Contact Whirling Vibration of a Rotating Shaft Supported by a Repulsive Magnetic Bearing and the Influence of the Axial Displacement on Its Suppression

2011 ◽  
Author(s):  
Tomohiro Sugai ◽  
Tsuyoshi Inoue ◽  
Yukio Ishida
Keyword(s):  
Rotational Speed ◽  
Critical Speed ◽  
Nonlinear Coefficient ◽  
Magnetic Bearing ◽  
Axial Displacement ◽  
Damping Coefficient ◽  
Rotating Shaft ◽  
Escape Speed

A rotating shaft supported by a repulsive magnetic bearing may contact with a backup bearing during the passage of the critical speed as the damping coefficient of the repulsive magnetic bearing is small. This paper investigates the contact vibration during passage of the critical speed. Particularly, the influence of the axial displacement of the repulsive magnetic bearing on the escape speed from the contact vibration is focused. As a result, it is clarified that the rotational speed of the escapement from the contact vibration decreases as the axial displacement increases. It is explained by the change of both the linear stiffness and nonlinear coefficient in the increase of the axial displacement.

Blade-Shaft Coupled Resonance Vibration by Using Active Magnetic Bearing Excitation

2008 ◽  
Author(s):  
Norihisa Anegawa ◽  
Hiroyuki Fujiwara ◽  
Osami Matsushita
Keyword(s):  
Natural Frequency ◽  
Rotational Speed ◽  
Critical Speed ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Dynamic Vibration Absorber ◽  
Blade Vibration ◽  
Lower Natural Frequency ◽  
Damped System ◽  
Spring System

The turbine generator requires sufficient reliability as a major component of the power plant. The rotor dynamics calculates the critical speed of the shaft-bearing system for design to avoid appearance of the critical speed, while the blade dynamics calculates the natural frequency of the blade to avoid nX resonance. For longer blades, however, the lower natural frequency requires that the design of the shaft and blade takes into account the coupling of the blade vibration mode with nodal diameter k = 0 and k = 1 with the vibration of the shaft. The present work analyzes the coupling of the parallel motion of the shaft with the in-plane vibration of the blade within k = 1 modes. More specifically, the existence of an unstable region due to coupling and the coupled resonance in an eight-blade (N = 8) where each blade is assumed to be a 1-DOF mass-spring system were analyzed in detail. Analysis was also made on the forced vibration of a stable damped system. At a rotational speed Ω = |ωs − ωb|, the vibration of the shaft was limited to a relatively small amplitude due to anti-resonance points resulting from the dynamic vibration absorber effect, while the resonance of the blades was relatively big amplitude. A violent coupled resonance resulting from the dynamic absorber effect of the blades and shaft was observed at a rotational speed Ω = ωs + ωb. The resonance in blade vibration at Ω = |ωb − ωs| was experimentally confirmed.

Vibration of the Vertical Rigid Rotor Supported by a Repulsive-Type Magnetic Bearing: Effects of Both the Axial Displacement and the Magnetical Anisotropicities of Magnets

2007 ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Yukio Ishida ◽  
Tomohiro Sugai
Keyword(s):  
Permanent Magnet ◽  
Magnetic Bearing ◽  
Axial Displacement ◽  
Rigid Rotor ◽  
Rotating Shaft ◽  
Restoring Force ◽  
Uniform Magnetization ◽  
Nonlinear Force ◽  
Linear And Nonlinear ◽  
Force Characteristics

Magnetic bearing is considered for the usage in various industries. This paper investigates vibration of the rotating shaft supported passively by a repulsive-type magnetic bearing. The permanent magnet on the market not only has strong nonlinear force characteristics, but also may have a few percents of non-uniform magnetization characteristics. Also nonlinear force characteristics change as axial displacement of the shaft. Restoring force of a repulsive-type magnetic bearing is evaluated numerically considering the effects of both the axial displacement of the shaft and the magnetical anisotropicities of the inner and outer magnets. The occurrences of not only the linear and nonlinear parametric characteristics, but also the excitational forces for each pattern of magnetical anisotropicities are observed and they are evaluated in terms of the axial displacement. Furthermore, the influence of each magnetical anisotropicity pattern on the occurrences of various resonance phenomena is clarified.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

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