As early as 1907, Frederick W. Taylor described machining vibrations as the most obscure and delicate of all the problems facing the machinist, an observation still true today, as shown in many publications on machining.
Mathematical models make it possible to simulate machining vibration quite accurately, but in practice it is always difficult to avoid vibrations.
Basic rules for the machinist for avoiding vibrations:
The use of high speed machining (HSM) has enabled an increase in productivity and the realization of workpieces that were impossible before, such as thin walled parts. Unfortunately, machine centers are less rigid because of the very high dynamic movements. In many applications, i.e. long tools, thin workpieces, the appearance of vibrations is the most limiting factor and compels the machinist to reduce cutting speeds and feeds well below the capacities of machines or tools.
Vibration problems generally result in noise, bad surface quality and sometimes tool breakage. The main sources are of two types: forced vibrations and self-generated vibrations. Forced vibrations are mainly generated by interrupted cutting (inherent to milling), runout, or vibrations from outside the machine. Self generated vibrations are related to the fact that the actual chip thickness depends also on the relative position between tool and workpiece during the previous tooth passage. Thus increasing vibrations may appear up to levels which can seriously degrade the machined surface quality.
Industrial and academic researchers  have widely studied machining vibration. Specific strategies have been developed, especially for thin-walled work pieces, by alternating small machining passes in order to avoid static and dynamic flexion of the walls. The length of the cutting edge in contact with the workpiece is also often reduced in order to limit self-generated vibrations.
The modeling of the cutting forces and vibrations, although not totally accurate, makes it possible to simulate problematic machining and reduce unwanted effects of vibration. Multiplication of the models based on stability lobe theory, which makes it possible to find the best spindle speed for machining, gives robust models for any kind of machining.