1、 Journal of Mechanical Science and Technology 24(2010)2932 DOI 10.1007/s12206-009-1134-5 A study on the bending stress of the hollow sun gear in a planetary gear train Kyung-Eun Ko*,Do-Hyeong Lim,Pan-Young Kim and Jinsoo Park Machinery Design Research Department,Hyundai Heavy Industries Co.,LTD,Ulsa
2、n,682-792,Korea (Manuscript Received May 2,2009;Revised September 21,2009;Accepted October 16,2009)-Abstract Generally,planetary gear type traveling reduction gear is composed of multiple planetary gear stages and has a hollow sun gear in the last stage planetary gear.In designing reduction gear,it
3、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 system.Although bending stress can be calculated easily using gear standard codes such as the American Gear Manufacturers Association(AGMA)and Inter
4、national Organization for Standardization(ISO)6336 for almost all 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 analysis(FEA)is carried out
5、 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 linearly with a constant slope for the backup ratio below 1.2.However,the effect of the rim thickness on bend
6、ing stress is more complex in the planetary gear system.Bending stresses calculated by FEA with various backup 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 thicknes
7、s-1.Introduction Planetary gear trains are used widely in the machinery industry,especially in automotive and aerospace applications,because of its advantages such as compactness,coaxial design,and high performance.The crawler excavator is equipped with a traveling reduction gear composed of multipl
8、e planetary gear stages.In the last planetary gear stage,the traveling reduction 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 linearly in
9、creases 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 for a crawler-type excavator.The bending stress is affected by the root fillet radius as well.
10、Thus,bending stresses are calculated for the various backup ratios and root fillet radii,and then compared with those 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
11、 the American Gear Manufacturers 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 bending stress are calculated by Eq.(1)and Eq.(2),in which the
12、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 and the stress correction factor of YS.In the standards,these factors are calculated independently.0FFAVFFK K KK=(1)0tFFSBDTnFY Y Y Y Ybm=(2)As shown
13、 in Fig.1,the rim thickness factor 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,June 2009.This paperwas recommended for publication in rev
14、ised form by Guest Editors Sung-Lim Ko,Keiichi Watanuki.*Corresponding author.Tel.:+82 52 202 0832,Fax.:+82 52 202 5495 E-mail address:kekopro78hhi.co.kr KSME&Springer 2010 30 K.-E.Ko et al./Journal of Mechanical Science and Technology 24(2010)2932 Backup ratioRim thickness factorBackup ratioRim thi
15、ckness factor/Rtsh=Backup ratioRim Thickness Factor YB Fig.1.The rim thickness factor versus backup ratio in the standard codes.Fig.2.Geometry parameters for the shape of the tooth root in the standard codes.Meanwhile,YF and YS are calculated from many geometry parameters related to the root fillet
16、radius according to Eq.(3)and Eq.(4).The parameters are shown in Fig.2.26coscosFeFennFFnnnhmYsm=(3)12.31.211.20.132FeFnhFnFnsSFeFssYh+=+(4)2.2 FEA for planetary gear train To investigate precisely the influence of rim thickness and root fillet shape in hollow sun gear design,an integrated finite element analysis(FEA)including gear contact,roller bearing,carriers,housing,and shafts was carried out.As there is always a contact point between two meshed gear surfaces,conventional FE analysis becomes
