Vibration analysis of various machines is a powerful diagnostic tool enabling to evaluate a dynamic behaviour and the status of the object under a test. For this purpose it is necessary to measure instant amplitudes and phase of vibrations of the surface of the investigated object. The measurements may be performed by various sensors, such as piezoelectric accelerometers, electromagnetic sensors, fixed to the vibrating surface. Most of the sensors measure acceleration or a vibration velocity, but not an absolute displacement of the vibrating surface. The most attractive are sensors, which used non-contact techniques. We have developed an ultrasonic sensor enabling to perform absolute measurements of surface displacements (vibration) by means of high frequency ultrasonic waves.
Principle of operation
For ultrasonic based measurement of vibrations different physical phenomena are used. The Doppler effect is exploited  for the measurement of high frequency vibrations, but it can not be used for measurement of low frequency vibrations or displacements. The Doppler frequency shift, created by vibration of the surface under test depends on a frequency of vibration.
The ultrasonic techniques, based on a phase-locked loop are used for measurement of surface displacements in short range of vibrations. The single transducer for transmitting and receiving of ultrasonic waves is used in this case . Disadvantage of this technique is a low resolution and sensitivity because of slow phase changes.
Objective of this investigation was development and analysis of a sensitive ultrasonic measurement method, suitable for measurement of static displacements and low frequency vibrations.
Principle of operation of the ultrasonic sensor is based on an interference phenomenon of continuos harmonic ultrasonic waves between a vibrating surface and the ultrasonic pick-up. The sensor consists of transmitting and receiving ultrasonic transducers, an exciting electric generator and a phase locked loop. Due to multiple reflections in the air gap between transmitting and receiving transducers a standing wave is created. Measurement of vibrations is based on tracking the selected interference peak, which is carried out by means of the phase-locked loop.
The transducer, used for radiation of ultrasonic waves, is fixed on the surface under a test and moves together with the surface. The receiver of ultrasonic waves is fixed on a rigid surface (support). When the ultrasonic waves are radiated, the standing waves between parallel surfaces of ultrasonic transducers are created. During vibration of the tested surface the distance z between the surfaces of transducers changes in the time domain:
Fig 1: Principle of vibration measurement|
Let us assume that the ultrasonic transducer radiates a continuous harmonic signal:
where w0 is the angular frequency of the signal. The signal received by another ultrasonic transducer is given by
where , a(f) is the frequency dependent attenuation coefficient of an ultrasonic wave in air and is the wavenumber.
If the period of the measured vibrations is much longer then the propagation time of ultrasonic wave in the air gap, then it is possible to assume that during the measurement the transfer function is time independent, that is, its value at the given time instant t=tm depends only on the "frozen" distance z(tm).
In Fig.3 the normalised transfer coefficient of the air gap is presented. The transfer coefficient was normalised with respect to the transfer coefficient of the gap when no standing wave exists. The position and separation of periodic resonances depends on the distance between transducers and an ultrasound velocity in air. When the distance between transducers fulfils the condition:
Fig 2: The amplitude of the received signal versus distance between ultrasonic transducers at the frequency f=270kHz.
Fig 3: The phase versus distance between ultrasonic transducers at the frequency f=270kHz|
where f1 the fundamental resonance frequency of air gap, the received ultrasonic signal obtains a maximal value. Note that the values of the transfer coefficient at the resonant peaks indicate the quality of the acoustic resonator, consisting of the air gap between ultrasonic transducers and the reflecting surfaces of these transducers. The higher the quality of the resonator, the higher sensitivity may be obtained.
In the vicinity of such a peak, not only the amplitude, but also the phase of the received signal depends on the distance between the transmitter and the receiver (Fig.2 and 3). In the developed meter the frequency of the exciting signal is adjusted in such a way that the phase difference between transmitted and received signal is kept constant. That is accomplished by means of the phase locked loop, which consists of the phase detector and voltage controlled oscillator (Fig.4).
Fig 4: Block diagram of the ultrasonic displacement sensor|
Sensitivity and linearity of the sensor developed were checked by means of static calibration. For this purpose transmitting transducer was fixed rigidly and receiving transducer was shifted by means of a micrometer screw. The measurements were performed in a vicinity of the resonance peak at the frequency f=270 kHz. The results of the calibration are presented in Fig.5. The results given indicate that the displacement meter possesses a quite good linearity and sensitivity S=100mV/µm. The resolution of the meter is limited by a noise and is 0.05 µm.
Fig 5: The output voltage Uout of the phase locked loop versus the displacement D
z in the case of a high gain of the controlled amplifier|
The technique proposed enables to measure vibrations in a wide frequency range from 0Hz up to a few kHz. The upper limit of the frequency range depends on features of the phase locked loop and the design of ultrasonic transducers and the object under a test. The technique developed enables to measure absolute displacements in the range of 0,05÷1000 µm at a selected distance from the vibrating surface.
- S-R.Huang, R.M.Lerner, K.J.Parker, "Time domain Doppler estimators of the amplitude of vibrating targets", .J. Acous. Soc. Am., 91(2), 965-974 (1992).
- J.Tapson, "High precision, short range ultrasonic sensing by means of resonance mode-locking", Ultrasonics, 33, 6, 441-444 (1995).