From: Sergio Montes
Date: Tue, 25 Oct 94 09:27:26 EST

To come to some logical conclusion on the suitability of the 90 degree cranks for a parallel twin, I have performed two sets of calculations using the standard balancing theory. The calculation of the unbalanced INERTIA forces is fairly straightforward for a two cylinder engine.

The theory is well explained in Taylor's book, " The Internal Combustion Engine",MIT Press 1968.Using this theory,I have calculated the vertical imbalance forces for a parallel twin with a a crank with phase difference between 0 and 180 degrees in steps of 18 degrees.The connecting rod is assumed to be represented by two equivalent masses,one located at the big end , rotating with the crank and another at the small end, moving in a vertical direction.The lower equivalent mass can be fully counterweighted,so that no imbalance results. The upper conrod equivalent mass, plus the mass of the piston,piston pin and rings, because of its reciprocating motion, cannot be balanced exactly by a rotating mass. I have assumed here that no partial balancing of this mass has been used, so that the different crank phase angles could be compared in their degree of imbalance.

This calculation takes into account both the primary forces due to the mass of the piston and the upper portion of the conrod, and the secondary forces due to the angularity of the connecting rod. The ratio of crank radius R to conrod length L is R/L=0.286, a value which I believe is typical or close to that of many engines.Also it is assumed here that the factor Z defined below:

To get the actual forces in pounds (or Newtons) at given rpm one multiplies the table figure by the appropriate Z factor for the engine.

As the imbalance force varies with the angular position of the crank, the number of interest is the maximum value of the vertical force This is the value reported in the table below. For a given phase difference (first column) the maximum vertical force is shown in the second column.

The 180 degree crank has perfect primary balance but NOT secondary balance,as shown in the table. The 90 degree crank , on the other hand is better than the 360 degree crank, but far inferior to the 180 degree crank in matters of balance. The fact that the power pulses in any but the 360 crank are not evenly distributed means that the torque is irregular and torsional vibrations may be set out in the crank, unless it is stiffer and heavier than the 360 crank.This may have been the reason that convinced Edward Turner to adopt the 360 crank, in spite of its inherent unbalance problems.

The secondary imbalance cannot be eliminated except with a balance shaft rotating at twice the crank speed, so that the performance of the 180 crank without the balancing shaft cannot be improved. The question remains what would be the performance of the 90 degree crank if the piston,etc. is partially counterweighted at the crank. Assuming a "balance factor" of 2/3, a figure widely used by many manufacturers, the vertical and horizontal force as a function of the crank angle for the 90 crank have been computed and are shown in the next table, alongside the vertical force for an UNBALANCED 180 crank (there is no horizontal force for this crank).
 
 

The comparison is interesting, as the partial balancing has improved the primary balancing of the 90 crank (column marked FV90), which is now better than the 180 crank (FV180)in the vertical force, BUT at the expense of considerable horizontal forces(FH90), which the 180 crank lacks.The sign of the force is unimportant.

The outcome of this comparison is not quite as clear as I thought initially.If the frame is cleverly designed, the horizontal forces present may not induce large amplitude vibrations, so that the 90 degree partially balanced crank is perhaps not a bad proposition. But is it better than the 180 crank ?

Sergio Montes Department of Civil and Mechanical Engineering
University of Tasmania

Return to the Contents Page