PARTIAL CANCELLATION OF SHAKING FORCE HARMONICS BY CAM MODIFICATION

An optimization procedure for minimizing the shaking force harmonics o f machinery is described. Because of constraints imposed by the specif ication, optimization is unlikely to make any significant reduction in the fundamental, machine frequency, term of the shaking force. That t erm, normally the largest, must be substantially reduced by other mean s for the procedure described here to be cost effective. Earlier work describing methods of reducing the fundamental term are cited. An extr usion press machine incorporating two planar mechanisms, one crank dri ven and one cam driven, provides an example. Two designs of the cam-dr iven mechanism, referred to here as cams 1 and 2, are in use in instal led extrusion press machines. Harmonic analysis of the shaking force a s a function of time shows that cam 2 produces smaller amplitudes of s haking force harmonics. The ten variables used in the optimization pro cess are the amplitudes and angles of the first five terms of a trigon ometric series defining the acceleration of a reciprocating mass drive n by a hypothetical third cam, cam 3, which is similar to cam 2 but st ripped of all harmonics of order higher than the fifth. The objective function is the sum of the amplitudes of the horizontal components of the second to fifth shaking force harmonics on the machine as a conseq uence of accelerations of the moving parts of both mechanisms. Several equality and inequality constraints must be met. For the extrusion pr ess machine the result is a reduction in the amplitudes that would be created if cam 3 were to be used by approximately 10, 75, 65 and 100 p er cent respectively. The improvement over cam 1 is greater. The proce dure is particularly suited as a retrofit measure where the number of installed machines is large in relation to the future rate of producti on of new machines: a cam that has been removed from one machine can b e re-cut for use on another machine.