a study on the bending stress of the hollow sun gear in a planetary gear train

1、 Journal of Mechanical Science and Technology 24 (2010) 29~32 www.springerlink.com/content/1738-494x DOI 10. 1007/s12206-009-1134-5 A study on the bending stress of the hollow sun gear in a planetary gear train? Kyung-E

2、un Ko*, Do-Hyeong Lim, Pan-Young Kim and Jinsoo Park Machinery Design Research Department, Hyundai Heavy Industries Co., LTD, Ulsan, 682-792, Korea (Manuscript Received May 2, 2009; Revised September 21, 2009; Accepted O

3、ctober 16, 2009) -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

4、----------------------------------------------------------------------------------- Abstract Generally, planetary gear type traveling reduction gear is composed of multiple planetary gear stages and has a hollow sun gear

5、 in the last stage planetary gear. In designing reduction gear, it is important to evaluate accurately the bending stress at the tooth root of the sun gear as the sun gear is the weakest component in the reduction gear

6、 system. Although bending stress can be calculated easily using gear standard codes such as the American Gear Manufacturers Association (AGMA) and International Organization for Standardization (ISO) 6336 for almost al

7、l gears, meticulous calculation is needed for the hollow sun gear because of its low backup ratio (rim thickness divided by tooth height) and comparatively large root fillet radius. In this study, a finite element analy

8、sis (FEA) is carried out to investigate the effect of rim thickness and root fillet radius on bending stress at the tooth root of the hollow sun gear. In standard codes, bending stress at the tooth root is calculated l

9、inearly with a constant slope for the backup ratio below 1.2. However, the effect of the rim thickness on bending stress is more complex in the planetary gear system. Bending stresses calculated by FEA with various back

10、up ratios and root filler radii are compared with the bending stresses calculated by the standard codes. Keywords: AGMA; Backup ratio; Bending stress; Fillet radius; Hollow sun gear; ISO; Rim thickness -----------------

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12、------------------------------------------------- 1. Introduction Planetary gear trains are used widely in the machinery industry, especially in automotive and aerospace applications, because of its advantages such as

13、compactness, coaxial design, and high performance. The crawler excavator is equipped with a traveling reduction gear composed of multiple planetary gear stages. In the last planetary gear stage, the traveling reducti

14、on gear has a hollow sun gear, which is usually the weakest component in the system for tooth bending stress because of its intrinsic low backup ratio (rim thickness divided by tooth height). Bending stress almost l

15、inearly increases as the backup ratio decreases. In this study, the actual effect of the backup ratio on the bending stress of the sun gear is investigated by direct structural analysis of a full reduction gear system

16、 for a crawler-type excavator. The bending stress is affected by the root fillet radius as well. Thus, bending stresses are calculated for the various backup ratios and root fillet radii, and then compared with thos

17、e calculated by the standard codes. 2. Bending stress calculation 2.1 Standard codes The most common methods of gear design and analysis are based on international gear standards such as the American Gear Manufacturers

18、 Association (AGMA) and International Organization for Standardization (ISO), where the formulas for gear tooth bending stress calculations are included. For example, for ISO 6336-3 [1], bending stress and nominal b

19、ending stress are calculated by Eq. (1) and Eq. (2), in which the effect of the backup ratio is considered by the rim thickness factor of YB, and the effect of root fillet radius is considered by the form factor of YF

20、 and the stress correction factor of YS. In the standards, these factors are calculated independently. 0 F F A V F F K K K K β α σ σ =(1) 0 tF F S B DTnF Y Y Y Y Y bm β σ =(2) As shown in Fig. 1, the rim thickness fac

21、tor is treated as constant 1.0 for the backup ratio above 1.2, and it almost linearly increases for the backup ratio below 1.2 in both AGMA and ISO standards. ? This paper was presented at the ICMDT 2009, Jeju, Korea

22、, June 2009. This paper was recommended for publication in revised form by Guest Editors Sung-Lim Ko, Keiichi Watanuki. *Corresponding author. Tel.: +82 52 202 0832, Fax.: +82 52 202 5495 E-mail address: kekopro78@hhi.

23、co.kr © KSME & Springer 2010 K.-E. Ko et al. / Journal of Mechanical Science and Technology 24 (2010) 29~32 31 (a) Backup ratio = 1.6, root fillet radius = 0.4 module (b) Backup ratio = 1.6, root fillet radius

24、 = 0.3 module (c) Backup ratio = 0.8, root fillet radius = 0.4 module Fig. 5. Maximum principle stress distributions in the hollow sun gear. in one mesh cycle. The bending stress occurred at the tooth root fillet as exp

25、ected. Some snapshots of the highest maximum principle stress occurrence are shown in Fig. 5, where the maximum normalized bending stress is the maximum bending stress divided by the maximum stress for a backup ratio

26、 of 1.32 and fillet radius of 0.4 module. Bending stress calculations by FEA have been attempted in some studies [4], but only two or three gear teeth have been modeled. In this study, all the structural effects of o

27、ther mechanical components and real contact conditions were considered. 3.1 Effect of rim thickness To compare the effect of backup ratio, all calculated maximum bending stresses are normalized by the maximum stress

28、for a backup ratio of 1.2 and plotted to a backup ratio in Fig. 6. It seems that the effect of the backup ratio above 1.2 may be negligible as indicated in the standards. However, the effect of the backup ratio belo

29、w 1.2 may be considerably overestimated. Backup RatioNormalized Bending Stresses0.5 0.8 1.0 1.3 1.5 1.8 2.0 2.31.01.31.51.82.02.32.5ISO standardFE analysisReference 4Fig. 6. Bending stress versus backup ratio (root fill

30、et radius = 0.4 module). Root Fillet Radius (module)Normalized Bending Stresses0.1 0.2 0.3 0.4 0.5 0.80.91.01.11.2ISO standardAGMA standardFE analysisFig. 7. Bending stress versus root fillet radius (backup ratio = 1.32

31、). For the range below 0.5, the standards do not give the guidelines. Meanwhile, it is noted in Ref. 5 that sudden catastrophic failure due to a crack through the rim thickness is prone to occur in case of a backup ra

32、tio below 0.5. Thus, the current standards seem to be conservative, as the backup ratio becomes smaller although the bending stress is not a direct cause of the rim through crack. 3.2 Effect of root fillet radius The

33、 influence of the root fillet radius on the bending stresses is summarized in Fig. 7. This figure plots the max. bending stresses normalized by the max. stress for a fillet radius of 0.3 module as a function of root f

34、illet radius. Bending stress increases as the root fillet radius decreases, and the effects of root fillet radius calculated by FEA are similar to those obtained by the formulas of the standards. Generally, 0.2~0.3

35、modules are recommended, and this study investigated comparatively larger root fillet radius up to 0.4, which results in notable stress reduction. 3.3 Interaction between the effects of rim thickness and root fillet r