三自由度纳米磨削微定位平台的运动学特性

Kinematic Characteristics of a 3-DOF Micropositioning Table for Precision Grinding

为了克服精密平面磨床进给系统分辨率低而难以实现纳米级磨削加工的不足,设计了一台三自由度微定位平台来实现纳米定位和振动误差动态补偿.该微定位平台采用3个高刚度压电陶瓷驱动器并联驱动,3个弹性铰链实现动平台的导向,利用3个高精度的电容式位移传感器测量动平台的实际位姿.为了深入研究三自由度微定位平台的运动学特性,分别利用欧拉角和RPY角描述动平台的姿态并基于空间解析几何理论,建立了微定位平台的正、逆解运动学模型,得到了传感器测量值和压电陶瓷驱动点的实际位移输出值间的映射关系,分析了不同姿态描述之间的内在联系,并研究了微定位平台受到压电陶瓷驱动器伸长量限制时的可达姿态空间.试验验证了三自由度微定位平台的特性和所建模型的正确性.试验表明该微定位平台的z向最大位移为12μm,章动角随进动角的不同而变化,最大可达130μrad.

In order to overcome the shortage that precision grinding machine can not realize nanometer level machining due to lower infeed resolution, a 3-DOF micropositioning table is utilized as auxiliary table for precision positioning and dynamic compensation. The micropositioning table is in parallel driven by three piezoelectric actuators with high stiffness and guided by three flexure hinges. Three high precision capacitive displacement sensors are used to measure the position and orientation of the moving platform. To better understand the kinematic characteristics of the 3-DOF micropositioning table, the direct and inverse kinematic models are obtained under Eular and RPY angle orientation description based on the spatial analytic geometry theory. The mapping relationship between the measurement values and the actual displacement of the driving points is given. The inherent relationship between different orientation descriptions is also investigated, and the reachable orientation space due to the limitation of the expansion of the piezoelectric actuators of the micropositioning table is achieved. The experimental tests are carried out to verify the performance of the micropositioning table and established models. It is noted that the maximum displacement in z direction is up to 12 μm. The nutation angle changes with the procession angle and the maximum nutation angle is approximately 130 μrad.