1、13FTM07 AGMA Technical Paper Finite Element Analysis of a Floating Planetary Ring Gear with External Splines By Dr. V. Kirov and Dr. Y. Wang, Caterpillar Global Mining, LLC 2 13FTM07 Finite Element Analysis of a Floating Planetary Ring Gear with External Splines Dr. Vanyo Kirov and Dr. Yun Wang, Cat
2、erpillar Global Mining, LLC The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract This study investigates the stresses and deflections of a floating ring gear with ext
3、ernal splines working in a large planetary wheel motor of a mining truck. Such calculations carried out with conventional engineering approaches described in popular standards and textbooks are not comprehensive because of the complexity of the problem. These approaches can give us good stress numbe
4、rs for non-floating gears and some guidance about the rim thickness factor but they lack the capabilities to effectively calculate the deflections and their influences on the stresses, especially for floating gears. Moreover they cannot calculate an entire gearing system and the interdependent influ
5、ences of the different components. The model studied consists of a floating ring gear driving a torque tube. The ring gear is driven through internal gear meshing by three planets and it transmits the torque to the torque tube through its external splines. The torque tube transmits the motion to the
6、 hub and the truck tires. A nonlinear static analysis of the ring gear and torque tube was conducted in ABAQUS. Linear 8-node hex elements and linear tetra elements were used to model the ring gear and torque tube. External torque was resolved into corresponding tangential force, which was then appl
7、ied directly onto three of the ring gears internal teeth. Contact pairs were used to capture the load transfer between the ring gear and torque tube through the splines. The results show that the deflections in the ring gear were so excessive that about one-tenth of the spline teeth were actually tr
8、ansmitting torque against the common engineering understanding that only half of the spline teeth are typically engaged. The crowning of the spline teeth had also effect on the stresses though quite small compared to the deflections. Conclusions and recommendations were made about the effectiveness
9、of the design. Copyright 2013 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 September 2013 ISBN: 978-1-61481-064-3 3 13FTM07 Finite Element Analysis of a Floating Planetary Ring Gear with External Splines Dr. Vanyo Kirov and Dr. Yun Wang, Caterp
10、illar Global Mining, LLC Introduction The design of a planetary ring gear is always a challenge due to the contradictive requirements which it must comply with. On one hand the ring gear should be strong and stiff enough to successfully carry the applied load. On the other hand, it should have as sm
11、all volume as possible to account for the radial restraints of a planetary gearbox imposed by the truck tires. Additionally, the ring gears are floating in many cases. Altogether, the designer job becomes very complicated. One of the design issues of the strength calculations of the ring gear is tha
12、t none of the American Gear Manufacturers Association (AGMA) standards, including ANSI/AGMA 2001-D04 1, rate internal gears. No acceptable methodology is defined to calculate geometry factor for internal gears, following the method for external gears in ANSI/AGMA 908-B89 2. ANSI/AGMA 2001-D04 provid
13、es guidelines for the calculations of the ring gear rim thickness by introducing the rim thickness factor. Very often the ring gears have external spline teeth which transmit the torque to the final driven member of the gearbox. ANSI/AGMA6123-B06 3 gives a methodology for calculating splines which i
14、nclude shear capacity, fretting and wear as well as ring bursting. The standard assumes that 50% of the splines are carrying the torque. Other approaches suggest different ways to calculate splines 7. The stresses in the gear and the spline teeth are influenced by the deflections of the gear itself
15、and also by the deflections of the entire gearbox. AGMA does not have published codes for calculating these deflections. It stresses in different standards like ANSI/AGMA 2001-D04 the importance of determining the deflections, and provides examples of using Finite Element Analysis (FEA) methods. Bec
16、ause of these difficulties in the engineering design of ring gears more and more researchers are using modern calculation methods like FEA. One researcher showed that when properly used, FEA and AGMA methods give closer results 6. In this study a ring gear assembly is evaluated using FEA software in
17、 order to determine the stresses and deflections in the system. Design model The assembly consists of a carburized ring gear and a through hardened torque tube (Figure 1) used in the wheel motor of large electrically driven mining truck. The torque path comes from three planet gears (not shown and u
18、sed in the study), whose teeth are meshed with the internal teeth of the ring gear. The ring gear transmits the torque to the torque tube through its external splines. The torque tube transmits the torque from its internal splines to the hub through a bolted joint and from there to the truck tires.
19、The meshing areas between each planet and internal gear teeth are marked as zones 1, 2 and 3 (Figure 2). Each one is modeled with different root radii and crowning of the external splines. The gear and spline teeth are ground to quality 6 per ANSI/AGMA 2015-1-A01 4 and ANSI/AGMA 20015- 2- A06 5. Loa
20、ding and constraints The applied torque is assumed to be equally divided among the three planets per ANSI/AGMA6123-B06 (Figure 3) which recommends a mesh load factor of “unity” for high speed and high quality gears for the presented case. For the purpose of this study the force acting on each tooth
21、is applied at the highest point of single tooth contact for each location (Figure 4) and assumed to be equally distributed along the line of contact which means using load distribution factor of “unity”. The application of the force transmitted through the splines is determined by the FEA software.
22、The ring gear is floating in all directions. The radial and circular movement of the gear is limited by the backlash in the assembly and the axial movement is restricted by axial stoppers, which are not shown. 4 13FTM07 Figure 1. Ring gear and torque tube assembly view Figure 2. Ring gear splines ro
23、ot radii and crowning 5 13FTM07 Figure 3. Force location on the internal gear teeth of the ring gear Figure 4. Force application on the internal gear teeth: Ft tangential component of the gear tooth force; Fc gear tooth force 6 13FTM07 FEA modeling A nonlinear static analysis of the ring gear and to
24、rque tube was conducted in ABAQUS. The ring gear teeth and the splines of the ring gear and torque tube were modeled with a fine mesh of 8-node brick elements. The model transitioned to a coarser mesh of linear tetrahedral elements away from the splines (Figure 5). Using a cylindrical coordinate sys
25、tem, the loads were applied on three internal teeth of the ring gear. Contact pairs were used to capture the interaction between ring gear and torque tube splines. These contact pairs were defined between the mating surfaces of the ring gears external splines and the torque tubes internal splines. T
26、he model had about 3.5 million nodes and the analysis was run on a supercomputer in order to obtain results in a reasonable time frame. Results FEA snapshots of only the overall displacement magnitude of the ring gear and the splines stresses are shown on Figure 6 and Figure 7. Von Mises, max and mi
27、n principle root stresses in locations I, II and III of only one tooth flank (Figure 8) of the ring gear teeth and external splines, and torque tube internal splines, are shown on the graphs of Figures 9 through 17. Figure 5. Picture on the right shows a zoom in view of the mesh around the ring gear
28、s external splines Figure 6. Overall displacement in inches of the ring gear 7 13FTM07 Figure 7. Von Mises stresses of the ring gear external splines in zone 1 Figure 8. Location of the root stresses presented in the table Figure 9. Von Mises root stresses of the ring gear external splines 8 13FTM07
29、 Figure 10. Von Mises root stresses of the ring gear internal teeth Figure 11. Von Mises root stresses of the torque tube internal splines Figure 12. Max principle root stresses of the ring gear external splines 9 13FTM07 Figure 13. Max principle root stresses of the ring gear internal teeth Figure
30、14. Max principle root stresses of the torque tube internal splines Figure 15. Min principle root stresses of the ring gear external splines 10 13FTM07 Figure 16. Min principle root stresses of the ring gear internal teeth Figure 17. Min principle root stresses of the torque tube internal splines Co
31、nclusions The analysis shows heavy triangulation of the ring gear (Figure 6). Only about 10% of the splines teeth carry most of the load at the same time. Close analysis of these stressed teeth (not shown) points out that the stresses are not evenly distributed and only few teeth at a time take the
32、highest load. This leads to the conclusion that the fatigue calculations of splines with similar behavior are as important as the shearing and wearing calculations. In many instances the principle stresses are higher than the allowable fatigue stress numbers per ANSI/AGMA 2001-D04. The higher crowni
33、ng increases the stresses and that is why the stresses in zone 2 are generally smaller than the other zones. The smaller root radius increases the stress and this is clearly seen in the highest stresses in zone 3. The results from the FEA study confirm the field feedback. 11 13FTM07 The FEA is an ef
34、fective method of analyzing and predicting the complicated deflections of floating planetary ring gears. Limitations of the study Only two parts of the entire wheel motor are used in this study the ring gear and the torque tube. If other parts like the hub, the wheel bearings, the planets, etc. and
35、stress influencing factors like the truck load were added, the stiffness of the investigated mechanical system would change and the results would be different. The force transmitted from the planets to the internal teeth of the ring gear was applied at the highest point of single tooth contact and u
36、niformly distributed along the tooth surface. In reality the force may not be at that point for flexible systems and certainly would not be distributed evenly. Only three zones of the ring gear were modeled with different crowning and root radii which limit the understanding of their influence on th
37、e stresses. Acknowledgements The authors would like to thank to Srinivas Rallabandi and Deepak Rotti who worked on the FEA modeling and analysis, as well as Nick Dame who worked on the solid models. References 1. ANSI/AGMA 2001-D04, Fundamental Rating Factors and Calculation Methods for Involute Spu
38、r and Helical Gear Teeth 2. AGMA 908 - B89, Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth 3. ANSI/AGMA 6123-B06, Design Manual for Enclosed Epicyclic Gear Drives 4. ANSI/AGMA 2015-1-A01, Accuracy Classification System - Tange
39、ntial Measurements for Cylindrical Gears 5. ANSI/AGMA 2015-2-A06, Accuracy Classification System - Radial Measurements for Cylindrical Gears 6. Kirov, V., Comparison of the AGMA and FEA Calculations of Gears and Gearbox Components Applied in the Environment of Small Gear Company, 10FTM05 7. Silvers, J., Sorensen, C.D., and Chase, K.W., New Statistical Model for Predicting Tooth Engagement and Load Sharing in Involute Splines, 10FTM07.
