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CSME 2021/02
Volume 42 No.1
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51-62
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Vibrations of Rotating Ring Under Electric Field
Tao Yua, Jiange Koua and Yuh-Chung Hub
aSchool of Mechatronics and Automobile Engineering, Yantai University, Yantai 264005, China
bDepartment of Mechanical and Electro-Mechanical Engineering, National ILan University, ILan, 26047 Taiwan
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Abstract:
The vibration of rotating ring has got attention due to its wide application in engineering, such as vibratory ring gyroscope. This paper proposes an analytical model for the vibration of a rotating ring subjected to uniform electric field. The static pull-in voltage of a stationary ring is derived ahead the vibration analysis of the rotating ring. Then, a linearized electric-field model is derived and agrees well with the non-linear model when voltage lower than the static pull-in voltage. It is then applied on the analysis of the vibrations and dynamic stabilities of the rotating ring before static pull-in. The electric field will introduce an equivalent negative stiffness, which is proportional to the square of the voltage, into the rotating ring and thereby soften the ring and probably makes the vibration of the rotating ring unstable. The most interesting is that once the voltage enters the unstable region, one can further raise the rotational speed higher than the so-called critical speed to escape the unstable region. This is due to the initial stress induced by centrifugal force, which is proportional to the square of the rotational speed, makes the ring more rigid.
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Keywords: Electrostatics, initial stress, MEMS, vibratory ring gyroscope, rotating ring, rotor dynamics, vibration.
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*Corresponding author; e-mail:
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©
2021
CSME , ISSN 0257-9731
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