由Bezier曲线构造的聚合物熔体剪切黏度模型

杨晓东; 申长雨; 李倩

doi:10.6052/0459-1879-13-163

由Bezier曲线构造的聚合物熔体剪切黏度模型

杨晓东^1,2,
申长雨¹,
李倩^1,2

1 郑州大学橡塑模具国家工程研究中心, 郑州 450002
2 郑州大学力学与工程科学学院, 郑州 450002

基金项目: 国家重点基础研究发展计划（973计划，2012CB025903）和河南省教育厅自然科学计划（2010A130002，12B130006）资助项目.

详细信息

作者简介:
杨晓东，教授，主要研究方向：聚合物成型过程数值模拟.E-mail：yangxd@zzu.edu.cn

中图分类号: O373
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出版历程
- 收稿日期: 2013-11-20
- 修回日期: 2013-12-10
- 刊出日期: 2014-03-17

A SHEAR VISCOSITY MODEL OF POLYMER MELT CONSTRUCTED BY BEZIER CURVE

1 National Engineering Research Center for Advanced Polymer Processing Technology, Zhengzhou University, Zhengzhou 450002, China
2 School of Mechanics and Engineering Science, Zhengzhou University, Zhengzhou 450002, China

Funds: The project was supported by the National Key Project for Basic Research of China（2012CB025903）and the Natural Science Program of the Education Department of Henan Province of China (2010A130002, 12B130006).

摘要

摘要: 为提高聚合物熔体剪切黏度模型的描述精度，提出了一个基于二次Bezier 曲线的黏度模型. 模型采用分段函数描述，在对数坐标系中，低剪切速率时的牛顿区和高剪切速率时的幂律区采用线性函数，介于二者之间的过渡区采用二次Bezier 曲线. 通过牛顿区和幂律区的直线延长线构造Bezier 曲线的控制多边形，从而保证三段曲线的光滑过渡. 模型可以明确给出任意温度下低剪切速率时牛顿区的结束点，以及高剪切速率时幂律区的开始点. 拟合算例表明，所提出模型的拟合精度明显高于Cross-Arrhenius 黏度模型.
- 黏度模型 /
- Bezier 曲线 /
- 聚合物熔体 /
- 剪切黏度 /
- 数据拟合
Abstract: A shear viscosity model of polymer melt is proposed based on a quadric Bezier curve to improve the model's descriptive precision. The model is characterized by piecewise functions in a logarithmic coordinate. Linear functions are adopted to represent the two linear sections of the Newton region at lower shear rates and the power law region at higher shear rates. A quadric Bezier curve is applied to describe the transitional region between the two linear regions. The three curves are connected smoothly by a control polygon which is formed through the extension lines of the two linear curves of the Newton region and the power law region. At any temperature, the end point of the Newton region at lower shear rates and the start point of the power law region at higher shear rates are predicted accordingly. The data fitting examples show that the precision of the proposed model turns out to be obviously higher than that of the Cross-Arrhenius model.
- viscosity model /
- Bezier curve /
- polymer melt /
- shear viscosity /
- data fitting

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