Rotors vibration

In a real rotor system the amount and location of unbalances cannot always be found. The only way to detect them is with the study of rotor vibration. Through careful operation, the amount and the phase angle of vibration amplitude can be precisely recorded by electronic equipment. The relation between vibration amplitude and its generating force for an uncoupled mass station is... 

Mechanical imbalance is not the only form of imbalance that affects rotating elements. It is the condition where more weight is on one side of a centerline of a rotor than on the other. In many cases, rotor imbalance is the result of an imbalance between centripetal forces generated by the rotation. The source of rotor vibration also can be an imbalance between the lift generated by the rotor and gravity. 

The main concerns in the design and operation of a power recovery system are catalyst fines and temperature. Catalyst fines will lead to serious blade wear, deposits, power loss, and rotor vibration. Deposit occurs most frequently where flue gas velocities are at maximum levels, such as blade outer diameter. 

Causes of Blade Wear, Power Loss, and Rotor Vibration... 

A second implication of the collective, moleculelike model concerns the states with excitation in the bending mode. The bending mode of the linear rotor-vibrator is of course doubly degenerate. Hence, there are two independent states with one quantum of bending, which should be very similar to one another and should differ markedly from the state with no excitation as with all first excited vibrational states, their probability distributions should be zero at the potential minimum where the density of the unexcited state is a maximum. In this case, the implication is that the two first excited bending states... 

Performance tests are those tests that need to be carried out on combined equipment such as a gas-turbine driven generator or a pump driven by a high-voltage motor. In such cases the dynamic relationship between the various equipments is of interest. For example, rotor vibration, critical speeds, run-up time to full speed, starting up and shutting down sequences, full-load and over-load performances, heat dissipation and cooling medium performance. 

It is apparent, on the basis of the properties presented here, that neither the rotor-vibrator nor the Hartree-Fock representation is overwhelmingly better than the other in all respects for all states, even for the states discussed here in which both electrons are in the same or adjacent shells. State by state, property by property, sometimes... 

What can be the outcome of this inference If the RV representation is indeed somewhat better, one might guess that expansion of the exact function in a (truncated) basis set of rotor-vibrator functions would converge faster than a conventional expansion in products of one-electron, independent-particle functions. An investigation of this question is in progress now. 

As the observed power deficit had been explained to a very large extent, several measures were identified to enable its reduction. One measure would be to optimize the flow conditions for the inflow and outflow areas of the compressor and turbine sections in order to minimize the pressure drop losses and to achieve an optimum inflow into the blading. Moreover, a reduction of the blade gap losses would be required. That could be achieved by a reduction in rotor vibration and better selection of materials. The materials for both the rotor and the stationary blade carrier should be selected to optimize thermal expansions to achieve minimum gaps at operating conditions. One approach would be the replacement of the non-cooled austenitic stationary blade carrier in favor of a ferritic one, with cooling provided at necessary locations. Preferably no cooling at 750 C should be provided at all, taking into account possible improvements in avaible blade and rotor materials. A third approach that seems to be possible would be a further optimization of the stationary blade profiles and rotor blade profiles. 

Pivoted-pads thrust bearing are commonly used to support axial load in rotating machinery. Analysis of such bearing is complicated by the ability of each pad to pivot, as the rotor is displaced and to translate axially due to the flexibility of the pad support. This leads to dependance of linearized stiffness and damping coefficients on rotor vibrational frequency, pad inertia and support dynamic characteristics. 

The rotor vibrations shown correspond to a common unbalance for all cases and, as might be expected, the stiff rotor system is much less sensitive than the flexible rotor system. It is common knowledge that a plain circular profile results in the best synchronous damping properties in hydro-dynamic bearings. The relative figures in table 1 show that the partially grooved bearings approach the circular in this respect. 

JE House, Fundamentals of Quantum Mechanics, Academic Press, San Diego, 1998. Excellent elementary yet complete discussion of the principles of quantum mechanics including particle-in-a-box, rotors, vibrations, and simple atoms. 

All shafts equipped with instruments are hoUow to take all the cables which are connected via special high-speed slip rings to the static analysis instruments. Rotor vibrations are to be surveyed by pic-up s all other instruments and sensors are as for a common industrial platform gear. The wheel of the slave gear is not equipped with sensors, but the hydraulic axial force device and the input motor drive are connected to it. At the input shaft, the total losses of both gears can be measimed by means of a torque meter coupling. 

---