a mathematical model to determine the convergent point in a rotor spinning machine

8/7/2019 A Mathematical Model to determine the convergent point in a Rotor Spinning Machine

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J Y O T I S W A R O O P R E P A K A R O L L N O : 0 7 0 1 0 0 4 2M E 7 5 4 - T E X T I L E S M A C H I N E S D E S IG N A N D

A U T O M A T I O NI N S T R U C T O R : P R O F . A . G U H A

A Mathematical Model to

determine the convergent point ina Rotor Spinning Machine


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Introduction to Rotor Spinning

y Open end spinning or open-end spinning is a technologyfor creating yarn without using a spindle. It was inventedand developed in Czechoslovakia in Vzkumn stav

bavlnsk / Cotton Researching Institute in st nad

Orlic in the year 1963.y There very few companies which can manufacture yarn

using this process, owing to its technical complexity. Alot of research & development has been done to increaseproductivity by them.

y The disadvantages of using Rotor spinning can beimproved by combining staple fibers with a continuousfilament yarn in the rotor spinning process


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AdvantagesAdvantages DisadvantagesDisadvantages

1. High yarn output rate

2. Reduced productioncost

3. Increased bulkiness

4. Improved evenness ofthe resultant yarn

1. Low breaking

strength2. Wrapper fibres of

yarn surfaces

3. Cloth made fromrotor spinning haslower wear resistance

Introduction to Rotor Spinning (2)


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Rotor spinning machine


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The Process in brief

Filament yarn is fed from a supplybobbin by means of a tension deviceand guide to the filament feed rollers.

Drawn into the rotor freely bysuction.

Filament combined with staple fibersto form composite yarn in rotor.

Composite yarn is drawn through thedoffing tube.

Composite yarn onto the take uproller.


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Basis of MathematicalmodelBasis of Mathematicalmodel

Diagram of force AnalysisDiagram of force Analysis

y The momentum in eachyarn in the rotor-spuncomposite yarn spinningprocess is acted by itscentrifugal force.

y The characteristics of thecomposite yarn depend

mainly on how and wherethe two strands of fiber andfilament are combined andmixed, so the convergentpoint is of crucialimportance.

Mathematical model


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Equations


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Chosen ParametersChosen Parameters ResultsResults

y R = 19 mm

y H = 0.9 mmy =45,000 rpm

y Input: 70D filament

y

Output: To produce58tex rotor-spuncomposite yarn.

y Coordinates of the

convergent point are:y x = 12.53 mm

y y = 0.47 mm

Results


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Phase diagram of theConvergent pointPhase diagram of theConvergent point

Trajectory of theConvergent pointTrajectory of theConvergent point

The position of convergent point with time andcalculation certainity


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References

y A nonlinear dynamic model for a rotor-spun compositeyarn spinning process.,Zhang, H. X., Xue, Y., and Wang,S. Y., Nonlinear Analysis 71 (2009) e98e102,doi:10.1016/j.na.2008.10.016.

y A Mathematical Model for Rotor-Spun Composite YarnSpinning Process., Rui-Hua Yang and Shan-YuanWang. , 2010 Textile Research Journal., doi:10.1177/0040517509099420.

y Mechanisms of wrapper fiber formation in rotorspinning: An experimental approach, Koc, E., and

Lawrence, C. A., J.Textil. Inst. 97(6), 483492 (2006).

a mathematical model to determine the convergent point in a rotor spinning machine

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