Crankshaft Design - Balancing

THIS PAGE IS WORK IN PROGRESS!

To minimise vibration in an engine, crankshafts need to be designed to achieve (or get as close as possible) static and dynamic balance. When speaking of rotating shafts, if there are eccentric masses on the shaft, then to achieve static balance, the vector sum resultant force must equal zero. i.e. the centre of mass must lie on the axis of rotation. When the shaft is spun, the eccentric masses create centrifugal forces which act on the shaft. If the masses are not all in the same plane, then rotating couples act on the shaft too. To achieve dynamic balance, both the vector forces and the rotating couples must sum up to equal zero.

Note that when dynamic balance is achieved, static balance is automatically achieved, therefore when calculating the balance of a rotating shaft, it is best to just go for satifying the dynamic balance requirements straight away.

One must determine if the crank is either symetrical or asymetrical and dependant on which it is will determine what forces need to be balanced out. An asymetrical crankshaft, for example, will always have a rotating couple to take care of first.

A crankshaft is considered symetrical if it is equal either side of the centreline (vertical plane midway between each end). For example, looking at an inline-4 crank, one side is a mirror image (symetrical) of the other side, therefore, as long as all the pins / throws / counterweights are equal, the crank is symetrical. If it is not a mirror image about the vertical centre plane, then it is considered asymetrical and will have a rotating couple to be balanced out.

Some image examples of symetrical / asymetrical needed here.

So as stated above, to achieve dynamic balance, the force vectors of any eccentric masses and rotating couples must all sum up to zero. So a generic way to approach any crankshaft design would be to sum up all forces and couples and see what state of dynamic balance it is in. Obviously sometimes you can tell just by looking at the layout of a crank that it is going to be inherently in dynamic balance, such as an inline-4, which is symetrical and in static balance, but it is alwaysbest to learn from basics and have an approach suitable to all.

There are three main areas to consider when balancing a crankshaft:

All these forces act on the crankshaft when it is rotating, so all should be used in calculations.

Reciprocating Forces are the forces associated with the movement of the piston assembly and little end of the con-rod. This force acts along the line of the cylinder and alternates in direction as the piston travels in one direction, then reverses its movement. There are primary and secondary forces to consider. These are the first and second order forces. There are third, fourth, fifth... and so on, but after the second, the force becomes relatively small and can be considered negligible.

The primary reciprocating force is a force that occurs once every crank rotation. It is basically the centrifugal force of the mass of the reciprocating components. This would be all we would need to calculate if the motion of the piston was sinusoidal. But due to the crank mechanism (the inclusion of the con-rod) this motion is not simple harmonic motion.

The con-rod introduces an effect which causes the secondary forces. When these forces are summed up, there is a greater force at TDC than there is at BDC. To take this effect into account, we calculate the secondary forces with the ratio of the crank throw radius to con-rod length in mind (r/l). The calculation of these inertia forces have been discussed on the Journal Sizing page.

The piston moves faster at the top than the bottom due to the link mechanism of the con-rod. To illustrate this, look at two extremes: one where the con-rod is equal in length to the crank throw radius and the other is an infinitely long con-rod.

The first option will result in piston motion in the top 180° of crank rotation, but when the crank angle (from TDC) reaches 90° the piston stops moving as the crank throw is the same as the con-rod. (need images/amins of this)

Then the other extreme is the infinitely long con-rod, which would make the movement in the top half the same as in the bottom half as the con-rod would be basically parallel with cylinder axis. This would result in simple harmonic motion (sinusoidal).

So somewhere inbetween is reality. Therefore the top half of the crank rotation will always result in greater piston motion than the bottom half. If we picture this in terms of inertia force, the faster motion in the top half, i.e. as the piston approaches TDC is greater than when the piston is approaching TDC. This is what is calcualted in the secondary force calculations and is why some seemingly balanced engines have secondary imbalance and require balance shafts (inline-4).

One way to eliminate secondary force problems is to use a scotch yoke type arrangement to achieve sinusoidal motion of the piston. This is not practical in engines though really.

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