A filament bundle is a kind of filament assembly with less twist or nontwist. It is a viscoelastic body and has a large aspect ratio. Its large deformation during motion over a wide range is a universal phenomenon in many textile processes. The dynamic viscoelasticity of the filament bundle, gravity, and air resistance are three important factors affecting the filament bundle's dynamic behavior. Taking account of these factors, a filament bundle dynamics analysis method is proposed in a series of three papers. This paper, the first in the series, presents an approach to model the dynamics of the flexible filament bundle with viscoelasticity and to analyze its dynamic behavior under the action of gravity and air resistance. The filament bundle element (FBE) is established based on absolute nodal coordinate formulation (ANCF), in which slope vectors and global coordinates are applied. The approach presented in this paper is well suited for the analysis of large deformation motions of filament bundles. As an example, a dynamic model was established to predict the filament bundle's trace during its swinging through large displacements under the action of gravity and air resistance, taking into account the filament bundle viscosity. The nonlinear differential equations of the filament bundle system were solved using MATLAB. Furthermore, the swing traces of the filament bundle in a closed Plexiglas box with different vacuum degrees were recorded using a high-speed camera to prove the validity of the established filament bundle model based on ANCF.

A new finite element dynamic model of a moving yarn segment has been proposed in this paper based on the absolute nodal coordinate formulation (ANCF). Apart from taking into account the elastic properties of the yarn in three dimensions, the model also considers the viscosity in the longitudinal direction and takes into account the effect of gravity and air resistance. In this paper, the simulation described the movement of the yarn segment that is pulled by the fixer on the guideway. Then, a corresponding experiment was proposed to evaluate the theoretical model. The theoretical and experimental comparisons of the motion tracing exhibited good agreement, demonstrating that the new model could predict the actual moving trace of the yarn segment. Moreover, another simulation of the spatial motion of the yarn segment was presented, to elucidate the role of the model in predicting the movement of the yarn segment. After considering the parameters of the actual process and its constraints, the authors established that the proposed model could be used to predict the trajectory of a yarn segment in the actual production process, which is vital when fabricating textile products.

A polyester filament winding spindle is the most complex winding rotor system, due to its high speed, heavy load, and frequency-dependent parameters; furthermore, the spindle's rotating speed constantly changes and it is continually crossing the critical speed points. This paper presents an approach to establish the finite element model of the winding spindle to predict its dynamic behavior characteristics during start-up. Firstly, three finite element models of the discrete single component were developed based on the Timoshenko beam theory. The bending, transverse shear effect, and gyroscopic moment were considered in these models. The flexible supporting system, which consists of a deep groove ball bearing and several rubber O-rings, is simplified by a nonlinear spring and damper. Its frequency-dependent dynamic supporting parameters are identified by experiment. Secondly, a fully dynamic model of the polyester winding spindle system, which consists of the cantilever supporting arm, shaft, and sleeve, as well as the flexible and rigid coupling elements, was established. Thirdly, the Newmark method was used to develop a program for solving the dynamic equations of the spindle system in MATLAB®. Based on the model of the spindle system and the computation program, the effects of the supporting stiffness, damping, and start-up time on the spindle's unbalanced response were investigated. The results indicate that the model of the spindle system presented in this paper is suitable for the prediction of the dynamic performance during its start-up.

This paper continues the previous study and presents a dynamic modeling approach for a high-speed winding system. To meet the requirements of high-speed winding, a twin-rotor coupling structure is adopted in the winding system. It is a complex spindle system, due to its high speed, heavy load, frequency-dependent coupling parameters, and time-varying rotational speed. In this paper, an approach to establishing a finite element model of the winding system is proposed to predict its dynamic behavior characteristics during the winding process. First, the spindle and contact roller models of the discrete single component are developed based on Timoshenko beam theory. Bending, transverse shear effects, and gyroscopic moment are considered in the models. The contact stiffness between the contact roller and the packages to be wound on the spindle is simplified by a nonlinear spring. The contact stiffness is identified by dynamics analysis in ANSYS® 17.0. Next, a fully dynamic model of the winding system, which consists of the spindle subsystem, the contact roller, and the flexible coupling elements, is established. Third, the Newmark method is used to develop the program to solve the dynamic equations in MATLAB® 2013b. Finally, the effects of the supporting system and contact state on the winding system's dynamic response are investigated. The results indicate the model of the winding system presented in this paper is suitable for predicting dynamic performance during the winding process.

A filament bundle is a type of yarn, which is composed of nearly parallel and highly oriented polymer monofilaments. Due to its nonlinearity both in material constitutive properties and structure, the filament bundle possesses nonlinear viscoelastic properties. It is important to study the dynamic behavior of the filament bundle accurately during its high-speed movement. Therefore, an accurate expression of the constitutive relation of the filament bundle is an essential prerequisite for its dynamic simulation and analysis. Continued the previous study in Part I: modeling filament bundle method, in this paper, an approach was proposed to identify the equivalent dynamic constitutive parameters of the filament bundle considering frequency-dependent characteristics. Firstly, the identification formulas of the dynamic elastic modulus and viscoelastic coefficients were derived based on the Kelvin model. Then, a testing method of the cross-sectional parameters of the filament bundle under a certain tension was proposed, and the testing device was developed to obtain the area of the filament bundle; The dynamic loading test of the bundle filament was conducted in a DMA Q800 dynamic mechanical tester. Thirdly, the equivalent dynamic elastic modulus and viscoelastic coefficients were obtained through the experimental test. Finally, an analytical method was proposed to verify the correctness of experimental results through simulation. The results show that the excitation frequency has a significant influence on the dynamic elastic modulus and viscoelastic coefficient, and the curves of the equivalent dynamic elastic modulus and viscoelastic coefficient present nonlinear variation characteristics.

To satisfy the requirements of high speed, large capacity and constant winding, a textile winding rotor needs to work in a wide rotation speed range and frequently pass through critical speed points. Thus, the winding rotor adopts the flexible long shaft coupling structure and flexible support with rubber O-rings. This kind of rotor has a multi-coupling structure and frequency-dependent parameters characteristics, especially representative and universal in the dynamic analysis method of the high-speed rotor. In this paper, an approach was proposed to investigate the dynamic behavior of the winding rotor considering the flexible coupling and frequency-dependent supporting parameters. Firstly, a dynamic model of the winding rotor was established by using a Timoshenko beam element. Its dynamic behaviors were simulated by considering the time-varying rotation speed and the frequency-dependent parameters of flexible support. Secondly, a non-contact measuring device was developed for measuring the vibration displacement of the winding rotor in three different speed-up times. Finally, based on simulation and measurement data, how flexible support parameters and the speed-up time affect the winding rotor passing through the critical speed point of the rotor smoothly is revealed. The methods and findings reported here can be used for theoretical and experimental vibration analysis of other types of high-speed flexible rotors.