Patte's model Limitation of Patte’s law

Platte Model Limitation of Patte’s law: 

 1The radius of yarn remains constant on yarn strain as Patte’s Model but it is not true because there is always some radical contraction on yarn strain.

2.A per Platte’s strain equation helix angle θ remain constant which means each filament maintains a fixed helical patch without changing radical position, but it is also not true.

3.Effect of twist is ignored here. That means the lateral force due to twist which effect the load transfers from fiber to fiber during extension is avoided.

4.Effect of fiber migration is ignored.

5. Poisson’s ratio is ignored.

Derivative of an equation for prediction of a filament strain under low yarn strain ∑▒〖y≤10%)〗

Derivative of an equation for prediction of a filament strain under low yarn strain (∑▒〖y≤10%)〗

This derivative was developed by Platte’s Model. The model shows the extension of filament in yarn under low tension.
 Let,    H = height of yarn having one turn of twist
         ∂h = yarn extension
          l = Length of the filament
         ∂l = Filament extension
         Θ = Helix or twist angle

Equation to predict filament strain for any given yarn strain ∑▒〖y≤10%)〗 at helix angle θ

Theory Of Eectricity Faradays and Modern Theories

Theories of Electricity: 

1. Two fluid theories 

2. One fluid theory 

3. Faraday’s theory 

4. Lorentz’s theory 

5. Modern theory 

Faraday’s Theory: according to this theory, charges produced by static electricity are moved by electron cell. As a result current electricity is obtained.

Modern Theory: At Present, modern theory is accepted everywhere, according to this theory every atom has a positively charged nucleus and negatively charged electron. Proton & electron are equal in neutral condition. If number of electrons increase the atom becomes negatively charged due to decrease of electrons. Electrons flow from higher level portion to lower level until the energy levels higher level portion to lower level until the energy levels same. Thus charge transfer is occurred by electron transfer

Riding Method Description The Fiber Migration

Measurementof Migration:

1.         Tracer fiber technique 
2.          Cross-sectional method 
3.          Riding Method.

The Description Riding Method:

Description: Riding method by measuring relative radial position. Riding used a liquid in which the yarn is immersed and when the same refractive index as that of viscose nylon ie: Continuous filament riding used mirror to carry out the experiment for analytical analysis. He has used one black filament in the yarn to study the migration behavior. He carried out measurement at interval of data turns of twist 200. Such as measurement were taken to get result:

Fig: Riding Method Fiber migration

From this equation Riding measured the amount of migration in the yarn.

Fiber Migration n Mechanisms causing fiber migration

Fiber Migration: The variation of the distance of a fiber or filament from the yarn axis along its length it is called fiber migration.

PARAMETERS FOR FIBRE MIGRATION:
  1. Staple Length of Fiber: With the increase of staple length migration will also increase.
 2. Tension: With the increase of tension of fiber migration will also increase.
 3. Mode of Spinning: - Fiber migration in yarn depends on the methods of manufacturing processes.


Mechanisms causing fiber migration: Morton proposed that one of the mechanisms which cause fiber migration is the tension differences between fiber at different radial positions in a twisted yarn. During the twist insertion fiber are subjected to different tensions depending on their radial positions. According to the principle of the minimum energy of deformation, fiber lying near the yarn surface will try to migrate into inner zones where the energy is lower. This will lead to a cyclic interchange of fiber position

Result showed that fiber migration can be influenced mainly by three groups of factor:

1.     Fiber related factor such as fiber type: fiber length, fiber fineness, fiber initial modulus, fiber bending etc.

2.      Yarn related factor, such as yarn count and yarn twist

3.      Processing factors such as twisting tension, drafting system & number of doubling.