On the Retrospective Balancing of Installed Planar Mechanisms

Abstract

The paper closely follows the work described in the preceding paper by Chiou and Davies (1) and shares with it the nomenclature and illustrative example. The results of that paper are used here to investigate the feasibility of providing retrospective balancing of existing machines on site. In reference (1) it is shown that unbalance of frequency that is a multiple k of driveshaft rotational frequency can be represented by contra-rotating force vectors Fk+, Fk- rotating about centres Sk+, Sk-, one of which can be chosen arbitrarily. As explained in reference (1) there are advantages in adding balance mass to existing shafts that rotate at driveshaft speed, notably of course the driveshaft itself, or shafts that rotate at an exact multiple k of that speed. The extrusion press machine described in reference (1) has a driveshaft balance mass. Space is available on the driveshaft to add additional mass as a retrofit measure, but the force exerted by the supplemented balance mass remains less than the first-order unbalance of magnitude F1+ that rotates in the same sense as the driveshaft. The residual unbalance still requires two contra-rotating forces to represent it, but one of these is less than it would otherwise have been without driveshaft balance mass. It will usually be found that there are boundaries to the regions where additional shafts can be located. This is particularly so within the frame of a machine where it is, to say the least, inconvenient to install shafts that span the width of the machine as a retrofit measure. Attention is therefore directed to balancing one or more frequency terms of the unbalance by additional masses installed external to the frame of the machine. Several means by which this can be done are described: they include the use of two or more additional shafts carrying balance masses and the use of dummy mechanisms. Means of driving the shafts and mechanisms are also briefly discussed.