Damping measurements, methods

Figure 4.20 Damped oscillation method for measuring surface viscosities...

This paper summarizes different methods of pulsation dampening in high pressure plants, and shows how to control and optimize the effectiveness of damping measures by numerical pulsation analysis. 

In order to test the predictions of the model, plates were made up from selected formulations and tested in air. The thicknesses of the various layers were as stated previously, while the length was one meter and the width was one-third meter. Damping measurements were made by two different methods. In both cases, the plates were suspended in a shock chord and accelerometers placed at different locations on the plate. The first used a reverberation meter and the half-power method (16). In the second, an impact hammer was used to tap the structure and the outputs of the accelerometers fed into a Fourier transform based spectrum analyzer to examine the envelope of vibration (17). The results presented here are based upon the second method. 

The measurement method described in this article is an embodiment of the non-resonance, direct-force-excitation approach that subjects a double-lap shear sample of damping polymer to force from a vibration shaker. In concept this approach can be applied irrespective of whether the material is in a rubbery, glassy, or intermediate state. Each material specimen is small in size and behaves as a damped spring over the entire frequency range. The small specimen size is in contrast with some alternate approaches in which the specimens have sufficiently large dimensions to be wave-bearing. 

Figure 7-13. Damped pendulum method for measurement of friction. A view of the moving specimen in the cradle of the fixed specimens. After Y. Tamai [13].

Torsional Damping - One of the methods to measure the crystallinity of polytetrafluoroethylene is torsional damping. Other methods include infrared spectroscopy, x-ray diffraction, and ultrasonics. 

Mechanical Damping. The elastic energy behavior of resins at low temperatures was determined from the stress-strain relation. Small inelastic contributions, not detectable with that method can be determined by damping measurements using a free torsion pendulum. The mechanical loss, tan 8m, is plotted vs. temperature in Fig. 10. Low-temperature values were similar for the resins considered. No major structural dependence is indicated. (It is not within the scope of this paper to consider the relaxation maxima of resins.)... 

Common Methods for Damping Measurement Logarithmic Decrement and Bandwidth Method... 

Mechanical, as opposed to viscosity, measurements on fats are comparatively rare. Often this is due to the brittle nature of the materials, for example chocolate. However, one approach is to observe the major transitions using the Triton materials pocket or constrained layer damped beam method. At present, however, absolute values of moduli cannot be obtained. Nevertheless, transitions between polymorphs in cocoa butter were measurable. 

Although the RSF contains matrix-dependent quantities, their variations are damped to some extent by virtue of taking ratios, and in practice the RSF is assumed constant for low concentrations of A (e. g. <1 atom%). It can be evaluated from measurements on a well-characterized set of standards containing A in known dilute concentrations. The accuracy of the method, however, is not as high as in laser-SNMS and XPS. 

Potential methods of measurement for dilatation parameters are the damping of transverse and longitudinal surface waves and the damping of vibrating bubbles. For theory and measuring techniques see Wiistneck and Kretzschmar [47]. 

There are other, less commonly used, methods for measuring hardness. One is an impact method in which an indenter is dropped from a known height onto a specimen, and either the size of the indentation, or the coefficient of restitution, is measured. Another is the pendulum method in which a rocking pendulum is applied to a specimen surface. The damping of the pendulum s oscillations is a measure of the hardness. Still another is Moh s scratch method in which the ability of one specimen to scratch another is observed. These methods are described in various books (McColm, 1990), but only the... 

Tan landa, a damping term, is a measure of the ratio of energy dissipated as heat to the maximum energy stored in the material during one cycle of oscillation. For small to medium amounts of damping. G is the same as the shear modulus measured by other methods at comparable time scales. The loss modulus G" is directly proportional to the heat H dissipated per... 

Viscosity, defined as the resistance of a liquid to flow under an applied stress, is not only a property of bulk liquids but of interfacial systems as well. The viscosity of an insoluble monolayer in a fluid-like state may be measured quantitatively by the viscous traction method (Manheimer and Schechter, 1970), wave-damping (Langmuir and Schaefer, 1937), dynamic light scattering (Sauer et al, 1988) or surface canal viscometry (Harkins and Kirkwood, 1938 Washburn and Wakeham, 1938). Of these, the last is the most sensitive and experimentally feasible, and allows for the determination of Newtonian versus non-Newtonian shear flow. 

An associated technique which links thermal properties with mechanical ones is dynamic mechanical analysis (DMA). In this, a bar of the sample is typically fixed into a frame by clamping at both ends. It is then oscillated by means of a ceramic shaft applied at the centre. The resonant frequency and the mechanical damping exhibited by the sample are sensitive measurements of the mechanical properties of a polymer which can be made over a wide range of temperatures. The effects of compositional changes and methods of preparation can be directly assessed. DMA is assuming a position of major importance in the study of the physico-chemical properties of polymers and composites. 

While there are many methods for measuring modulus and damping, one of the simplest involves using a torsion pendulum (23, 24, 25) as illustrated in Figure 11. 

For methods which measure Young s modulus, , instead of the shear modulus, G, the analogous term for the damping is given by ... 

The successful numerical solution of differential equations requires attention to two issues associated with error control through time step selection. One is accuracy and the other is stability. Accuracy requires a time step that is sufficiently small so that the numerical solution is close to the true solution. Numerical methods usually measure the accuracy in terms of the local truncation error, which depends on the details of the method and the time step. Stability requires a time step that is sufficiently small that numerical errors are damped, and not amplified. A problem is called stiff when the time step required to maintain stability is much smaller than that that would be required to deliver accuracy, if stability were not an issue. Generally speaking, implicit methods have very much better stability properties than explicit methods, and thus are much better suited to solving stiff problems. Since most chemical kinetic problems are stiff, implicit methods are usually the method of choice. 

Surface viscosity has an important influence on the deformation of films and can also provide information about structure. Gaines [14] describes various methods of measuring this quantity. The damped torsion pendulum as developed by Langmuir and Schaefer [65] is probably the best device for making such measurements. Recent measurements of this type have been made by Buhaenko et al. [66]. Malcolm [67, 68] and Daniel and Hart [69] have carried out experiments which illustrate the important influence which viscosity has on the study of isotherms. 

Dynamic testing DMTA, DMA, torsional braid analysis (Enns and Gillham, 1983) is first used as a thermal analysis method to detect the transitions, using dissipation peaks. Certain commercial DMTA instruments have a relatively low accuracy in measuring forces and/or strains. In contrast, they give relatively accurate values of the damping factor tan 5, so that dissipation spectra tan 8 = f (oo, T), are very useful analytical tools. 

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