Definition of Increasing the Fibre Capturing Surface of Saw Teeth of Cotton Ginning Machine through Mathematic Modelling

Theoretical and the experimental researches executed in Uzbekistan and abroad explored some ways of a substantiation of a rational profile of a tooth of a saw and its fibre capturing ability. Despite that, untill now, optimum parameters of a saw gin which provides high quality ginning without harming the quality of cotton fibre have not been found. Considering the stated above in the given job the influence of the changed form of saw teeth on fibre-capturing area is examined. The analytical formulas for the additional area promoting to double the fibre capture quantity by saw teeth are received.


Introduction
It is known, that productivity of saw gin depends on the structure of teeth or on other parameters of saw gin.On defined selection of saw teeth's profile or other parameters, it is possible to achieve the maximum capture of fibre.It promotes the increase of the productivity of a saw gin.Theoretical experimental researches in Tashkent textile institute noted some ways of substantiating the rational profile of saw teeth and its fibre capturing capacity.
On Figure 1 the circuit of meeting saw teeth with cotton roll in the zone of seed combing developed by G.I. Boldinskiy is given.A centrifugal force influences on fibre seized by saw teeth trying and forces the fibre to escape from the teeth.At the same time another forcefriction force influences on fibre which helps to hold the fibre at front lines of the saw teeth [1,2].
Defining the corner, at which the fibre is held on saw teeth, by ψ, we can write following formula: where  -a front corner of a tooth  -corner between a radial surface of a saw and surface of shift of a fibre.For defining the corner  , an equation is developed on the movement of the element of fibre, descending from a tooth of a saw, in relation to mobile axes OXY:

Materials and Methods
This Table 1 shows the values of parameters in Figure 1 [3,4].This Table 2 shows the values of parameters in  Table 1 for Figure 1.

Figure 2. Schematic diagram and parameters of the pro-
The capturing ability of a tooth is proportional to the ar 1 (5) -The area of a triangle with-applicable in- Here ner between vectors of relative speed and ta -Linear speed of cotton roll in its meeting point b v with saw; 1  -Corner between the radius of a saw and vector of lacing the received figures by formula ( 6) and ( 7) on speed.
To increase the area of capturing surface of s offer a new changed profile of saw of saw cylinder.This w tip will be about 25 ˚ -30 ˚.
rch ВВ ; t arc and str s; ich is kept in a   aw we ork examines the influence of the changed form of tooth of saw cylinder on the area of fibre capturing surface (Figure 2).
The profile of a tooth resembles an arch, on which the corner of tooth's Vв-Speed of a particle of cotton roll at the moment of its meeting with saw tooth; V-Linear speed of the end of a saw tooth; θ-The central corner of an a As we see, fibre capturing ability of saw te termined by the areas of triangles AВС 1 and АВВ 1 , and al (10 eth is deso the segment ВВ 1 .Last two areas are additional to the basic area of a triangle AВС 1 .
The area of a triangle АВВ1 is determined as follows: From a triangle ΔВВ 1 С under e theorem of sine we can define СВ 1 : th The additional area of a triangle АВВ1: Now we pass to definition of the area of a seg ВВ1, chord which is determined der the formula: The central corner of a segment arccos A

 
where: Then the area of a segment: (16) From the formula (16), it can be seen that the area S dop mainly depends on corners γ, γ 1 and ξ.
At the appropriate selection of these corners, the optimum additional area of fibre capture by saw teeth is achieved.ssion ndence of a corner ξ between a tangent of re means anges θ = θ (ξ) at R = 20 cm.The yellow line on a fig-

Numerical Results and Discu
Figure 3 shows changes of the central corner θ arches ВВ 1 , in depe the spent bow-shaped and direct back of a profile of teeths [6,7].The red line on a schedule figu ch ure shows changes θ = θ (ξ) at R = 10 cm.We take corner radius from the given schedule R = 10 cm because at this value the tooth height will be equal h =4mm and a tooth step t = 4mm.At these data the most optimum value is θ = 25 ˚ -30 ˚ at ξ = 14 ˚.If we accept optimum value θ = 25 ˚ -30 ˚ and ξ = 14 ˚ and radius R = 20 cm that leads to increase of a step and tooth heights.It leads to seed jamming in a backlash between teeth.As a result it will lead to intensive crash of seeds between tooth of a saw and a grid-iron saw gin.From this follows that the central corner θ arches ВВ 1 should be in θ = 25 ˚ -30 ˚ limits and not exceed these values.Change of the additional area of a segment depending on a corner ξ pi various radiuses of curvature of a new profile of teeth.Optimum value of the area of a segment is S seg = 0.01 cm 2 which corresponds R = 10 cm, ξ = 14 ˚.
In Figure 3 when the maximum value of ξ eqauals to 14 ° and when the maximum value of θ equals to 30 ˚, the level of teeth capturing fiber reaches its maximum de- Thus, the additional areas promoting the increase of fibre capture by saw tooth is determined by the formula: In Figure 4, the area of S seg (S 1 ) has been determined at different radiuses according to the value of ξ.
In Figure 5, the area of (S 2 ) triangle has been found at different radiuses to the value of ξ.In Figure 6, in order to find S (S ), we have added the area of S seg (S 1 ) to the area of (S 2 ) triangle.Since we know the area of S 4 ) triangle, we have added the area of S4 to the area of S3 and as a result, we have determined the pturing fiber of new profiled teeth based on t ematic modeling and graphics (Figure 7).There are icron fibers in the area of Using the n profile, we can inc 4.

Conclusions
Th al resea eoretical and the experim rches executed at    The values have been checked and prepared in Maple 9.5.Drawings have been prepared and projected through T-Flex CAD programm using th alculated values.
Stemming from these facts, it can be concluded that the application of the ity of ginnng, and also will bring to saving of power resources.

Figure 1 .
Figure 1.Schematic diagram and parameters of saw teeth developed by G.I.Boldinskiy.

1 ξ-
Corner between a tangent carried ou aight line shoulder of teeth structure; β 1 -Corner between the radius of saw and direction of movement of light fibre approaching saw φ-Corner of friction of fibre on fibre; γ-Front corner of tooth.The tooth of a saw will seize a fibre wh tri an additional triangle АВВ 1 an angle AВС 1 , and also in d a segment described by arch ВВ 1 .The area of the triangle 1 ABC S  is determined by well-known formula:
ABB S  according dop 3 1 ABB S  S ( 1 ABC  area of ca he math 100 m ew teeth

Figure 7 .
Figure 7. Variance of the area of capturing fiber of the new in Table2show that the area of fibre capturing surface of saw tooth widened two times.The highest figure of the area of the surface is achieved at R = 10.Proportionally, at R = 20 the area of segment decreases and fibre capturing capacity also decreases.Through this additional area, 200 -250 mkr of fibre is achieved.Thus the offered new profile of a tooth of a saw gin will increase fibre capture 2 -3 times.e c offered new design of a saw on cotton processing industry will increase the productiv of .Azizov and A. I. Karimov, "Defining the Interaction of Cotton with Hilly Ginning Kolosnic," Journal of echanical Engineers, Vol. 3, 2005.] G. I. Miroshnechenko, "Bases of Designing of Machines shev and A. I. Karimov, "The Analysis of Work-