Factor mechanical damping

Fatigue resistance is a major factor in industrial applications of textile materials (conveyer belts, automobile tyres, etc.). The fatigue resistance depends on the viscoelastic properties (mechanical damping) of the material, but equally on the soundness of bonds between the surfaces or interfaces. 

Quantitative relationship of chemical structure to physical properties in network polymers has received considerably less attention and study than in the case of thermoplastics. However, in recent years, progress has been made towards elucidation of the quantitative relationships between structure and properties. We have chosen to illustrate the quantitative effect of structural factors on physical properties in four representative areas glass transition temperature, modulus of elasticity, mechanical damping, solvent resistance. 

Vibration forces applying a dynamic stress load to viscoelastic materials results in a phase shift by the phase angle 8 between stress a and elongation e. The tangent of 8 is called the mechanical loss factor d or mechanical damping. Damping is thus a measure of the heat produced by application of dynamic loads as a result of internal friction (dissipatiOTi) (Fig. 24). 

Internal friction (IF), e.g. [102]. IF is a mechanical testing procedure which may be understood as a special technique of DMT A. The mechanical damping of the free oscillation is measured depending on the temperature at a constant frequency. The internal friction parameter is proportional to the natural logarithm of the ratio of two subsequent amplitudes of the oscillation and hence is also related to the damping factor tan (5, (see also section 12.1). 

With the closed-loop feedback mechanism, the bid price submitted by a robot for a task being auctioned can be regulated and fine-tuned to mitigate deviations of cost estimation due to operational uncertainties. Moreover, a series of adjustment values are averaged with related time-discounting factors to damp out possible fluctuations of adjustments, further safeguarding the robustness of the closed-loop regulation mechanism. Therefore, the stability of the proposed approach can be effectively secured. 

Viscoelastic properties may be expressed in terms of a dynamic storage modulus (E ), dynamic loss modulus (E ) and mechanical damping factor (tan8). Mathematically, they are defined as follows ... 

Figure 15.11. Variation of mechanical damping factor with temperature for (a) PP, PET, neat blend and MFCs, and (b) PP, neat blend and MFCs...

The energy loss due to interaction of the propagating plane wave with the coupling media can be calculated from the change of the quality factor (q) of the resonance on substitution of the reference liquid by the unknown (2,5). The quality factor Q is defined as the frequency of the resonance f. divided by the half power peak width Af., The observed width is a function of both th mechanical damping in the cavity, the effects of diffraction due to the finite size of the transducer and the attenuation per wavelength of the elastic displacement. The... 

These predictions of the simple phenomenological model are in accord with experimental dielectric data for amorphous solid polymers (4-7). The model does not specify detailed mechanisms for a and B processes, so, historically, the next stage was to develop such models. Many attempts were made and Table 1 summarizes a number of one-body models and their generalizations to include chain dynamics. Those for chain dynamics incorporate the basic models for one body motion e.g. the theory of Yamafuji and Ishida (22) is for coupled units each undergoing small-step rotational diffusion, while those of Jernigan (29) and Beevers and Williams (30) are for coupled units each undergoing motion in local (conformational) barrier systems. All the models in Table 1 exclude the short time effects associated with inertial factors and damped librations in a local potential. 

Dynamic mechanical testers apply a small sinusoidal stress or strain to a small sample of the polymer to be examined and measure resonant frequency and damping versus temperature and forced frequency. Instrument software computes dynamic storage modulus (G ), dynamic loss modulus (G") and tan delta or damping factor. Measurements over a wide range of frequency and temperature provide a fingerprint of the polymer with sensitivity highly superior to DSC. 

Note that if j = 1, (9.12) is formally identical with the classical expression (9.7) the classical multiple oscillator model, which will be discussed in Section 9.2, is even more closely analogous to (9.12). However, the interpretations of the terms in the quantum and classical expressions are quite different. Classically, o30 is the resonance frequency of the simple harmonic oscillator quantum mechanically 03 is the energy difference (divided by h) between the initial or ground state / and excited state j. Classically, y is a damping factor such as that caused by drag on an object moving in a viscous fluid quantum mechanically, y/... 

The variation of the damping factor (tan 5) with temperature was measured using a Polymer Laboratories Dynamic Mechanical Thermal Analyzer (DMTA). The measurements were performed on the siloxanfe-modified epoxies over a temperature range of — 150° to 200 °C at a heating rate of 5 °C per minute and a frequency of 1 Hz. The sample dimensions were the same as those used for flexural modulus test specimens. 

Other factors, such as mechanical clamping, damping in the electrical circuit, and temperature also affect the absolute accuracy. For this reason it is necessary to use calibration curves for quantitative work. In spite of these limitations, the quartz microbalance is an extremely sensitive and versatile sensor. 

---