There are three basic types of vibrations experienced by milling machine:
(a) Free or transient vibrations resulting from impulses transferred to the structure, where the structure is deflected and oscillates in its natural modes of vibration until the damping present in the structure causes the motion to die away;
(b) Forced vibrations that come from periodic forces within the system. The machine tool will oscillate at the forcing frequency and if this frequency corresponds to one of its natural frequencies of the structure.
(c) Self-excited vibrations, usually resulting from the dynamic instability of the cutting process.
One of the most important effects causing poor surface quality in a cutting process of cnc milling machine is vibration arising from a delay. Due to some external disturbance, the tool starts a damped oscillation relative to the workpiece thus making the surface uneven. After one revolution of the workpiece (lathe), the chip thickness will vary at the tool. The cutting force thus depends on the current position of the tool and workpiece and also a delayed value of the displacement. This is the so-called regenerative effect. The corresponding mathematical model is a delay differential equation but added that the analysis does not account for nonlinear phenomena as the tool leaves the material also in machine tools like machining center.
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