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This technology is very compact and can be used on every conventional machine tool. However, experiments on these tools are quite difficult and long because of the numerous parameters influencing the vibration. Therefore, in order to guide the experiments a dimensionless approach has been used to choose the cutting conditions and vibratory tool holder properties.

This approach permits the number of tests to be reduced, since the machining process can be entirely described with only three dimensionless parameters instead of nine physical parameters

Self excited vibratory drilling

At first glance, it seems that the drilling process is well known and has been mastered for a long time. However, in industrial series it is very difficult to obtain holes with regular geometrical and technological parameters, and to increase the productivity without quality loss. It becomes critical for deep drilling because the chip removal process remains the main obstacle to quality and productivity.

Chip fragmentation is due to axial vibration of drill creating discontinuous cutting. The two main advantages of the process are the following:

• Chips are naturally fragmented to small pieces implying that there is no need to perform the stripping operations classically used to split up chips.

• The friction of chip on the manufactured hole surface is limited which leads to improved hole quality.

The idea of assisting the drilling process by low frequency axial vibration has been around for more than 30 years in the world. However, in all studies the vibrations were forced type; they were generated by an external source of energy.

[Mechanical excitation, piezoelectric translator etc ]. Such technologies have an advantage in controlling vibrations. However, they are relatively cumbersome and expensive, and are limited in frequency and amplitude. In order to solve this problem a new drilling technology, self-excited drilling was developed based on the mechanism of self-excited vibration.

This phenomenon is particularly well known. It was identified as one of the principle causes of chattering. Therefore, studies made on the subject always saw this phenomenon as harmful with the cut and thus sought to identify the cutting conditions without chattering. The step used was reverse the aim was to look at controlling the phenomenon to split chips up.

Self-excited vibratory drilling is a dynamic process extremely difficult to control because of non-linear forces vary in time. The regenerative vibrations naturally appear at certain revolution frequency of drill. These natural axial vibrations are used to fragment chips. The challenge is to keep them stabilized at a suitable frequency and magnitude for good quality cutting.

The mathematical model of self-excited vibratory drilling tried to sole this problem with dimensionless parameters. This model allowed the operating conditions required for the setup to be forecast.

The theoretical study aimed at obtaining the equations governing the creations of work piece surface and making it possible to forecast the operating conditions of the vibratory drilling. This study has been base on specific modeling of drilling. The basic equations are obtained in a dimensionless form in order to decrease significantly the number of parameters of the system for simplicity of study and practical use of this technology.