Forces acting on yarn and traveller

FORCES ACTING ON YARN AND TRAVELLER

BY, KALEESWARAN .P

• INTRODUCTION

• SPINNING TENSION

• AIR DRAG FORCE

• SKIN FRICTION DRAG

• AIR PRESSURE DRAG ON BALLOONING YARN

• CONCLUSIONS

• REFERENCES

CONTENTS

• In ring spinning, the yarn is wound on the spindle by having the force against many natural forces acting on the yarn and also the traveller.

• The forces that are acting are frictional force, centrifugal force, skin friction drag, air pressure drag, gravitational force.

INTRODUCTION

SPINNING TENSION

S - Tension on the traveller directed towards the balloonScs - Winding tension,C = mrω - Centrifugal force acting on the traveller where m - Mass of the traveller T - Radius of the ring,mg - Weight of the traveller, andα’ – Angle between force S and coordinate axis y

Multiplying the first equation by sin γ the second one by cos γ and adding the same

Multiplying the first equation by μ the third one by cos γ and summing up both

Multiplying the second equation by - μ, the third one by sin γ and summing up

For approximation, considering,

Wingding Tension,

Winding Angle,

• With decreasing winding angle the angle between the reaction force substituting the constraint P and the spindle axis will be smaller, thus the winding tension increases.

• As a consequence of the reduced effect of the centrifugal force the traveller is being pressed against the top edge of the ring, in contrast to the former case, where it is lying on the inner side of the ring.

• With increasing winding angle, the direction angle of the reaction force P decreases, thus the force P plays a more important part in balancing the centrifugal force, and consequently the winding tension decreases.

RESULTS OBTAINED

• The air drag on a body is due to the sum of pressure drag and skin friction drag. In many cases, one or the other of these two drags is predominant.

• In ring spinning, air drag on the rotating yarn package is mainly due to skin friction drag on the package surface, while pressure drag is the dominant one on the ballooning yarn.

AIR DRAG FORCE

• For an incompressible and laminar flow, there is a relationship between the skin friction coefficient (Cf) and the Reynolds number (Re),

ρ [kg/cubic metre] is air density ν [m/s] is linear velocityμ [kg/m.s] is air viscosity

Cfo – Skin friction coefficient on the surface of the package with diameter do

Cf - Skin friction coefficient on thesurface of the package with diameter d.

SKIN FRICTION DRAG

Pi - Total power consumed by a rotating yarn package of diameter di, Pfi - Power consumption due to skin friction drag on the surface of a yarn package of diameter di (i = 1, 2, and d1 < d2)Po - Power consumed by driving the spindle.

Total Skin friction drag on the package surface

Power required to overcome Skin friction drag

Sp [m ] is the surface area of the yarn package.

As spindle of height h,

Skin friction coefficient at varying spindle speeds for three diameters.

Spindle Speed Vs Skin Friction Coefficient

Skin friction coefficient [Cf (scalar)] on a rotating yarn package surface without hairiness

Skin friction coefficient [Cf (scalar)] on a rotating yarn package surface with hairiness

H (scalar) is the yarn hairiness index a, b, a1 and b1 are constants

Fd – Air Dragρ (kg/m )- Air density = 1.197 kg/m3ΔCD (scalar) - Drag coefficient at PΔA (m ) - projected frontal area of the yarn segment ds,ΔA - yarn diameter * the length of dsυ (m/s) - linear velocity of the ballooning yarn at P.

dy (m) -Yarn diameters1 (m) - Yarn length in balloonrmax (m) - Maximum radius of the balloonV (rps) is the spindle speedCD (scalar) is the air drag coefficient on the ballooning yarn

AIR PRESSURE DRAG ON BALLOONING YARN

Relationship between the Normalization form [p0 (scalar)] and dimensional form [CD (scalar)] of the air drag coefficient on a rotating yarn,

CDs and Fds are the air drag coefficient and air drag on a ballooning yarn which has been singed CDn and Fdn are the respective air drag coefficient and air drag on a ballooning natural yarn

If the effects of hairiness on the diameter and mass of yarn in the balloon are ignored

m – Linear Density of yarn(kg/m)a – Ring radius(m)

The hairiness on a ballooning cotton yarn increases the air drag by around 8.7% for a 38 tex cotton yarn at 5300 rpm . This can be considered to be skin friction drag increase due to hairiness when the effects of hairiness on the diameter and mass of yarn in balloon are ignored.

Air drag between packages of natural and singed cotton yarns at different rotating speeds

• The effect of yarn hairiness on skin friction coefficient on the surface of a rotating yarn package is inversely proportional to spindle speed; specifically, for the cotton yarn package, the skin friction coefficient increased from about 16% at a spindle speed of 16 000 rpm to about 98% at a spindle speed of 2000 rpm.

• The air drag on a ballooning yarn and the average air drag on the surface of a rotating yarn package both increased with an increase in yarn hairiness. For instance, singeing the surface hairs off the cotton yarn packages reduced the average air drag on the rotating packages by about 26 %, similarly, air drag on the ballooning cotton yarn was reduced by about 9% when the yarn was singed to remove surface hairs.

RESULTS OBTAINED

• Winding Tension is inversely proportional to Winding angle

• Skin Friction Coefficient is inversely proportional to Spindle speed

• Air Drag is directly proportional to Yarn Hairiness

These forces, if gone more, will cause the end breakages and more power consumption. The researches are done mainly to reduce these and to have more efficiency.

CONCLUSIONS

• Investigation of the tension relations in ring spinning between Traveller and Yarn Package, By B. Grega, June 3, 1972, Presented by Prof. G. Szasz

• Skin Friction Coefficient on a Yarn Package Surface in Ring Spinning, By Zheng-Xue Tang, Xungai Wang and Barrie Fraser, Textile Research Journal 2004 74: 845

• Recent Studies on Yarn Tension and Energy Consumption in Ring Spinning, By Zhengxue Tang, Xungai Wang and W. Barrie Fraser, RJTA Vol. 9 No. 4 Nov 2005

• The Effect of Yarn Hairiness on Air Drag in Ring Spinning, By Zheng-Xue Tang, Xungai Wang, Lijing Wang and W. Barrie Fraser, Textile Research Journal 2006 76: 559

REFERENCES

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