Damping Theory
Terminology of vibration mechanics
To evaluate the damping unit requires familiarity with the basic fundamental theory of vibration. Common terminology of vibration mechanics is listed below to assist you in understanding issues related to vibration.
- Free Vibration
- Free vibration takes place when a system oscillates under the action of forces inherent in the system itself and when externally impressed forces are absent. Based on the initial displacement or speed, the kinetic force and the restoring force of the whole system change each other periodically. Therefore, the system moves with simple harmonic motion.
- Natural Frequency(fn)
- Natural frequency is the frequency at which a system naturally vibrates once it has been set into motion. In other words, natural frequency is the number of times a system will oscillate within a period of time between its original position and its displaced position, if there is no outside interference. In a system, the magnitude of natural frequency is equal to the degree of freedom. The frequency of the lowest mode of vibration is called fundamental natural frequency. Two types of natural frequency are most used and listed as follows:
- Rotational frequency (f): unit is cycle/sec or Hz
- Radius frequency (w): unit is rad/sec
The relation between rotational frequency and radius frequency is described as w=2πf
- Natural frequency is the frequency at which a system naturally vibrates once it has been set into motion. In other words, natural frequency is the number of times a system will oscillate within a period of time between its original position and its displaced position, if there is no outside interference. In a system, the magnitude of natural frequency is equal to the degree of freedom. The frequency of the lowest mode of vibration is called fundamental natural frequency. Two types of natural frequency are most used and listed as follows:
- Resonance
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If a system’s natural frequency of vibration is equal to the frequency of forced vibration, dangerously large oscillations may result. This phenomenon is called resonance.
※ In designing a damping unit, it is very important to avoid resonance in order to protect your equipment from being damaged.
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- Damping and damping ratio (tanδ)
- Since friction and other resistance will dissipate energy, the amplitude of free vibration will decrease with time and finally become zero. This energy dissipation mechanism is called damping. Damping ratio is the ratio of the actual resistance in damped harmonic motion to that necessary to produce critical damping. For general damping, the damping is small, while at the resonance position, the damping ratio is zero and dangerously large oscillation may result. If we can increase the damping a little at the resonance point of vibration, the amplitude of oscillation can be immediately decreased markedly. General speaking,the higher the damping ratio, the better the shock absorbing capabilities.
- Dynamic stiffness Kd Ratio of force to unit displacement during dynamic loading condition.
- Static stiffness Ks Ratio of force to unit displacement during static loading condition.
- ※ The data of Kd & Ks can be provided as a reference for shock absorbing unit design.
