Development of Warp Yarn Tension During Shedding: A Theoretical Approach

Abstract

Theoretical investigation on the process of development of warp yarn tension during weaving for tappet shedding is carried out, based on the dynamic nature of shed geometry. The path of warp yarn on a weaving machine is divided into four different zones. The tension developed in each zone is estimated for every minute rotation of the bottom shaft. A model has been developed based on the dynamic nature of shed geometry and the possible yarn flow from one zone to another. A computer program, based on the model of shedding process, is developed for predicting the warp yarn tension variation during shedding. The output of the model and the experimental values of yarn tension developed in zone-D i.e. between the back rest and the back lease rod are compared, which shows a good agreement between them. The warp yarn tension values predicted by the model in zone-D are 10–13 % lesser than the experimentally measured values. By analyzing the theoretical data of the peak value of developed yarn tension at four zones i.e. zone-A, zone-B, zone-C and zone-D, it is observed that the peak yarn tension value of A, B, C-zones are much higher than the peak tension near the back rest i.e. at zone-D. It is about twice or more than the yarn tension near the back rest. The study also reveals that the developed yarn tension peak values are different for the extreme positions of a heald. The impact of coefficient of friction on peak value of yarn tension is nominal.

Appendices

Appendix A: The Formulation of Model for Development of Warp Yarn Tension during Shedding Process

Appendix B

r′

r′ is the distance between two lines parallel to the yarn axis and passing through centers of circular surfaces carrying the yarn. This variable changes according to the arrangement of yarn on two surfaces. There are two possibilities arrangements;

• (i) When the yarn lies above and below the two surfaces (Fig. 18)

  Fig. 18

  

  Definition variables r′

• (ii) When the yarn lies either above or below both the surfaces where it is the difference between the two radii (Fig. 19).

  Fig. 19

  

  Definition of variable r′

h′

h′ is the difference in heights of two yarn carrying surfaces (Fig. 20).

Fig. 20

Definition of variable h′

α

α is the angle made by the line joining centers of two circular elements carrying the yarn with the horizontal line (Fig. 21).

$$ \alpha \, = { \tan }^{ - 1} \left( {{\text{h}}'/{\text{d}}} \right) $$

Fig. 21

Definition of α

β

β is the angle made by the line parallel to yarn axis in the straight portion with the line joining the centers of two circular elements carrying the yarn (Fig. 22).

$$ \beta \, = { \tan }^{ - 1} \left( {{\text{PQ }}/{\text{ OQ}}} \right) \, = { \tan }^{ - 1} \left( {{\text{r}}'/{\text{l}}} \right) $$

Fig. 22

Definition of β

Half Wrap Angle on an Element in a Zone (A/B/C/D)

It is the angle made by a line perpendicular to the yarn axis with the vertical line that divides two zones. For example half wrap angle in zone B is represented in the figure (Fig. 23).

Fig. 23

Half wrap angle or wrap angle in a zone

Total Wrap Angle on an Element (W)

Wrap angle on any element that divides into two zones is the sum of the two half warp angles on either side of it (Fig. 24).

Fig. 24

Definition of total wrap angle on an element

Geometrical Length of Yarn in a Zone (1)

It is the length of straight portion of yarn measured in any zone between two contacting points i.e., excluding the wrap length. It is represented by “l” in the chapters (Fig. 25).

Fig. 25

Geometrical length of yarn

Total Geometrical Length of Yarn in a Zone (L)

It is the sum of straight length and wrap length calculated by multiplying warp angle with the radii of respective yarn holding elements. It is represented by “L” in the chapters. Say in zone B (Fig. 26).

Fig. 26

Total geometrical length of a yarn in a zone