• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.925-934
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• 2005

The dynamic response due to the unbalance and crack and the quasi-static response due to gravity are analytically derived based on the complex transfer matrix. The additional slope is expressed as function of the bending moment at crack position based on the fracture mechanics concept, and inversely the bending moment is expressed as function of the additional slope at the crack position. At each angle step during the shaft revolution, the additional slope and bending moment are calculated by an iterative method. The transient behavior is considered by introducing Fourier series expansion concept for the additional slope. Simulation is carried out for a simple rotor similar to those available in the literature and comparison of the basic crack behavior is shown. Using the additional slope, the cracked rotor behavior is explained with the crack depth increased: the magnitude of the additional slope increases and the closed crack duration during a revolution decreases as the crack depth increases. The direction of unbalance is also shown as a factor to affect the crack breathing. Whirl orbits are shown near the sub-critical speed ranges of the rotor.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.3
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• pp.277-283
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• 2008

Balance shaft module contributes to reduce the engine-born vibration by compensating it from a unbalance mass with opposite phase but practically, this device has some problems during the operation in a high speed owing to the considerable amount of unbalance mass that leads to the large quantity of bending deformation as well as torque fluctuation at the balance shaft. To tackle two main problems, the design strategy on balance shaft is suggested by addressing the optimal location of unbalance mass and supporting hearing based on the formulation of objective function that minimizes critical issues, both bending deformation as well as torque fluctuation. The boundary condition of balance shaft assumes to be free such that any external force or contact component is not taken into consideration in this study.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1137-1147
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• 2005

The dynamic response due to the unbalance and crack and the quasi-static response due to gravity are analytically derived based on the complex transfer matrix. The additional slope is expressed as function of the bending moment at crack position based on the fracture mechanics concept, and inversely the bending moment is expressed as function of the additional slope at the crack Position. At each angle step during the shaft revolution, the additional slope and bending moment are calculated by an iterativemethod. The transient behavior is considered by introducing Fourier series expansion concept for the additional slope. Simulation is carried out for a simple rotor similar to those available in the literature and comparison of the basic crack behavior is shown. Using the additional slope, the cracked rotor behavior is explained with the crack depth increased: the magnitude of the additional slope increases and the closed crack duration during a revolution decreases as the crack depth increases. The direction of unbalance is also shown as a factor to affect the crack breathing. Whirl orbits are shown near the sub-critical speed ranges of the rotor.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.801-806
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• 2008

Large quantity of bending deformation as well as rotating torque fluctuation at the balance shaft are main struggles during the operation in a high speed rotation and thereby, two issues should be cleared at the design process of balance shaft module. Since two issues are highly related with balance shaft itself and particularly much sensitive to the location of both supporting bearing and unbalance mass, the design strategy on balance shaft should be investigated at the aspect of controlling two critical issues at the early stage of balance shaft design. To tackle two main problems, the formulation of objective function that minimizes critical issues, both bending deformation as well as torque fluctuation, is suggested to derive the optimal information on balance shaft. Then, optimal informations are reviewed at the practical logics and the guideline at the selection of locations, both supporting bearing and unbalance mass, is addressed at the final chapter.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1214-1221
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• 2009

A high-speed spindle can be very sensitive to rotating mass unbalance which has harmful effect on many machine tools. Therefore, the balancing procedure to reduce vibration in rotating system is certainly needed for all high-speed spindles. So, balancing procedure was performed with a spindle-bearing system for CNC automatic lathe by using numerical procedure. The spindle is supported by the angular contact ball bearings and the motor rotor is fixed at the middle of spindle. The spindle-bearing system has been investigated using combined methodologies of finite elements and transfer matrices. The balancing was performed through influence coefficient method and the comparison was made by whirl responses between before balancing and after balancing. As a result, balancing of simple spindle model reduced whirl orbit magnitude in case of a completely assembled spindle model.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.11 no.4
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• pp.104-110
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• 2012

The spindle with a built-in motor can be used to simplify the structure of machine tool system, while the rotor has unbalance mass inevitably. A high-speed spindle can be very sensitive to rotating mass unbalance which has harmful effect on many machine tools. Therefore, the balancing procedure to reduce vibration in rotating system is certainly needed for all high-speed spindles. So, it was performed with a spindle-bearing system for CNC automatic lathe by using numerical procedure. The spindle is supported by the angular contact ball bearings and the motor rotor is fixed at the middle of spindle. The spindle-bearing system has been investigated using combined methodologies of finite elements and transfer matrices. The balancing was performed through influence coefficient method and the comparison was made by whirl responses between before balancing and after balancing. As a result, balancing of simple spindle model reduced whirl orbit magnitude in case of a completely assembled spindle model.

• Transactions of the Korean Society of Automotive Engineers
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• v.18 no.4
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• pp.1-7
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• 2010

Large quantity of bending deformation as well as irregular rotating torque fluctuation are the main struggles of the balance shaft module during a high speed rotation. Since two issues are much sensitive to the location of both supporting bearing and unbalance mass at a balance shaft, it is recommended to construct a design strategy on balance shaft at the early stage so as to save developing time and effort before approaches to the detailed design process. In this paper, an optimal design formulation is proposed to minimize the elastic strain energy due to bending as well as the kinematic energy of polar moment of inertia in rotation. Case studies of optimal design are conducted for different mass ratio as well as linear combination of objective function and its consequence reveals that global optimum of balance shaft model is existed over possible design conditions. Simulation shows that best locations of both supporting bearing and unbalance are globally 20% and 80%, respectively, over total length of a balance shaft.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.5
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• pp.305-312
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• 2000

This study deals with the dynamic response of a rotor in Switched Reluctance Motor(SRM) caused by the unbalance force such as the unbalanced mass and electromagnetic force. The method to analyze the mechanical response of the rotor supported on the bearing is based on an extension of the 3-dimensional Transfer Matrix Method(TMM) coupled with the electromagnetic force calculated by Maxwell stress tensor. The displacement of the rotor as a function of frequency according to the position of the unbalanced mass is evaluated from the frequency response function (FRF). The rotor behaviour with the electromagnetic force is compared with that without the electromagnetic force. In addition, the resonance speeds and the vibration modes are analyzed and demonstrated in this paper. These results are useful in designing the mechanical rotor and in balancing properly the rotor to reduce vibration and noise.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.4
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• pp.511-519
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• 2013

Switching controllers for active magnetic bearings are claimed to minimize the copper losses because they do not use bias currents. In this study, we compare the performances of the switching controller with those of the widely used proportional-derivative (PD) controller. The PD controller is combined with a synchronous notch filter to reduce the effect of the unbalance disturbance. For a fair and objective comparison, the PD controller is designed systematically. The switching controller is designed so that the dynamics of the two controllers are almost identical. A system model is developed. This model includes the flexible modes of the rotor and the dynamics of the sensors and amplifiers. The simulation results show that the switching controller indeed reduces the copper loss at lower speeds. However, it fails to operate around the speed close to the bending mode of the rotor.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.22-29
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• 2011

Critical speed of high thrust liquid rocket engine turbopump is obtained through a rotordynamic analysis and a unloaded turbopump test is peformed for validation of the numerical model. The first critical speed predicted by the numerical analysis is correlated well with the test result for the bearing unloaded rotor condition only considering mass unbalance load. Using the previous rotordynamic model, critical speed variation is estimated as a function of varied bearing stiffness due to pump and turbine radial loads with relative angle difference. From the numerical analysis, it is found that the relative angle difference of pump and turbine radial loads greatly affects the critical speed. However, additional axial load reduces the effect derived from the relative angle difference of radial loads.