Study on Vibration Characteristics of TPU Film Guided by Inclined Support
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摘要: TPU薄膜在生产过程中有斜支承导向辊对薄膜起导向传输和支承作用，此外还需要有加热烘干系统进行即时干燥，这些过程都不可避免的引起TPU薄膜的横向振动，从而影响薄膜的制备精度和质量。根据D'Alembert原理，建立具有运动速度的TPU薄膜的动力学模型及热传导方程，解耦后得到含有热弹耦合系数的运动TPU薄膜振动方程；考虑薄膜导向辊斜支承作用，建立无量纲化的斜支承下TPU薄膜的振动方程；采用微分求积法对耦合方程进行离散，研究运动TPU薄膜复频率变化对无量纲速度、斜支承角度、热弹耦合系数、张力比的影响，定量分析各参数对运动TPU薄膜振动稳定性的影响，从而提高汽车TPU薄膜的涂布精度和制备质量。Abstract: In the production process of TPU film, there are inclined supporting guide rollers to guide and support the film; In addition, a heating and drying system is required for instant drying. These processes inevitably cause the transverse vibration of the TPU film, thereby affecting the film′s preparation precision and quality. Based on D'Alembert principle, the dynamic model and heat conduction equation of TPU film with motion velocity are established. After decoupling, the vibration differential equation of TPU film with thermoelastic coupling coefficient is obtained; The motion differential equation of TPU film with oblique support was established; The complex characteristic motion equation is obtained by using differential quadrature method. The relationship between the motion complex frequency and dimensionless velocity, inclined support angle, thermoelastic coupling coefficient, aspect ratio and tension ratio is studied. The influence of each parameter on the vibration stability of motion TPU film is analyzed quantitatively, so as to improve the coating accuracy and preparation quality of automobile TPU film.
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图 6 无量纲速度
$ c $ 随$ {\omega _1} $ 、$ {\omega _2} $ 、$ {\omega _3} $ 的变化曲线（$ \theta = \dfrac{{5\text{π} }}{{12}} $ ，$ {r_0} = 1 $ ，k=0.8，$ \vartheta = 0.3 $ ）Figure 6. Variation curve of dimensionless velocity
$c $ with the first three modes（$ \theta = \dfrac{{5\text{π} }}{{12}} $ ，$ {r_0} = 1 $ ，k=0.8，$ \vartheta = 0.3 $ ）
图 7 无量纲速度
$ c $ 随$ {\omega _1} $ 、$ {\omega _2} $ 、$ {\omega _3} $ 的变化曲线（$ \theta = \dfrac{\text{π} }{2} $ ，$ {r_0} = 1 $ ，$k = 0.8$ ，$\vartheta = 0.3$ ）Figure 7. Variation curve of dimensionless velocity
$c $ with the first three modes（$ \theta = \dfrac{\text{π} }{2} $ ，$ {r_0} = 1 $ ，$k = 0.8$ ，$\vartheta = 0.3$ ）
图 8 无量纲速度
$ c $ 随无量纲复频率变化曲线（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$\vartheta = 0.1$ ）Figure 8. The curve of dimensionless velocity
$c $ changing with dimensionless complex frequency（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$\vartheta = 0.1$ ）
图 9 无量纲速度
$ c $ 随无量纲复频率变化曲线（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$ \vartheta = 0.2 $ ）Figure 9. The curve of dimensionless velocity
$c $ changing with dimensionless complex frequency（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$ \vartheta = 0.2 $ ）
图 10 无量纲速度
$ c $ 随无量纲复频率变化曲线（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$ \vartheta = 0.3 $ ）Figure 10. The curve of dimensionless velocity
$c $ changing with dimensionless complex frequency（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0.1$ ，$ \vartheta = 0.3 $ ）
图 11 无量纲速度
$ c $ 随无量纲复频率变化曲线（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0$ ，$ \vartheta = 0.2 $ ）Figure 11. The curve of dimensionless velocity
$c $ changing with dimensionless complex frequency（$ \theta = \dfrac{{2\text{π} }}{3} $ ，$ {r_0} = 1 $ ，$k = 0$ ，$ \vartheta = 0.2 $ ）表 1 陕西北人TB1350精密涂布机基本参数
Table 1. Basic parameters of Shaanxi Beiren TB1350 precision coating machine
承印物 涂布机最大
幅度/m涂布机最高
速度/（m·min−1）张力
Tx/（N·m−1）TPU薄膜 1.25 400 120 
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