By Duncan Walker
Textual content provides worthy recommendations built over the author's life of paintings and examine in controlling torsional vibrations in rotating equipment. For mechanical engineers. DLC: Turbomachines--Vibration.
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Additional info for Torsional Vibration of Turbomachinery
It is assumed that the cross-sectional dimensions and material properties are constant along the length of the element. The element stiffness k can be obtained from the geometric and material properties presented in the torsional stiffness definition in Sec. 1. 4 shows the stiffness element free-body diagram with nodal displacements 1 and 2 and nodal torques T1 and T2. This element would be used in conjunction with the two-node inertia element developed in Sec. 1. The stiffness between nodes 1 and 2 is k.
For turbine-generator shaft response and subsynchronous natural frequency calculations, the inertia of components such as blades can be added to the inertia of the rotor that supports them (rigid connection). However, for accurate calculation of the supersynchronous modes in the vicinity of twice the electrical transmission system frequency, it is generally necessary to flexibly couple the inertia of the more flexible steam turbine blades to the rotor that supports them. These branched, coupled models are outside the scope of this book, because the book focuses on shaft response for which the subsynchronous modes generally dominate.
Torsional Vibration Mathematical Modeling Torsional Vibration Mathematical Modeling 35 An equivalent single angular velocity mathematical model is derived in App. A that will provide the same natural frequencies, and after back substitutions, the correct mode shapes and forced response results. The results are summarized here: ■ The equivalent inertia of each element is its actual value times its velocity ratio squared. The equivalent stiffness of each shaft span is obtained in the same way. ■ At a gear cluster the equivalent gear inertias are now summed to produce one equivalent gear inertia.