Cryogenic cooling helps to improve the machining performance and reduce the tool wear. Cryogenic condition could activate these substructures such as deformation twins and dislocation cells. The effects of the substructures are not taken into consideration in the conventional machining models. The conventional models cannot characterize the dynamics in cryogenic machining, i.e., the evolutions of cutting force and temperature with time. Here, considering the effect of the substructures, a new analytical model for metal cutting was proposed to predict the dynamics in cryogenic orthogonal machining. To validate the applicability of the proposed model, the experiments of orthogonal cutting copper at liquid nitrogen temperature and room temperature were conducted. Transmission electron microscope observations show that nanotwins formed in cryogenic cutting copper. The comparisons between experimental cutting forces and the proposed model or the conventional models validate the rationality of the nanotwin-based analytical model. Numerical calculations were further carried out to reveal the underlying mechanism. The periodic oscillation of cutting force in liquid nitrogen condition is a phenomenon of Hopf bifurcation resulting from the formation of nanotwins.

低温冷却有助于改善加工性能并减少刀具磨损。低温条件可以激活这些亚结构，例如变形孪晶和位错细胞。在传统的加工模型中未考虑子结构的影响。传统模型无法描述低温加工中的动力学特性，即切削力和温度随时间的变化。在此，考虑到子结构的影响，提出了一种新的金属切削分析模型，以预测低温正交加工中的动力学。为了验证该模型的适用性，在液氮温度和室温下进行了正交切削铜的实验。透射电子显微镜观察表明，在低温切削铜中形成了纳米孪晶。实验切削力与所提出的模型或常规模型之间的比较证实了基于纳米孪晶的分析模型的合理性。进一步进行了数值计算以揭示其潜在机理。液氮条件下切削力的周期性振荡是由于纳米孪晶形成而引起的Hopf分叉现象。