General: 

Because the condition of the cylinder of my engine was not optimal, I decided to have it bored and honed. I needed to make my own oversized piston, as I could not find one that fits. See http://www.geutskens.eu/neracar/description4.htm
In addition, the motorcycle showed quite some vibrations, like the other Model A’s.
So I decided to make a piston which weighs as much as the calculations show, viz. 504 g instead of the weight of the original piston, which is 389 g, so 115 g heavier.
The ultimate piston could always be made lighter and subsequent vibration tests are planned to make a piston with a weight that results in minimal vibrations.

 Balancing the engine

 Mass of reciprocating parts (g):

 Mass of rotating parts (g):

 Calculating the theoretical counter weight in the crank web for balancing:

Assume a balance factor of 58%.
The counter weight in the crank web is calculated as follows:
Take 100% of the rotating mass + 58% of the reciprocating mass
= 182.6 + 0.58*560.9 = 507.9

 Reverse engineering:

Calculating the optimal piston weight for correct balancing with the actual counterweight.
· Assume a balance factor of 58%.
· Determine the counter weight of the crank web by making a test weight that fits around the crank pin with a weight such, that when the crank shaft rotates between    two centre points, it is in balance. This means that it can be left in any position without rotating back or fro.
·This weight was found to be 574.4. This means the current balance factor is not 58% but as high as 70%. It looks like the engine is overbalanced.
· If we choose a balance factor of 58%, without reducing the weight of  the crank cheek (we do not want to spoil the originality of the crankshaft), the weight of the piston should be 504, hence 115 heavier than the current 389 (rounded figures).
· Remarks:

o   Balancing the rotating parts for 100 % is ideal.

o   Not balancing the reciprocating parts makes the engine to vibrate in a direction equal to the piston movement.

o   Balancing the reciprocating parts for 100% makes the engine vibrate in a direction with a right angle to the piston movement.

o   The optimal balancing of the reciprocating parts is with a balance factor around 50%. In that case the total of the vibrations in both directions is minimal.

·    Determination of the direction of engine vibration.If the calculated value for the new piston is about correct, the current piston, fitted in the engine, must be too light, or, in other words, the counterweight of the crank-web is too heavy.In order to check that assumption, vibration measurements have been carried out. This part of the project was lead by Rob Poestkoke. We bought an AD22037 dual axis acceleration sensor with a range of +/- 18 g (gravitational force) which was firmly attached to the engine. The two analog outputs were fed into a scope and it was apparent that at certain speeds the horizontal acceleration exceeded the vertical acceleration (read: vibration) by far. Hence we decided to carry on with the ‘heavy piston’, as it looks like the current engine is overbalanced. For details see Vibe Measurement

     The new piston.
A new piston was made to fit the oversized cylinder.
For details see http://www.geutskens.eu/neracar/piston.htm
The weight of the piston is 533.9 g, 4.2 g less than the targeted 538.1 g.
The balancing figures are now as follows: 

Mass of reciprocating parts (g):

Mass of rotating parts (g):

Calculation of the balance factor
The balance weight of the crankweb, 574.4 g, is equal to the sum of of the weight of the rotating mass, 182.6 g and the balance factor times the mass of the reciprocating mass, 675.2 g.
Or, the balance factor = (574.4 – 182.6) / 675.2 = 58% 

Conclusion:
By increasing the weight of the piston with piston rings from 423.3 to 533.9 g, the balance factor was reduced from 70% to 58%, like our plan was.
By comparing the graphs of the vibrations of the ‘light’ and the ‘heavy’ piston we can see that the engine is no longer overbalanced; the vibrations, which were originally merely in a horizontal direction are now smaller and about equal to the vertical vibrations. It looks like the balance is now optimal for a one cylinder engine. Test runs told us so.

Some final words about vibrations:
An unbalanced engine will vibrate in the reciprocating direction (assuming that the easy-to-balance rotating masses have been balanced for 100%). For vertically placed motorcycle engines this direction is up-and-down, When we compensate for the full 100%, the up-and-down vibration will be replaced by a comparable vibration perpendicular to the piston movement and perpendicular to the crank shaft.
The optimum balance is achieved with a balance factor of 50 – 60%, where 50 - 60%  of the reciprocating masses are compensated for, with an extra weight in the crank web. This results in less vigorous vibrations in both directions, in the horizontal and the vertical plane.
For motorcycle engines with a vertical cylinder, where the crank shaft points into the left-right direction, which is common practice, the horizontal component results into a back-and-fro vibration, which can hardly be noticed.
Balancing the engine cannot be seen apart from the frame.

For a Neracar the orientation of the engine is such, that the crank shaft points into the driving direction, which will cause the horizontal component of the vibration to make the frame shake in the left-right direction, which is much more noticeable than a the back-and-fro vibration. The up-and-down vibrations will have the same effect as for all other engines with a vertically oriented cylinder. 

An extra problem for the Neracar is that we are dealing with a floppy frame that does not give sufficient stiffness and does not have sufficient mass to damp the vibrations generated by the engine. Hence, the effect of balancing is limited.