This Data Item presents four procedures for the design of
counterweights which, when fixed to shafts rotating with constant
angular velocity, improve the balance of machines that incorporate
single degree-of-freedom, planar, multibar linkage mechanisms. The
frame shaking force^† and/or the frame shaking
moment^† may be reduced by using the procedures contained
in this Item to determine the optimum sizes and locations of the
counterweights which form the following devices.

(a) Lanchester Balancer – in which two rotating masses are sized
and aligned to eliminate a single frequency term of the frame
shaking force in a chosen direction fixed with respect to the frame
and in the plane of the linkage (see Section 3).

(b) Single Counterweight Balancer – in which one rotating mass
is sized and aligned to minimise the average frame shaking force
(see Section 4).

(c) Generalised Lanchester Balancer – in which two rotating
masses are sized and aligned to eliminate a single frequency term
of the frame shaking force in the plane of the linkage (see Section
5).

(d) Moment Balancer – in which two rotating masses are sized and
aligned to eliminate a single frequency term of the frame shaking
moment (see Section 6).

Computer program, ESDUpac A9007, supplied with this Data Item
can be used to carry out all the required calculations (see
Sections 9 and 10). The criteria for choosing an appropriate method
are included in ESDU 89043 (Reference 6). The use of rotating
counterweights to improve balance has, in general, the following
advantages.

(i) Often these methods require little extra space and so are
especially suited to retrofitting existing machinery.

(ii) Linkage joint forces, other than those connecting
counterweighted shafts to the fixed frame are unchanged and so
bearing re-design is not usually necessary.

(iii) Peak-to-peak input torque during steady-state operation is
not altered.

It should be noted, however, that balancing by the methods
presented in this Item will not necessarily provide the best
possible improvement in dynamic performance. The use of rotating
counterweights can give only a partial reduction in frame shaking
force. The attainable degree of reduction is dependent on the
particular application and is difficult to predict without detailed
calculation. If extra shafts, gears and bearings are necessary then
costs may be high and space may not be available. The torque
required to accelerate and decelerate the machine will be increased
so more powerful prime movers and more effective brakes may be
required.

^† See Section 2.1.1 for definition.