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This paper presents theoretical modeling for predicting the optimum twist angle on yarn made by open end rotor spinning machine in textile industry. Fiber movement on yarn can be used for predicting the optimum twist angle which can be used to reduce yarn breaking in spinning process. In this research the twist angle has been found and the result of this research shows the twist angle around 45 °; and the theoretical result of the ratio of rotor diameter to fiber length is .

In textile industry the study of the fiber movement inside yarn has been researched of many researchers. According to Rohlena [

Rohlena [

measure of radial position against the yarn length

where

Thus, for the probability

Yarn properties can be analyzed and determined from the fiber movement which is shown by the ratio of yarn length to fiber length,

where _{o} (tenacity of take off roller) which makes the yarn will not break during the spinning process. By extensive experiment, Trommer [

Suppose a fiber moves in cylindrical coordinate and twist is defined as turns per unit yarn length H (in unit m).

Suppose a cotton fiber with length

Suppose that the acceleration of fiber accelerates

Twist is defined as turns per unit length, hence

Another way to derive the relation of twist and the yarn number is by using this formula

substitute Equation (17) to Equation (9)

Suppose the angle twist

Taking

According to Trommer [_{o} which makes the yarn will not break during the spinning process, hence Equation (24) is agree with the experimental result. Using the twist angle 45˚ it can be explained and determined the relationship of fiber movement inside yarn and also the limitation of the ratio of rotor diameter to fiber length is more than 0.7 and the fiber substansce strength (the ratio of yarn strength to fiber strength is 50%).

A simple model of fiber movement would be a made in a cylindrical coordinate. Pretend that a fiber moves inside a yarn in a cylindrical coordinate which can be written as below

During a certain time

Let

Hence

which has solutions

For

For

Let

Defined that

Hence Equation (28) can be written as

For the value of

Based on

The prediction of the theoretical model is appropriate enough comparing the experimental having done by Trommer [

The value of

The prediction of fiber movement and the influence of the kinematic inside of yarn which is worked by a fiber has been derived and determined accurately according to the experimental data of Trommer [_{o} (tenacity of take off roller) which makes the yarn will not break during the spinning process. By extensive experiment, Trommer [

The value of _{o} (tenacity of take off roller) which makes the yarn will not break during the spinning process.

It has been shown via classical mechanics (Lagrange and geodesic methods) that fiber movement on yarn can be

used for predicting the optimum angle twist which can be used to reduce yarn breaking in spinning process. In this research the angle twist has been found and the result of this research shows the angle twist around 45˚ and

the theoretical result of the ratio of rotor diameter to fiber length is