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Another method is the impact excitation technique, in which a magnet and the rotation of the spindle are used to provide the excitation. The measurements of the FRF are most commonly based on the impact testing when an instrumented hammer is used to strike the tool tip, and the force of the impact is measured or the “pop-off” device in which the impact is created by using an explosive device. In practice, it is necessary to have steplessly variable spindle speed to be able to select the most stable speed. But as the spindle speed approaches the values of n=0.5 f n/ m (and mainly n= f n/ m), which denotes one wave between the subsequent teeth, substantial increase of the stability may be achieved by exact selection of the right rotational speed. This means that for low spindle speeds, the peaks of stability are not very high and are localized close to each other. 8.6C that peaks of stability are close to values of p=1( N+1). The highest stability, permitting the highest value of stable depth of cut, is obtained with the spindle speed at which the tooth frequency equals the natural frequency of the system (for p=1). In contrast, at the high-speed end, on the right, gaps of increased stability occur. The upturn of the stability boundary on the left end of the horizontal scale is the effect of process damping. The practical interpretation of the graph is to consider the envelope of all the lobes as the boundary between the stable field below the envelope and the chatter field (shaded areas) lying above the envelope. It should be pointed out that the individual “lobes” in the diagram correspond to a different integer N in Eq. 8.6C, the vertical coordinate is the ratio q= b lim/ b cr, where b cr is the lowest b lim obtained for phasing most favourable for chatter generation, and the horizontal scale expresses the value of the number p being the ratio of the tooth frequency over the natural frequency of the system. Two-dimensional stability lobe diagram for a milling operation: waviness generation for increased spindle speed (A), variations of chip thickness (B) and stability lobe (C). In contrast, no chip thickness and force variations were obtained with exactly one wave between the teeth being in phase.įigure 8.6. In addition, cases (B1) and (B2) illustrate that a substantial variation in chip thickness (twice the vibration amplitude) occurs with one and a half waves between the teeth, for the same amplitude. Cases (A1), (A2), and (A3) were recorded for increased spindle speed and it can be seen that for higher spindle speed (A3) only one and a small fraction of a wave occur. 8.8A and B that in milling the waviness, which is cut into the surface during chatter vibrations by a tooth, gets recut by the subsequent tooth. An example of a two-dimensional stability chart for an end-milling operation with characteristic unstable ranges shown as lobed areas is presented in Fig. In milling operations, both 2D and 3D stability lobes that consider the axial depth of cut or the axial and radial depths of cut together are used.
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The SLD visualizes the border between a stable zone (i.e., chatter free) and an unstable zone (i.e., with chatter).
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In practice, stability of a machine tool can be represented graphically in the form of a special chart called the stability lobe diagram (SLD), which depicts the effect of the depth of cut in milling, drill diameter, and so on, versus the rotational speed of the tool or workpiece.