以希爾伯特轉換設計多頻多模態壓電線性馬達

Abstract

本研究發展以希爾伯特轉換(Hilbert Transform)設計壓電線性馬達之驅動參數，將本團隊過去開發之雙頻雙模態激發行進波的研究延伸至多頻多模態的行進波驅動研究，在一維的有限結構中設計並製作出壓電線性馬達，透過在不鏽鋼平板上兩端以並聯的方式貼合壓電陶瓷片作為馬達的致動源，並發展出解析解來進行馬達設計及共振頻率及模態的模擬計算。本研究將所使用到的共振頻率彼此具有為整數倍的關係，如此一來各個驅動模態的相位差不會隨著時間變化，而能夠使行進波更加穩定且為週期性，較以往選擇兩個相鄰共振模態來激發的雙頻雙模態為驅動方式更為穩定。多頻多模態驅動方法為使用較高頻的模態相疊加來增加行進波單位時間內的驅動次數，行進波速度也會較驅動低頻模態更快，同時也能做到改變載物行進的速度，進而達到變速的功能。本研究也導入了希爾伯特轉換(Hilbert Transform)來分析空間中行進波與駐波的比例來定義行進波之效率，同時能從理論推導出之通解析解中計算出最佳之行進波驅動參數，並控制行進波方向，希爾伯特轉換不只能對理論進行分析，並同時也對實際雷射振動計量測到的行進波數據作分析，以與理論作相互對照。 本研究完成以兩組多頻多模態驅動的壓電馬達驅動一線性馬達平台，使用兩組鏡像之馬達架構出雙邊驅動的方式來增加125.5克滑塊移動效率，在無載重的情況下，以第三模態和第四模態所疊加之行進波平均驅動速度可到2.2mm/s，而滑塊行進之距離為41mm。而載物驅動實驗的部分為在滑塊上放上不同克重的砝碼，而最重可推動之砝碼重量達到160g，總重量為285.5克，平均速度達到0.59mm/s，行徑距離為22mm，驗證此多頻多模態壓電線性馬達之驅動效能。

This study developed a new driving method named “Multi-Integer-Frequency Multi-Mode” for generating traveling waves on a one-dimensional finite structure for the application of motorization. It is based on the two-frequency two-mode method that reported by our research team. In this paper, a piezoelectric linear motor is designed and fabricated by using a simply-supported one-dimensional finite plate. Two piezoelectric PZT sheets are attached on two ends of the plate froming two parallel bimorphs. Resonant frequencis of the first 4 bending modes are designed to have an integer multiple relation. In this way, the phase difference of each driving mode does not change with time, and it can make the traveling wave more stable and periodic. Different from the two-frequency two-mode method that used two adjacent resonance modes for excitation, the multi-integer-frequency multi-mode method uses the superposition of higher frequency modes to increase the number of driving modes per unit time to generate the traveling wave. The traveling wave speed can be faster. To optimize the design, the Hilbert transform is used to analyze the ratio of the traveling wave to the standing wave in space. Then, it is used to optimize the driving parameters and is estimated by using the derived analytical solution. The Hilbert transform not only can analyze the solution of theory, but also can use to analyze the data measured by laser scanning vibrometer. Finally, two designed linear motor are integrated to construct a piezoelectric motor that suspended by two rails of ball bearings. The weight of the slider is 125.5g. Experimental results show that the average driving speed of the traveling wave superimposed by the third mode and the fourth mode can reach 2.2mm/s, and the distance of the slider travels 41mm. The maximum loading is 160g with an average speed of 0.59mm/s and a travel distance of 22mm. In summary, the analytical, numerical, and experimental analyses verify the concept of the multi-frequency multi-mode piezoelectric linear motor, and its performace is much improved than the two-frequency two-mode method.