• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.7
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.11
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• pp.1064-1069
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• 2015

Control Moment Gyro (CMG) has been used as an indirect actuator of a single-wheel robot system GYROBO, developed at Chungnam National University. The flip motion of the gimbal system produces the gyroscopic motion onto the body system while the body motion also produces the gyroscopic motion onto the gimbal system inversely. In this paper, the intuitive equation of the inverse gyroscopic effect is derived as the direct relation between the rate of the body system and the rate of the gimbal system. Experiments on the inverse gyroscopic effect under the chaotically generated disturbance are conducted. Experimental data are approximated by a linear equation using the least square method.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.11
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• pp.1027-1033
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• 2015

For the attitude control of spacecraft, two variable-speed control moment gyros are proposed as main actuators in the article. Since a variable-speed control moment gyro (VSCMG) makes two control torques (gyroscopic torque and reaction torque), two VSCMGs are sufficient for controlling 3-axes attitude. Additionally, there are no singular conditions for two non-parallel VSCMGs. Since gyroscopic torque is usually much greater than reaction torque, the control performances of approximately 3 axes may not be the same. However, several missions can be accomplished by controlling two axes. For such missions, a selective axes control method is proposed. The method selects two axes for a certain task and controls the attitude of the selected axes. For the remaining axis, angular speed is controlled for stabilization. A hardware-in-the-loop simulation has been used to test VSCMG modules and to verify the proposed method. Two VSCMGs can be alternative actuators for small satellites.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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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.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.6
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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.

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

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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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.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4E
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• pp.20-25
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• 1999

To get accurate natural frequencies of an engine crankshafts, finite element equations of motion are developed, taking real geometries of the shaft into account. For the crankshaft with wide crank webs, a specialized rotating web element is developed. This includes the effects of rotary inertia, gyroscopic moment, and shear. After the finite element equations are constructed, eigenvalues are extracted from the system equations to get natural frequencies, based on the Sturm sequence method which exploits the banded forms of the system matrices to reduce computations. The scheme developed can be used for the free vibration analysis of any type of spinning structures which include skew symmetric gyroscopic moment matrix in the system matrices. The results are compared with experimental data in order to confirm the study.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.16 no.3
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• pp.188-196
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• 2016

For the balancing control of a one-wheel mobile robot, CMG (Control Moment Gyro) can be used as a gyroscopic actuator. Balancing control has to be done in the roll angle direction by an induced gyroscopic motion. Since the dedicated CMG cannot produce the rolling motion of the body directly, the yawing motion with the help of the frictional reaction can be used. The dynamic uncertainties including the chattering of the control input, disturbances, and vibration during the flipping control of the high rotating flywheel, however, cause ill effect on the balancing performance and even lead to the instability of the system. Fuzzy compensation is introduced as an auxiliary control method to prevent the robot from the failure due to leaning aside of the flywheel. Simulation studies are conducted to see the feasibility of the proposed control method. In addition, experimental studies are conducted for the verification of the proposed control.

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