Before we start, a small experiment on the subject of 'oscillations'. Belonging to the above picture, is the respective video at the bottom of the page. It shows, very briefly, how in the beginning, the black Mercedes still reverberates, then by adding weights, it calms down again.
Did you know, that basically no part of the motor car is simply rigid? Sooner or later every part is put under strain and becomes deformed, even if the deformation is minimal. This more often happens to the parts in the drive-train region, which are strained by torsion. Indeed, the parts are returned to their original shape and then deformed once more, over and over again, this process is called elasticity.
Oscillations in elastic systems, whether they are caused by twisting, or bending or perhaps even both, are difficult to calculate. It is however, particularly necessary, because they occur when movement takes place and the solving of possible problems by oversizing, is not particularly favourable.
The first question is: Which parts actually oscillate? After all, in the automobile field we are very seldom dealing with simple shafts. Some of these may have cranks, cams or thickenings, they may be bearings or simply gear-wheels. If one turns the gear-wheels on the shaft around, the shaft itself will also be somewhat twisted.
Regardless of of whether it's caused by the shaft or the gear-wheels, if the gear-wheels are placed on the ends of the shaft, the greatest twisting angle will be found between them. The point where no twisting takes place, is the nodal point, which by the way, does not necessarily have to be the mid-point of the shaft. The important thing is, that now we're not dealing with twisting, but with oscillations.
As soon as we speak of oscillations, their frequency becomes important. They, on the other hand, are determined by the moment of inertia. Thus, should the gear-wheel on one side have a greater mass, the nodal point has a tendency to move in that direction. If indeed, we're speaking of a twisting, we could call the whole thing a 'torsion-spring', which means that we could determine the already known spring-rate.
This on the other other hand, has to do with the frequency. The more the above system resists against twisting and the greater the spring-rate is, the greater the frequency is as well. It decreases when the inertial moment of the involved masses increases. This is where the problems arise, because oscillations can overlay the acceptable torsion forces in such a manner that damage can be caused.
Most of the time the shaft itself doesn't actually break, it does however, cause a recurring strain on the bearings Should one have the choice, one would place the bearings on the zero-crossing point of the oscillations, i.e. on the nodal point. Astonishingly, oscillations also generate heat. This always takes place when a mechanical system is slowed down through friction. In our case, this occurs through the bearings, but also, through internal friction, e.g., in the shaft.
According to Newton, the oscillations should always remain the same, in fact, with the consistant influence of force, they should continually increase. In the drive-train of a motor car however, these occur more periodically. Now we have a further source of disturbance. If two oscillation-waves overlap each other unfavourably, the resulting greater oscillations can, under certain circumstances, lead to a concrete fracture. 11/13