Analysis of Changes in Tension in Leading Branch Belt Drive

This paper presents method of determination in the regularity change in the branches of a belt drive with an eccentric tensioning roller. On the basis of analysis in the research results identified the recommended belt transmission parameters.


Introduction
On a number of technological machines, in particular of small cotton cleaners litter is important in kolkova drum rotation angular speed of a variable at a certain frequency and amplitude, allowing effect intensification cotton cleaning [1,2].
Therefore, in the drive of the machine used belt transmission with belt tension [3].Thus in the belt drive (Figure 1) is mainly driven pulley is rotated at variable angular speed.
The theoretical task of the problem: In the process of transmission branches are extended on the values depend on the change of angular speeds pulleys.According to the work of the branches in the belt drive extension determined from the expression: Where, , σ σ ∆ ∆ -changes in belt stress transmission branches Pа; Е-modulus belt, Pа; 1 2 , D D -the diameters of the guiding and driven pulleys, mm; f-the coefficient of friction of the belt on the pulley surface; 0 φ -elastic slip angle.Furthermore, lengthening pulleys branches can be determined by the angular displacement of pulleys: ( ) Thus according to Figure 1 can be determined

Abstract
This paper presents method of determination in the regularity change in the branches of a belt drive with an eccentric tensioning roller.On the basis of analysis in the research results identified the recommended belt transmission parameters.
Differential equations describing the motion of the belt drive pulleys are of the form Where, M g -drive moment to the drive pulley shaft, M 1 М 0 -the amplitude hesitation of the driving and disturbing moments.Decision of system (4) differential equations belt drive found in the form: sin , sin t t ϕ ϕ ω ϕ ϕ ω = = (5) Supplying (5) with respectively, in the equation (4) we obtain the expression for determining the values the amplitudes ripple of the belt drive pulleys ( ) Where, When this tension will change Then, full of tension in the branches of a belt drive get
Figure 2 shows a graphic pattern of the belt tension changes in the leading branches on the transfer at σ 10 =40 kg/sm 2 M 1 =5,2 Nм, M 0 =18 Nм.
Analysis of the resulting pattern shows that the amplitude of the low component match, depending on the disturbing M 0 resistance force and frequency ω, high-frequency components is dependent on the value of M 1 and j.
The amplitude of the ripples reaches 0,373 10 2 kg/sm 2 , low frequency rippling occur in the range of (9,0….11)s - .It should be noted that the value of σ 10 not affect the nature of the change in time σ 1 in time (Figure 2b).Thus, from the graphs in Figure 2b.It is seen that the graphs 1, 2 and 3 are shifted in parallel relative to the axis t. Figure 2 presents the patterns of change in σ 1 changing M 0 and σ 10 =40 kg/sm 2 .
It is common knowledge the amplitude of the disturbing moment increases the deformation of the belt, and by the tense Ascending.Besides the increase in the moments of inertia of pulleys in the variable driving modes lead to cyclic changes in load in the branches of a belt drive (Figure 3a).Therefore, the recommended value is I 1 =(0,03…0,04) kgm 2 and I 2 =(0,05…0,06) kgm 2 .
It is common knowledge that driving with increasing force values and accordingly increases the belt tension deformation particularly in the leading branch, which transmits the motion from the driving pulley to the driven (Figure 3b). Figure 4 shows the pattern of the belt voltage fluctuations in the leading branches of the transmission by varying the values of ω, j, М 1 and М 0 .An analysis of the laws shows that with the change in the frequency of the driving values of j and the frequency ω resistance on the shaft of the driven pulley is also changed form σ 1 voltage fluctuations in the leading branches of the belt drive.
At the same time with the increase in М 1 and М 0 increases the amplitude of the fluctuations σ1 as the high-frequency and lowfrequency components (Figures 4a and 4b).It should be noted the phase shift with increasing fluctuations σ 1 j with respect to ω.

Conclusion
An analytical method for determining the laws of the belt voltage fluctuations in the leading branches of the belt drive with tensioning roller.Substantiates the numerical values of the parameters in the belt transmission.

Figure 1 :
Figure 1: Scheme of belt drive with an eccentric tensioning roller.

Figure 2 :
Figure 2: Laws of change of tension in the leading branches of the belt drive from time to time σ 1 fluctuations.

Figure 3 :
Figure 3: Graphic changes depending on the amplitude of the vibrations on the belt tension in the leading branches of the transmission changes in amplitude on the disturbing force to the driven pulley (a) and the maximum belt tension on the voltage variation of the pre-tensioning of the belt (b).