Various comments on the idealized geometry | twist factors of typical textile yarns

yarn geometry has been discussed by Schwarz and later by Woods and Treloar. Schwarz argued that in the measurement of yarn diameter, the value obtained corresponds to the diameter of the circle (d), which circumscribes the outer layer of fibers as shown in image. But in the measurement of twist angle (by a

microscopy technique), it is the edges of the fibers in the outer layer that are observed. Therefore, the effective twist angle measurement is made at a diameter represented by the cylinder containing the

centers of fibers in the outer layers. The modified equation (B) then becomes:

                     tan α    = π (d -  d’ / h)/ h  ……………………………………….( 8)

                                 =  π dk’ T          ………………………………………..     (9)

                               where d  = yarn diameter;

         

                                         d’  =  fiber diameter; and

                                          k = (d  -  d’  ) / d  = Schwarz’ constant.

The value of  k  approaches unity for large number of fibers .Schwarz has reported the values of k for single, plied, and cabled yarns and has pointed out its usefulness in twist analysis.

In real yarns, the assumptions (2) and (3) made are incompatible in view of the observations made by Morton on “fiber migration” in staple yarns. His observations suggest that the path of a fiber in a yarn ( continuous filament as well as staple yarn) is in fact not a cylindrical helix, but one whose radius changes along the length of the yarn.

Riding has reported an experimental study in which he examined the validity of the eq.(2) in determining the relationship between twist and yarn structure .He points out that the agreement between the experiment and the theory is very good for continuous-filament yarns twisted by the continuous method.

that “except for small values of  r/h (i.e. small amplitudes), where the experimental errors are relatively large, there is no systematic deviation from the theoretical formula”

YARN SIZE AND TWIST MULTIPLIER:

Textile yarns are generally specified by their count or size, namely, mass per unit length or linear density. The reason for this is that the diameter (or radius) of a yarn is very difficult to define because of its hairiness and indefinite packing density; on the other hand, linear density is easier to measure and control during spinning.

Twist multiplier or twist factor is a measure of the twist-hardness of a yarn; it is given by the product of yarn twist and square-root of yarn size in the direct system, or the division of the turns per unit length by the square-root of the count in an indirect system. Expressed mathematically:

1.      Direct system (tex system) – turns per centimeter multiplied by

                                                                                   

          root(count of tarn,tex)  = turns/cm  x tex^1/2     .

2.      Indirect system(cotton or worsted, etc., count system) – turns per inch

      divided by

                                                                                                                                                 root(count of yarn,worsted) = TPI/Count^1/2

     .

Some examples of the major yarn count systems and the twist multipliers and their relationships (Conversion of one system to another).

OPTIMUM TWIST FACTOR:

There is certain minimum value of twist factor below which it is impossible to spin a staple yarn. Above this minimum twist factor, which is strongly influenced by staple length, fineness, and fiber surface (frictional) characteristics, the cohesiveness (yarn strength) between fibers increases at a fairly rapid rate initially. At low twist factors, the initial increase in yarn strength is determined by the resistance of fibers to slippage.

At high twist factors, the contribution because of resistance to slippage reaches a steady maximum. However, as the twist factor becomes high, the effect of fiber obliquity comes into play, and this has a tendency to cause a decrease in yarn strength.

The twist factor at which maximum strength is achieved at any given staple yarn is sometimes called the “optimum twist factor”. The optimum twist factor and the lowest practicable twist will both depend on such fiber characteristics as fiber length, fineness, bending , flexural rigidity and frictional properties. The optimum twist factor will also vary with the count of yarn being spun, and it is entirely possible for the maximum value of breaking load and breaking extension to occur at different levels of twist.

Hearle has given values for twist factors and twist angles as given below:

    

                                                                                 

Specific                                              Twist Factor, Tex^1/2    Turns/cm

Volume(cm²/g)        0         20        40        60          80         100          120

                                                            Twist Angles (degrees)                 

0.5                            0          9          18        25          32          38            44

1.0                            0         13          24       34          42          48            53

1.5                            0         15          29       39          48          54            59

Some typical values of twist multiplier used in the textile industry are given below:-

              TWIST FACTORS OF TYPICAL TEXTILE YARNS

                                           Twist Factor                    Twist Factor (traditional units                                                                                                    

                                          (tex^1/2       turns/cm)                   tpi/count^1/2    )

Cotton yarns

Doubling weft                          29-32                             3.0 – 3.3

Ring weft                                 32-35                             3.3 – 3.6

Ring twist                                38 – 43                           4.0 – 4.5

Voile                                        49   - 53                         5.5 -  5.5

Crepe                                       57  - 77                           6.0  6.8

Worsted Yarns

Hosiery                                             17                              1.4

Soft worsted                                      20                             1.7

Medium worsted                               23                              1.9

High worsted                                    26                               2.2

Extra hard twisted                             29                               2.5