Fund Project:Project supported by the National Natural Science Foundation of China (Grant Nos. 11674206, 11874253)
Received Date:17 August 2020
Accepted Date:03 September 2020
Available Online:21 December 2020
Published Online:05 January 2021
Abstract:Radial vibration transducer has the advantages of large radiation area, high radiation efficiency, uniform radial radiation, and wide range of action. Therefore, it is widely used in the technical fields of ultrasonic liquid treatment such as underwater acoustics, ultrasonic degradation and sonochemistry. On the other hand, the 2-2 piezoelectric composite material is one of the most commonly researched piezoelectric composite materials with the best development prospects. Compared with traditional pure piezoelectric ceramics, this new type of material has the advantages of low impedance, low mechanical quality factor, and frequency bandwidth. Therefore, in this paper we propose a new broadband radial vibration ultrasonic transducer based on 2-2 piezoelectric composite material, which is mainly composed of an inner metal ring and an outer piezoelectric ceramic composite ring. First, the Newnham series-parallel theory and the uniform field theory are used to derive the equivalent parameters of the 2-2 piezoelectric composite material. Second, the radial vibration of the combination of the metal ring and the radially polarized piezoelectric composite ceramic ring are analyzed by the analytical method. The six-terminal electromechanical equivalent circuit of the transducer is obtained, and the frequency equation of the transducer is also obtained. And then the relationship between the resonant frequency and anti-resonant frequency of the transducer, as well as the effective electromechanical coupling coefficient, geometric size, and two-phase volume ratio are analyzed. It is concluded that in order to obtain higher electromechanical conversion efficiency, the design of the transducer radius ratio should be as close as possible to 0.35. Although the higher proportion of polymer phase will lead the electromechanical conversion efficiency to decrease, it can also bring better acoustic matching ability. Therefore, the lower proportion of polymer phase can be selected in the transducer design. The finite element method is used to numerically simulate the radial vibration of the new transducer. The results show that the resonance frequency and anti-resonance frequency obtained by the analytical method are in good agreement with the numerical simulation results. In addition, the acoustic field of the transducer under water is simulated numerically. The results show that compared with the traditional pure ceramic radial transducer, the new composite radial transducer has a large emission voltage response amplitude, the working bandwidth is nearly doubled, and the acoustic matching is better. Keywords:composite material equivalent parameters/ radial vibration/ bandwidth/ acoustic matching
基于以上推导, 可以得到径向极化压电陶瓷复合材料圆环径向振动的六端机电等效电路如图4所示. 图 4 径向极化压电陶瓷复合圆环径向振动的机电等效电路 Figure4. Electromechanical equivalent circuit of radial vibration of a piezoelectric ceramic composite ring with radial polarization.
表1新型径向复合材料换能器共振频率的理论及数值模拟结果(一阶径向振动) Table1.Theoretical and numerical simulation results of the resonance frequency of the new radial composite transducer(first-order radial vibration).
图 8 (a) 换能器共振频率为53198 Hz时的振动模态; (b) 换能器共振频率为47552 Hz时的振动模态; (c) 换能器共振频率为52675 Hz时的振动模态; (d) 换能器共振频率为47901 Hz时的振动模态 Figure8. (a) The vibration mode of the transducer when the resonance frequency is 53198 Hz; (b) the vibration mode of the transducer when the resonance frequency is 47552 Hz; (c) the vibration mode of the transducer when the resonance frequency is 52675 Hz; (d) the vibration mode of the transducer when the resonance frequency is 47901 Hz.
24.3.相比传统径向换能器的性能提升 -->
4.3.相比传统径向换能器的性能提升
为了验证新型换能器相比传统径向换能器的性能提升, 利用仿真软件(COMSOL Multiphysics 5.4)对换能器在水下的辐射声场进行了仿真研究[18], 假设换能器处在无限大水域内工作. 在53到65 kHz范围内, 同一尺寸($a = $6 mm, $b = $16 mm, $c = $24 mm, $h = $6 mm, ${v_{\rm p}}/{v_{\rm c}} = 0.429$)的新型换能器的发射电压响应相比传统径向换能器幅值更大, 其原因在于采用压电复合材料以后, 换能器的声阻抗匹配得到了改善. 另外, 以中心频率对应发射电压响应左右下降3 dB取换能器工作带宽[19,20], 由数值模拟结果可知该尺寸下新型径向换能器在水中振动的中心频率在53082 Hz, 振动模态如图9(a)所示, 传统径向换能器的中心频率在55356 Hz, 振动模态如图9(c)所示, 则由图10可见, 新型换能器工作带宽为6000 Hz左右, 即为图10中两蓝线间隔, 而传统径向换能器工作带宽为3000 Hz左右, 即为图10中两绿线间隔, 两者相差接近一倍, 因此新型换能器相比传统径向换能器性能上有很大的提升, 是一种针对传统换能器性能提升的改进方案. 另外在图10中可以看到新型换能器和传统换能器在68和73 kHz左右出现峰值, 因此对利用仿真软件对两种换能器在对应峰值频率附近寻找特征频率, 其振动模态分别如图9(b)和图9(d)所示, 由图可见此时两种换能器的振动模态非常复杂, 存在径向振动和弯曲振动的耦合振动, 且振动位移较大, 因此在水中发射电压响应出现了一个峰值, 但由于振动模态复杂, 并非本文所研究模态. 图 9 (a) 换能器共振频率为53082 Hz时的振动模态; (b) 换能器共振频率为68070 Hz时的振动模态; (c) 换能器共振频率为55356 Hz时的振动模态; (d) 换能器共振频率为73747 Hz时的振动模态 Figure9. (a) The vibration mode of the transducer when the resonance frequency is 53082 Hz; (b) the vibration mode of the transducer when the resonance frequency is 68070 Hz; (c) the vibration mode of the transducer when the resonance frequency is 55356 Hz; (d) the vibration mode of the transducer when the resonance frequency is 73747 Hz.
图 10 新型复合材料径向换能器与传统纯陶瓷径向换能器的发射电压响应曲线 Figure10. The emission voltage response curves of the new radial transducer and the traditional radial transducer.
图 1 新型径向振动复合材料圆环换能器
图 2 2-2型压电复合材料
图 3 压电陶瓷复合材料圆环
图 4 径向极化压电陶瓷复合圆环径向振动的机电等效电路
图 5 径向振动金属圆环的机电等效电路
图 6 径向振动压电陶瓷复合材料圆环换能器的机电等效电路
图 7 (a) 换能器的一阶共振频率和反共振频率与几何尺寸之间的关系; (b) 换能器的有效机电耦合系数与几何尺寸之间的关系; (c) 换能器的一阶共振频率和反共振频率与两相占比之间的关系; (d) 换能器的有效机电耦合系数与两相占比之间的关系
图 8 (a) 换能器共振频率为53198 Hz时的振动模态; (b) 换能器共振频率为47552 Hz时的振动模态; (c) 换能器共振频率为52675 Hz时的振动模态; (d) 换能器共振频率为47901 Hz时的振动模态
图 9 (a) 换能器共振频率为53082 Hz时的振动模态; (b) 换能器共振频率为68070 Hz时的振动模态; (c) 换能器共振频率为55356 Hz时的振动模态; (d) 换能器共振频率为73747 Hz时的振动模态
图 10 新型复合材料径向换能器与传统纯陶瓷径向换能器的发射电压响应曲线
