• 한국정밀공학회지
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• 제17권2호
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• pp.58-63
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• 2000

The dynamics of spindle-bearing-workpiece system significantly affects the cutting condition and stability in milling process. The present paper investigates the chatter stability of milling process due to the change in the dynamics of spindle-bearing-workpiece systems. In particular, the present paper focuses on chatter stability due to the presence of gyroscopic effect. An eigenvalue problem approach to the stability of milling process is extensively used in this paper. To incorporate the rotational speed dependent gyroscopic effect, an iterative algorithm is proposed. A numerical example is provided for examining the chatter stability problem in the presence of gyroscopic effects.

• 한국지진공학회논문집
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• 제2권2호
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• pp.1-12
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• 1998

여섯 성분의 지진에 의한 지반속도를 받는 회전기계-기초시스템의 거동을 해석하기 위해 회전기계-기초시스템을 회전원판, 회전축, 윤활유막 베어링, 주각, 그리고 뼈대기초로 구성된 것으로 이상화한다. 이때 회전기계-기초의 동적거동을 나타내는 지배운동방정식은 Gyroscope 효과와 Coriolis 효과, 윤활유막의 동적특성 그리고 지반의 병진과 회전거동을 고려하여 얻는다. 지반의 회전거동, Gyroscope 효과, 그리고 Coriolis 효과들이 회전기계-기초시스템의 전체거동에 미치는 영향을 해석예젤르 통해 고찰한다. 해석결과 회전기계-기초시스템의 지진해석에 있어서 지반의 회전거동 성분과 Gyroscope 효과의 영향을 포함하여야함을 알 수 있다.

• 한국소음진동공학회논문집
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• 제11권7호
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• pp.275-286
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• 2001

The research presents an analytical theory to calculate the characteristics of the bal bearing with waviness in its rolling elements considering the centrifugal force and gyroscopic moment of bal. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. and the waviness of rolling elements is modeled by sinusoidal function to calculate the contact force at each ball. The numerical solutions of governing equation of berating due to waviness are calculated by using the Newton-Raphson method. The accuracy of the research is validated by comparing the contact force. contact angle in case of considering the centrifugal force and gyroscopic moment of bal and the contact force and vibration frequencies in cases of considering waviness with the prior researches respectively. It investigates the stiffness, contact force. displacement and vibration frequencies of the ball bearing considering not only the centrifugal force and gyroscopic moment of ball but also the waviness of the rolling elements.

• 한국정밀공학회지
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• 제29권6호
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• pp.671-679
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• 2012

This paper presents an estimation procedure for axial displacement in spindle equipped with angular contact ball bearings due to rotational speed. High-speed spindle-bearing system experiences axial displacement due to thermal expansion and rotational speed-dependent characteristics of angular contact ball bearings. This paper deals with the axial displacement caused by the rotational speed-dependent effects such as centrifugal force and gyroscopic moments. To this end, a bearing dynamic model is established that includes all the static and dynamic properties of angular contact ball bearing. An analytical formula to calculate the axial displacement based on contact angles between ball and races is derived to discuss the physics regarding the axial displacement in spindle. The proposed dynamic model is compared with a reference and a commercial program. Numerical examples are presented to show the effects of centrifugal force and gyroscopic moment on the axial displacement. The proposed model is also validated with an experimental result.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권1호
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• pp.17-35
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• 2016

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.

• Journal of Advanced Marine Engineering and Technology
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• 제30권8호
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• pp.885-893
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• 2006

A dynamic model of turbo air compressor having multi-helical gear pairs is developed by transfer matrix method. The model accounts for the shaft and bearing flexibilities, gyroscopic effects and the force couplings among the transverse, torsion, and axial motions due to gearing. The program which can be used to analyze and predict the vibrational characteristics by the mass unbalance of the rotors and gear transmission error of turbo compressor is developed with this system model We expect this developed program to contribute the reduction of the vibration/noise on turbo compressor in the field of both design and manufacturing and can be used as a basic sub-program for CAD/CAM of low-noised gear teeth also.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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• pp.297-303
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• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Steel and Composite Structures
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• 제51권4호
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• pp.457-471
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• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• 제어로봇시스템학회논문지
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• 제19권6호
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• pp.501-507
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• 2013

This paper presents the development and balancing control of GYROBO, a one wheeled mobile robot system. GYROBO is a disc type one wheel mobile robot that has three actuators, a drive motor, a spin motor, and a tilt motor. The dynamics and kinematics of GYROBO are analyzed, and simulation studies conducted. A one-wheeled robot, GYROBO is built and its balancing control is performed. Experimental studies of GYROBO's balancing abilities are conducted to demonstrate the gyroscopic effects generated by the spin and tilt angles of a flywheel.

• 한국정밀공학회지
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• 제23권2호
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• pp.113-121
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• 2006

This paper established the dynamic model of a flexible Timoshenko beam capable of geometrical nonlinearities subject to large overall motions by using the finite element method. Equations of motion are derived by using Hamilton principle and are formulated in terms of finite elements using CO elements in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. In the final formulation are presented Coriolis and Gyroscopic forces as well as linear and nonlinear stiffnesses effects for the forthcoming numerical computation.