Loss factor tan

By monitoring the insulation condition of the windings during maintenance, at least once a year, which can be carried out by measuring (a) the polarization index (Section 9.5.3) and (b) the dielectric loss factor, tan S (Section 9.6) and making up the insulation as in Section 9.5.2, when the condition of the insulation is acceptable and only its level is less than permissible. 

For lower voltage systems, say. 2.5 to lU kV, measurement of dielectric loss factor tan 5. along similar lines, to those recommended... 

Fig. 4. Effect of nanocomposites on mechanical loss factor tan 8 vs temperature...

Both rolling resistance and heat buildup are related to hysteresis that is the amount of energy that is converted to heat during cychc deformation. It is well known that hysteresis of tread compounds, characterized by the loss factor, tan 8, at high temperature, is a key parameter. It not only governs heat buildup of the compounds under dynamic strain but also shows a good correlation with the... 

A coincidence between r and Tf, accompanied by the formation of a maximum of energy losses (peak of the loss modulus G" or of the loss factor tan <5 = G7G ), can be achieved by varying either the period Tf at constant temperature (isothermal experiment) or t (by changing the temperature) at the constant period Tf (isochronous experiment). The latter procedure is experimentally easier to implement and is therefore more frequently used. 

This equation implies that the relaxation strength of a molecular motion passes through a maximum at AH° = 2.4 RT and that for AH° = 0 no relaxation process can exist. An equation for the loss factor tan 6 derived from this theory was attempted81 for the... 

Figure 6.4 Decrease in the loss factor (tan 8) during cure, for the same epoxy-diamine system as that represented in Fig. 6.3, at different frequencies of the dynamic measurements. T] =70°C. (Matejka, 1991 - Copyright 2001 -Reprinted by permission of Springer-Verlag)... 

The loss factor, tan 8, can be measured with the aid of dynamic-mechanical experiments (such as the torsion pendulum). The deformation in such a test varies as indicated in Figure 7.13 the damping follows from the logarithmic decrement , A, it can be easily shown that... 

The most important dielectric properties are the dielectric constant, e, and the dielectric loss factor, tan 8. These properties are of interest for alternating currents indicates the polarizability in an electric field, and, therefore, it governs the magnitude of the alternating current transmitted through the material when used in a capacitor. For most polymers e is between 2 and 5, but it may reach values up to 10 for filled systems. 

Of more importance is the loss factor, tan 8, denoting the fraction of the transmitted alternating current lost by dissipation in the material. Here large differences occur between polymers, as indicated in Figure 8.10. It appears that polymers with the highest specific resistance also show the lowest dielectric losses. It should be remarked, that the values given are very schematical the losses are strongly dependent on frequency and temperature. 

Fig. 9.28 Influence of SiOz and CaO additions to the ferrite Mn0 6SZn0 2Fe204 on (a) resistivity (flm) and (b) loss factor ((tan 8)/fj n x ICC6) at 100 kHz (after [9]).

As discussed in Section 9.3.1, the quality of the ferrite is measured by its loss factor (tan <5)//tri which should be as small as possible, and in the following discussion it is assumed that this is the case. 

Figure 9.10. Viscoelastic Properties of Solid and Microcellular PLAand PLA-MWCNT nanocomposites (a) Storage Modulus as a Function of Temperature (b) Loss Factor (Tan-6) as a Function of Temperature. Reprinted with permission from S. Pilla et al., International Polymer Processing, XXII, p. 418,2007, 2007, Polymer Processing Society.

The second point is to compare the appropriateness of PD measurements with that of more conventional loss factor (tan 8) measurements. In general, tan 8 measurements show an integral over the insulating material in its entirety. Deviations from tan 8 due to an insulation impairment restricted to a small (local) area cannot be detected to have been caused by the limited... 

For the DMA trace in Fig. 35—typical for almost all reported literature data—it is obvious that both ac- and -relaxations are more pronounced for the /1-nucleated material than for its non-nucleated counterpart suggesting both its amorphous and crystalline phases to be more mobile. Varga showed the progressive increase of the maximum of the loss factor, tan 8, as Kfj was progressively increased from 0 to 75% [137]. This improved damping obviously favors fracture resistance [48,72,77,190]. Detailed correlations between the intensity of the relaxations and the impact strength in -nucleated PP would be beyond the scope of this review they are published elsewhere [111, 191]. 

The extensional dynamic storage modulus E and the loss factor tan 8 for a series of linear polyethylene tapes of different draw ratios are shown in Fig. 30(a) and (b). There are two features worthy of particular note. First, the modulus at low temperatures is about 160 GPa, which is about one half of the theoretical modulus and the maximum value obtained from neutron diffraction and other measurements. Secondly, the a and y relaxations are both dearly visible even in the highest draw ratio material, although the magnitude of tan 5 for the y relaxation reduces with increasing draw ratio. 

Fig. 33a. Storage modulus, E (at 5 Hz), as a function of temperature for drawn and isotropic POM Delrin 500) samples. Numbers on curves refer to deformation ratio b. The mechanical loss factor, tan 6. corresponding to the data of (a)...

A most useful measure of the degree of damping is the loss factor, tan 6, as defined in Eg.12 in terms of the energy dissipated per cycle, E, and the total... 

When a dielectric resonator is coupled with microwave circuits, the dielectric material responds to the frequency. The frequency selectivity of the microwave device depends on the loss quality of the materials. The selectivity Q ) of the dielectric materials is defined as the ratio of/ to A/, and the Q approximates the reciprocals of the loss factor (tan 5). The loss in DR (l/2 ) is the sum of the loss of dielectric materials (I/Qm). surface conduction HQ, and radiation loss (1/2,) ... 

The angle 8e describes the deviation of the phase shift between current and applied potential from the ideal value of 90°. Its projection on the real part of the total impedance Z therefore describes the ohmic part of the capacitor characteristic corresponding to a series resistance in the equivalent circuit. In practice, this number is used to specify the polarization losses of a capacitor. Analogously, the total loss factor tan 8C of a capacitor is defined by the ratio of the real and imaginary part of the total impedance Z. In addition to the polarization loss, this number considers unavoidable resistances due to lead wires and losses due to an imperfect insulation, plus the capacitive inductance I ... 

---