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For self locking, N 1 remains nonzero when F c is removed therefore:
sin f ¼ m 1 cos f
i.e., if sin f , m 1 cos f ; then anegative force F c is required to extend the rod.
From this inequality it can be seen that for self locking:
tan f , m 1
Therelationship betweenwedge angleand friction coefficient can therefore be plottedasshown
in Figure 9.12.
Further insight can be gained if the equations relating the wedge forces to the coupler force and
polymer spring force are developed, again assuming saturated friction states and direction shown in
Case 1for m 1 N 1 giving:
F c ¼ F s ð m 1 cos f þ sin f Þ = ½ðm l 2 m 2 Þ cos f þð1 þ m 1 m 2 Þ sin f � ð9 : 12Þ
Coefficient of Friction
2.5
2
1.5
1
0.5
Self Locking Zone
FIGURE 9.12 Friction wedge self locking zone.
F c
F c
m 1 N 1 (case 2)
m 1 N 1 (case 1)
0
0 20 40 60 80
f
N 1
f
N 1
N 2
Wedge Angle, Degrees
Handbook of Railway Vehicle Dynamics
m 1 N 1 (case 1)
m 1 N 1 (case 2)
m 2 N 2
FIGURE 9.11 Free body diagram of asimplified draft gear rod–wedge–spring system.
© 2006 by Taylor & Francis Group, LLC
F s