SEED Guides Tutor's Guide - Cam Mechanisms < >
6. Forces on the Follower5.1 The force acting along the path of the translating follower consists of the following components:-
5.1.1 the force to accelerate the lumped mass of the following system at the roller centre, [for brevity subsequently called the "inertia" force]
5.1.2 the external load; which may be approximated to one, or a combination of:
5.1.2.1 "constant",
5.1.2.2 varying linearly*, or
5.1.2.3 varying sinusoidally*. * - zero at start and finish.
5.1.3 the gravitational force acting on the mass of the following system,
5.1.4 the frictional resistance, and
5.1.5 the sum of the spring pre-load and spring deflection force which must always be sufficient to ensure that the resultant force always acts to maintain force closure of the "higher pair" connection between the roller and the profile.
Alternatively, a second ["cognate"] cam profile driving the follower in the opposite direction can be provided. This is more expensive than sprung force closure; NB - the implications for precision manufacture.
The gravitational and frictional forces may be negligible in comparison with the magnitudes of the "inertia" force and the external load.
5.2 In general, the lumped mass can be estimated, e.g., from the layout drawing, [how accurately?] to determine the greatest negative inertia force acting to separate the roller from the profile at the position of greatest follower retardation, 'Cam Mechanisms - Unit Design' Guide Fig 24 and Appendix E. Hence the spring preload and stiffness can be estimated to counteract this separating force with a sufficient margin. NB - This is likely to be sensitive to cam speed!
5.3 For spring design, see SEED 'Specify and Choose Springs' Guide. To determine the spring preload and stiffness: their relative proportions depend upon stress, natural frequency, etc.
5.4 Usually the external load is arranged to assist force closure but can only be included in the spring design calculations if there is no possibility of an idle cycle. This is a good example of the idle condition providing the worst case.
NB - determining the critical spring force from the maximum "inertia" force is not strictly accurate: if no force margin factor is allowed, i.e., if KA = 1, then a small negative loop will exist in the resultant force curve.
5.5 Analysis. [For Notation see 'Cam Mechanisms - Unit Design' Guide pages 8 & 9].
FI = My" (T1) [where y" = d2y / dt2]. FS = FPL + ksy (T2) FPL + ks(y)c > ABS[M(y")c] (T3) FPL + ks(y)c = KA M(y')c (T4)
