Example 2 : Self-excited Vibration due to Dry Friction.

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Fig 4.3: Variation in friction force with relative velocity

Figure 4.3 shows the variation of the dry friction force (between two bodies in relative motion) with a relative velocity. The negative slope of this curve, as opposed to the positive slope for viscous damping, is important. It implies that the friction force does positive work in every cycle of oscillation of the driven member. This work manifests itself in the oscillatory instability of the driven member, i.e., the member oscillates at its natural frequency with its amplitude increasing gradually. This type of oscillation, normally referred to as chatter, is frequently encountered in machining and similar situations. Such friction-induced oscillations in disc brakes of automobiles give rise to "brake-squeal", control of which is an important topic of current research. Providing a lubricant which essentially reduces the friction at the tool-job interface, sometimes controls the chatter of a cutting tool.

A machine can be made less susceptible to chatter by improving the

surface finish   dimensional tolerance and   lubrication standard of the machine elements (e.g., guideways) that are in contact but move      relative to each other.