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• SPINNING TENSION
• AIR DRAG FORCE
• SKIN FRICTION DRAG
• AIR PRESSURE DRAG ON BALLOONING YARN
• 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,
S - Tension on the traveller directed towards the
Scs - 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, and
α’ – 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,
• 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.
• 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
ρ [kg/cubic metre] is air density
ν [m/s] is linear velocity
μ [kg/m.s] is air viscosity
Cfo – Skin friction coefficient on the surface of
the package with diameter do
Cf - Skin friction coefficient on the
surface 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.
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 Drag
ρ (kg/m )- Air density = 1.197 kg/m3
ΔCD (scalar) - Drag coefficient at P
ΔA (m ) - projected frontal area of the yarn segment ds,
ΔA - yarn diameter * the length of ds
υ (m/s) - linear velocity of the ballooning yarn at P.
dy (m) -Yarn diameter
s1 (m) - Yarn length in balloon
rmax (m) - Maximum radius of the balloon
V (rps) is the spindle speed
CD (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
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
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
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
• 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.
• Winding Tension is inversely proportional to Winding
• Skin Friction Coefficient is inversely proportional to
• 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.
• 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