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Rotating moment for statically unbalanced rotor with elastic shaft

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Category: Geotechnical and mining mechanical engineering, machine building

Last Updated on 10 July 2014

Published on 10 July 2014

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Authors:

V.P. Franchuk, Dr.Sci.(Tech.), Professor, State Higher Educational Institution “National Mining University”, Dnepropetrovsk, Ukraine

O.Yu. Zhyvotov, Yuzhnoye State Design Office, Yuzhnoye SDO, Group Head, Dnepropetrovsk, Ukraine

Abstract:

Purpose. Study of total rotational moment components for statically unbalanced system of the “rotor – supports” type with a bent elastic shaft.

Methodology. In this paper, theoretical approaches of classical mechanics were used to study a process of unbalanced rigid body rotation. These approaches are based on a methodology to determine axial moments of inertia of statically unbalanced system of the “rotor – supports” type with a rigid (non-deformable) shaft and an elastic (deformable) shaft.

Findings. The conducted researches show that a statically unbalanced rotating system of the “rotor – supports” type, with an elastic shaft, is a system with variable moments of inertia that depend on the rotor’s rotation velocity. Therefore, moments that impede the rotor’s rotation occur in the system. The obtained general equation of moments makes it possible to find total rotational moment of the drive in each particular case. Total rotational moment is defined as the sum of rotational moments needed to ensure the “rotor –supports” system’s rotation and the production process.

Originality. The equation of rotation for the “rotor – supports” deformed system, which is given in the paper, reflects the behavioral features of a statically unbalanced rotor with a bent elastic shaft at different rotation velocities, such as the bent shaft’s middle line position with respect to the rotational axis, the rotor’s center of mass position with respect to the bent shaft’s middle line and the rotational axis, and the rotor’s angle of turn around the shaft’s middle line. The equation of total rotational moment, which is obtained in this paper, confirms and explains why the rotational moment, with rotor’s shaft bend, exceeds the rotational moment sufficient for rotor rotation with no shaft’s bend.

Practical value. The equation of total rotational moment can be used as a master equation in computer software to calculate required rotational moment of the drive or to process experimental results.

References:

1. Timoshenko, S.P. (2007), Kolebaniya v inzhenernom dele [Oscillations in Engineering] trans. from the third American edit., ed. by D.H. Young, URSS. KomKniga, Moscow, Russia.

Тимошенко С.П. Колебания в инженерном деле / С.П Тимошенко; пер. с 3-го амер. изд., перераб. совместно с Д.Х. Янгом. – М.: URSS. КомКнига, 2007. – 439 с.

2. Franchuk, V.P. and Antsiferov, A.V. (2000),“Use of Volterra principle and elasticity complex module for accounting of non-elastic resistances in oscillating systems with considerable asymmetry”, Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 2, pp. 30–32.

Франчук В.П. Использование принципа Вольтерры и комплексного модуля упругости при учете неупругих сопротивлений в колебательных системах с существенной асимметрией / В.П. Франчук, А.В. Анциферов // Науковий вісник НГУ. –2000. – № 2. –С. 30–32.

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2014-07-08  524.02 KB  1271

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