Numerical Simulation of Fiber Motion in the Condensing Zone of Lateral Compact Spinning with Pneumatic Groove


 Lateral compact spinning with pneumatic groove is a spinning process to gather fibers by common actions of airflow and mechanical forces. Compared with ring spinning, it can more effectively reduce yarn hairiness and enhance yarn strength. However, fiber motion in the agglomeration area is complex. And, it is important to establish a new fiber model to accurately describing the fiber motion. The objectives of this research were to create a new fiber model to simulate the agglomeration process, to analyze yarn properties of the lateral compact spinning with pneumatic groove, and to compare with other spinning yarns through a series of tests. The new fiber model was based on the finite element method implemented in MATLAB and was to show the fiber motion during the agglomeration area. The simulation generated results were close to the real motion of fibers in spinning. In the lateral compact spinning with pneumatic groove, fiber bundle through the agglomeration area can be gathered, and the output of the fiber bundle was nearly to cylinder before yarn twisted. The experiments demonstrated that the lateral compact spinning with pneumatic groove can improve the yarn properties: increase the yarn twist, enhance the yarn strength, and reduce the yarn hairiness.


Introduction
Spinning plays an important role in determining the mechanical properties of yarns. And, fi ber motion is important for the theoretical research for yarn generation during the spinning process. Yarn is a linear assembly of twisted short fi bers or fi laments [1]. In order to describe the fi ber motion during spinning, a fi ber model needs to be established. Fiber is a fl exible continuum material with certain elasticity and a large length-diameter ratio. When a fi ber is considered as an elastic thin rod, the multiple segments can be deformed relative to others. Thus, the motion of a fi ber in the airfl ow fi eld is nonlinear with large deformation [2]. In the past decades, a fi ber was usually simplifi ed by a variety of mechanical models for fi ber property characterization, particularly with particles or rigid cylindrical rods being model's elements. For instance, a chain model was used to simplify a fi ber into many hinged short rigid rods [3][4]. However, a simple model may not be effective enough to describe the physical characteristics of fi bers [5]. In the late 1980s, mechanical modeling of fi ber had made some breakthroughs because of widespread applications of computer. Cheng established a series of mechanical models with multiple spheres for fi bers, containing almost all the physical characteristics of fi bers [6][7]. But, the expression of the mechanical behaviors from these models was not applicable for fi bers in the airfl ow fi eld. In the 1990s, many scholars continued to study the mechanical models of fi ber. Yamamoto and Matsuoka proposed a bead-spring-chain model, which was similar to a polymer chain; it can better describe the rigidity and fl exibility of fi ber [8]. Zeng and Wang improved this model, but it could not be applied to fi bers of a large length-diameter ratio (about 1000:1), and its computation was rather complex and diffi cult [9,10,11].
In this article, we present a fi nite element model with continuous elastic fi ne rods established in MATLAB to simulate the motion of fi ber in the three-dimensional space. In this model, a fi ber is regarded as the elastic thin rod, and it is used to simulate the large deformation and to analyze the infl uence of its axial force on the bending. From this new fi nite element model, the fi ber movement can be calculated and visualized, and the simulation result can be more closely to the real fi ber movement.

Numerical simulation of fi ber motion
In order to describe the fi ber movement during the gathering zone in the spinning process, a proper mathematical model for fi bers should be established to numerically simulate the statics of the fi ber under lateral mechanical force in the general stress state. This fi ber model regards a fi ber as elastic fi ne rods so that the fi nite element method can be used to solve the nonlinear large deformation of an elastic thin rod.

Abstract:
Lateral compact spinning with pneumatic groove is a spinning process to gather fi bers by common actions of airfl ow and mechanical forces. Compared

Keywords:
Compact spinning; fi ber motion; agglomeration process; yarn properties

Fiber fi nite model and simulation
In this paper, we compared the fi ber movement of lateral entry compact spinning with pneumatic groove, intermediate entry compact spinning with suction groove, and ring spinning. First, we used the Ansys 15.0 to get the velocity of fi ber bundle and then established the fi ber fi nite element model by MATLAB. Finally, we simulated the fi ber motion in the agglomeration area.
In the new fi ber fi nite element model, the fi ber was regarded as an elastic thin rod. The whole elastic thin rod was decomposed into a combination of micro-section rigid mass unit and massless elastic rod unit, and the analysis of the elastic thin rod by fi nite element method was carried out. The deformation of the rod unit in three-dimensional space can be decomposed into axial tensile deformation and the combination of bending and torsional deformation in two principal planes.  Figure 1 showed the establishment of an overall coordinate system O -xyz for the entire elastic thin rod. The local coordinate system of each rod unit was O'-abc, a was the axis direction of the rod unit, aO'b and aO'c were the two principal plane orientations of the rod unit. The node i and node j were the ends of rod unit e, each of the nodes had six degrees of freedom (displacement component). After the elastic rod unit was deformed by force, the relative displacement of node i in the local coordinate system was calculated by the following formula: (1) where means the axial displacement of node i, and mean the bending defl ection in two transversely curved principle planes, means the torsion angle of the crosssection of the node, and mean the two laterally curved bending corners in the main plane.
In the meantime, the relative displacement of node j in the local coordinate system was calculated by the following formula: The displacement of the two nodes of the rod unit in the local coordinate system was calculated by the following formula: The force received by node i and node j in the unit local coordinate system was calculated by the following formula: where , , and , , were the force of the node; , , and , , were the force couple of the node.
The combination of forces received by the two nodes of the rod unit was called the rod end force. It was calculated by the following formula: Figure 2 showed the connection of quality spatial elastic rod unit. The external force on the elastic thin rod was simplifi ed to the node coordinate system on the node. Each node coordinate system had six degrees of freedom with respect to the fi xed global coordinate system. There were six independent coordinate parameters to determine their relative position, and three of them described the moving line displacement of the node, the other three described the angular displacement of the node cross-section. The entire elastic thin rod had 6(n+1) degrees of freedom.

Initial parameters
The diameter d of the fi ber was 0.02 mm; the length of the fi ber in agglomeration area was 42 mm; the elastic modulus E of the fi ber was 2,224.6 cN/tex; the shear elastic modulus G of the fi ber was 106.2 cN/tex; the density of the fi ber was 1,510 kg/m 3 ; the number of fi ber division units was 500; the left lateral angle was 15°; the initial position of the fi ber in lateral entry compact the motion theorem of center of mass, the dynamic equation of rigid body moving with the center of mass is: (7) where: m is the mass of the rigid body mass unit; a is the absolute acceleration of the mass center relative to the inertial reference frame, where the inertial reference frame is O-xyz; and F is the principal vector of external force on the rigid body mass element.
The dynamic equation of the motion of mass element of a rigid body in a micro segment around its center of mass in space can be established by using the momentum moment theorem: (8) Or (9) where: J is the tensor of inertia of the rigid body to the center of mass O.
M is the principal moment of the external force on the rigid body to the center of mass.
is the angular velocity of the rigid body.
is the derivative of with the coordinate system O-xyz to time.
The entire elastic thin rod had 6(n+1) degrees of freedom. So, combining the formulae (7) and (9), it can be written as: (10) where The fi ber model was established based formula (10) by MATLAB; it was shown as Figures 3 and 4. From that way, the new fi ber model was not only can reduce the complex computation but also will more closely to show the characteristic of real fi ber. Figure 6 shows the movement of single fi ber. It is obvious that lateral entry compact spinning with pneumatic groove spinning twisted obviously than intermediate entry compact spinning with suction groove spinning or the ring spinning. And, ring spinning almost has no additional twist. Because of the lateral direction of fi ber bundle during the agglomeration area, the fi ber, especially the edge fi ber, would move closer to the center. The fi ber bundle would be more inseparable, and it would improve the yarn properties.
The condensing zone is for better gathering fi ber. And, the best condition is that when the fi ber bundle is totally gathered in this place and the twist form is to be cylinder. Then, the yarns spinning with suction groove was Z=-1 mm; the initial position of the fi ber in intermediate entry compact spinning with suction groove and ring spinning was Z=0 mm; The time integral step was 10-6s.
Then, the initial parameters will type in the MATLAB fi nite fi ber simulation model.

Simulation results and analysis
According to the specifi c value, we calculated the fi ber motion in the agglomeration area by MATLAB software. http://www.autexrj.com/ will avoid the triangle, and the yarn properties will be better. Figure 7 shows the fi ber motion of two compact spinning. As Figure 3 shows, the x,y coordinate of the condensing zone is from A(20,10)mm to B(10,-20)mm. Figure 7 (d) shows the fi ber motion of intermediate entry compact spinning with suction groove and (e) shows the fi ber motion of lateral entry compact spinning with pneumatic groove. In Figure 7 (d), the fi ber is totally condensing during the x,y coordinate of (10,-20) mm and (e) is (15,-10) mm. The fi ber of lateral entry compact spinning with pneumatic groove is totally condensed during the condensing zone but the fi ber of intermediate entry compact spinning with suction groove is condensing at the edge of condensing zone. Fiber bundles will not get total gathered in case (d). The twists of spindle will pass forward and breakdown the gathered fi ber bundles. Finally, the twist triangle cannot be avoided. It will lead the yarn hairiness and the fi nal yarn properties worse. At in the case of Figure 7 (e), the fi ber bundle will totally be gathered during the condensing zone. The output fi ber bundle looks like near-cylindrical, and the yarn will be tighter, and the hairiness will less after twisted.

Results and discussion
In order to compare the yarn properties of the lateral entry compact spinn ing with pneumatic groove, intermedia entry compact spinning with suction groove and ring spinning, the yarns were spun, and the yarn properties tests were carried out. The spinning machine and raw materials used in the experiment were, respectively, provided by two different companies (Hunan Huashen Group and Ningbo Dechang Precision Textile Machinery CO., LTD). The spinning yarn was 36 Nm ramie yarn. According to the experimental program, the twist, strength, and hairiness of yarn were compared. During the experiment, the experimental test instruments were unchanged.

Basic experimental parameters and testing instruments
The raw material was ramie roving. The mass of the roving was 4.70 g/10m; the moisture regain of the roving was 8.07%. All the spinning was fi nished by the domestic FZ501-type spinning machine. The pressure of pneumatic groove was -2,600 (Pa), the twist was 680 (T/m), the spinning speed was 7,000 (r/min). The count of yarn was 36 Nm.
The tests were performed at the standard atmosphere pressure, when the relative humidity was 65%±3% and the temperature was (20±2)℃. Before testing, the specimen should be humidifi ed for 48 hours in a constant temperature and humidity laboratory. The type of yarn evenness test instrument was UT4 evenness meter. Uster UT4 adopts capacitive sensor and photoelectric sensor to measure yarn diameter unevenness, slub, detail, and ramie yarn number. The test speed is 400 m/min, and each tube yarn was tested 10 replications. The yarn tension of different counts was adjusted by (0.5±0.1) cN/tex. The tested specimens were 3 kinds of bobbins that have 10 replications per bobbin when tested. The type of the yarn hairiness test instrument was YG172A yarn hairiness tester. The testing condition is according to FZ/T01086-2000 [12]. During the yarn hairiness tests, the length of the test fragment was 10 m, the number of tests was 1 tube per 10 times. The test speed was 10 m/min. The type of yarn strength test instrument was YG063T, according to GB/T4711-1984 [13]. During the yarn strength test, the clamp distance was 500 mm, and the tested speed was 500 mm/min. The type of yarn twist test instrument was YG331A yarn twist test tester. According to GB/T2543. 2-2001 [14], the experiment adopted a method of untwist-retwist method, which was to test the yarn with a certain length under the specifi ed tension and measure the number of rounds when returning to the starting length after untwisting and reversed twisting. The experiment used counterclockwise running direction, the speed was 800 r/min, the length of the sample was 500 mm, and the pre-tension was calculated according to the formula of the yarn was 500 mm, and the pre-tension was calculated according . The allowable elongation limit was 4.0 mm. For the mean±sd (standard deviation), the standard deviation was mainly decided by the test equipment and environment.

Comparison of yarn evenness
The essence of yarn linear density unevenness is the unevenness of fi ber arrangement along the length direction in the yarn sliver. It is an important factor that directly affects the yarn breaking strength and elongation, yarn twist distribution, and yarn thickness unevenness. Therefore, it is very important to measure the evenness of yarn.
In Table 1, all the indicators of II are best. On calculation, CVm of II has reduced 7.32% compared to that of I and reduced 20.4% compared that of III. The thick place and the thin place have the same tendency. The lateral entry compact spinning with pneumatic groove could improve the parallelism of fi ber arrangement. In the meantime, the reduction of thick place and thin place will lead the yarn more evenness. hairiness of II was better than I. The hairiness of I was 72.39% lower than III, and the hairiness of II was 80.21% lower than III. Compared with I, II, the hairiness of II was 28.46% lower than I. So, the reduction of hairiness of lateral entry compact spinning with pneumatic groove was the best. The ramie yarn had high hairiness because of its high stiffness and low elongation. The lateral entry compact spinning with pneumatic groove made the free-end fi bers on the edge attached to the yarn more effi cient. Therefore, the hairiness was lower. Through the compact spinning, the hairiness of ramie yarn reduced. It was good for the fi nishing process and the post-procedure process.
To comment on the degree of difference between the average values of yarn hairiness of I and II, the statistic t is calculated as follows: (11) where is the average value of I, is the average value of II, n1 is the number of I, n2 is the number of II, and n1=n2=30. The degree of freedom is df=n-1=29, and t=0.000<t (29)0.05 from the t critical values. According to this, the spinning method of lateral entry compact spinning with pneumatic groove and intermediate entry compact spinning with suction groove has a statistically signifi cant effect on the yarn hairiness.

Comparison of yarn strength
Yarn strength is an important technical indicator of yarn quality assessment. It has a positive meaning to guide the production, formulation, and adjustment of the spinning process through testing of yarn strength.
In Table 2, the yarn breaking strength was increasing for the lateral compact spinning with pneumatic grooves. For the same count yarn, the strength of the lateral compact spinning with pneumatic grooves spinning yarn was the highest. Because it is gathered in the condensing zone and is totally assembled in this place, the output fi ber bundle is tighter and so the fi nal yarn. With highly gathered, the yarn could resist the external force and had the highest breaking tenacity. And, the breaking elongation of these types of spinning was almost the same. It showed that compact spinning could not improve the ramie yarn's breaking elongation.

Comparison of yarn hairiness
Yarn hairiness is one measure of the yarn quality. The reduction in hairiness is a key indicator of this test and is the biggest advantage of compact spinning. While not all hairiness is harmful, in a certain range, the shorter hairiness can smooth the appearance of the yarn and fabric. In this paper, the hairiness length above 3 mm is regarded as the main basis of evaluate the effect of spinning experiment.
The tested number of hairiness length was 1-10 mm and 4-10mm was compared. From Table 3, the number of hairiness of length 4-10mm for I, II was signifi cantly less than III. Comparing the yarn hairiness of I, II, it also showed that the with pneumatic groove has better shape and properties. When the fiber is getting through condensing zone of the lateral groove, the fiber bundle can be arranged into the ideal shape, and after twisting the yarn, it can get better yarn properties. Compared with the intermediate compact spinning with suction groove, the lateral compact spinning with pneumatic groove can reduce yarn hairiness and increase yarn strength, thus improving the overall performance of the yarn.

Comparison of yarn twist
Yarn twist is a major factor that will affect the yarn strength. However, the unreasonable twist will lead to some problems. Yarn twist will lead to the hairiness problems and the later process, such as weaving.
As seen in Table 4, all the twists were below the designed twist, but the twist of lateral compact spinning with suction grooves was highest. The loss of twist was attributed to the low elongation and high stiffness of ramie. During the spinning time, because of the high stiffness and low elongation, the fiber was harder to be twisted and easily broken than cotton fibers. The lateral entry compact spinning with pneumatic groove could reduce the loss of twist.
The next 3 figures showed the yarn forms of the three different spinning methods.

Conclusions
Compact spinning is the consequence of airflow and mechanical actions on fibers. The new finite element method simulates the fiber motion during the fiber bundle through the agglomeration area and proves that the lateral groove can gathered the fiber bundle efficiently during yarn agglomeration. From the simulation results, the gathering point of the lateral compact spinning with pneumatic groove is assembling in the gathering area, and it can be a better cluster fiber. The experiment results fit the numerical analysis: The yarn of lateral compact spinning