The vast majority of crank&slider systems worldwide are in piston engines. This discussion of balancing the forces and moments in crank and slider systems thus inevitably centres around common engine configurations.
A little background knowledge will help in interpreting questions about crankshafts and pistons as well as providing an insight into the design process.
There are 3 “apps” that run in Matlab:
- long_balance.m is to refresh your memory of the shaft balancing lab that you did in second year. It shows how a vector diagram can help you visualise the angular relationships between forces (or moments) - this in turn shows what calculation you need to do to get a numerical answer.
- fr_masses.m helps you imagine a pair of shafts, each carrying an out of balance mass, but rotating in opposite (“forwards” and “reverse”) directions. If the centripetal forces are equal in magnitude, their resultant is a force that does not rotate - instead it is a vector of constant direction but varying in amplitude (cosine wave). In fact it is equivalent to the reciprocating forces generated by a crank-slider mechanism (long connecting rod so sinusoidal acceleration). Like an "equivalent circuit" in electronics, this gives one a mathematical model that is much easier than summing all the trigonometric relationships for out of phase cosine waves.
- balancing_app.m combines these two approaches to show how the state of balance can be found for any configuration of piston engine. The phasor diagram approach gives you a visual model for understanding why forces or moments cancel that is often more useful that an algebraic approach. Typically an engine designer will aim to make the reverse-rotating phasors cancel out (otherwise his engine needs a counter-rotating balancer shaft) - the forwards rotating phasors matter much less because one can just add balance weights to the crankshaft.
balancing_app can model over 300 combinations of cylinder numbers, bank numbers and crankshaft types, times an infinite set of crank angles, bank angles etc. I know from last year that people like to memorise particular cases and questions - this is not a good idea. As far as ES3C3 is concerned, all that matters is understanding the basic concepts and being able to analyse simple situations.
I have also added here, for interest and general knowledge, some very simple notes and hyperlinks about different kinds of engine. Some of you, I’m sure, already know far more than this: for people who know nothing about engines it may be interesting. It is tempting to “write off” old designs as having no modern relevance but the art of engineering is, in part, knowing what has been tried previously and understanding what worked and what didn’t.