• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.11 no.7
• /
• pp.275-286
• /
• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11a
• /
• pp.297-303
• /
• 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.

• Journal of the Korean Society for Precision Engineering
• /
• v.29 no.6
• /
• pp.671-679
• /
• 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.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• pp.2636-2646
• /
• 2002

This research presents an analytical model to investigate vibration due to ball bearing waviness in a rotating system supported by two or more ball bearings, taking account of the centrifugal force and gyroscopic moment of the ball. The waviness of rolling elements is modeled by the sinusoidal function, and it is incorporated into the position vectors of the race curvature center. The Hertzian con tact theory is applied to calculate the elastic deflection and nonlinear contact force while the rotor has translational and angular motions. Both the centrifugal force and gyroscopic moment of the ball and the waviness of the rolling elements are included in the kinematic constraints and force equilibrium equations of a ball to derive the nonlinear governing equations of the rotor, which are solved by using the Runge-Kutta-Fehlberg algorithm to determine the new position of the rotor. The proposed model is validated by the comparison of the results of the prior researchers. This research shows that the centrifugal force and gyroscopic moment of the ball plays the important role in determining the bearing frequencies, i.e. the principal frequencies, their harmonics and the sideband frequencies resulting from the waviness of the rolling elements of ball bearing. It also shows that the bearing vibration frequencies are generated by the waviness interaction not only between the rolling elements of one ball bearing but also between those of two or more ball bearings constrained by the rotor.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.20 no.3
• /
• pp.376-383
• /
• 2017

This paper describes the gyroscopic stability and the drag characteristics of the smart munition with a course correction fuze(CCF). A ballistic analysis was conducted to figure out the effect of the canards on the gyroscopic stability of the projectile. The analysis used the commercial ammunition performance evaluation software: Projectile Design and Analysis System(PRODAS). In particular, we compared the PRODAS analysis results to real field test results to investigate the influence of the CCF mounted projectile. In addition, some ballistic simulations were carried out to provide the conditions suitable for wind tunnel tests. Experimental results show that the added drag force by the canards is almost uniform regardless of the Mach number when the projectile is at the normal position where the angle of rotation and the angle of attack are both 0 degrees. However, as the angle of attack of the projectile increases, the additional drag force depends on the deflection of the canards.

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.2 s.179
• /
• pp.113-121
• /
• 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.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.49 no.8
• /
• pp.459-466
• /
• 2000

In this paper, we propose an attitude controller for an unstructured object using CMG(Control Moment of Gyro) subsystem, which has a stabilizer function. The CMG subsystem consists of one motor for spinning the wheel and the other motor for turning the outer gimbal. While the wheel of CMG subsystem is spinning at high speed, applying force to the spin axis of the wheel leads the torque about the vertical axis. We utilize the torque to control the attitude of object in this study. For the stabilizer function, in additiion, holding the load at the current position, the power applied to the gimbal motor of CMG will be cut, which result in the braking force to stop the load by gyro effect. However, due to the gear reduction connected to outer gimbal, slow load motion cannot generate the braking force. Thus, in this study, we are willing to make a holding force by applying control power to the gimbal motor from the signal of piezoelectric gyroscopic sensor that detected the angular velocity of the load. These two features are demonstrated in experiment, carrying a beam with crane. As a result, load was started to rotate by controlling gimbal positiion and was stopped by turning off the gimbal power. Moreover, slow movement of the load was also rejected by additional control with gyroscopic sensor.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.18 no.4 s.70
• /
• pp.385-393
• /
• 2005

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 in which the nonlinear constraint equations are adjoined to the system using Lagrange multipliers. The Newmark direct integration method and the Newton-Raphson iteration are employed here for the numerical study which is to demonstrate the efficiency of the proposed formulation.

• Journal of Magnetics
• /
• v.16 no.1
• /
• pp.6-9
• /
• 2011

Spin-motive force has drawn attention because it contains a fundamental physical property. Spin-motive force creates effective electric and magnetic fields in moving magnetization; a vortex is a plausible system for observing the spin-motive force because of the abrupt profile of magnetization. However, the time-averaged value of a spin-motive force becomes zero when a vortex core undergoes gyroscopic motion. By means of micromagnetic simulation, we demonstrates that a non-zero time-averaged electric field induced by spin-motive force under certain conditions. We propose an experimental method of detecting spin-motive force that provides a better understanding of spin transport in ferromagnetic system.

• Tribology and Lubricants
• /
• v.14 no.2
• /
• pp.26-34
• /
• 1998

This paper presents a high-speed performance analysis of ball bearings with ceramic balls under thrust loads. The sliding velocity profiles between a ball and raceways were obtained by the 3-D quasi-dynamic equations of motion including both centrifugal force and gyroscopic moment derived by vector matrix algebra. The friction at the contact areas was obtained by the Bair-Winer's non-Newtonian rheological model and the Hamrock-Dowson's central film thickness in EHL analysis. The nonlinear equations were solved by the Newton-Raphson method and the underrelaxation iterative method. The friction torques and ball behaviors with various loads, ball materials, and contact angles were predicted by this model. It was shown that the friction torque was sensitive to thrust load and contact angle, and that the friction torque and the pitch angle of the bearing with ceramic balls are smaller than those of the bearing with steel balls.