Rotation frequency

Varberg T D and Evenson K M 1992 Accurate far-infrared rotational frequencies of carbon monoxide Astrophys. J. 385 763-5... 

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. 

Torsional criticals should be at least 10% away from the first or second harmonics of the rotating frequency. Torsional excitations can be excited by some of the following ... 

If there are real frequencies of the same magnitude as the rotational frequencies , mixing may occur and result in inaccurate values for the true vibrations. For this reason the translational and rotational degrees of freedom are nonnally removed from the force constant matrix before diagonalization. This may be accomplished by projecting the modes out. Consider for example tire following (normalized) vector describing a translation in the x-direction. 

Other forces, such as the side-load created by V-belt drives, also generate unique frequencies or modify existing component frequencies. For example, excessive belt tension increases the side-load on the machine-train s shafts. This increase in side-load changes the load zone in the machine s bearings. The result of this change is a marked increase in the amplitude at the outer-race rotational frequency of the bearings. 

In most cases, a defective cable or transducer generates a signature that contains a ski-slope profile, which begins at the lowest visible frequency and drops rapidly to the noise floor of the signature. If this profile is generated by defective components, it will not contain any of the normal rotational frequencies generated by the machine-train. 

With the exception of mechanical rub, defective cables and transducers are the only sources of this ski-slope profile. When mechanical rub is present, the ski slope will also contain the normal rotational frequencies generated by the machine-train. In some cases, it is necessary to turn off the auto-scale function in order to see the rotational frequencies, but they will be evident. If no rotational components are present, the cable and transducer should be replaced. 

Turbines use both rolling-element and Babbitt bearings. Narrowbands should be established to monitor both the normal rotational frequencies and failure modes of the specific bearings used in each turbine. 

Process rolls are commonly found in paper machines and other continuous process applications. Process rolls generate few unique vibration frequencies. In most cases, the only vibration frequencies generated are running speed and bearing rotational frequencies. 

Rolling-element bearings The ability to monitor rolling-element or anti-friction bearing defects requires the inclusion of multiples of their rotating frequency. For example, with ball-pass inner-race bearings, the bandwidth should include the second harmonic (2x). 

Variable-speed machinery Variable-speed machine-train narrowband windows should be converted to their relationship to the running speed (lx). For example, if the frequency of the ball-pass inner-race rolling-element bearing is calculated to be 5.9 times the primary shaft running speed, then the narrowband window should be set as 5.3x to 6.2x. This allows the microprocessor to track the actual bearing rotational frequency regardless of the variation in running speed. 

With sleeve or Babbitt bearings, looseness is displayed as an increase in sub-harmonic frequencies (i.e., less than the actual shaft speed, such as 0.5x). Rolling-element bearings display elevated frequencies at one or more of their rotational frequencies. Excessive gear clearance increases the amplitude at the gear-mesh frequency and its sidebands. 

There are four normal rotational frequencies associated with rolling-element bearings fundamental train frequency (FTP), ball/roller spin, ball-pass outer-race, and ball-pass inner-race. The following are definitions of abbreviations that are used in the discussion to follow. 

The speed of the ball/roller rotating relative to the inner race generates the ball-pass inner-race rotational frequency (BPFl). The inner race rotates at the same speed as the shaft and the complete set of balls/rollers passes at a slower speed. They generate a passing frequency that is determined by ... 

Rolling-element bearing defect frequencies are the same as their rotational frequencies, except for the BSF. If there is a defect on the inner race, the BPFl amplitude increases because the balls or rollers contact the defect as they rotate around the bearing. The BPFO is excited by defects in the outer race. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

Let us consider first quantum J-diffusion. It is carried out by purely non-adiabatic collisions realized for anc is the average rotational frequency. A semiclassical analogue of the infinite-order sudden... 

The principal advantage of SCS in comparison with IOS is that the adiabaticity of collisions may be taken into account. The difference between actual cross-sections and their purely non-adiabatic estimation is not large but increases with rotational frequency. As shown in Fig. 5.5 the adiabatic correction improves even qualitatively the high-frequency alteration of cross-sections by minimizing the discrepancy between SCS... 

One also needs to be careful when using the slope of the Koutecky-Levich plot to determine av of the catalytic film. Examples of metaUoporphyrin-catalyzed ORR have been reported where, above a certain value of the electrode rotational frequency, the catalytic currents became independent of Koutecky-Levich model, either because the rate of charge or substrate transfer within the film became rate-limiting or the catalyst became partially samrated with O2 [Boulatov et al., 2002 Song et al., 1998 CoUman et al., 1980]. In other cases, the versus graphs may remain mostly linear within the experimental... 

The induced dipole moment in a given direction fluctuates at double the rotational frequency of the molecule as shown schematically below. The upper diagram shows the electric field in phase with a rotating polar molecule. 

---