(Question 3 is in three parts A, B and C)

Analysis of Vibratory Feeder. The track is considered to move bodily with simple harmonic

motion along a straight path:

F-

mp8

mp4,00²

Maximum inertia force acting on a part in vibratory feeding when the track is at its upper

limit for motion. Forward sliding is shown.

90²

8

A. Assuming that the motion of the part is independent of its shape and that air resistance

is negligible and that the part does not roll down the track, show that for backward

sliding to occur during the vibration cycle:

u, cos 0 - sin 0

cos -u, sin

Include in your answer your own diagram, drawn for backward sliding and all your

working out./nInclude in your answer your own diagram, drawn for backward sliding and all your

working out.

B. The operating conditions of a vibratory feeder can be expressed in terms of the

dimensionless normal track acceleration An/gn. For values of us = 0.8,0 = 3° (0.05

rad), and y = 30° (0.52 rad) what must the ratio of An/gn be greater than for backward

sliding?

C. Without reference to the specific conditions in B, but including the assumptions in A,

describe the general motion of a part in a vibratory bowl feeder. Does hopping always

occur in the vibration cycle? Does hopping occur after forward sliding or after

backward sliding? Fully Justify your answer. Include in your answer your own

diagrams, and all your working out.