Torsional Vibration of Turbomachinery
Including application case studies and in-depth interpretation of computer-generated results, this book offers practical answers to preventing excessive damage, failure and noise due to vibrations in machines.
TABLE OF CONTENTS Torsional Vibration of Turbomachinery
9.2: Torsional Natural Frequency Calculation Case Studies
9.2 Torsional Natural Frequency Calculation Case Studies
9.2.1 Case study: Model creation and model adequacy
A uniform solid-steel shaft of cylindrical cross section is built in at one end and has a very short steel impeller at the other end, which has a polar moment of inertia of 1000 lb in 2. The steel shaft is 100 in in length and 5 in in diameter. The density and rigidity modulus of steel for this example are 0.283 lb/in 3 and 1.1538 10 7 lbf/in 2, respectively.
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How should this system be best modeled to determine its first five torsional natural frequencies using the finite elements defined in this book?
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How can the adequacy of the model be confirmed?
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What are the natural frequencies?
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If a new material was used for the shaft and the impeller, how would the frequencies change?
Solution to Case Study 9.2.1
1. The shaft should be modeled as a series of distributed finite elements (preferably with three nodes per element), and a point inertia should be used to represent the short impeller. The fixed-end condition can be simulated by placing an artificial point inertia of very high value relative to the total inertia of the system (e.g., 10 8 lb in 2). In this case the rigid-body mode calculated at 0 Hz is fictitious. All other modes will have virtually zero displacement at the fixed end, representing a nodal point for the simulated built-in end condition. The...
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