近年来，压电驱动因其响应时间短、推力密度高、无电磁干扰、无需润滑和变速机构等显著优势，逐渐成为精密驱动领域的研究热点。与传统的电磁式电机相比，压电驱动器在航空航天、科学仪器、精密定位等领域展现了广阔的应用前景。随着工作环境和工作空间的复杂化与狭小化，机械臂的功能需求从单一的定点作业扩展到自主作业。然而，传统电磁电机驱动的机械臂每增加一个自由度，通常需要增加一套减速系统，这不仅导致体积增大，还降低了系统的抗干扰能力。为此，本文提出了一种两自由度压电驱动器，直接驱动超冗余度机械臂，仅需一套驱动器即可实现机械臂的多自由度运动，解决了传统驱动方式体积大、结构复杂的问题。本文设计的两自由度压电驱动器具有直线自由度和旋转自由度，能够实现沿机械臂轴向运动和旋转机械臂关节的双重功能。通过纵弯复合与弯弯复合振动的结合，驱动器能够在平面内实现高精度、高效率的两自由度运动。主要研究内容与结论如下：

(1)本文基于逆压电效应，以简单金属梁的纵弯振动为原型，设计了一种新型压电驱动器。通过纵弯复合与弯弯复合振动原理，设计了压电陶瓷的基本结构与极化方向；确定压电驱动器的结构尺寸，不同位置的材料与压电陶瓷的排布方式和数量等参数，阐明压电驱动器的纵向振动与弯曲振动激励方法和多模态的简并方式。通过纵弯复合与弯弯复合振动的模态叠加，产生不同平面的椭圆运动，从而实现压电驱动器的两自由度运动。

(2)建立基于ANSYS的两自由度压电驱动器有限元模型，对建立的模型进行模态分析，选出不同方向的纵向振动与弯曲振动模态以实现多种模态的复合振动。为了满足多种振动模态被同时激发，通过对压电驱动器进行不同结构尺寸的参数敏感度分析，确定各个结构对于共振频率的影响，最终调节参数实现了频率简并。最后通过瞬态分析，提取驱动足上不同位置的点的位移，验证了工作原理的正确的与可行性。

(3)基于Greenwood-Williamson接触理论，假设压电驱动器与被驱动表面的微观特征，并引入周期性接触的非线性特性。通过将压电驱动器驱动足表面的椭圆运动轨迹分解为切向和法向，然后通过库伦摩擦定律建立摩擦模型。利用该模型，分析材料特性如弹性模量、泊松比、表面粗糙度等对摩擦系数影响规律。并通过仿真计算了不同状态下的稳态输出力，为压电驱动器的摩擦界面选择与性能优化提供了理论支撑。

(4)搭建压电驱动器实验测试平台，完成压电驱动器的加工与装配，并测试其阻抗特性。在纵弯复合振动模式下，驱动器的最佳工作频率为40.00 kHz，在150 V_p-p激励电压下，速度达到330.56 mm/s。驱动器在低输出力区间(0-15 N)运行稳定，即使在35 N的最大输出力下，仍能保持40.10 mm/s的运动速度。在弯弯复合振动模式下，最佳工作频率为40.60 kHz，150 V_p-p激励电压可使速度达到317.06 mm/s。输出力为30 N时速度为66.85 mm/s。通过摩擦实验，测试了不同材料和粗糙度的输出性能，为后续机械臂系统的设计提供了数据支持。在闭环控制实验中，跟踪位移正弦信号的最大误差分别为0.096 mm和0.073 mm，在跟随阶跃速度信号时到达稳态时间最小为0.34 s，稳态误差低于0.6%。最后，搭建了两自由度压电驱动器与机械臂的整机系统，并测得该款压电驱动器可以实现超冗余度机械臂274.37 mm/s的直线速度和6.43 rad/s的旋转速度。该压电驱动器实现了两自由度运动，具备高速、高精度的特点，为压电驱动器驱动超冗余度机械臂的研究提供了重要支持。

In recent years, piezoelectric actuation has emerged as a research focus in precision drive systems due to its notable advantages including rapid response time, high thrust density, absence of electromagnetic interference, and elimination of lubrication and transmission mechanisms. Compared with conventional electromagnetic motors, piezoelectric actuators demonstrate broad application potential in aerospace, scientific instrumentation, and precision positioning fields. As operational environments become increasingly complex and workspaces more confined, robotic arm functionality has evolved from single-point operations to autonomous tasks. However, each additional degree of freedom (DOF) in traditional electromagnetic motor-driven robotic arms typically requires an additional reduction system, which not only increases volume but also compromises anti-interference capability. To address these limitations, this study proposes a novel two-DOF piezoelectric actuator for directly driving hyper-redundant robotic arms, achieving multi-DOF motion with a single actuator while overcoming the bulkiness and structural complexity of conventional drive systems. The designed two-DOF piezoelectric actuator integrates both linear and rotational freedom, enabling axial motion along the robotic arm and joint rotation simultaneously. By combining longitudinal-bending hybrid vibrations with bending-bending coupled vibrations, the actuator achieves high-precision, high-efficiency planar two-DOF motion. The main research contents and conclusions are as follows:

(1) This study presents a novel piezoelectric actuator design based on the inverse piezoelectric effect, using the longitudinal-bending vibration of a simple metal beam as the fundamental prototype. The actuator's core structure incorporates strategically arranged piezoelectric ceramics with optimized polarization directions to enable both longitudinal-bending hybrid vibration and bending-bending coupled vibration modes. Through systematic parameter optimization, we determined critical design specifications including the actuator's dimensional parameters, material distribution, and the spatial configuration of piezoelectric ceramic elements. The working mechanism involves precise excitation of longitudinal and bending vibrations through carefully designed driving signals, coupled with a degenerate multimodal vibration approach to achieve motion control. By superimposing these carefully tuned vibration modes, the actuator generates elliptical trajectories in orthogonal planes, thereby realizing two-DOF motion output. This innovative design approach successfully integrates multiple vibration modes into a compact structure while maintaining precise motion control capabilities.

(2) A finite element model of the two-DOF piezoelectric actuator is established using ANSYS finite element analysis software. Modal analysis is performed to extract longitudinal and bending modes in different directions, facilitating the realization of multi-modal hybrid vibrations. To achieve simultaneous excitation of multiple vibration modes, a parametric sensitivity analysis was conducted to investigate the influence of various structural dimensions on resonant frequencies. This analysis identified critical structural parameters affecting the resonance characteristics, ultimately leading to successful frequency convergence through parameter optimization. The operational principle was validated through transient analysis by extracting displacement data at multiple key points on the driving foot. The obtained results confirmed both the correctness and feasibility of the proposed working mechanism.

(3) Based on the Greenwood-Williamson contact theory, this study models the microscopic characteristics of the contact interface between the piezoelectric actuator and rotor while incorporating the nonlinear behavior of periodic contact. The elliptical motion trajectory was decomposed into tangential and normal components, and an intermittent friction model of the piezoelectric actuator was established by integrating the Coulomb friction law. Through this model, quantitative analysis was performed to investigate the influence of material properties (including elastic modulus, Poisson's ratio, and surface roughness) on the friction coefficient. Furthermore, steady-state output forces under different operating conditions were systematically calculated through numerical simulations. These results provide theoretical foundation for both the frictional interface design and performance optimization of the actuator.

(4) An experimental test platform for the piezoelectric actuator was established to complete its fabrication and assembly, followed by impedance characterization tests. Under the longitudinal-bending hybrid vibration mode, the actuator demonstrated an optimal operating frequency of 40.00 kHz, achieving a velocity of 330.56 mm/s at 150 V_p-p excitation voltage. The actuator maintained stable operation in the low output force range (0-15 N), while retaining a velocity of 40.10 mm/s even at the maximum output force of 35 N. In the bending-bending coupled vibration mode, the optimal operating frequency was 40.60 kHz, with a velocity of 317.06 mm/s under 150 V_p-p. At an output force of 30 N, the velocity reached 66.85 mm/s. Friction experiments were conducted to evaluate the output performance with different materials and surface roughness, providing essential data for subsequent manipulator system design. In closed-loop control experiments, the maximum tracking errors for sinusoidal displacement signals were 0.096 mm and 0.073 mm, respectively. When following step velocity commands, the minimum settling time was 0.34 s with a steady-state error below 0.6%. Finally, an integrated system incorporating the two-DOF piezoelectric actuator and the manipulator was assembled. Experimental results confirmed that the actuator enabled the hyper-redundant manipulator to achieve a linear velocity of 274.37 mm/s and a rotational velocity of 6.43 rad/s. This two-DOF piezoelectric actuator successfully realized high-speed, high-precision motion, providing critical support for research on piezoelectric-driven hyper-redundant manipulators.

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