ทฤษฎีของการแกว่ง (Damping Vibration)
ความนิยมของผู้ชม: / 14
แย่มากดีมาก 

ระบบสั่นสะเทือนที่สปริงแข็งเกินไป

hard suspension

   Too hard suspension system of a car results in throwing of the car on uneven road, while too soft suspension system will swing the car, which results in lost of the contact between the wheels and the road.

คลิกค่ะ   download  จากฟิสิกส์ราชมงคล  


หยุดการสั่น 5 ครั้ง หลัง จากสั่นไป 2 คาบ

    Response of the passive vibration isolation system to unit impulse excitation. Parameters of the spring and damper are chosen by such a way that the amplitude of oscillation diminishes 5 times after 2 periods of oscillation.

คลิกค่ะ   download  จากฟิสิกส์ราชมงคล  


เพิ่มความถี่การสั่นจาก 0 ถึง 7.5 ครั้งต่อวินาที

เกิดการเรโซแนนท์

   Video-animation (AVI) shows the response of the system to a sinusoidal mechanical excitation with the frequency increasing from 0 to 7.5 Hz (transmissibility). Small GIF-animation in text shows the excitation of the system with the resonance frequency.

คลิกค่ะ   download  จากฟิสิกส์ราชมงคล  


ยังหลงเหลือการสั่น ที่ความถี่น้อย

    Response of the passive vibration isolation system to noise mechanical excitation. High-frequency vibrations are suppressed entirely. Residual oscillations occurs mainly at low frequencies.

คลิกค่ะ   download  จากฟิสิกส์ราชมงคล  


การสั่นของหัวเข็มที่ระบบควบคุมแบบป้อนกลับ

    Active vibration isolation system. Among the spring and damper there are feedback circuit which consists of accelerometer, actuator and signal processing electronics.

คลิกค่ะ   download  จากฟิสิกส์ราชมงคล  


การทดลองเสมือนเรื่องการแกว่งที่ถูกแรงบังคับ

ให้คุณทดลองดูดังนี้

  1. ถ้าความถี่ของแรงมีค่าต่ำมากๆ  ตอนแรกการสั่นสะเทือนจะไม่เท่ากัน รอไปสักครู่  ความถี่และแอมพลิจูดของกล่องจะลดลงจนเท่ากับความถี่และแอมพลิจูดของแรงจากภายนอกที่ใส่เข้าไป

  2. ถ้าเลือกความถี่ของแรงให้เท่ากับความถี่ของระบบ   ระบบจะเกิดปรากฎการณ์เรโซแนนท์  แอมพลิจูดจะเพิ่มขึ้นทุกๆรอบของการแกว่ง  

 คลิกที่รูปภาพหรือที่นี่เพื่อเข้าสู่การทดลอง


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. 

car.gifAnimation 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. 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.

spri.gifMotions 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. 

sprl.gifNext 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. 

sprr.gifIncreasing 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.

sprh.gif 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. video 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.

sprn.gif 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.

sprt.gif 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. 

Next figure shows the difference in transmissibility of passive and active damping systems simulated with the aid of computer. The  signal of accelerometer was integrated, so the feedback signal applied to electromagnetic actuator was proportional to velocity of the table top. Red curve corresponds to the case when feedback was switched off. We can see the resonance pick at frequency of about 0.6 Hz. Green curve shows the case when weak feedback was switched on. This weak feedback removed the resonance pick, while the transmissibility at low and high frequencies was about the same. And, finally, blue curve shown the influence of the strong feedback signal. We can see that residual vibrations are considerably suppressed  from low frequencies up to about 10 Hz.  Feedback coefficients for green and blue curves are related as 1 to 15. Maximal advantage of active vibration isolation system can be achieved in the middle frequency region, near resonance, which is very important for most of practical applications. More detail information on Active Vibration Control can be found on the website of Halcyonics GmbH


Animations on  active vibration isolation system were developed for and belong to company Accurion Scientific Instruments.




 
< ก่อนหน้า   ถัดไป >

 

Statistics

สถิติผู้เยี่ยมชม: 42462863

Who's Online