基于突变理论的两类切屑形态突变现象建模及控制方式优化

In-depth study is conducted on modelling and optimized controlling of two newly found types of mutation in chip morphology on account of the researchers’ observations that those mutations have not only overturning impact on relative conventional theories and viewpoints but also great influence on process effects and thus have great potential for application. After an effort to improve the analytic models and the experimental means, methods are put forward for the theoretical and the empirical modelling of cutting catastrophe, which are based on the catastrophe theory, various cutting analysis models or critical conditions got by experiments, and rational combinations of status/control parameters. Models of the two types of mutation are established so as to reveal the mechanisms of their occurrence. Various types of experimental data reflecting their process effects are obtained. The relational models are established that illustrate the relationships between process effects and status/control parameters and thus reveal how the two types of mutation influence the process effects. With the above models, the processing controllability of the two types of mutation is analyzed, and a procedure to optimize both control parameters and the ways to achieve their values is proposed. With the procedure, an energy-saving threading tool which is expected to reduce energy consumption by about 30% and its matched machining process are designed, and thus the difficulty with thin-walled workpieces thread processing in quality guarantee is solved. A significant breakthrough in research on cutting catastrophe has been made, with theoretical findings being introduced into the application study. Thus the current engineering optimization theories and process control theories are enriched. On this basis, some defective traditional controlling conceptions are improved, and research methodology regarding modelling and controlling of cutting catastrophe based on catastrophe theory is established, which has great scientific significance in stimulating the development of metal cutting and cutting tool design theories, and broad application prospects in reducing energy-consumption and increasing efficiency in manufacture industry.

鉴于新发现的两类切屑形态突变现象对现有理论和传统观点的颠覆性冲击、巨大的工艺影响和可利用潜力，拟对其建模与控制问题进行深入研究。思路是：从改进切削分析模型和实验手段入手，应用突变理论，提出基于分析模型/临界条件实验数据和状态/控制参数合理组合的切削突变理论/实验建模方法，建立两类新突变的数学模型，揭示其发生机制；通过实验研究，获得两类新突变以多种形式体现的工艺影响数据，建立相应的工艺效果与控制和状态参数关系模型，探明突变的影响规律；利用所建模型，分析两类新突变的工艺可控性，提出控制参数及其变化路径优化设计方法，设计出预计节能约30%的螺纹车刀和配套工艺，解决薄壁工件螺纹加工工艺难题，实现应用突破，丰富工程优化和工艺控制理论。在此基础上，澄清错误的传统观点，构建基于突变理论的切削突变建模与控制方式研究方法体系。具有促进金属切削与刀具设计理论发展和制造业节能增效的科学意义和广阔的应用前景。

双刃切削时所发生的流屑角突变和切屑分叉突变，会导致切削力和切屑形态的突跳性改变，具有利用潜力。应用突变理论，对该两类切屑形态突变的建模与控制技术进行了研究。以提高模型预报精度为目标，分别改进了Oxley模型、不等分剪切区模型和非平行边不等分剪切区模型，建立了基于切削过程仿真数据的、根据切削控制参数计算部分切削状态参数的经验模型，推导了能较好体现切削过程的非线性影响、相对准确的双刃切削功率计算函数。完成了多轮通过切削控制参数连续变化条件下的双刃外圆、端面、锥面和V形槽车削，来观测两类突变及其影响的切削实验，获得了一批突变临界条件、切削状态参数和工艺影响的实验数据，发现了3种新切屑形态突变和一批有价值的研究线索。应用差分原理，提出了求解以复杂分段超越函数表示的切削功率函数偏导数的方法，扫清了流屑角突变建模的算法障碍。应用突变理论的理论和实验建模法，采用从切削分析模型出发，经切削力到切削功率即势函数的推导过程，建立流屑角突变数学模型，以及从突变临界条件实验数据出发，拟合出从实际控制参数到理论控制参数微分同胚变换系数，获得分叉集方程，建立切屑分叉突变数学模型两条建模路径，建立了两类切屑形态突变的尖点型、燕尾型或蝴蝶型突变数学模型。为了将流屑角突变数学模型化为符合突变理论的标准形式，提出了基于分段泰勒展开的模型正则化，并计算相应的正则化误差的方法。根据所建数学模型，分析了两类切屑形态突变的发生机制、规律和控制方法。验证实验发现，所建突变模型对突变临界条件的预报误差均小于±20%，优化控制参数的变化路径，可以实现最高达60%的切削过程节能目标。应用所发现的突变规律，设计了预计可节能约35%的陶瓷螺纹车刀，改进了节能型曲折刃带槽麻花钻的结构。发表论文4篇，其中3篇为Sci、Ei收录，授权发明专利1项，培养研究生18名，其中8名已毕业。受疫情影响，4篇论文尚在审稿，相关研究还在进行之中。

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