Boosting the Speed and Accuracy of Vibration-Prone Manufacturing Machines at Low Cost through Software

质量、生产率和成本是制造业的三大支柱。为了在日益全球化的经济中保持竞争力，美国制造商必须找到方法，在保持低成本的同时，提高制造过程的质量和生产率。由于机械结构的弱点，大多数制造机器在移动时往往会振动。由此产生的运动引起的振动对制造机器的精度和速度产生不利影响，从而降低了相关制造过程的质量和生产率。涉及生成运动命令以避免机器不必要的振动的软件解决方案在实践中非常有吸引力，因为它们成本低，并且与硬件解决方案不同，它们不会增加机器的重量和尺寸。然而，现有的软件解决方案牺牲了运动速度和/或精度，或者是不切实际的，因为它们不能正确地处理在机器的正常使用期间发生的不确定性和变异性。该奖项支持对基于软件的减振方法的科学调查，该方法显示出克服现有软件解决方案的技术和实践缺陷的巨大前景。该方法包括用B-样条线表示所需的机床，然后根据机床的特性对其进行修改。为了使计算易于管理，不会计算整个零件的刀具运动，而是计算当前刀具位置周围的一个窗口。通过这项科学研究创造的知识将使工业能够以低成本提高制造机器的精度和速度，从而增加它们在全球市场上的竞争力。这直接影响到一些经济部门，包括医疗器械、汽车、航空航天和国防；因此，它直接和积极地影响经济竞争力和国家安全。更广泛的影响计划包括：通过课程开发和(在线)教程，教育学生和行业有关基于软件的减振方法；以及K-12推广活动，通过在台式3D打印机上演示基于软件的减振技术的好处，激励未被充分代表的少数族裔学生进入STEM领域。该工作的目标是从数学上表征并实验验证B-Spline的有限预览过滤对遭受运动命令诱导振动的制造机器的精度和速度的影响。易于振动的机器的运动命令将表示为B样条线。为了便于计算高效的在线振动补偿，将使用机器动力学模型对B-Spline进行小批量过滤(有限预览)。然而，B-样条曲线的有限预览滤波引入了逼近误差，对在线振动补偿的精度和通用性的影响鲜为人知。将使用线性系统理论的方法来表征和减轻逼近误差的影响。此外，还将从数学上分析机器动力学中的不确定性对滤波B样条线精度的影响，以最大限度地提高在线振动补偿对系统动力学变化的鲁棒性。最后，将利用模型预测控制技术来开发一种科学的方法，在不牺牲定位精度的情况下最大限度地提高易振动机器的速度。通过这项研究开发的理论理解和方法将在3D打印机和各种其他易振动的制造机器上进行实验验证。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quality, productivity and cost are three key pillars of manufacturing. To stay competitive in an increasingly global economy, U.S. manufacturers must find ways of improving the quality and productivity of their manufacturing processes while keeping costs low. Most manufacturing machines tend to vibrate as they move, due to weaknesses in their mechanical structures. The resultant motion-induced vibration adversely affects the accuracy and speed of the manufacturing machines, thus degrading the quality and productivity of the associated manufacturing processes. Software solutions that involve generating motion commands to avoid unwanted vibration of the machines are very attractive in practice because they are low cost and, unlike hardware solutions, they do not add to machine weight and size. However, existing software solutions sacrifice motion speed and/or accuracy, or are impractical because they cannot properly handle uncertainties and variabilities that occur during normal usage of the machines. This award supports a scientific investigation into a software-based vibration mitigation approach that shows great promise to overcome the technical and practical shortcomings of existing software solutions. The approach involves representing the desired machine tools in B-splines, then modifying them to account for characteristics of the machine. To keep calculations manageable, tool motions will not be calculated for the entire part but will be calculated for a "window" around the current tool location. Knowledge created through this scientific investigation will enable industry to boost the accuracy and speed of manufacturing machines at low cost, thus increasing their competitiveness in the global marketplace. This directly affects a number of economic sectors, including medical devices, automotive, aerospace and defense; it therefore directly and positively impacts both economic competitiveness and national security. The broader impact plan includes: educating students and industry about software based vibration mitigation methods through curriculum development and (online) tutorials; and K-12 outreach to motivate underrepresented minority students to STEM fields by demonstrating the benefits of software-based vibration mitigation techniques on desktop 3D printers.The objective of the work is to mathematically characterize and experimentally validate the effects of limited-preview filtering of B-splines on the accuracy and speed of manufacturing machines that suffer from motion-command-induced vibration. The motion commands for a vibration-prone machine will be represented as B-splines. To facilitate computationally efficient online vibration compensation, the B-splines will be filtered in small batches (limited preview) using a model of machine dynamics. However, limited-preview filtering of B-splines introduces approximation errors with poorly understood effects on the accuracy and versatility of online vibration compensation. Methods from linear systems theory will be employed to characterize and mitigate the effects of the approximation errors. Moreover, effects of uncertainties in machine dynamics on the accuracy of filtered B-splines will be analyzed mathematically with a goal of maximizing the robustness of online vibration compensation to variations in system dynamics. Lastly, techniques from model predictive control will be leveraged to develop a scientific methodology for maximizing the speed of vibration-prone machines without sacrificing positioning accuracy. The theoretical understanding and methods developed through this research will be validated experimentally on 3D printers and various other vibration-prone manufacturing machines.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.