Stability charts

W. Krebs, P. Flohr, B. Prade, and S. Hoffmann. Thermoacoustic stability chart for high intense gas turbine combustion systems. Combustion Science and Technology, 174 99-128, 2002. 

For the synthesis of CIO carba derivatives, a better leaving gronp than hydroxyl is nsnally preferred. The anomeric finoride , bromide, acetate, benzoate and phenyl-snlphonyl gronps have all been nsed and some of the chemistry that has been achieved is shown in Scheme 25. AllylsUanes tend to provide /S-confignred prodncts by axial attack on the oxoninm ion species (Scheme 25C) whereas larger nncleophiles snch as electron-rich aromatics add by attack on the a face (Scheme 25D). For nitrogen nncleophiles, Haynes and CO workers have employed the CIO anomeric bromide intermediate that gives the ClO-a hemi-aminal prodncts (Scheme 25E), some of which exhibit remarkable stability (Chart 1) . ... 

N. G. Lordi and M. W. Scott, Stability charts, design and application to accelerated stability testing of... 

Figure 16 shows the practical region of the stability chart (i.e., for positive depths of cut) and the associated frequency ratio diagram, where / = coHn is the frequency of the arising self-excited vibrations at the stability boundaries in [Hz]. The stabihty lobes are usually characterized by their index the lobe of index j is called theyth lobe. The minimum points of the lobes can be given as... 

A terthiophene-functionalized guanine base 2.203 was synthesized for its incorporation into the minor grove of DNA without alteration of duplex stability (Chart 1.41) [293]. Pulse radiolysis measurements of 2.203-modifled oligodeoxynucleotides showed the formation of a stable terthiophene radical cation in DNA. The authors further proposed that the incorporation of several terthiophene moieties along the DNA sequence may be useful to carry holes along the modified DNA. 

The simplest way of demonstrating the Intrinsic stabilizing character of a bearing Is by means of the stability charts of fig. 7. A light load of 70 kN Is used to enable a comparison of all four bearing designs to be made. 

The relative performance of the overarm is determined by performing cutting tests, resulting in a stability chart of the machine with each of the three overarms in situ. These charts, shown in Fig. 1.10, are obtained by plotting the width of cut W corresponding to the threshold of stability versus the cutter speed. From these stability charts, the maximum width of cut which is stable at all speeds is extracted. 

Fig. 1.10. Experimental stability charts, (a) Cast-iron overarm, (b) Welded overarm, (c) Bonded overarm.

The method for the dynamic evaluation of machine tools under test conditions has been described. The procedure evolved, covering the determination of the response data (and from this that of the operative receptance locus ), the prediction of the stability chart, the concept of the coefficient of merit describing machine quality, will be summarised in relation to the particular case of the bonded machine. 

By using the theory and method discussed in the literature," the stability charts shown in Fig. 1.19 (rows I) are obtained. It must be stressed that these are valid for a particular machining process specified by the geometry of the tool/workpiece and the material properties, as specified in Table 1.2. Both relate to the bonded machine. Fig. 1.19(a) for machining with a slot cutter and Fig. 1.20(a) when a helix cutter is used. 

The horizontal asymptotes of the hyperbolic line dividing the unconditionally and conditionally stable regions of the stability charts, at and W oi are related to the maximum negative in-phase amplitudes of the operative response locus ... 

Fig. 1.19. Theoretical and experimental stability charts of bonded machine with slot cutter, (a) Theoretical stability chart = 0-63 X 10" N/jum/jum C = 0 0021 Zc = 2). (b) Experimental stability chart.

For the calculation of the stability chart for the helix cutter a depth of cut ratio of d/R = 0-2 was chosen. The number of cutting teeth in continuous contact varied between = 1 and = 2-0 though, for reasons previously explained," the maximum was z<, = 1-1. It was thus taken to be z = 1. 

With these data, and those in Table 1.6, the stability chart was calculated and it is presented in Fig. 1.20(a), row I. Note the very much greatervalueof IFmoi = 24-8 mmandlF o2 = 3-5 mm compared to those obtained in the case of the slot cutter (Fig. 1.19(a)). However, the two stability charts are not comparable since they correspond to different values ofz and d/R (Table 1.6). As far as the d/R ratios are concerned, the very much smaller value of the helix cutter was necessary since otherwise the available drive power would have been exceeded, as will be seen from the experimental results. 

The experimental stability charts for the bonded machine, determined with the slot and the helix cutters, are presented in Figs 1.19(b) and 1.20(b), respectively. A comparison with the theoretically predicted charts shown in Figs 1.19(a) and 1.20(a) indicates good correspondence, both as far as the variation of the width of cut and that of the chatter frequency are concerned. Note that the existence of two sets of unstable lobes is confirmed. Similarly, the chatter frequency of these varies as predicted. 

In the theoretical stability charts (Figs 1.19(a) and 1.20(b)) there is a speed range in which the two sets of unstable lobes overlap. The question arises as to the physical meaning of this. 

Using the data contained in Fig. 1.18(c) and (d), the stability charts of the cast-iron machine can be predicted with the method outlined previously. Figure 1.25(a) is the chart for the slot cutter and Fig. 1.25(c) is for the helix cutter. In these, for simplicity, only the lobes corresponding... 

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