PASSIVE AND ACTIVE VIBRATION ISOLATION SYSTEMS

Vibrations accompany us everywhere and in most cases these vibrations are undesirable. First of all we can mention the vibration of cars and carriages, motors and machine tools, oil and gas platforms, buildings and constructions in a zone of seismic activity, undesirable vibrations of laboratory tables (especially optical), setups, etc. In all these cases an object has to be isolated  from the source of vibrations. Despite of all constructional distinctions the essence of vibration isolation systems are identical. The passive vibration isolation system consists of a spring and damper (dash-pot). The spring is intended to soften vibrations and pushes, and damper has to terminate the oscillation which is excited in system. The active system uses also accelerometers and electromagnetic drivers which allows higher degree of vibration isolation to be achieved. 

Let us consider the work of passive vibration isolation system by the example of a suspension bracket of the automobile. In any suspension bracket there are elastic elements, which soften pushes and impacts of the road. Other not less important element of a suspension bracket is the shock-absorber -- the device which is intended to terminate excited the oscillation. Many drivers think that shock-absorbers is only the means to maintain comfort. Actually functions of this element of a suspension bracket are directly connected to maintenance of contact of a wheel with road, i.e. with controllability of the automobile and traffic safety. 

Animation shows that too hard suspension system of a car results in throwing of the car on unevenness of the road, while too soft suspension system will swing the car, which results in lost of the contact between the wheels and the road. Whether you have a Mercedes or a lower price vehicle or even if you buy expensive or low price Accord car parts, keeping your suspension system is a vital part of car maintenance, and you should worry as much or more about safety as about price. On the other hand too strong damping also has the negative consequences. Figure shows transmissibility of the passive vibration isolation system for three damping coefficients related as 1 (blue): 3 (green): 10 (red). We can see in the figure that when the value of damping is big the vibration isolation properties of the system are practically vanish, while when the damping is week the considerable resonance peak is observed. The optimum value of damping corresponds to the case when the amplitude of oscillation increases only insignificantly (<3 dB) near to resonant frequency (green line). Such value of damping was chosen for computer simulations shown below.

Motions of a suspension bracket caused by roughnesses of the road are of various character, from individual pushes to periodic oscillation. For this reason shock-absorbers have to satisfy different and mutually exclusive characteristics. For example, on a wavy road the resonance oscillation can be excited and dash-pots have to provide the maximal damping to keep contact of the wheels to road. At unitary sharp pushes the damping should be minimal to soften them as much as possible.  Therefore parameters of a spring and dash-pot have to be carefully calibrated. If the shock-absorber is serviceable, then the amplitude of oscillation has to diminish 5 times after 2 periods of oscillation. Push a corner of the car in vertical direction. If the car makes no more than one oscillation, this does not speak yet about serviceability of shock-absorbers. But if there are several oscillations of a car, then it is time to change the shock-absorbers. 

Next we shall consider the response of passive vibration isolation system to sinusoidal excitation of oscillation. A platform oscillates in the vertical direction with growing frequency. At low frequencies (below the resonant frequency of the system) the amplitude of stabilized table oscillation (top part in animation) coincides with amplitude of platform oscillation. The phases of these oscillations coincide too. 

Increasing the frequency of the platform oscillation we achieve the resonance. In resonance the amplitude of the table oscillation increases. The acceptable value of transmissibility in resonance is +3 db (i.e. amplitude of oscillation in resonance can exceed the amplitude of low-frequency oscillations no more than 2 times). In resonance the phase of stabilized table oscillation is shifted by 90 degrees as compared to platform oscillation.

And, finally, at frequencies much higher than the resonance frequency the amplitude of stabilized table oscillation considerably diminishes and occurs in antiphase with platform oscillation. The response of system to harmonious influence with the frequency rising from 0 up to 7.5 Hz can be seen in the following video - animation (click the icon in the right). In resonance the amplitude of oscillation increases about twice, and then it considerably decreases at high frequencies.

Next animation shows the response of system to noise excitation.  Real excitation force applied to vibration isolation system consists of many frequencies. Vibrations with frequencies higher than resonant frequency of the system are exposed to significant damping, while the low-frequency oscillation of the stabilized table is about the same as the amplitude of platform oscillation. We can conclude that the resonant frequency of the system has to be as low as possible and the damping should be big enough to avoid a substantial growth of amplitude of resonance oscillation. We can see in animation, that residual vibrations occur mainly at low frequencies, while high-frequency vibrations of the stabilized table are practically absent.

		A revolutionary concept in low-frequency vibration isolation is the passive negative-stiffness isolator. These isolators typically use three isolators stacked in series: a tilt-motion isolator on top of a horizontal-motion isolator on top of a vertical-motion isolator. The first animation is the vertical-motion isolation system provided by a stiff spring that supports a weight load, combined with a negative-stiffness mechanism. It uses a conventional spring connected to a negative-stiffness mechanism consisting of two flexures connected at their inner ends to the spring and supported at their outer ends, and loaded in compression by forces P. The spring is compressed by weight W to the operating position of the isolator
		The next animation shows a horizontal-motion isolation system consisting of two beam-column isolators. Each isolator behaves like two fixed-free beam columns loaded axially by a weight load. With the weight load the lateral bending stiffness is reduced by the "beam-column" effect. This behavior is equivalent to a horizontal spring combined with an negative-stiffness mechanism. Horizontal stiffness can be made to approach zero by loading the beam-columns to approach their critical buckling load.
		A tilt pad serves as the tilt-motion isolator. The result of all three, the tilt pad, beam-column and negative-stiffness mechanism is a compact passive isolator capable of very low vertical and horizontal natural frequencies and very high internal structural frequencies. A vertical stiffness adjustment screw is used to adjust the compression force on the negative-stiffness flexures thereby changing the vertical stiffness. A vertical load adjustment screw is used to adjust for varying weight loads by raising or lowering the base of the support spring to keep the flexures in their straight, unbent operating position.
		The transmissibility curve shows the transmissibility of a negative-stiffness passive isolation systems and a high performance air table system. The dashed curve shows air table and the solid curve is the performance of a typical negative-stiffness 1/2-Hz performance isolator. Once adjusted to 1/2 Hz, they achieve 93% isolation efficiency at 2 Hz, 99% at 5 Hz, and 99.7% at 10 Hz. The negative-stiffness isolators require no air or electricity. They also perform better than active or electronic-cancellation systems. More detail information on negative-stiffness passive vibration control can be found on the website of Minus K Technology.
		Animations on negative-stiffness passive vibration isolation system were developed by and belong to Minus K Technology.

In active vibration isolation system among the spring there is feedback circuit which consists of a piezoelectric accelerometer, an analog control circuit, and an electromagnetic transducer. The spring supports the weight of the table top and the device which is mounted on the table. The motion of the table top is detected by a highly sensitive piezoelectric accelerometer consisting of a mass resting on a piezoelectric disc and covered by a housing. The acceleration signal is processed by analog control circuit and amplifier. Then it feeds the electromagnetic actuator, which is designed analogously to loudspeaker. The magnet of actuator is located on a movable table, and the electrical coil is connected with platform. As a result of such feedback system we can achieve considerably stronger suppression of vibrations as compared to ordinary dampine. Animation shows one of variants of active vibration isolation system with two accelerometers and electromagnetic transducers. The track in the bottom part of animation shows the record of the noise displacement of a vibrating platform. The top track is the residual displacements of the stabilized table enlarged 100 time. We can see in animation that such a system allows considerable reduction of amplitude of the table oscillation to be achieved, especially in high-frequency region.