非线性再生切削的多稳态、安全性和定向切换

This project is a fundamental research in both theory and application, focusing on regenerative cutting process with complex nonlinearity. Three main scientific problems are to be studied: (1) analysis of multi-stability in nonlinear regenerative cutting dynamics; (2) analysis and assessment of cutting safety based on basin of attraction; (3) control of multi-stability and attractor selection in cutting process. The influences of nonlinear time-delayed cutting force and non-smooth frictional force on cutting dynamics are to be revealed, which play major roles in the multi-stability near stability boundaries and in stability islands. Physics in the cutting process will be considered in the construction of basin of attraction and attractability, which will be used to assess the cutting safety. Then, various methods of controlling multi-stability and attractor selection will be introduced to improve cutting efficiency and safety. This project, based on the analysis of nonlinear cutting process and its inherent multi-stability, will construct basin of attraction and safety assessment of time-delayed cutting process and establish the theoretical framework for controlling multiple-stability and attractor selection. The achievements will upgrade the method of theoretical analysis of multi-stability in delayed differential systems, and improve the cutting efficiency and safety from the viewpoint of industrial application.

本项目定位于应用基础性研究，针对具有复杂非线性特征的再生切削过程，通过对（1）非线性再生切削动力学的多稳态分析；（2）基于吸引域的切削安全性分析和评估方法；（3）切削多稳态的控制和定向切换这三个科学问题的研究，深入认识非线性时滞切削力和非光滑摩擦力对切削动力学的影响，重点探索线性稳定边界附近和稳定孤岛内的切削多稳态。针对时滞非线性切削的物理过程构建合理的吸引域和吸引性计算方法，并以此为基础评价切削安全性，最后引入恰当的稳态控制和定向切换方法，提高切削效率和安全性。在本项目中，对非线性切削过程的复杂多稳态研究是基础，其关键在于为时滞切削过程构建吸引域计算和安全性评价方法，为稳态控制和定向切换奠定理论基础。本项目的研究意义在于从理论上突破现有的时滞非线性系统的多稳态分析方法，从工程应用上为提高切削效率和安全性提供评价标准。

本项目旨在深刻揭示时滞非线性动力系统的多稳态，提出新的吸引域评估切削安全性，在此基础上定向切换切削响应，通过对（1）非线性再生切削动力学的多稳态分析；（2）基于吸引域的切削安全性分析和评估方法；（3）切削多稳态的控制和定向切换；其核心科学问题就是对非线性再生切削的多稳态、安全性和定向切换的研究，深入详尽的讨论了机械加工中的再生切削多稳态问题。针对典型的车销加工，提出了具有再生时滞、Stribeck摩擦和过程阻尼的新模型，提升了切削加工的稳定性预测精度。将模型推广到具有两个和多个时滞的磨削和钻削动力学模型中，为非均布刀刃的高稳定裕度提供了理论支撑。扩展了切削失稳的局部分析，发现具有切削多稳态的不安全区域也可以由具有非光滑特征的摩擦颤振导致。提出概率吸引盆的新理念，将无穷多维的时滞初始状态压缩为一维的能量特征，并用具有相同能量特征的初始条件发生颤振的概率来构造统计吸引盆。在统计吸引盆中发现了颤振依概率不会发生的安全盆，对应于速度和能量较小的时滞初始条件，依据该条件构造了状态依赖反馈控制，即当切削状态进入安全盆以后可以撤销外部干扰，使得大振幅切削颤振在内部特征的引导下自发稳定下来。与基于颤振幅值的状态依赖反馈控制相比，基于概率吸引盆的多稳态调控方法更加有效，所需的控制反馈也更小。在此基础上提出了人工智能算法用于增强概率吸引盆的计算，并通过灵敏度分析找到了影响切削多稳态走向的关键初始特征。