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Research Papers

Multibody Dynamic Model of Web Guiding System With Moving Web

[+] Author and Article Information
Lei Yu

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, Chinayulei05@mails.tsinghua.edu.cn

Zhihua Zhao, Gexue Ren

Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

J. Dyn. Sys., Meas., Control 132(5), 051004 (Aug 12, 2010) (10 pages) doi:10.1115/1.4001797 History: Received August 26, 2009; Revised March 21, 2010; Published August 12, 2010; Online August 12, 2010

In this paper, a multibody dynamic model is established to simulate the dynamics and control of moving web with its guiding system, where the term moving web is used to describe thin materials, which are manufactured and processed in a continuous, flexible strip form. In contrast with available researches based on Eulerian description and beam assumption, webs are described by Lagrangian formulation with the absolute nodal coordinate formulation (ANCF) plate element, which is based on Kirchhoff’s assumptions that material normals to the original reference surface remain straight and normal to the deformed reference surface, and the nonlinear elasticity theory that accounts for large displacement, large rotation, and large deformation. The rollers and guiding mechanism are modeled as rigid bodies. The distributed frictional contact forces between rollers and web are considered by Hertz contact model and are evaluated by Gauss quadrature. The proportional integral (PI) control law for web guiding is also embedded in the multibody model. A series of simulations on a typical web-guide system is carried out using the multibody dynamics approach for web guiding system presented in this study. System dynamical information, for example, lateral displacement, stress distribution, and driving moment for web guiding, are obtained from simulations. Parameter sensitivity analysis illustrates the effect of influence variables and effectiveness of the PI control law for lateral movement control of web that are verified under different gains. The present Lagrangian formulation of web element, i.e., ANCF element, is not only capable of describing the large movement and deformation but also easily adapted to capture the distributed contact forces between web and rollers. The dynamical behavior of the moving web can be accurately described by a small number of ANCF thin plate elements. Simulations carried out in this paper show that the present approach is an effective method to assess the design of web guiding system with easily available desktop computers.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of web guiding system

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Figure 2

Schematic of 36 deg of freedom plate element coordinates

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Figure 3

Projection of g onto the master surface

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Figure 4

A velocity-based friction model

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Figure 5

Schematic of revolution and its motion

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Figure 6

Block diagram of control for the web simulation

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Figure 7

Schematic of steering angle θC and lateral position S3

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Figure 9

Steering angle θD of the guide1

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Figure 10

Snapshot of moving web animation

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Figure 11

von Mises stress contour of moving web (Pa) (Eqs. 3,4,5)

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Figure 12

Lateral displacement at S1–S3

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Figure 13

Driving moment (N m) for enforcing the rotation angle θD

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Figure 14

Lateral displacement at S3 without control

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Figure 15

Lateral displacement, steering control angle θC, and driving moment with control

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