ANCF Analysis of Textile Systems

Abstract

This paper presents a new flexible multibody system (MBS) approach for modeling textile systems including roll-drafting sets used in chemical textile machinery. The proposed approach can be used in the analysis of textile materials such as lubricated polyester filament bundles (PFBs), which have uncommon material properties best described by specialized continuum mechanics constitutive models. In this investigation, the absolute nodal coordinate formulation (ANCF) is used to model PFB as a hyperelastic transversely isotropic material. The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy–Green deformation tensor. Using this energy decomposition, the second Piola–Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. The constitutive equations are used to define the generalized material forces associated with the coordinates of three-dimensional fully parameterized ANCF finite elements (FEs). The proposed approach allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to describe the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between the rollers and PFB.

Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate Formulation

“…When a yarn is defined as having square-symmetric and transversely isotropic homogeneous continuum, the elastic compliance matrix can be expressed by the modulus and Poisson's ratios [33]:…”

“…The modulus and Poisson's ratio in the other directions could be determined using the method in the literature [33]. The viscosity coefficient used the parameters that were found in the literature [30].…”

A dynamic modeling approach to the moving filament during high-speed winding by absolute nodal coordinate formulation

“…The modeling of slender flexible bodies, such as yarn and filaments, firstly started with the ball chain model and the string model. [18][19][20][21] Based on the multi-body system method, Wang et al 22 conducted modeling and analysis around the drafting process in the production of polyester filaments, and applied absolute nodal coordinate formulation (ANCF) to model continuous filament bundles in three-dimensional and large deformation motion. Wang et al 23 further proposed a mathematical modeling method, which included air resistance, and described the free swing process of filament bundles.…”

An analytical approach of filament bundle swinging dynamics, Part I: Modeling filament bundle by ANCF

“…Furthermore, with the development of research, ANCF is no longer limited to assumptions of isotropy and homogeneity, as long as the appropriate constitutive relation of the material is given. 19 These characteristics make the dynamic model established by ANCF more suitable for describing flexible multibody systems, such as the large deformation of yarn during motion in a wide range, than the model using the floating reference frame formulation. By coincidence, for the dynamics analysis of a yarn system, one may pay more attention to the motion trace, deformation, and axial tension of the yarn than to the centrifugal force and the Coriolis force.…”

“…Yoo et al 24,25 and Dmitrochenko et al 26 analyzed a rotating paper strip or yarn-shaped string using the ANCF; in particular, the combination of theoretical analysis and experimental verification proved the validity of the ANCF. Wang et al 19 investigated a new flexible multibody system approach for modeling textile systems, including roll-drafting sets used in the textile machinery, and simulated the dynamic behavior of lubricated polyester filament bundle textile systems, whose cross-section was rectangular, shedding light on the complexity of such a textile drawing system. Gerstmayr et al 27 and Nachbagauer et al 28 reviewed the development and application of ANCF over the past decade.…”