Influence of Gyroscopic Moments on the Unbalance Force in Rotor Systems Abstract- This paper the unbalance excitation force is analyzed to be used as excitation medium in the dynamic characterization of rotors. Analytical and numerical models were used to obtain frequency response Bode and Campbell diagram using unbalance excitation force. With the obtained results of the models is concluded that the gyroscopic effects affect the effectiveness of the unbalance force in the excitation of rotors and spite of the force of unbalance does not excite the backward precessional whirl mode in rotors with isotropicbearings; Despite these circumstances, unbalance forceisuseful and easy to apply for the modal characterization of rotordynamic systems. Keywords—gyroscopic moment, unbalance force, dynamic characterization, unbalance rotors I. INTRODUCTION The identification of spatial and modal properties ofa dynamic system is a common practice in modal analysis and rotordynamic [1]. To achieve the identification of dynamic properties, it is necessary toexcite the dynamic systems by a natural input force or a controlled artificial force. In addition, the measure the input and output response signal to be analyzed on the time or frequency domain [2]. When a rotating structureis in operation, the structuralexcitationis the principal problem to apply identification techniques in rotordynamic. Different excitation devices have been developed and used for real machines o experimental prototypes, these can be preload shaft, magnetic bearing, impact hammer, unbalance of a second shaft, electromagnetic shaker (by an shaft rider) and unbalance force device [3]. The unbalance forces occur on rotating structures for their own operation and can be used for dynamic characterization. The unbalance is the main principal cause of vibration on rotating machines but this onecan also be used to excite a rotating system without connecting it to excitation equipment as electromagnetic exciters or inertial motors. excitation by unbalance is atechnique very easy to apply and depends onthe rotation speed. The unique disadvantage is that only can be applied in balancing planes [4, 5, 6]. However, the ability of unbalance forceto excitation a rotor depends onfactors such as: the forceapplication point, the gyroscopic effects and bearing characteristics of the rotor. This work present an analysis of gyroscopic effects and unbalance force in the excitation for rotors in order to dynamic characterization. For thisreason, analytical models and models of finite element of rotors are used to introduce response diagrams and Campbell diagrams using unbalance excitation force. II. SYNCHRONOUS UNBALANCE EXCITATION The unbalance force occurs when an eccentric mass spin around a principal axis of inertia and this is the reason of the conversion of rotating energy in passive lateral vibrations. This is a condition of unequal distribution of mass in the radial direction to each section of the shaft. This establishesa condition of unbalance in the center of mass of the rotor, which does not coincide with its axis of rotation. If the first lateral mode of vibration in an isotropic rotor is considered then the unbalance distribution may be considered as an average of a force composed of a mass m at a radius r. The magnitude of the unbalance force depends directly on the speed of rotation of the body and it is expressed as: = Ω 2 (1) The magnitude of unbalance force can be represented as the addition of components of one vector around each reference axisand it can be expressed as: = 0 cos Ω + 0 Ω (2) = Ω = Ω (3) Whereand are components of the unbalance force to each axis. The unbalance excitation force can also be represented using a harmonic excitation force within movement equation as: Pedro Cruz Departmentof Mechanical Engineering The Autonomous University of San Luis Potosí. San Luis Potosí, México. Jose Luis Arguelles Departmentof Mechanical Engineering The Autonomous University of San Luis Potosí. San Luis Potosí, México. Rafael Figueroa The Sonora Institute of Technology (ITSON) Sonora, México. Josefa Morales Applied Mathematics Institute for scientific and technological Research of San Luis Potosi. San Luis Potosí, México. International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 www.ijert.org IJERTV3IS100884 (This work is licensed under a Creative Commons Attribution 4.0 International License.) Vol. 3 Issue 10, October- 2014 971
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Influence of Gyroscopic Moments on the Unbalance …...Keywords—gyroscopic moment, unbalance force, dynamic characterization, unbalance rotors I. INTRODUCTION The identification
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Influence of Gyroscopic Moments on the
Unbalance Force in Rotor Systems
Abstract- This paper the unbalance excitation force is analyzed
to be used as excitation medium in the dynamic characterization
of rotors. Analytical and numerical models were used to obtain
frequency response Bode and Campbell diagram using
unbalance excitation force.
With the obtained results of the models is concluded that the
gyroscopic effects affect the effectiveness of the unbalance force
in the excitation of rotors and spite of the force of unbalance
does not excite the backward precessional whirl mode in rotors
with isotropicbearings; Despite these circumstances, unbalance
forceisuseful and easy to apply for the modal characterization of