In some bikes, the crank, chain ring, and bottom bracket spindle are integral, a

Question

In some bikes, the crank, chain ring, and bottom bracket spindle are integral, and the spindle is joined to the second crank (on the left side) via a spline. Say the spline has 6 ridges, and that the mean diameter of the spline face is Ds = 0.95 in. Find the length of each spline groove. Let the width of the splined section of the crank be w - 1.25 in. If the torque to be transmitted is 3000 lb-in., find the force acting on each groove in the crank, assuming it is distributed uniformly among the splines. Finally, determine the maximum shear stress tow in the splines of the crank. You only need to do one problem set-up (knowns, unknowns etc.)

Explanation / Answer

Length of each spline groove (L) = circumference of spline / 2*no of grooves

                                           = pi * Ds / 2*6

                                           = pi * 0.95 / 12     = 0.2487 in

Torque    = 6 * Force acting on each spline groove * Ds / 2

Force acting on each spline groove = T / 1.5 * Ds     =   3000 / 1.5 * 0.95

                                                                             = 2105.263 lb

shear stress = force / w * L

                   = 2105.263 / (0.2487 * 1.25)   = 6.772 ksi

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