0
Research Papers: Design of Mechanisms and Robotic Systems

Effects of Tooth Indexing Errors on Load Distribution and Tooth Load Sharing of Splines Under Combined Loading Conditions

[+] Author and Article Information
J. Hong

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
201 W. 19th Avenue,
Columbus, OH 43210
e-mail: hong.383@osu.edu

D. Talbot, A. Kahraman

Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
201 W. 19th Avenue,
Columbus, OH 43210

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 22, 2014; final manuscript received November 27, 2014; published online January 9, 2015. Assoc. Editor: Qi Fan.

J. Mech. Des 137(3), 032601 (Mar 01, 2015) (10 pages) Paper No: MD-14-1252; doi: 10.1115/1.4029282 History: Received April 22, 2014; Revised November 27, 2014; Online January 09, 2015

In this paper, influences of tooth indexing errors on load distribution and tooth load sharing of spline joints are investigated by modifying an existing semi-analytical load distribution model for side-fit involute splines. Two commonly observed loading conditions, namely (i) combined torsion and radial loads representative of a spline joint of a spur gear with shaft and (ii) combined torsion, radial loads, and tilting moment representative of a spline joint of a helical gear with shaft are considered in this study. Numerical results of an example spline having (i) no tooth indexing error, (ii) a single tooth with indexing error, and (iii) a random sequence of tooth indexing errors under these two loading conditions are presented to demonstrate the effects of tooth indexing errors. In addition, a practical study of the robustness to manufacturing tolerances is also presented where probability distributions of load sharing factor of the critical tooth of an example spline designed to certain manufacturing tolerance classes are obtained with a large number of randomly generated indexing error sequences.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Volfson, B. P., 1982, “Stress Sources and Critical Stress Combinations for Splined Shaft,” ASME J. Mech. Des., 104(3), pp. 551–556. [CrossRef]
Barrot, A., Paredes, M., and Sartor, M., 2006, “Determining Both Radial Pressure Distribution and Torsional Stiffness of Involute Spline Couplings,” Proc. Inst. Mech. Eng., Part C, 220(12), pp. 1727–1738. [CrossRef]
Barrot, A., Paredes, M., and Sartor, M., 2009, “Extended Equations of Load Distribution in the Axial Direction in a Spline Coupling,” Eng. Fail. Anal., 16(1), pp. 200–211. [CrossRef]
Chase, K. W., Sorensen, C. D., and DeCaires, B. J. K., 2010, “Variation Analysis of Tooth Engagement and Loads in Involute Splines,” IEEE Trans. Autom. Sci. Eng., 7(4), pp. 746–754. [CrossRef]
Kahn-Jetter, Z., and Wright, S., 2000, “Finite Element Analysis of an Involute Spline,” ASME J. Mech. Des., 122(2), pp. 239–244. [CrossRef]
Tjernberg, A., 2001, “Load Distribution in the Axial Direction in a Spline Coupling,” Eng. Fail. Anal., 8(6), pp. 557–570. [CrossRef]
Tjernberg, A., 2001, “Load Distribution and Pitch Errors in a Spline Coupling,” Mater. Des., 22(4), pp. 259–266. [CrossRef]
Ding, J., Leen, S. B., Williams, E. J., and Shipway, P. H., 2008, “Finite Element Simulation of Fretting Wear-Fatigue Interaction in Spline Couplings,” Tribol. -Mater., Surf. Interfaces, 2(1), pp. 10–24. [CrossRef]
Medina, S., and Olver, A. V., 2002, “Regimes of Contact in Spline Coupling,” ASME J. Tribol., 124(2), pp. 351–357. [CrossRef]
Medina, S., and Olver, A. V., 2002, “An Analysis of Misaligned Spline Coupling,” Proc. Inst. Mech. Eng., Part J, 216(5), pp. 269–279. [CrossRef]
Hong, J., Talbot, D., and Kahraman, A., 2014, “Load Distribution Analysis of Clearance-Fit Spline Joints Using Finite Elements,” Mech. Mach. Theory, 74, pp. 42–57. [CrossRef]
Hong, J., Talbot, D., and Kahraman, A., 2014, “A Semi-Analytical Load Distribution Model for Side-Fit Involute Splines,” Mech. Mach. Theory, 76, pp. 39–55. [CrossRef]
STANDARD ANSI B92.1, 1996, Involute Splines and Inspection, SAE, Warrendale, PA.

Figures

Grahic Jump Location
Fig. 1

(a) Schematic side view of a spline joint consisting of an external spline and an internal spline and (b) schematic representation of tooth indexing errors of a few example external spline teeth

Grahic Jump Location
Fig. 2

Schematic side view of the external spline under combined loading condition at four sample rotational positions of (a) 0 deg, (b) 90 deg, (c) 180 deg, and (d) 270 deg

Grahic Jump Location
Fig. 3

Load distributions of the example spline having no tooth error under combined torsion and radial loads, at different rotational positions

Grahic Jump Location
Fig. 4

Load sharing factors of (a) tooth #5, (b) tooth #10, (c) tooth #15, and (d) tooth #20, at different rotational positions spanning a full rotational cycle, for the example spline having no tooth error under combined torsion and radial loads

Grahic Jump Location
Fig. 5

Load distributions of the example spline having single tooth indexing error under combined torsion and radial loads, at different rotational positions

Grahic Jump Location
Fig. 6

Load sharing factors of (a) tooth #10, (b) tooth #13, and (c) tooth #15, at different rotational positions spanning a full rotational cycle, for the example spline having single tooth indexing error (tooth #13) and comparison to the no tooth error case, under combined torsion and radial loads

Grahic Jump Location
Fig. 7

Load distributions of the example spline having random tooth indexing errors under combined torsional and radial loads, at different rotational positions

Grahic Jump Location
Fig. 8

Load sharing factors of (a) tooth #6, (b) tooth #14, (c) tooth #17, and (d) tooth #18, at different rotational positions spanning a full rotational cycle, for the example spline having random tooth indexing errors and comparison to the no tooth error case, under combined torsion and radial loads

Grahic Jump Location
Fig. 9

Load sharing factors of the example spline design to (a) tolerance class 7 and (b) tolerance class 6, at different rotational positions for 100 sets of random tooth indexing errors, under combined torsional and radial loads

Grahic Jump Location
Fig. 10

The probability distribution of the load sharing factor of the critical tooth of the example spline designed to (a) tolerance class 7 and (b) tolerance class 6, under combined torsional and radial loads

Grahic Jump Location
Fig. 11

Load distributions of the example spline having no tooth error under combined torque, radial loads, and tilting moment loading, at different rotational positions

Grahic Jump Location
Fig. 12

Load sharing factors of (a) tooth #5, (b) tooth #10, (c) tooth #15, and (d) tooth #20, at different rotational positions spanning a full rotational cycle, for the example spline having no tooth error under combined torque, radial loads, and tilting moment loading

Grahic Jump Location
Fig. 13

Load distributions of the example spline having single tooth indexing error under combined torque, radial loads, and tilting moment loading, at different rotational positions

Grahic Jump Location
Fig. 14

Load sharing factors of (a) tooth #10, (b) tooth #13, and (c) tooth #15, at different rotational positions spanning a full rotational cycle, for the example spline having single tooth indexing error and having no tooth indexing error, under combined torque, radial loads, and tilting moment loading.

Grahic Jump Location
Fig. 15

Load distributions of the example spline having random tooth indexing error under combined torque, radial loads, and tilting moment loading, at different rotational positions

Grahic Jump Location
Fig. 16

Load sharing factors of (a) tooth #6, (b) tooth #14, (c) tooth #17, and (d) tooth #18, at different rotational positions spanning a full rotational cycle, for the example spline having random tooth indexing errors and having no tooth indexing error, under combined torque, radial loads, and tilting moment loading

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In