# Increasing the frequency variation at position p 1 to

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Increasing the frequency variation at position P 1 to position P 2 and P 3 in X direction shows an increase in stiffness . Figure 7: Waterfall frequency diagram for X direction in P 3 position The same situation existed for 50.5 Hz frequency, which P 1 position is similar to the frequency of the electric network. This frequency increases reaching 53 Hz for P 2 and 55Hz for P 3 .The same evolution is finder in the case of 130-230 Hz frequency range. This observation shows that the X direction (the axial direction), the stiffness presents an increase when the TCP (tool center point) of robot go through the different position P 1 ,P 2 and P 3 .
6 ICASAAM 2011 7-10 September 2011 Bucharest Romania Figure 8: Waterfall frequency diagram for Y direction in P 1 position For the Y direction (Figure 1) frequencies decrease slightly as the robot arm goes away from the position P 1 , (figure 8). Frequencies show a similar behavior, where the fundamental frequency from 12 Hz for P 1 position decrease to 10 Hz in position P 2 (figure 9) and 8 Hz for P 3 position (figure 10). Figure 9: Waterfall frequency diagram for Y direction in P 2 position
7 7-10 September 2011 Bucharest Romania ICASAAM 2011 Figure 10: Waterfall frequency diagram for Y direction in P 3 position Figure 11: Waterfall frequency diagram for Z direction in P 1 position Figure 12: Waterfall frequency diagram for Z direction in P 2 position
8 ICASAAM 2011 7-10 September 2011 Bucharest Romania Figure 13: Waterfall frequency diagram for Z direction in P 3 position The self excited frequencies in the Z direction (figure 1) show the same trend as the Y direction. The robot arm rigidity decreases, from position P 1 (figure 11) in relation with P 2 position (figure 12) and the P 3 position (figure 13). After analyzing the self-excited frequencies measured from the impact test to see a sensible increase in stiffness in the X direction and a decrease in stiffness in the direction Y and Z. The variation of the low frequency is about 10% at position P 1 to position P 2 respectively P 3 in the three directions. The analysis of the static frequency aims to impact frequency location of the robot in different configurations and their variation according to different position on the robot to perform. Thus obtain an overview of the self-excited frequency, where there is slight increase frequency in the X direction and a very small decrease of frequency in the Y and Z direction at P 1 position from P 2 and P 3 position. 4 Vibrations analysis during the spindle rotation Frequency analysis is performed in the dynamic case for the rotation speed of 12,032 rpm which can be identified both LFR and HFR frequency range, figure 12 in the P 1 position. The choice of tool speed is considering cutting parameters for testing and also the comparative material will be made between the behavior of the robot during the cutting process and outside the cutting process. The range of the high frequency represents the excitation of the component elements of the robot arm, representing one of the prospects of this research [10], [11]. By the spectrum analysis synchronized with rotational speed can identify

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