General aspects regarding the kinematic and dynamic analysis of the fabric take up/cloth roller

The aim of this paper is to presents different aspects regarding the kinematic and dynamic behaviour of the fabric winding at the weaving loom. In this paper shall be presented the kinematic diagram for operating the cloth roll on the weaving machine, making the study of kinematic and dynamic cloth behaviour, setting up the expression of fabric tension. Finally, where drawn the charts of the variation of the fabric load depending by kinematic and constructive parameters.


Introduction
In present days, the request for the high quality garments imposes certain trends in the weaving loom development/construction.The modern weaving loom uses positive take-up mechanisms, acted by individual c.c. motors and clutches, protecting the fabric for over loading.
The paper presents a kinematical and a dynamical analysis of the take-up and cloth roller mechanism.The command schema and the kinematic chain that acting the take up cylinder contain the computer, gears, chain and frictional clutch as is shown in Figure 1 [1][2], where: 1 -loading cell, 2 -computer, 3 -d.c. motor, 4 -zi gears, 5 -cloth take up roller, 6 -chain and chain wheels, 7 -clutch, 8 -cloth roller.

Theoretical kinematical and dynamical aspects of the fabric loading
In the fabric take up and rolling process, the fabric element is extracted with a constant velocity.The characteristics of the cloth (from the paper's point of view) are: -specific weight "U"; -fabric thickness "G"; the length of the cloth roller "l0"; -the diameter of the fabric roller "d0"; -the axial moment of inertia "J0".In the process of the rolling cloth, its axial momentum of inertia (J') represents a sum of the both empty fabric roller and fabrics' axial momentum of inertia (1) [3][4].
The axial moment of inertia of the empty fabric roller (J0) could be calculated using: Where: mcil plin , mcil gol -the mass of the filled/empty fabric roller, [kg], r0, rintexternal/internal radius of the fabric roller, [m].
Using the constructive particularities of the beam and the density of its material (aluminium), the equation (2) became: Where: ρ -Aluminium density [2700 kg/m 3 ], h -Length of the fabric beam [m], r0, rint -external/internal radius of the fabric beam, [m].
The fabrics' axial momentum of inertia , JΔ tes depends by time (indirectly) and could be calculate using the relation:   n -the number of cloth layers at a specific moment.Finally, will obtain: The elements of the fabric winding are show in the figure 3.
The theorem of the kinetic moment variation, calculated in relation with the rotation axis of the fabric beam, is given by: It results: Replacing in (20), it became: Replacing the calculated sized in relation (15), the final relation will be:

Experimental aspects to calculate fabric loading
The theoretical values were applied to the Somet Thema weaving loom, with the main parameters shown in table 1.

The Clutch's influence
As is seen in the weaving process, the fabric load is falling down according with the rising of the radius, as shown in table 4 and figure 4.  Based on the Table 3, the graphical variation of the slippage is presented in figure 5.

Conclusions
Starting from kinematical and dynamical analysis, it results a calculus formula of the fabric loading in the wrapping process, depending by the geometrical dimensions of the cloth roller.Also, we obtained the mathematical equation and diagrams of speed variation and clutch's slip, depending by the radius of the cloth roller, too.
As is seen in the weaving process, the fabric load is falling down according with the rising of the radius, as shown in table 2 and figure 4. On the other hand, using the gear ratio between take up roller and the cloth beam, the peripheral speed of the fabric roller is rising, overloading the fabric.This overload of fabric could be eliminated by the worker by using a clutch (raising the slippage of the clutch's discs).
The worker's action in the fabric rolling is more often with the radius raising and it decrease the number of weaving loom surveyed by a worker.
The state-of-the-art weaving looms use an electronic controlled take up and individual motors [6][7].
-the radius of the empty fabric beam, [m], R -maximal radius of the fabric roller, [m], r -the radius of the fabric roller at a specific time, [m], dm -elementary mass, [kg].
Where dl -elementary length of cloth roller.

Fig. 4 .
Fig. 4. The variation of the fabric loading depending by winding radius.

Table 1 .
Combination of gears to calculate maximal fabric density.