Compact spinning with pneumatic grooves is a spinning process to gather fibers by blended actions of airflow and mechanical forces. Modified from the ring spinning system, the lateral compact spinning with pneumatic grooves can improve yarn appearance and properties due to generated additional twists. In this study, we investigated additional twists of the lateral compact spinning with pneumatic grooves via a finite element (FE) method. An elastic thin rod was used to model a fiber to simulate its dynamic deformation in the three-dimensional space, and the space bar unit was used to simplify the fiber model for the dynamic analysis. The stiffness equation of the elastic rod element and the dynamic equation of the rigid body mass element were derived from the differential equation of the elastic thin rod. In the analysis of the nonlinear geometric displacement of the space elastic thin rod unit, the large deformation problem was solved with the stepwise loading successive approximation. The simulation results explained the mechanism of generating additional twists, and the experiment results proved the existence of additional twists. The study demonstrated that the FE model is effective for predicting additional twists of fiber bundles in the agglomeration zone, and for simulating the fiber motion in the compact spinning with pneumatic grooves.

Yarn twist, or the number of twists per unit length of yarn, directly affects yarn’s structure and mechanical properties, and fabric styles [

In order to study additional twists, Feldman [

There is still a large gap between the performances of these existing fiber models and the actual mechanical behavior of a fiber. In this paper, we would like to introduce a continuous elastic thin rod to study the structure and dynamics of the fiber flexible body. The simultaneous partial differential equations of general nonlinear mechanics of the elastic thin rods are used to express the small deformation behavior of the rods. Based on the spatial elastic thin rod unit, we establish the fiber finite element (FE) model to explore the additional twists of lateral compact spinning with pneumatic grooves. The FE model of continuous elastic fine rods is used to simulate the fiber motion in compact spinning for both efficient calculations and effective visualization in the three-dimensional space. The FE method is applied to solving the dynamic problem of the large deformation of an elastic thin rod. The stiffness equation of the elastic rod element and the dynamic equation of the rigid body are derived from the dynamic analysis of a combination of mass units and elastic rod units. The nonlinear geometric large deformation problem of the spatial elastic thin rod unit is studied by solved the method of step-by-step loading and successive approximation. The goal of the research is to present an effective and feasible theoretical model and method for examining the twist formation process and mechanism of flexible fibers under the mechanical force of lateral grooves.

In order to solve the nonlinear large deformation problem and to realize the large draw ratio (fiber length/fiber diameter) of fibers, a finite element model is established with spatial elastic thin-rod units., as shown in

To analyze the dynamics of the elastic thin rod, the elastic thin rod is divided into

Any general motion of the rigid body in space can be decomposed into the translation with its centroid and the rotation relative to the centroid. According to the centroid motion theorem, the dynamic equation of the rigid body translation with centroid

where

According to the momentum quadrature theorem, the dynamic equation of the rigid body rotating around the centroid

where

In coordinate

where

Assume that the inertia of a micro rigid body relative to

Then

where the direction cosine matrix of

The influence of the axial force on bending deformation must be considered in a large deformation of the elastic thin bar. The bending deformation of the elastic thin rod unit is shown in

where _{n}_{n}_{ui}_{uj}

Given that the displacement of the rod element is small and in the limits of elastic deformation, plastic (unrecoverable) deformation can be ignored. The deflection of the rod

where

If the displacement of the rod element is relatively small in the local coordinate system

where _{w}

According to

Similarly, the bending deformation matrix equation of the elastic rod unit in the plane uO0w can be derived.

For the axial tension compression and torsion deformation of the rod unit, the following relationships can be derived

where

The relationship between the deformation displacement of the elastic rod element and the force of the rod end relative to the overall coordinate system

where the end force and deformation displacement of the element relative to

where

Taking the coordinate system

Let

For the dynamic equation of all the nodes,

where the vacancy element is zero, and

The dynamic equation of each elastic rod unit

where

Substituting

where,

The differential equation of the dynamic FE model is solved by a specially developed MATLAB program to simulate the additional twists of yarn in the condensing zone. In the simulation, the ramie fiber was taken as an example where the fiber diameter along the fiber length was assumed to be uniform, the elastic modulus ^{3}, and the fiber length in the agglomeration area was 40 mm. The other parameters used in the analysis included the size of the fiber AB division unit of 0.5 mm, the number of fiber AB division units of 200, and the time integral step of 10^{−6}. The gathering roller was made of rubber and supported by a copper sleeve, and thus the friction coefficient

When an edge fiber was connected with central fibers and the lateral pneumatic grooves, the contact was treated as a flexible connection constraint with sufficient stiffness in the simulation. Each node was subjected to the normal elastic connection occurring on the central cylinder, and the wall surface was constrained by the reaction force

where

where

To implement the numerical calculation for the FE dynamic differential equations of the elastic thin rods, the implicit difference scheme Euler method was adopted. The calculation process was stable and the calculation results were reliable [

In order to solve the problem of large deformation, this paper adopts the load incremental step loading method. The load is divided into N loading steps from zero, which ensures that the load increment for each step is a small amount. For the first load step at which the load is zero, the position of the entire non-loaded state of the elastic rod unit is taken as the initial position. Establishing a local coordinate system at the initial position, the second step is taken. The displacement of each elastic rod unit under the load is solved by the element stiffness equation established under the small displacement condition, and the new position of the whole fiber after the first deformation will be obtained. For any N loading step calculation, the position of the elastic rod unit in step

In order to determine the additional twist, yarns of the lateral compact spinning of pneumatic grooves were spun and compared with the intermediate compact spinning with pneumatic grooves yarns. The raw material was ramie roving. The roving linear density was 4.70 g/10 m, and the moisture regain of the roving was 12.0%. All the spinning was finished by the FZ501 spinning machine. The pressure of pneumatic grooves was −2600 (Pa), the twist was 680 (T/m), the spinning speed was 7000 (r/min), and the count of yarn was 36 Nm.

The tests were performed in the standard climate where the relative humidity was

Twist (T/m) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Average |
---|---|---|---|---|---|---|---|---|---|---|---|

I | 643 | 632 | 633 | 648 | 645 | 637 | 632 | 640 | 645 | 621 | 637.6 |

II | 572 | 573 | 578 | 587 | 571 | 592 | 575 | 593 | 586 | 599 | 582.6 |

Notes: I refers as lateral entry compact spinning with pneumatic groove and II refers as intermediate compact spinning with pneumatic grooves.

In the paired

This paper provided a theoretical method for modeling the dynamic motion that simulates fibers driven by mechanical forces in the lateral compact spinning. In the study, we established a fiber FE model to simulate the large deformation process of the elastic thin rod element, and deduced the dynamic equilibrium equation of the spatial elastic thin rod unit in the model. We numerically obtained the movements of fibers under agglomeration and visually displayed additional twists generated in the lateral compact spinning with pneumatic grooves. The experiments demonstrated that the lateral compact spinning could produce smoother and tighter yarns that the intermediate compact spinning due to additional twists. Thus, the fiber FE model may be used to solve the large deformation problem of fiber motion in the three-dimensional space.