7103 -.OU8929 - a19385 W Figure 6-22 Gear 5, Tooth 1, Tangential Displacement (UY, Inch) Page 17 of 22 COPYRIGHT Americ
33、an Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGHA 97FTMLO-ENGL 1997 m Ob87575 0005Lb2 340 m Figure 6-23 Gear 5, Tooth 1, Axial Displacement (UZ, Inch) Figure 6-24 Gear 5, Tooth 1, Total Displacement, Inch Figure 6-25 Gear 6, Tooth 1, Radiai Displacement (UX, In
34、ch) t Figure 6-26 Gear 6, Tooth 1, Tangential Displacement (UY, Inch) Figure 6-27 Gear 6, Tooth 1, Axial Displacement (UZ, Inch) Figure 6-28 Gear 6, Tooth 1, Total Displacements, Inch Page 18 of 22 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services STD-A
35、GHA 97FTHLO-ENGL 1797 = Ob87575 0005Lb3 287 D w Figure 6-29 Typical Locations For Displacement Evaluations 7.0 MODEL SIMPLIFICATION The analytical models discussed in Section 4 and 5 are significantly large therefore requiring considerable time in model development, analysis and post processing resu
36、lts. In an attempt to increase efficiency and cut down modeling and analysis time, we developed a simplified model of Gear 5. This modified model shown in Figure 7-1, includes the four fine mesh teeth of Gear 5 modei as is and simulates the remaining gear rim, web and shaft with beam elements. The r
37、im and the web are simulated by beam elements forming two circular rings and the shaft is modeled with a set of beams forming three circular rings connected by beams placed on the shaft circumference and running in the gear axial direction. The bearings were simulated by two RBE2 element each consis
38、ting of 14 rigid elements as in Gear 5 model. The properties used for the beam elements were generally based on approximate cross-sectional area the component simulated by the beam under consideration and on judgement. Note that these beam properties provided only an approximate simulation of the ge
39、ar component they represented; no additional effort was made to scientifically derive precisely accurate properties for this exploratory attempt at model simplification. This simplified model consist of 8048 solid elements, 186 beams and 2 RBE2 elements in a mesh of 10631 nodes. This modified or sim
40、plified model is significantly smaller than Gear 5 model which included 30900 nodes and 24248 solid elements. A static analysis was performed with the modified model of Gear 5 using the same loading as that for Gear 5 model. Figure 7-2 shows a plot of predicted major principal stress for tension (lo
41、aded) side of Tooth 1. The stress pattern predicted by the simplified model is generally similar to results obtained by the detailed Gear 5 model shown in Figure 6-9. However, the magnitude of predicted stresses by the simplified model are generally higher indicating that the beam properties used to
42、 simulate gear components may be stiffer than the actual components. Figure 7- 1 Gear 5, Simplified Model Figure 7-2 Gear 5, Simplified Model Tooth 1, Tension Side, Major Principal Stress This is confirmed by smaller displacements predicted by this model, shown in Figure 7-3, as compared to those pr
43、edicted by the detailed model shown in Figure 6-24. The simplified model also shows displacement fringe lines running parallel to the axis of rotation (that is displacements are constant across the face width at any given radius) while the detailed model predicts displacement fringes running diagona
44、lly across the face width. These differences in displacement response indicate that: a) the simplified modei beam stiffness representation is inaccurate since it cannot predict the shaft bending response and the resulting effect on gear tooth, rim and web displacements and b) the properties used for
45、 beam elements are simulating a gear stiffer than the actual. At this point it became apparent that a more involved and dedicated effort would be required to develop an acceptable simplified model that provides good correlation of Page 19 of 22 COPYRIGHT American Gear Manufacturers Association, Inc.
46、Licensed by Information Handling ServicesSTD-AGMA 77FTMLO-ENGL 1997 predicted stress and displacement response with the detailed model. Since developing a simplified model was beyond the scope of the current task, it was decided to drop this effort and continue to use the detailed simulation of sele
47、cted gear configurations with solid finite elements. .o005838 Figure 7-3 Simplified Gear 5 Model, Tooth 1, Displacement Magnitude 8.0 BASIC GEAR TOOTH OPTIMIZATION The main reason for investigating the dual rim concept described herein is to provide a fully redundant load path for the entire toothed
48、 element section. In addition to this approach, the safety of the gear can be further improved by providing a multiplicity of contact points within the gear mesh itself, thus providing a kind of internal load path redundancy. ?his approach is not competitive to the dual rim concept but rather it is
49、complementary and, in some cases, actually makes the implementation of the dual rim concept simpler. Focusing on tooth mesh design then, several approaches for multiple load paths in gear meshes have been investigated, including: 1 High profile contact ratio designs which are spur or helical gears with a minimum two teeth in contact at all times in the transverse plane. 2 High axial or face contact ratio designs - helical gears with a minimum of two teeth in contact (across face) at all times. These concepts were explored by analysis to determine their relative merit. In each c
