Rotor inertia

All turbomaehinery models eonsider rotor inertia, bearing losses, and windage. The intereonneeted piping is modeled as a pressure drop and a volume. 

A generator load drop of 100% is shown in Figure 4-89. For a valve elosure time of 1 see, a 5% overspeed is predieted. Note the eompari-son to the power reeovery string in Figure 4-83, where a 10% overspeed was predieted with a 10 see valve elosure. The mueh larger rotor inertia of the full power reeovery string allows the use of a slower and less expensive valve. 

The results shown in fig. 55a pertain to situations in which account was taken of the fact that constraints are commonly imposed on the overall diameter and length, as well as on the rotor inertia, while Q will ultimately be limited by thermal considerations. Region 1 corresponds to a maximum length limit. In this case a... 

WlC = total system inertia, lb ft (i.e., the equivalent WK plus rotor inertia)... 

A major limitation in controlled stress rheometers is instrument inertia. It is very similar to the transducer inertia described with eq. 8.2.1. The torque imposed on the drag cup must overcome reluctance torque, air bearing friction, and rotor inertia as well as the sample viscosity. The inertia portion dominates with low viscosity samples (Kreiger, 1990). Figure 8.2.11a illustrates the problem. Stress was commanded to increase linearly from 0 to... 

Rotor inertia affects all transient measurements on low viscosity fluids. Figure 8.2.1 lb illustrates the problem in sinusoidal oscillation testing. Even for this relatively high viscosity standard, it was not possible to obtain accurate data above about 0.2 rad/s without compensating for inertia. The most difficult corrections are for step changes in torque like start-up and recovery. Even for these cases, Franck (1992) reports that his correction software yields true values less than 2 seconds after the step for a very low 5 mPa s, viscosity standard. 

The formulation of the dynamics of a flexible mainipulator has been applied to a 1-link arm driven by a 30 Nt.m maximum torque actuator through an elastic joint (or transmission). The rotor inertia is Im = 0.15 kg,m. The joint torsional stiffness is Kt = 2500 Nt,m/rad, The link is an aluminium beam of cross section dimensions 0.001 X 0.066 m and length L = 1 m. The first 2 natural frequencies of the clamped-free beam representing the link are 0.8 and 5 Hz. These modes have been obtained from a discretization of the link in 6 Euler-Bemoulli beam elements. Material damping ratio is set equal to 0.02. 

For a symmetric rotor, or symmetric top as it is sometimes called, two of the principal moments of inertia are equal and the third is non-zero. If... 

A spherical rotor has all three principal moments of inertia equal ... 

An asymmetric rotor has all principal moments of inertia unequal ... 

In a molecule such as the asymmetric rotor formaldehyde, shown in Figure 5.1(f), the a, b and c inertial axes, of lowest, medium and highest moments of inertia, respectively, are defined by symmetry, the a axis being the C2 axis, the b axis being in the yz plane and the c axis being perpendicular to the yz plane. Vibrational transition moments are confined to the a, b or c axis and the rotational selection mles are characteristic. We call them... 

Cup anemometers have shaped cups mounted on the spokes of a wheel. The cups, under the action of the fluid forces, spin in a horizontal plane about a vertical shaft mounted in bearings. Vane or propeller types use a multibladed rotor, the axis of which is parallel to the flow direction as the rotating member. Both designs are commonly used for wind speed measurement or similar appHcations such as the velocity in ventilation ducts. Because of inertia, anemometers are most accurate under steady conditions. Velocity fluctuations cause readings that are too high. 

Reactive control is also possible through synchronous condensers. As they rotate, the rotor stores kinetic energy which tends to absorb sudden Huctuations in the supply system, such as sudden loadings. They are. however, sluggish in operation and very expensive compared to thyristor controls. Their rotating masses add inertia, contribute to the transient oscillations and add to the fault level of the system. All these factors render them less suitable for such applications. Their application is therefore gradually disappearing. 

An expander-eompressor unit must be meehanieally tested and all meehanieal tests should be witnessed by the owner-purehaser or his representative. If the manufaeturer does not have the eapability of testing with the fully bladed eontraet rotor, a dummy wheel may replaee the eompressor impeller. This dummy wheel is a disk with no blades, designed to duplieate the weight, eenter of gravity, and moment of inertia of the aetual eompressor wheel. 

If the load eonsists of a rotor of moment of inertia / and a damping deviee of damping eoeffieient C, then the load dynamies are... 

The torque after breakaway for acceleration to full speed must be considerably greater than the torque required by the driven machine. The greater the margin, the shorter will be the time to accelerate the inertia (Wk ) of the driven equipment and of the motor rotor to full speed. The Wk of the driven equipment must be obtained from the equipment manufacturer and given to the motor manufacturer. 

Design A produces exceptionally high breakdown torques but at the expense of high locket rotor currents that normally require provision for starting with reduced voltage. This motor is suitable for machines in which the friction and inertia loads are small. 

Strictly speaking, / is the reduced moment of inertia for the relative rotational motion of the system. For the case of a relatively light rotor such as CH3 it is the moment of inertia of the hindered rotor that appears in Eq. (143). 

In Chapter 3, a formula was presented which connects the normal vibrational frequencies of two rigid-rotor-harmonic-oscillator isotopomers with their respective atomic masses m , molecular masses Mi and moments of inertia (the Teller-Redlich product rule). If this identity is substituted into Equation 4.77, one obtains... 

E.3.3.3 Rotor systems that have low inertia and are subject to accidental unloading should be equipped with a quick-acting brake to prevent damage from overspeed. 

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