论文标题
非牛顿对电影铸造中抽奖共振的影响
Non-Newtonian effects on draw resonance in film casting
论文作者
论文摘要
在本文中，研究了非牛顿材料特性对胶片铸造中抽奖共振不稳定性的影响。无限宽度膜铸造的粘弹性模型是在渐近扩展之后系统地得出的，并使用两个众所周知的本构方程：Giesekus模型和简化的Phan-Thien/Tanner/Tanner〜（PTT）模型。基于稳态分析，制定了入口应力的数值边界条件，这抑制了模具流的未知变形历史。 Deborah数字和非线性参数的依赖性的临界拉力比通过线性稳定性分析来计算。对于这两种模型，最不稳定的不稳定模式可能会在控制参数的变化下切换，从而导致关键时振荡频率的不连续变化。只要Deborah数量不太高，就将有效的延长粘度仅取决于局部Weissenberg数量。通过使用广义的牛顿流体模型近似PTT模型来证明这一点。基于这种广义的牛顿流体模型，最终探索了应变硬化和应变变薄的影响，从而揭示了非牛顿稳定性行为的两个相对机制。
In this paper, the influence of non-Newtonian material properties on the draw resonance instability in film casting is investigated. Viscoelastic models of infinite width film casting are derived systematically following an asymptotic expansion and using two well-known constitutive equations: the Giesekus model and the simplified Phan-Thien/Tanner~(PTT) model. Based on a steady state analysis, a numerical boundary condition for the inlet stresses is formulated, which suppresses the unknown deformation history of the die flow. The critical draw ratio in dependence of both the Deborah number and the nonlinear parameters is calculated by means of linear stability analysis. For both models, the most unstable instability mode may switch under variation of the control parameters, leading to a non-continuous change in the oscillation frequency at criticality. The effective elongational viscosity, which depends exclusively on the local Weissenberg number, is analyzed and identified as crucial quantity as long as the Deborah number is not too high. This is demonstrated by using a generalized Newtonian fluid model to approximate the PTT model. Based on such a generalized Newtonian fluid model, the effects of strain hardening and strain thinning are finally explored, revealing two opposing mechanisms underlying the non-Newtonian stability behavior.
