Undamped free system

The physieal eonfiguration and bloek diagram representation of a CNC maehine-tool is shown in Figures 1.10 and 1.11. The fundamental eontrol problem here is that, by design, the lead-serew (by the use of re-eireulating ball-bearings) is frietion-free. This means that the positional eontrol system will have no damping, and will oseillate eontinuously at the undamped natural frequeney of the elosed-loop system. 

The boundary conditions established by the machine design determine the freedom of movement permitted within the machine-train. A basic understanding of this concept is essential for vibration analysis. Free vibration refers to the vibration of a damped (as well as undamped) system of masses with motion entirely influenced by their potential energy. Forced vibration occurs when motion is sustained or driven by an applied periodic force in either damped or undamped systems. The following sections discuss free and forced vibration for both damped and undamped systems. 

Because of the linear restoring force of the spring, a deflection of the system will result in a harmonic oscillation. This becomes obvious by considering the free vibration Eq. 1 of the undamped system... 

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