2.1. Preparation of yarn samples

Viscose rayon staple fibre (44 mm, 1.67 dtex) was processed on an L R blow room line & a Texmaco Howa card, and given two passages on an L R DO/6 draw frame (breaker and finisher). The samples were prepared according to the L8 mixed orthogonal array as shown in Table 1. The design variable array shows that the two levels of lap hank, four levels of card draft and two sets of draft/doublings at the breaker and finisher drawframe were selected. The factor levels at various stages were chosen on the basis of certain practical considerations. The prepared finisher sliver samples of eight different linear densities were processed into two different types of rovings, and 24^s Ne rotor and air-jet yarns. The direction of the sliver fed to the air-jet machine was reversed for feeding the majority of hooks as trailing. The established trend in spinning preparatory for air-jet spinning is to use three passages of drawframe before yarn preparation, so as to feed the majority of hooks in the trailing direction. In the present research work, only two drawframe passages were used to produce equivalent ring and rotor yarns. For roving-type I, the draft at speed frame was kept constant in all the samples; while for roving-type II, the draft at speed frame was changed in such a way so as to produce the same roving hank for all the eight samples. These rovings were processed into two types of ring yarns, types I and II, in such a way so as to produce 24^s Ne yarn. The effect of uncontrollable variables, such as spindle to spindle variation and doff position, was duly taken into consideration.

Table 1. Sample preparation plan

2.2. Measurement of packing density in the yarns

The parameters needed to calculate packing density, such ashelix angle, helix twist, yarn diameters, were measured by using the classical tracer fibre technique [3]. Tracer fibres of red and green colour, each 0.03% by weight, were mixed with parent grey viscose fibres while laying the stack. The configuration of tracer fibre was studied at 100× under a projection microscope. Benzyl alcohol was used to optically dissolve the grey fibres in the yarn. Four different replications for fibre orientation parameters were measured at the yarn stage, in order to take the effect of uncontrollable factors (noise) into account. The packing density in the yarns was further calculated from the values of these parameters using Ishtiaque’s formula as given below. The schematic view of a tracer fibre seen under the projection microscope for the study of yarn structure is given in Figure 1, where D = 2R = yarn diameter (in mm); d = 2r = helix diameter (in mm); θ = helix angle (in degrees) = tan^-1 (π d Z / 25.4); Z = number of turns of twist in the fibre helix per mm; n = actual number of fibres in the yarn cross-section, obtained by multiplying the theoretical number of fibres in 24^s Ne yarn by the cosine of the helix angle (θ); The theoretical number of fibres in the yarn cross section = 148, calculated by {5315 / (yarn count (Ne) x fibre denier)}.F’ the cross-sectional area of the viscose fibre used (mm²) = 1.0964 x

. Finally, the formula used for calculating the packing density from the above defined parameters is as follows:

2

2

Packing density of yarn = µ= 2πnFZ /( 1+ (πDZ) −1)

Figure 1. Schematic view of a tracer fibre seen under projection microscope

A total of 100 tracer fibres per sample (25 tracer fibres per replication and a total of 4 replications per sample) were studied to calculate the packing density parameters in ring, rotor and air-jet yarns.

2.3. Analysis of the response

Analysis of the response depends upon whether a smaller or larger response value is desired. The helix angle and yarn diameter were classified under the response type of ‘smaller is better’, because the smaller are the values of these parameters, the higher the packing density of the yarn will be. The helix twist was classified under the response type of ‘larger is better’, because higher values of these parameters are required to obtain a higher packing density for the yarn. The packing density itself was classified under the response type of ‘larger is better’ because a higher packing density value contributes positively toward yarn tenacity. The formulae used for the calculation of the S/N ratio for the above response types are given below.

n

2

1. for ‘smaller is better’ S / N =−10.log₁₀ .(1/ n_∑ y_i ) ;

i=1

where: yi = the ith value of the result, and n = the number of replications;

n

2

2. for ‘larger is better’ S / N =−10.log₁₀ .(1/ n_∑1/ y_i ) ;

i=1 The actual values of S/N ratio maximum were also evaluated directly from the curves of the S/N ratio with a change in the process variable by using the equation:

S / N max = S / N + (S / NAmax− S / N) + (S / NB max− S / N) + (S / NC max− S / N)

where: S/ N max = the maximum actual value from the graph,

S /N = the overall average value of the S/N ratio,

S / NAmax = the maximum value of the S/N ratio in the plot of the lap hank,

S / NB max = the maximum value of the S/N ratio in the plot of the card draft,

S / NC max = the maximum value of the S/N ratio in the plot of draft/doublings.

The calculated value is statistically compared with the actual value of S/N ratio at a 95% confidence level for a significant difference between the two values. As previous researchers did [4], the rule followed was that if there was a significant difference in the two values, the experiment had to be repeated by maintaining the process variables at the optimum level observed from the graphs. Note that S/N ratios of the various parameters should be maximised to obtain the optimum set of process variables; that is, for reading the plot, the highest values of S/N ratio are looked up in order to determine the optimum value of the process variables in all the cases.