• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.3-6
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• 2000

The magnetic bearing system are intrinsically unstable, and need the feedback control of electromagnetic forces with measured displacements. So the controller design plays an important role in constructing high performance magnetic bearing system. In case of magnetic bearing system, the order of identified model is high because of unknown dynamics included in closed loop systems - such as sensor dynamics, actuator dynamics - and non-linearity of magnetic bearings itself. In this paper the identification and robust control of flexible rotor supported by magnetic bearing are discussed. We measure and identify overall system that contains not only flexible rotor model but also magnetic bearing and time delay. The structured and unstructured uncertainties are modeled that cover variations of natural frequencies, uncertainties in sensor and actuator gains and unmodeled dynamics. And desired performances are specified with several weighting function. Using augmented system that includes identified model, uncertainties, and weighting functions, μ-synthesis is applied to flexible rotor supported with magnetic bearing. The flexible rotor was spin up over the first flexible critical speed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.791-791
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• 2009

Hybrid air-foil magnetic bearing combines two oil free bearing technologies to take advantage of the strengths of each bearing with minimizing each other weaknesses. This paper presents bending mode vibration control of a flexible shaft supported by the hybrid air-foil magnetic bearing. An experiment set-up of a flexible shaft supported by the hybrid air-foil magnetic bearing is built. In order to verify the effectiveness of the hybrid bearing, unbalance responses of the flexible shaft supported by three different bearings: air-foil, magnetic and hybrid bearings are compared. Effect of load sharing between air-foil and magnetic bearings are investigated through changing control gain and offset displacements of magnetic bearing.

• Tribology and Lubricants
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• v.27 no.2
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• pp.57-64
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• 2011

Hybrid air-foil magnetic bearing integrates two oil free bearing technologies synergetically to adopt the strengths of two bearings with minimizing their weaknesses. This paper presents bending mode vibration control of a flexible shaft supported by the hybrid air-foil magnetic bearing. An experiment set-up of a flexible shaft supported by the hybrid air-foil magnetic bearing is built. In order to verify the effectiveness of the hybrid bearing, unbalance responses of the flexible shaft supported by three different bearings: air-foil, magnetic and hybrid bearings are compared. Effect of load sharing between air-foil and magnetic bearings are investigated through changing the control gain and the rotor center position of magnetic bearing. The experimental results shows that the hybrid bearing can control the bending mode vibration of the flexible shaft effectively and an optimal performance can be achieved with an appropriate load sharing between the air-foil and the magnetic bearings.

• Geomechanics and Engineering
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• v.35 no.1
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• pp.41-54
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• 2023

The use of a skirt, a vertical projection attached to the footing, is a recently developed method to increase the bearing capacity of soils and reduce foundation settlements. Most of the studies were focused on vertical skirted circular footings resting on clay while neglecting the rigidity and inclination of skirts. This study employs finite element limit analysis to investigate the bearing capacity enhancement of flexible and rigid inclined skirts in cohesionless soils. The results indicate that the bearing capacity initially improves with an increase in the skirt inclination but subsequently decreases for both flexible and rigid skirts. However, the rigid skirt exhibits more apparent optimum skirt inclination and bearing capacity enhancement than the flexible one, owing to differences in their failure mechanisms. Furthermore, the bearing capacity of the inclined skirted foundation increases with the skirt length, footing depth, and internal friction angle of the soil. In the case of rigid skirts, the bearing capacity increases linearly with skirt length, while for flexible skirts, it reaches a stable value at a certain skirt length. The efficiency of the flexible footing reduces as the footing depth and soil internal friction angle increase. Conversely, the efficiency of the rigid skirt decreases only with an increase in the depth of the footing. The paper also presents a detailed analysis of various failure patterns, highlighting the behaviour of inclined skirted footings. Additionally, nonlinear regression equations are provided to quantify and predict the bearing capacity enhancement with the inclined skirts.

• Journal of Power System Engineering
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• v.16 no.3
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• pp.22-28
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• 2012

Active magnetic bearings(AMBs) present a technology which has many advantages compared to traditional bearing concepts. However, they require backup bearings in order to prevent damages in the event of a system failure. In this study, the dynamics of an AMB supported rotor during impact on backup bearings is studied employing a detailed simulation model. The backup bearings are modeled using an accurate ball bearing model, and the model for a flexible rotor system is described using the finite element approach with the component mode synthesis. Not only the influence of the support stiffness, clearance and friction coefficient on the rotor orbit, but also bearing load are compared for various rotor system parameters. Comparing these results it is shown that the optimum backup bearing system can be applicable for a specific rotor system.

• Journal of KSNVE
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• v.8 no.3
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• pp.450-456
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• 1998

A rotordynamic analysis is performed with a centrifuge rotor-bearing system for the raing speed of 100,000 rpm. The system is composed of a centrifuge rotor(or simply the rotor), flexible shaft, motor rotor and shaft, and two support rolling element bearings of the motor shaft. Design goals are to achieve wide separation margins of critical speeds and favorable unbalance responses of the rotor at the associated critical speeds. The latter requirements are especially important as the system crosses multiple numbers of critical speeds and as the system may not have enough separaton margins around the rating speed. As the system adopts an extra-flexible shaft, it is shown that the rotor has satisfactory small unbalance responses over higher criticals while having an unsatisfactory large one at the first critical. To supress this a bumper ring or guide bearing needs to be installed at a suitable location of the flexible shaft. It is also shown that even with the flexible shaft the dynamics of the motor must be incoporated into the full system model to accurately identify the fourth critical speed, which is close to the rating speed, and higher ones. The analysis is based on the finite element method.

• Geomechanics and Engineering
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• v.30 no.1
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• pp.51-66
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• 2022

The article presents the results of finite element analyses carried out on skirted footings. The bearing capacity increases with the provision of the flexible and rigid skirt, but the effectiveness varies with various other factors. The skirts are more efficient in the case of cohesionless soils than cohesive and c-ϕ soils. Efficiency reduces with an increase in the soil strength and footing depth. The rigid skirt is relatively more efficient compared to the flexible skirt. In contrast, to the flexible skirt, the efficiency of the rigid skirt increases continuously with skirt length. The difference in the effectiveness of both skirts becomes more noticeable with an increase in the strength parameters, skirt length, and footing depth. The failure mechanism also changes significantly with the inclusion of a rigid skirt. The rigid skirt behaves as a solid embedded footing, and the failure mechanism becomes confined with an increase in the skirt length. Few small-scale laboratory tests were carried out to study the flexible and rigid skirt and verify the numerical study results. The numerical analysis results are further used to develop nonlinear equations to predict the enhancement in bearing capacity with the provision of the rigid and flexible skirts.

• Journal of Mechanical Science and Technology
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• v.16 no.12
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• pp.1583-1593
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• 2002

This paper discusses the model validation and vibration suppression of an AMB flexible rotor via additional LQG controller. The main difficulty in the vibration suppression of the flexible rotor using AMB is to realize a controller that can minimize resonance without injuring the stabilized rigid modes. In order to solve this problem, simple scheme for system modeling and controller design are developed. Firstly, the AMB flexible rotor is stabilized with a PID controller, which leads to a new stable rotor-bearing system. Then, authors propose the model validation procedure using measured open-loop frequency responses to obtain an accurate model of the AMB flexible rotor system. After that, LQG controller with modal weighting is designed to suppress resonances of the stable rotor-bearing system. Due to the poor controllability and observability of flexible modes compared to rigid ones, balancing of two Gramians is prerequisite for the fair LQG controller design. Simulation with step disturbance and experimental results of unbalance response up to 10,000 rpm verified the effectiveness of the proposed scheme.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.255-259
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• 1989

A suboptimal output feedback controller is designed and applied to a flexible rotor bearing system in order to control the unstable or lilghtly damped vibrations. The reduced order model is the truncated modal equation of the distributed parameter system obtained through the singular perturbation. The instability problem arising from the spillover effects caused by the uncontrolled high frequency modes is prevented through the constrained optimization by incorporating the spillover term into the performance index. The efficiency of the proposed method is demonstrated experimentally with a flexible rotor by using a magnetic bearing.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.6
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• pp.80-87
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• 1998

In this study, the effects of residual shaft bow and flexible bearings of a single disk rotor are investigated. The stiffness coefficients of a shaft with initial deflection are different from those of a straight shaft. The stiffness coefficients are calculated using Castigliano theorem considering initial deflections. The stiffness coefficients, which are obtained in this study, are in good agreement with FEM results. The speed which causes zero amplitude is shown to be the square root of the ratio of residual bow amplitude to unbalance eccentricity in the case of rigid bearings and isotropic flexible bearings, but not in anisotropic bearings.