Regimes of Contact in Spline Couplings

[+] Author and Article Information
S. Medina, A. V. Olver

Tribology Section, Department of Mechanical Engineering, Imperial College of Science, Technology, and Medicine, London SW7 2BX, England

J. Tribol 124(2), 351-357 (Jul 19, 2001) (7 pages) doi:10.1115/1.1403456 History: Received February 01, 2001; Revised July 19, 2001
Copyright © 2002 by ASME
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Ku, P. M., 1974, “Design of Spline Couplings for Fretting Mitigation,” NATO, AGARD Conference Proceedings, Vol. 161, NASA, p. 11.
Weatherford,  W. D., Valtierra,  M. L., and Ku,  P. M., 1968, “Mechanisms of Wear in Misaligned Splines,” ASME J. Lubr. Technol., 90F, p. 42.
Newley, R. A. 1978, “The Mechanisms of Fretting Wear of Misaligned Splines in the Presence of a Lubricant,” Ph.D. thesis, University of London, Imperial College.
Hyde, T. R., Leen, S. B., McColl, I. R., Williams, E. J., and Taylor, J. W., 2000, “A Representative Model for Life Assessment of Spline Couplings,” in Proceedings of the International Conference on Gearing and Transmission Systems, Daizhong Su, ed., Nottingham, UK, July 2000, Professional Engineering Publishing, UK.
Hyde, T. R., Leen, S. B., and McColl, I. R., 2000, “Experimental Determination of Crack Initiation in Frictional Contact Regions of Spline Joint Couplings,” in The Mission of Tribology Research, December 2000, London UK.
Brebbia, C. A., 1980, Boundary Element Method for Engineers, Pentech Press, London, UK.
Baker,  R. F., and Olver,  A. V., 1997, “Direct Observations of Fretting Wear of Steel,” Wear, 203–204, p. 425.
Archard,  J. F., and Hirst,  W., 1956, “The Wear of Metals under Unlubricated Conditions,” Proc. R. Soc. London, Ser. A, 236, p. 397.


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Spline coupling connected to elastic shaft with angular misalignment (schematic)
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(a) Typical model spline coupling, (b) showing boundary element mesh and sequence of applied loads and (c) detail of contact elements
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The relationship of the distribution of pressure on the male spline tooth to the pressure maps shown in Figs. 4, 6, 7, and 10
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Typical distribution of pressure on each of the spline teeth as a function of tooth position and the angular position of the shaft during rotation. (E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg)
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Variation of tooth load and axial position of center of pressure as a function of tooth position. Conditions as in Fig. 4. (E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg)
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Tooth pressure distributions for a range of parameters showing the effects of torque and misalignment angle: (a) E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg; (b) E*=32.8,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg; (c) E*=3.28,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg; and (d) E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.01 deg.
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Tooth pressure distributions for a range of parameters showing the effects of geometric effects and of coefficient of friction: (a) E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.1 deg; (b) E*=6.56,b*=5.4,z=18,α=30 deg,μ=0.3,θ=0.1 deg; (c) E*=3.28,b*=10.8,z=18,α=30 deg,μ=1.0,θ=0.1 deg; and (d) E*=6.56,b*=10.8,z=27,α=30 deg,μ=0.3,θ=0.1 deg.
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Local friction conditions showing stick slip: (a) E*=6.56,b*=10.8,z=18,α=30 deg,μ=0.3,θ=0.01 deg. and (b) E*=3.28,b*=10.8,z=18,α=20 deg,μ=1.0,θ=0.1 deg.  
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Shape of the path of slip over tooth surface. The main figure, left shows the trajectories of relative displacement of the contacting surfaces for a range of points on the tooth. The orientation of the diagram is the same as for the pressure distributions (Fig. 3) with the axis of the coupling to the left. The insets, right, show the heavily loaded part of the path for two selected points on the tooth.
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Tooth pressure distributions for spline with lead crowning. Conditions as described in Table 3, (as for Figs. 5 and 6(a), except for crowning radius of 3.6 m).



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