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.
As the intermediate component and fundamental constituent of the process of turning fiber into fabric in the textile industry, the quality of the yarn directly affects the quality of the final textile product. There are different types of yarn, such as twisted yarns or continuous filaments that are not twisted. Hereafter, in this paper, both types have been collectively referred to as “yarn”.
In the process of producing textiles, in addition to the continuous moving yarn, there is another state in which the yarn is clamped by a machine at one end and the rest of the yarn keeps moving under the pulling action of the machine, for example, a yarn segment that protrudes from the nozzle of the machine during air-jet weft insertion (Figure
Different yarn segments in the textile process: (a) yarn segment in the spinning when yarn-breaking; (b) yarn segment in the spinning when yarn-breaking; (c) yarn segment in filament winding starting process.
Of the above cases, yarn splicing, especially during the pneumatic yarn splicing process and the coupling of the yarn and the airflow, is of particular concern to researchers. However, when studying the yarn-breaking and filament winding starting processes, researchers focused on the dynamics of the mechanical parts rather than looking at the process from the perspective of the yarn. In addition to the pneumatic yarn splicing process, automatic yarn-splicing robots are now a research hotspot with regard to the spinning process. For this process, the yarn segments are not only coupled with the airflow, but this also includes different types of motions as the yarn is pulled by the gripper. Currently, few researchers have investigated this topic.
The modeling and simulation of the yarn begin with the ball-chain model in the early stage of research [
The movements of the yarn segments are three-dimensional, and, during the movement, the yarn segment undergoes deformation such as stretching, torsion, bending, and shearing in the various processes, and they are affected by air resistance. A three-dimensional description is needed to fully consider the yarn’s deformation and motion in the longitudinal direction as well as its cross-section dimensions. This has led to an exciting attempt to simulate the yarn segment using a three-dimensional beam element. Meanwhile, the viscosity of the yarn in the longitudinal dimension, which is the main direction of tension, cannot be ignored in the analysis. In finite element beam theories, there are classical models that come from Euler-Bernoulli’s and Timoshenko’s theories. As the beam becomes less and less slender or flexible, its mechanics is increasingly three-dimensional, and the classical models cannot yield accurate results [
Based on the ANCF, the moving yarn segment element was then established, that is, the yarn segment which is pulled and moves. The simulation of the movement and deformation of the moving yarn segment, with the end node point pulling motion, was then carried out. The effects of gravity on the yarn and air resistance were taken into consideration during this process. When modeling the moving element of the yarn segment, the elastic characteristics of each direction were fully considered, and the viscous characteristics in the longitudinal direction were also computed, so that the established model was more consistent with the actual conditions. Finally, in order to show the validity of the model, a corresponding experiment was conducted. This new finite element dynamic model can be used to analyze the movement and deformation of a yarn segment in textile processes, such as air-jet weft insertion, the yarn piecing up process, and the filament winding starting process. The ultimate goal of this research was to ensure that the yarn moves as expected.
Yarn is thin but has a considerable length to diameter ratio. In order to create a generally described model, it was assumed that the yarn was an ideal continuum with a circular cross-section, as shown in Figure
The moving yarn segment.
In this section, the theoretical model of the moving yarn segment has been established based on the ANCF [
In this section, the three-dimensional element of a moving yarn segment has been proposed based on the ANCF [
The moving yarn segment element model.
As shown in Figure
Configurations of moving yarn.
Since the cross-section of the element of the moving yarn segment is assumed to be circular, for the convenience of calculation, the following coordinate transformation can be performed, as shown in Figure
Based on continuum mechanics, there are two kinds of configurations that are used to describe the deformation and motion of the moving yarn segment, as shown in Figure
The two configurations can be defined in the global coordinate system
The kinetic energy of a yarn element can be defined as
The element of the moving yarn segment will move and change from one configuration to another, which can be described by the Jacobian matrix
The stored strain energy density function in the element can be written as
The elastic energy of the yarn element
The elastic forces can be obtained as gradients of the elastic energy
The dissipated energy due to viscosity can be written as
The generalized viscosity force can then be written as
When the yarn is moving in the processing space, the yarn is subjected to the force due to gravity. If the principle of conservation of mass or the continuity condition is assumed, the virtual work of the inertial force can be written as
From formula (
Apart from the body forces, the yarn is subject to surface forces such as air resistance, which plays a vital role during the movement of the yarn. Figure
Air resistance of the moving yarn.
The vectors
When the yarn is moving with a given velocity
The exact formula of the air resistance of the yarn element can be written as
Under the action of gravity
In this section, the constitutive model of the yarn has been discussed. The yarn, which is the fiber assembly, has a special structure in comparison to traditional materials. In the existing research, and, depending on the state of the yarn, there have been different descriptions of the yarn: pure elasticity, viscosity, and viscoelasticity. For instance, when discussing the coupling of the fiber and the airflow [
Therefore, the total strain energy of the yarn consists of two parts, the first is the elastic strain energy, and the second is the dissipation energy. Correspondingly, the stress can be written as
In the case of transverse isotropy,
The yarn also exhibits viscosity during large deformation and movement. In particular, the yarn has a damping effect of the nonnegligible viscous force in the longitudinal direction due to its tension. Moreover, since the yarn has a sizeable tensile modulus in the longitudinal direction, it also exhibits a particular form of oscillation during movement, which further indicates that the energy dissipated by the viscous force in the longitudinal direction cannot be ignored. When considering the viscosity of the yarn in the longitudinal direction, the stress-strain relationship can be written as follows:
In this study, the governing equation for the yarn segment motion Equation (
Solution procedure.
In this section, the results of the simulation and the experiments with a moving yarn segment have been presented. The results have been shown here to demonstrate the effectiveness of the proposed moving yarn segment model. For this reason, a polyester filament bundle, which is the most basic type of the yarn, was used as the object for the simulations and experiments. As the cross-section of the polyester monofilament is circular and the bundle of filaments is approximately parallel when arranged in the straightened state, this is more in line with the assumption that was made for the constitutive relationship.
Figure
Moving yarn model for simulation and experiment.
Firstly, the clamped end of the filament bundle was fixed with a porcelain eye that is commonly used to guide yarns in the process. The porcelain eye is a ceramic workpiece with a diameter of 0.5mm, as shown in Figure
Clamped filament bundle.
The purpose of the simulation and the experiment was to verify the accuracy of the moving yarn segment model. Since the length of the simulated filament bundle was 0.32mm, in order to observe the trajectory of the movement more clearly, it needed to be moved at least 1/3 of its length during the experiment. Combined with the simulation time and the data store capacity of the high-speed camera, the speed of the traction motion was determined to be 0.1 m/s, according to the stroke length.
The POY filament bundle had a nominal denier of 220dtex/72f. For better observation, 24 bundles of these POY filaments were combined into a bundle. Therefore, the actual linear mass density of the filament bundle was 5280dtex. A precision length measuring instrument (YG086) used to measure the length of the sample which was 320mm. According to the product manual, the density of the polyester was 1.38 g/m3. Before the experiment, the actual linear mass density of the filament bundle was measured using a precision balance (PRACTUM2102-1CN) according to the standard method of testing linear mass density [
The tensile modulus of the filament bundle was measured using a large-scale single yarn strength gauge (SITHAI ST-D100). According to the assumed idealized conditions, the shear modulus and Poisson’s ratio were determined using equation
The modulus and Poisson’s ratio in the other directions could be determined using the method in the literature [
The parameters of the filament bundle used in simulation and experiment.
Parameter | Value and unit |
---|---|
The density of the polyester material | 1320 kg/m3 |
Linear mass density (measured value) | 614.2 tex |
Tensile modulus | |
Viscosity coefficient | |
Fiber volume fraction | 70.16% |
Length | 320mm |
Cross section diameter | 0.92 mm |
Air density | 1.2 kg/m3 |
Moving yarn model for simulation and experiment. (a) schematic diagram and (b) test site.
When the traction fixer, which clamped the endpoint of the filament bundle, began to move, the other endpoint was released. A high-speed camera recorded the moving trace of the filament bundle, which was used to validate the model of the yarn. The motion states of the filament bundle at 0.05, 0.1, and 0.6 s were shown in Figures
Experimental validation. (a) Motion comparison at 0.05s. (b) Motion comparison of 0.1s. (c) Motion comparison of 0.6s. (d) Experimental and simulation comparison.
The filament bundle moved under the pulling action of the fixer. Figures 10 have shown that the positions of the filament bundle, for the different times that were obtained from the simulation and the experimental test, were very similar. The moving trace of the filament bundle at 0.6s was almost the same but they diverged at 0.25 s especially in the middle section. The experimental results showed a more curved result than that from the simulated results. The reasons for the difference were most likely as follows: (a) the motion of the filament bundle was affected by the air resistance. Thus, the appropriate air resistance coefficient should be incorporated into the simulation. The simulation in this paper used the results from the literature [
Automatic yarn piecing technology is the key technology needed to realize the intelligent spinning process. The development of an automatic piecing robot would play a significant role in enhancing the yarn spinning efficiency and guaranteeing the spinning quality. Already, relatively mature automatic piecing devices have been developed such as the FIL-A-MAT automatic piecing device (based on the Zinser 320 spinning machine), Fiasol automatic piecing device (Came Italy), Heathpan automatic piecing device, AYPT type automatic piecing device, and ROBOFIL automatic piecing device, and these devices can usually complete the detecting and piecing up process in less than 30 seconds. While developing automatic piecing technology, the design and control of the yarn piecing up module are major concerns. The yarn segment is pulled through the yarn guide hook and fed into the twist zone during this process. Finding the best method to complete the yarn piecing action quickly and accurately is the primary issue.
Taking the working process of the automatic yarn piecing robot during ring spinning as an example, the automatic piecing up work is performed by a robot arm. Figure
The parameters of the cotton yarn used in the simulation.
Parameter | Value and unit |
---|---|
The density of the cotton yarn | |
Linear mass density (measured value) | 324.2 tex |
Tensile modulus | |
Viscosity coefficient | |
Fiber volume fraction | 69.55% |
Length | 320mm |
Cross section diameter | 0.66 mm |
Air density | 1.2 kg/m3 |
The velocity of the robot arm (which gripped the endpoint of the yarn).
Position statement of the yarn segment | Velocity in the | Velocity in the | Simulation time/ moving time (s) | Corresponding configuration in Figure |
---|---|---|---|---|
Straight position to position 1 | 1.5 | 1.5 | 0.08 | (b) |
Position 1 to position 2 | -4 | 1 | 0.05 | (c) |
Position 2 to position 3 | -2 | -0.4 | 0.05 | (d) |
Yarn spinning process.
Automatic yarn-jointing robot.
Yarn segment motion during the piecing up process by the robot arm. (a) Winding on the bobbin. (b) Passing through the yarn guide hook. (c) Feeding into the twisting rollers.
The spatial motion of the yarn segment under the pulling of robot arm. (a) The process of passing through the yarn guide hook. (b) The first position of the yarn segment. (c) The second position of the yarn segment. (d) The third position of the yarn segment.
As shown in Table
The case described above has shown that the model that has been introduced in this paper can predict the trajectory of the yarn segment under different pulling motions from the robot arm. On the basis of this model, and by modifying its boundary conditions or expanding the coupling condition of the yarn with the mechanical parts, it is now possible to predict other movement behaviors of the yarn segment of the automatic piecing process, such as winding the yarn onto the bobbin and feeding into the twisting zone.
This paper has proposed a dynamic model of a yarn segment to predict the yarn’s motion trajectory based on the ANCF. When establishing the moving yarn segment model, the elasticity in the longitudinal direction and cross-section directions were considered, as well as the viscosity characteristic in the longitudinal direction. In order to enable the model to analyse the moving yarn segments for the actual processes, the effect of both air resistance and gravity were taken into consideration during the creation of the model.
As an example used to verify the simulation of the model, a model of the filament bundle where the gripper pulled it from one end on the guideway has been implemented this paper. The simulation and the corresponding experiment verified the accuracy of the model. Apart from this and in order to better understand how to use the model to predict the motion process of the moving yarn segment, another simulation was implemented which described the movement of the cotton yarn when it was pulled at different velocities during the automatic yarn piecing up process. This simulation described the yarn segment pulled from the horizontal position to the centre of the yarn guide hook. During this process, the yarn segment could not contact the support arm of the yarn guide hook. Thus, it was possible to check whether the designed velocity of the robot arm satisfies the requirements by observing the trajectory of the yarn segment.
On this basis, this model can be used effectively to provide a reference for the analysis of yarn segment motion during the textile process by extending the model with specific boundary conditions and constraints. Compared with modeling the yarn as either a moving string or a pure elastic body, the model that has been established in this paper is able to more effectively simulate the actual moving trace of the yarn segment when it is being pulled in the processes: such as the yarn segment protruding from the nozzle during air-jet weft insertion and the filament bundle segment during the start of the winding process. Through the use of the equations in this model, it is also possible to calculate the distribution of the tension in the yarn segment during movement. This has laid the groundwork for the establishment of a multibody system model for the coupling of the moving yarn segment with the mechanical part. For example, in order to simulate the dynamic behaviour of the yarn segment coupled to the gripper of the automatic yarn-jointing robot when in operation. Outlines for further research have been proposed as follows: Accurate parameter identification is vital when dealing with the modeling of a specific yarn. Furthermore, the actual state of the yarn during the production process should be taken into consideration, such as its tension and temperature when determining the yarn’s parameters. It is of interest to try to account for the viscosity of the cross-section dimension of the yarn, as well as using the three-dimension viscoelastic model to describe the constitutive relationship of the yarn. However, there is no doubt that this will also increase the amount of calculation inherent in the model.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This work was supported by the National Key R&D Program of China (2017YFB1304000), Natural Science Foundation of Shanghai (16ZR1401900), and Applied Foundation Research of China National Textile and Apparel Council (J201504).