Torsional resonance

Expander-compressor shafts are preferably designed to operate below the first lateral critical speed and torsional resonance. A flame-plated band of aluminum alloy or similarly suitable material is generally applied to the shaft in the area sensed by the vibration probes to preclude erroneous electrical runout readings. This technique has been used on hundreds of expanders, steam turbines, and other turbomachines with complete success. Unless integral with the shaft, expander wheels (disks) are often attached to the shaft on a special tapered profile, with dowel-type keys and keyways. The latter design attempts to avoid the stress concentrations occasionally associated with splines and conventional keyways. It also reduces the cost of manufacture. When used, wheels are sometimes secured to the tapered ends of the shaft by a common center stretch rod which is pre-stressed during assembly. This results in a constant preload on each wheel to ensure proper contact between wheels and shaft at the anticipated extremes of temperature and speed. 

Appears on gears like rotor critical speed. Vibration Torsional resonance Usually occurs only during startup... 

Besides the inherent lateral natural frequency characteristic, compressors are also influenced by torsional natural frequencies. All torsionally flexible drive trains are subject to non-steady or oscillatory excitation torques during normal operation of the system. These excitation torques can be an inherent function of either the driver or the driven equipment and, when superimposed on the normal operating torque, may appear to be of negligible concern. However, when combined with the high inertia loads of many turbomachinery trains and a torsional resonant frequency of the system, these diminutive ripples can result in a tidal wave of problems. 

The torsional resonant response of a system is an interaction of all the components in the train. Calculation of torsional natural frequencies is based on the entire system and these frequencies are valid only for that given arrangement. If any component of the train is replaced by an item with torsional characteristics different from the original, the system tor sional response must be recalculated and new torsional natural frequencies determined. Occasionally, an original equipment manufacturer is requested to calculate the torsional and lateral critical speeds of the supplied item. Unfortunately, the purchaser is unaware that this request is of limited value since the torsional response of a single item in a train is meaningless. Likewise, a torsional shop test will yield meaningless results if the train is not assembled and tested with every item destined for the field. 

Analogous studies can be done with torsional resonators in the kHz range. These have a lower sensitivity, but can bridge the frequency gap. 

Attenuation measurements are relatively easily obtained in the laboratory using various techniques (standing wave, pulse, torsional resonance, and torsional cyclic loading techniques— e.g., Hampton, 1967 Badiey et al., 1988 Bennell and Taylor-Smith, 1991 and other papers in Hovem et al., 1991). In-situ measurements are relatively rare compared with measurements of other soil properties (e.g., Hamilton, 1972, 1976 Taylor-Smith, 1974 Dunlop and Whichello, 1980 Dunlop, 1992). Attenuation, a, of both compressional and shear waves in surface sedi-menfs, is sfrongly dependenf on the frequency as presented in Equation 7.9... 

M. Reinstaedtler, U. Rabe, V. Scherer, J.A. Turner, and W. Arnold, Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry. Surface Science, (2003) in print... 

M. Reinstadtler, U. Rabe, V. Scherer, U. Hartmann, A. Goldade, B. Bhushan, and W. Arnold, On the nanoscale measurement of friction using atomic force microscope cantilever torsional resonances, Appl. Phys. Lett. 82, 2604 2606 (2003). 

G. Fritz, B.J. Maranzano, N.J. Wagner, and N. WUlenbacher High frequency rheology of hard sphere colloidal dispersions measured with a torsional resonator J. Non-Newtonian Huid Mech., 102 (2002) 149-156... 

Measurement of dynamic modulus of elasticity (Young s modulus, E) and modulus of rigidity (G) can be determined by measurement of the fundamental longitudinal and fundamental torsional resonant fi-equencies of regular shaped test specimens. Resonant frequencies are detected by means of either a mechanical or electrostatic drive or detection technique by means of a commercially available apparatus. 

In an ambitious study, the AIMS method was used to calculate the absorption and resonance Raman spectra of ethylene [221]. In this, sets starting with 10 functions were calculated. To cope with the huge resources required for these calculations the code was parallelized. The spectra, obtained from the autocorrelation function, compare well with the experimental ones. It was also found that the non-adiabatic processes described above do not influence the spectra, as their profiles are formed in the time before the packet reaches the intersection, that is, the observed dynamic is dominated by the torsional motion. Calculations using the Condon approximation were also compared to calculations implicitly including the transition dipole, and little difference was seen. 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Assume that oscillatory excitation torque of Tq sin cot is applied to the system in Figure 9-14. By definition, when the excitation frequency coincides with the torsional natural frequency of the model, all torques will balance and the system will be in a state of resonance. 

Once the driver and driven equipment have been chosen and it is deter mined that none of the items will be subject to any lateral vibration problems, the system torsional analysis is performed. If a calculated torsional natural frequency coincides with any possible source of excitation (Table 9-21, the system must be de-tuned in order to assure reliable operation. A good technique to add to the torsional analysis was presented by Doughty [8 j, and provides a means of gauging the relative sensitivity of changes in each stiffness and inertia in the system at the resonance in question. 

Hafner, K. E., Torsional Stresses of Shafts Caused by Reciprocating Engines Running through Resonance Speeds, ASME 74-DGPl, New York American Society of Mechanical Engineers, 1974. 

In this chapter, we first present a brief overview of the experimental techniques that we and others have used to study torsional motion in S, and D0 (Section II). These are resonant two-photon ionization (R2PI) for S,-S0 spectroscopy and pulsed-field ionization (commonly known as ZEKE-PFI) for D0-S, spectroscopy. In Section HI, we summarize what is known about sixfold methyl rotor barriers in S0, S, and D0, including a brief description of how the absolute conformational preference can be inferred from spectral intensities. Section IV describes the threefold example of o-cholorotoluene in some detail and summarizes what is known about threefold barriers more generally. The sequence of molecules o-fluorotoluene, o-chlorotoluene, and 2-fluoro-6-chlorotoluene shows the effects of ort/io-fluoro and ortho-chloro substituents on the rotor potential. These are approximately additive in S0, S, and D0. Finally, in Section V, we present our ideas about the underlying causes of these diverse barrier heights and conformational preferences, based on analysis of the optimized geometries and electronic wavefunctions from ab initio calculations. 

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