Abstract
Bending stiffness variation (BSV) is a common problem causing vibration in large rotating machinery. BSV describes lateral bending stiffness and its variation as a function of the rotational angle. It has been observed that BSV causes excitation exactly twice per revolution, which leads to vibration problems, especially at half critical speed. BSV is caused by rotor geometry errors if the material is assumed to be homogeneous and linearly elastic. Therefore, the study investigated BSV with harmonic roundness components, which are commonly used in industry to describe the geometry of a rotor. Hence, the results are easily applicable in the industry. The research was conducted primarily by analytical means, but also static simulations and numeric calculations were used. The results clearly showed that when the effect of single harmonic roundness components in rotor cross-sections were observed, only the second component could produce BSV. However, when component pairs were studied, they produced BSV also without the second component. If the second component was included, the profile produced BSV the most aggressively. A generated arbitrary roundness profile, including components 3–50 with random phases and amplitudes, indicated that BSV occurs always twice per revolution despite different components in the profile. The results improve the possibilities of eliminating excessive BSV in the industry, when certain components and component pairs can be avoided.
Highlights
Bending stiffness variation (BSV) is an interesting area of research, as the phenomenon has long been a common problem within industry
This paper focuses solely on BSV caused by static geometry errors, which can be described with harmonic roundness components
The results demonstrate that the superposition principle, in which the effect of two or more components can be solved separately by combining the effects of single components, is not applicable when calculating BSV
Summary
Bending stiffness variation (BSV) is an interesting area of research, as the phenomenon has long been a common problem within industry. This research paper tackles the BSV problem, providing novel tools to identify and eliminate BSV already at a manufacturing phase inspecting rotor geometry. This is achieved by investigating BSV from the perspective of the common definition of roundness, which is used to describe the manufacturing quality of round workpieces. Machining or casting can produce significant roundness errors to a rotor affecting second moment of area of each cross-section and eventually BSV of a rotor. A correlation between roundness and BSV provides a universal method to estimate BSV caused by geometry errors. The method can be generalized for symmetrical rotors, whose geometry can be measured and defined using roundness components
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