摘要
超精密加工与纳米加工技术是现代制造技术的前沿,随着加工精度的不断提高,对超精密加工机床的性能要求也随之提高。伺服定位系统是超精密机床的核心部件,其性能直接决定了超精密机床的加工精度。超精密加工技术的持续发展,要求伺服定位系统能够在数百毫米的行程范围内实现纳米级的定位分辨率。由于机械摩擦的影响,基于滚珠丝杠的纳米定位系统的行程一般比较小。采用双重驱动或者静压技术可以获得大行程的纳米定位,但是系统非常复杂和昂贵。
本文通过对超精密滚珠丝杠驱动机构的机械结构、摩擦特性进行理论和实验研究,推导控制器算法,建立了计算机闭环控制定位系统,采用单个控制器实现了大行程纳米定位,避免了摩擦辨识和补偿以及双模控制策略的应用。该研究为纳米定位技术的实现提供了一个经济可靠的手段,对于超精密定位系统的研究和应用具有重要的理论意义和实用价值。
本文首先设计和组建了基于滚珠丝杠副的定位系统,该系统采用DC伺服电机驱动,直线滚珠导轨导向,滚珠轴承支撑,激光干涉仪测量反馈。通过结合实体单元和弹簧单元建立滚珠丝杠驱动机构模型,采用有限元方法对机械系统进行动力学分析,包括模态分析和谐响应分析,得到了其低阶固有频率和在外扰动作用下的频率响应,为定位系统的设计和改进提供了理论指导和依据。
通过理论推导得到了滚珠丝杠驱动机构的线性数学模型,它可以很好的描述驱动机构在宏观运动范围内的动力学特性。然而,在微小的运动范围内,摩擦等非线性因素极大地影响定位系统的响应性能,是实现纳米定位的关键因素。通过微驱动特性实验和频率响应特性实验对系统在静摩擦阶段的运动特性进行研究,分析微动特性对定位精度的影响,辨识系统在微观范围内的动力学特性,建立了驱动机构微动特性的数学模型。为滚珠丝杠定位系统实现纳米定位提供了理论和实验依据。
闭环控制系统的结构和算法是定位系统设计的主要环节,对定位系统的性能起着决定性的作用。通过将摩擦等非线性因素作为系统的外部扰动,在定位系统的线性数学模型基础上,设计了高增益PID闭环控制算法,并对其进行了理论分析和仿真。在此基础之上,编写了计算机控制程序,构建了计算机闭环控制系统,对大行程范围内纳米精度的点位控制进行了实验研究,实现了10nm~10mm范围内的阶跃响应。并对实验结果和定位系统的鲁棒性进行了分析。
由于存在功率放大器的饱和,采用抗积分饱和算法可以保证高增益PID闭环控制滚珠丝杠定位系统的稳定性,却无法解决大幅值阶跃响应的超调现象。通过将轨迹规划思想和Bang-Bang控制理论与PID闭环系统结合起来,针对滚珠丝杠定位系统设计变结构控制来消除饱和导致的超调现象,实现了时间最优的无超调纳米定位。
Ultra-precision machining and nanotechnology are at the forefront of modern manufacturing industry. When the accuracy of machined part approaches nanoscale, machine tools have to be improved gradually. Positioning system is the key technology for realizing high accuracy. Precision positioning system with nanometer resolution and long stroke are becoming more important in industrial applications. Usually nanometer positioning systems based on ballscrews are of short stroke because of friction. Even positioning systems with dual-model control strategy or aerostatic mechanism can realize nanometer positioning with long strok, it is every expensive because of suppression or elimination of mechanical friction.
In this thesis, a positioning system based on ballscrew and linear ball guides is designed and constructed. The mechanism, friction phenomenon and control strategy of the system are investigated. Experimental and simulated results indicate that the sigle-step nanometer positioning with long stroke can be realized on such a cheap frictional system with computer control closed-loop system, friction identification and compensation or dual-model control strategy are avoided. The fulfillment of this study proposes a simple and inexpensive method for realizing nanometer positioning. It will contribute to the improvement of theoretic and experimental method of nanotechnology for its further development.
The precision positioning system based on ballscrew consists of ballscrew, linear ball guides, DC-motor and ball bearings, et al. Combining solid elements and spring elements, accurate model of the mechanism is built and Finite Element Analysis is carried out for calculating the system dynamics. The modal analysis and frequency response analysis are performed. The first four modals and natural frequencies are obtained. The frequency analysis of the positioning system under motor output is also obtained. The computation results provide theoretical basis for mechanism design and improvement.
For ballscrew mechanism, models that do not account for friction can only be used to describe the macrodynamic behavior. However, because of friction, the behavior of the system prior to continuous slipping at the friction interface is completely different from that of its macrodynamics. Friction becomes the main obstacle for realizing nanometer positioning. The torque/displacement experiments and frequency response analysis experiments are executed for studying friction phenomenon and identifying the microdynamic characteristics of the positioning system. The theoretic model is founded including microdynamics of the mechanism. This provides the basis of controller design and theoretical analysis for nanometer positioning.
Control strategy is the most important for nanometer positioning system design and it determines performance of the system. Based on the macrodynamics of the ballscrew mechanism alone, a high-gain PID control structure with proportional and derivative items placed in the feedback path is designed. Friction is considered as the outer disturbance of the closed-loop system. The controller is implemented on a personal computer. Experiment and simulation of point-to-point (PTP) positioning for step height from10nm to 10mm are examined and analyzed. Robustnes of the positioning system also be researched.
Because of saturation of the amplifier in the system, even the anti-windup technique can guarantee stability of long stroke positioning, overshoot appeared in long stroke PTP positioning is unavoidable with the high-gain PID controller. Input trajectory design method and Bang-Bang control strategy are combined with the PID closed-loop system respectively. Time optimum nanometer positioning is realized without overshoot.
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