基於撓性接頭的雙驅龍門平台數學建模與實驗分析

Abstract

隨著精密製造對高速度、高精度及高推力的需求不斷提升，雙軸線性馬達驅動的龍門平台成為巨量轉移等應用的主流選擇。然而，剛性結構易導致雙軸耦合效應強烈，限制系統頻寬並產生同步誤差。本研究以「撓性接頭」取代傳統剛性連接，系統性地探討其對龍門平台動態特性的影響。 首先，分別建立剛性與撓性接頭龍門結構的數學模型，推導其頻率響應函數（Frequency Response Functions, FRFs）；再以新式交叉耦合控制（Cross-Coupled Control, CCC）架構下在MATLAB/Simulink中進行模擬分析，並於實驗機台上驗證理論模型，並比較理論與實測之 FRFs 及時域響應。最後評估不同偏擺方向剛性及質量比對系統頻寬與穩定度的影響。 結果顯示，引入撓性接頭可將偏擺模態頻率由剛性結構的258 Hz顯著降低至約7 Hz，並於 CCC 控制下達成更高的開迴路頻寬與更佳的穩定裕度。此外，旋轉剛性及平台與滑塊質量比為龍門結構之關鍵參數，適當調整可進一步提升系統動態性能。本研究成果為高精度龍門平台之結構設計與控制策略提供了理論依據與實務參考。

In response to the ever-increasing demands for high speed, high precision, and large thrust in precision manufacturing, dual-axis linear-motor-driven gantry platforms have become the mainstream solution for applications such as mass transfer. However, rigid structures tend to produce strong coupling effects between the two axes, limiting system bandwidth and inducing synchronization errors. This study systematically investigates the use of compliant joints in place of traditional rigid connections and their influence on the dynamic characteristics of gantry platforms. First, mathematical models of both the rigid-joint and compliant-joint gantry structures are developed, and their frequency response functions (FRFs) are derived. Next, simulations under a novel cross-coupled control (CCC) framework are carried out in MATLAB/Simulink, and the theoretical models are validated experimentally on a test rig by comparing both the FRFs and the time-domain responses. Finally, the effects of varying stiffness and mass ratio in different parasitic motion directions on system bandwidth and stability are evaluated. The results show that introducing compliant joints reduces the yaw mode frequency from 258 Hz in the rigid structure to approximately 7 Hz, and under CCC achieves higher open-loop bandwidth and improved stability margins. Furthermore, rotational stiffness and the mass ratio between the platform and sliders are identified as key design parameters, whose proper adjustment can further enhance dynamic performance. The findings provide both theoretical basis and practical guidance for the structural design and control strategy of high-precision gantry platforms.