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

In this paper, we compared the fiber 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 fiber bundle and then established the fiber finite element model by MATLAB. Finally, we simulated the fiber motion in the agglomeration area.

In the new fiber finite element model, the fiber 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 finite 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) {Δ¯i}e={Δai,Δbi,Δci,Δθai,Δθbi,Δθci}T {\left\{ {{{\bar \Delta }_{\rm{i}}}} \right\}^{\rm{e}}} = {\left\{ {\Delta {{\rm{a}}_{\rm{i}}},\Delta {{\rm{b}}_{\rm{i}}},\Delta {{\rm{c}}_{\rm{i}}},\Delta {\theta _{{\rm{ai}}}},\Delta {\theta _{{\rm{bi}}}},\Delta {\theta _{{\rm{ci}}}}} \right\}^{\rm{T}}} where Δa_i means the axial displacement of node i, Δb_i and Δc_i mean the bending deflection in two transversely curved principle planes, Δθ_ai means the torsion angle of the cross-section of the node, Δθ_bi and Δθ_ci mean the two laterally curved bending corners in the main plane.

Figure 1

In the meantime, the relative displacement of node j in the local coordinate system was calculated by the following formula: (2) {Δ¯j}e={Δaj,Δbj,Δcj,Δθaj,Δθbj,Δθcj}T {\left\{ {{{\bar \Delta }_j}} \right\}^e} = {\left\{ {\Delta {a_j},\Delta {b_j},\Delta {c_j},\Delta {\theta _{aj}},\Delta {\theta _{bj}},\Delta {\theta _{cj}}} \right\}^T}

The displacement of the two nodes of the rod unit in the local coordinate system was calculated by the following formula: (3) {Δ¯}e={Δ¯iΔ¯j} {\left\{ {\bar \Delta } \right\}^{\rm{e}}} = \left\{ {{{{{\bar \Delta }_{\rm{i}}}} \over {{{\bar \Delta }_{\rm{j}}}}}} \right\}

The force received by node i and node j in the unit local coordinate system was calculated by the following formula: (4) {F¯i}e={Fai,Fbi,Fci,Mai,Mbi,Mci}T {\left\{ {{{{\rm{\bar F}}}_{\rm{i}}}} \right\}^{\rm{e}}} = {\left\{ {{\rm{F}}{{\rm{a}}_{\rm{i}}},{\rm{F}}{{\rm{b}}_{\rm{i}}},{\rm{F}}{{\rm{c}}_{\rm{i}}},{{\rm{M}}_{\rm{a}}}_{\rm{i}},{{\rm{M}}_{\rm{b}}}_{\rm{i}},{{\rm{M}}_{\rm{c}}}_{\rm{i}}} \right\}^{\rm{T}}} (5) {F¯J}e={Faj,Fbj,Fcj,Maj,Mbj,Mcj}T {\left\{ {{{{\rm{\bar F}}}_{\rm{J}}}} \right\}^{\rm{e}}} = {\left\{ {{\rm{F}}{{\rm{a}}_{\rm{j}}},{\rm{F}}{{\rm{b}}_{\rm{j}}},{\rm{F}}{{\rm{c}}_{\rm{j}}},{{\rm{M}}_{\rm{a}}}_{\rm{j}},{{\rm{M}}_{\rm{b}}}_{\rm{j}},{{\rm{M}}_{\rm{c}}}_{\rm{j}}} \right\}^{\rm{T}}} where Fa_i, Fb_i, Fc_i and Fa_j, Fb_j, Fc_j were the force of the node; M_ai, M_bi, M_ci and M_aj, M_bj, M_cj 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: (6) {F¯}e={F¯iF¯j} {\left\{ {{\rm{\bar F}}} \right\}^{\rm{e}}} = \left\{ {{{{{{\rm{\bar F}}}_{\rm{i}}}} \over {{{{\rm{\bar F}}}_{\rm{j}}}}}} \right\}

Figure 2 showed the connection of quality spatial elastic rod unit. The external force on the elastic thin rod was simplified to the node coordinate system on the node. Each node coordinate system had six degrees of freedom with respect to the fixed 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.

Figure 2

Any general motion of a rigid body in space can be divided into the translation and rotation to its center of mass. According to the motion theorem of center of mass, the dynamic equation of rigid body moving with the center of mass is: (7) ma=F ma = F 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) Jα+ω×(J⋅ω)=M J\alpha + \omega \times \left( {J \cdot \omega } \right) = M Or (9) Jα+R=M J\alpha + R = M 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.

ω is the angular velocity of the rigid body.

α is the derivative of ω with the coordinate system O-xyz to time. R=ω×(J⋅ω) R = \omega \times \left( {J \cdot \omega } \right)

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) {Fm}=[mb]{α}+{Rb} \left\{ {{F_m}} \right\} = \left[ {{m^b}} \right]\left\{ \alpha \right\} + \left\{ {{R^b}} \right\} where [mb]=∑i=1n+1[mb]6(n+1)×6(n+1)i \left[ {{m^b}} \right] = \sum\nolimits_{i = 1}^{n + 1} {\left[ {{m^b}} \right]_{6\left( {n + 1} \right) \times 6\left( {n + 1} \right)}^i} {Rb}=∑i=1n+1{Rb}6(n+1)×1i \left\{ {{R^b}} \right\} = \sum\limits_{i = 1}^{n + 1} {\left\{ {{R^b}} \right\}_{6\left( {n + 1} \right) \times 1}^i}

The fiber model was established based formula (10) by MATLAB; it was shown as Figures 3 and 4. From that way, the new fiber model was not only can reduce the complex computation but also will more closely to show the characteristic of real fiber.

Figure 3

Figure 4

Figure 5

The diameter d of the fiber was 0.02 mm; the length of the fiber in agglomeration area was 42 mm; the elastic modulus E of the fiber was 2,224.6 cN/tex; the shear elastic modulus G of the fiber was 106.2 cN/tex; the density of the fiber was 1,510 kg/m³; the number of fiber division units was 500; the left lateral angle was 15°; the initial position of the fiber in lateral entry compact spinning with suction groove was Z=−1 mm; the initial position of the fiber 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 finite fiber simulation model.

According to the specific value, we calculated the fiber motion in the agglomeration area by MATLAB software.

Figure 6 shows the movement of single fiber. 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 fiber bundle during the agglomeration area, the fiber, especially the edge fiber, would move closer to the center. The fiber bundle would be more inseparable, and it would improve the yarn properties.

Figure 6

The condensing zone is for better gathering fiber. And, the best condition is that when the fiber bundle is totally gathered in this place and the twist form is to be cylinder. Then, the yarns will avoid the triangle, and the yarn properties will be better. Figure 7 shows the fiber 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 fiber motion of intermediate entry compact spinning with suction groove and (e) shows the fiber motion of lateral entry compact spinning with pneumatic groove. In Figure 7 (d), the fiber is totally condensing during the x, y coordinate of (10, −20) mm and (e) is (15, −10) mm. The fiber of lateral entry compact spinning with pneumatic groove is totally condensed during the condensing zone but the fiber 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 fiber bundles. Finally, the twist triangle cannot be avoided. It will lead the yarn hairiness and the final yarn properties worse. At in the case of Figure 7 (e), the fiber bundle will totally be gathered during the condensing zone. The output fiber bundle looks like near-cylindrical, and the yarn will be tighter, and the hairiness will less after twisted.

Figure 7

Figure 8

Figure 9

Figure 10

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 finished 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)°C. Before testing, the specimen should be humidified 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 specified 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 1.8Tt-1.4cN 1.8\sqrt {{\rm{Tt}}} - 1.4{\rm{cN}} . 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.

The essence of yarn linear density unevenness is the unevenness of fiber 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 fiber arrangement. In the meantime, the reduction of thick place and thin place will lead the yarn more evenness.

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 fiber bundle is tighter and so the final 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.

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 significantly less than III. Comparing the yarn hairiness of I, II, it also showed that the 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 fibers on the edge attached to the yarn more efficient. Therefore, the hairiness was lower. Through the compact spinning, the hairiness of ramie yarn reduced. It was good for the finishing 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) t=|X¯1-X¯2|∑x12+∑x22n1+n2-2×n1+n2n1×n2 {\rm{t}} = {{\left| {{{{\rm{\bar X}}}_1} - {{{\rm{\bar X}}}_2}} \right|} \over {\sqrt {{{\sum {{\rm{x}}_1^2 + } \sum {{\rm{x}}_2^2} } \over {{{\rm{n}}_1} + {{\rm{n}}_2} - 2}} \times {{{{\rm{n}}_1} + {{\rm{n}}_2}} \over {{{\rm{n}}_1} \times {{\rm{n}}_2}}}} }} where X̅₁ is the average value of I, X̅₂ 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 significant effect on the yarn hairiness.

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.