ESDU - Procedures for balancing planar linkages using rotating counterweights
|Publication Date:||1 July 2010|
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.