以希爾伯特轉換最佳化之自走式壓電行進波旋轉致動器

Abstract

本研究目的為開發可產生旋轉運動之壓電自走式致動器，過去自走式致動器的研發以線性為主，故若可在有限的結構中達到旋轉效果，將可大幅提升自走式致動器之移動自由度。本研究以50 mm*41 mm矩形結構，以驅動Φ12、Φ22與Φ21、Φ22疊加產生行進波，當Φ12、Φ22疊加時，因x方向為第一及第二模態，疊加後可於x方向產生行進波，而y方向則皆為第二模態，故可使其疊加後因y方向第二模態具有180度空間相位差而產生一組位置相對且傳遞方向相反之x方向行進波，使致動器產生旋轉的驅動；而當Φ21、Φ22疊加時，則因y方向為第一與第二模態，故可於y方向產生行進波，亦因 x方向皆為第二模態，可使兩模態疊加後於y方向之對邊產生相反方向行進波，亦可使致動器產生旋轉運動。透過此兩組不同模態的疊加可產生不同之轉動效果，因x方向之行進波在簡支邊界間產生，振幅較大可產生較大之推動力。而y方向行進波在自由邊界間產生，振幅較小可產生微小角度之旋轉。本研究採用整數倍頻驅動的方式，以產生穩定的旋轉行進波，在x方向使用1600 Hz與3200 Hz兩頻率驅動，在y方向則是使用1675 Hz與3350 Hz兩頻率驅動。為能準確的找出最佳之驅動參數，本研究以希爾伯特轉換確認電壓比與相位差之最佳驅動參數，並進一步開發以希爾伯特圓的虛部差值來進行最佳化自由端行進波之電壓比。為驗證上述方法之可行性，本研究以實驗及有限元素法進行驗證。首先分析驅動支腳位置對於行進效果的影響，並以實驗驗證以x方向行進波推動時順時針與逆時針角速度可達-17.44 deg/s(100Vpp)與17.37 deg/s (100Vpp)，使用y方向行進波推動時可達順時針與逆時針角速度-5.78 deg/s與6.00 deg/s，其最大荷重皆為15g。在以支腳進行自走實驗時，以x方向行進波達到最大順時針與逆時針角速度分為-33.61 deg/s(100Vpp)與29.25 deg/s(100Vpp)，其最大荷重為35g。而以y方向行進波推動時，最大順時針與逆時針角速度分別為-10.78 deg/s與7.30 deg/s，最大荷重為30g。不論是圓盤實驗或是自走實驗，x方向之轉動角速度皆大約為y方向行進波之3倍，驗證可於單一結構達成兩種轉動效果。

This study aims to develop a self-propelled piezoelectric actuator for rotational motion. It is different from reported self-propelled piezoelectric actuators that focused on linear movement. The structure of the rotary piezoelectric actuator is a rectangular plate with a dimension of 50 mm by 41mm. The developed method is to superpose bending vibrations of Φ12 and Φ22 modes and Φ21 and Φ22 modes of a double simply supported (x-direction) and doubly free edge (y-direction) rectangular piezoelectric actuator. Using Φ12 and Φ22 modes, the first and second modes are generated in the x-direction to superpose into two traveling waves in opposite directions. Similarly, using Φ21 and Φ22 modes, the first and second modes are generated in the y-direction, and two traveling waves can be generated in the y-direction with opposite directions. The amplitude in the x-direction is greater than in the y-direction due to simply supported boundary conditions, so higher angular velocities can be generated. In this study, the two-integer-frequency-two-mode (TIF-TM) driving method is adopted, and 1600 Hz and 3200 Hz are used for driving in the x-direction, and 1675 Hz and 3350 Hz are used for driving in the y-direction. The voltage ratio and phase difference to drive the traveling wave is optimized using the Hilbert transform. Finite element analysis and experimental studies are conducted for verifications. To interact with a surface, protrusions were added to the actuator surface, and the influence of protrusion positions is analyzed. A small disk is first placed on the protrusions, and the maximum clockwise (CW) and counterclockwise (CCW) angular velocities are -17.44 deg/s (100Vpp) and 17.37 deg/s (100Vpp) using x-direction traveling waves. The maximum CW and CCW angular velocities are -5.78 deg/s and 6.00 deg/s using y-directions traveling waves. The maximum loading for both conditions is 15g. For the self-propelled experiments, the maximum CW and CCW angular velocities are -33.61 deg/s (100Vpp) and 29.25 deg/s (100Vpp) for x-direction traveling waves, and the maximum load is 35g. They reduced to -10.78 deg/s and 7.30 deg/s using y-direction traveling waves with a maximum loading of 30g. In summary, the rotational speed generated by x-direction traveling waves is about 3 times higher than that by y-direction traveling waves. It is verified that this self-propelled piezoelectric actuator can generated two different rotational speeds using different mode selections.