theoretical analysis of vibration mode ultrasonic transducers

When the axial and radial electromechanical factors of the disc-type piezoelectric vibrator are relatively strong, the one-dimensional theory established by the pure radial model or the pure thickness model is not accurate enough. Between the theoretical calculated value and the experimental value. The error of ultrasonic transducers is large. Therefore, it is necessary to understand the equivalent circuit of the radial/thickness coupling vibration mode of the disc-type piezoelectric vibrator, and derive the isotropic free vibration mode of the disc-type piezoelectric vibrator under some approximate conditions. Compared with the one-dimensional theory, the two-dimensional theory more accurately reflects the vibration process diameter of the disc-type piezoelectric vibrator and the equivalent circuit of the piezoelectric vibrator when is thick-coupling. In order to analyze the electromechanical characteristics of the disc-type piezoelectric vibrator, I represent the excitation supply voltage and current, respectively, and F represents the displacement and total pressure on the respective surfaces, respectively.

 It is known that a piezoelectric vibrator is made of a PZT-piezoelectric ceramic disk and is polarized along the z-axis, and a silver layer is plated on both end of the disk as an electrode, and an excitation voltage is applied to both ends of the electrode. When the thickness dimension of the disc differs greatly from the radial dimension, it can be treated as a pure thickness vibration mode or a pure radial vibration mode; conversely, the electromechanical coordination problem between the thickness and the radial direction of the piezoelectric ceramic disk should be considered. From the equation of motion, it is the piezoelectric equation and the free charge equation, the total pressure acting on the three surfaces of the disc can be derived.

The operating frequency range of the piezoelectric disc type ultrasonic transducer is between 2225 kHz. When there is relative motion between the transducer and the target is being measured, the frequency of the echo signal may fall outside the operating band of the transducer due to the doppler effect. There are two ways to solve this problem: first, using two or more transducers with different resonant (central) frequencies to form an array, that is, superimposing frequency bands of multiple transducers is to expand the transducer and bandwidth of the array;  the combined transducer structure is used to make the receiving frequency of the transducer bandwidth in the transmitting band of the ultrasonic distance measurement sensor.

 The former is a large array structure often used by underwater sonar; the latter is the structural scheme proposed in this paper, which takes advantage of the small size, low cost and high sensitivity of the transducer, and distributes the transducer as an auxiliary receiver at the pressure. Around the electric disc transducer (receiving and transmitting type), a circular array of transducers is formed,which is enabling the combined transducer to receive echo signals outside the band of the piezoelectric disc transducer. As a vehicle-mounted ranging sensor, it is more practical to be able to reliably detect a moving object that is approaching at a high speed than to detect a moving object that is far away. It can be known from the doppler effect that when the ultrasonic wave acts on an oncoming high-speed moving target, the frequency of the echo signal reflected back will be shifted upward (higher than the frequency of the transmitted signal). To this end, the lower operating frequency of the ultrasonic distance sensor annular array must be higher than the upper operating frequency of the primary transducer.