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50
DOI: http://dx.doi.org/10.20534/ESR-17-1.2-204-207
Mamatova Dilrabo Alisherovna, Teacher Tashkent Institute of Textile and Light Industry E-mail: Mda4580@inbox.ru Djuraev Anvar Djuraevich Professor Tashkent Institute of Textile and Light Industry
Dr.Sci.Tech., the professor E-mail: Mda4580@inbox.ru
The analysis of change belt tension in the slack side of belt transmission
Abstract: The article is produced the results of determining in the belt tension in slack side of belt transmission. The analysis of laws changes belt tension in the slack side of belt transmission, Justify the parameters of transmission.
Keywords. Belt transmission, slack side of, tension, moment, lengthening of oscillation frequency, amplitude, moment of inertia.
Introduction. The belting used in drives of technological ma- expense of choice materials for belt is important to determine the chine having variable load [1]. At the same time due to complex belt tension, particularly in the slack side of belt transmission. On deformation belt, especially in lengthening occurs irregularities op- fig. 1 is a diagram for alternating transmission of belt tension [2; 3]. eration work in the transmission. To ensure the durability belt at the
Figure 1. Diagram of the belt transmission with an eccentric tension roller
The analytical solution of the problem. According to the work of lengthening side of belt transmission determined from the expression:
M = Act,
AL = Act
I + A_ (1 - e - f A )
E 2 fE '
1 + A(-fo - !)
E 2 fE '
(1)
When, ACTj, Act2-changing the belt tension in strand of transmission, Pa; E-modulus of elasticity belt, Pa; Dl, D2 - the diameter of the drive and driven pulleys, mm; f - friction factor of belt on the surface of the belt pulleys; - elastic slip angle.
Differential equations describing the motion of the belt pulleys are of the form
Mg - moving moment on the shaft to the drive pulley M1 M0 - the motion of the amplitude hesitation and disturbing moments
The solution of system (2), differential equations belt drive as form:
fa = fa0 sin cot, fa2 = fa20 sin cot (3)
Supplying (3), respectively, in the equation (2) we obtain the expression for determining the values of the amplitude hesitation of the belt pulleys
- £ r Msinl+J© V a (J ©+M 0) l sin ©f J v '
m A = b
A2 - B2
J 2co2 + M. B
J 2
d2 fa KFD2 k3D.D2F ^
J1 +"Vfa - ^Dr2- fa2=M,
d2fa k,iDlD2F M i k3D22F
~dtr 4
^20 =
B M^sinjf + j^\ A( + Mo)
smrnt J v y
A2 - B2
(4)
fa +-
-fa = M sin a>t
(2)
Where, A = K3 ^ ; B = K3 ^^ F ; 3 4 3 4
Where, k3 = (k1 + k2)—; k = - + -^(1 - ef') ; 31 2 klk2 1 E 2fE
k = - + ■D^(ef"° -1), M = M, sin jt. 2 E 2 fE
Herewith tension will change Act10 =
Mo - Mo
k
=
Mo - Mo k
(5)
Then, full of tension in the slack side of belt transmission gets
&i = a10 + Ac10 sin cot, < 2 = <20 + A<20 sin rnt (6)
Analysis of the results. Numerical solution and analysis of results change on o1 and o2 carried out under the following initial values of the parameters belt drive with variable gear ratio:
R=1,540"3 m; R2=2,04Q-3 m; I=0,02 kgm 2; I2=0,033 kgm 2;
F=2,5 sm 2; o0=22 kg/sm 2; w=0,75P2; o10=40 kg/sm 2; o20=40 kg/sm 2; M0=25 Nm; E=1240 2 kg/sm 2; l=0,18540-3 sm; M^8,5 Nm.
It is important in the study of oscillating voltage in slack side of belt transmission with glance on the tensioning device.
Research are shown that the character of the oscillating voltage in the slack side of belt transmission actually does not affect the value of the pre-tensioning o20 (see. Fig. 2a, b).
Where, a: 1-Aff2O=0,040-102 Kg/sm2, to ff20=0,01-102 Kg/sm2;
2-Aff2O=0,028-102 kg/sm2, to ff20=0,32402 kg/sm2;
3-Aff2°=0,026-102 kg/sm2, to ff20=0,48402 kg/sm2
O S,102kg/snr
1.10 s
Where, b: 1-Aff20=0,12-102 kg/sm2; 2-Aff20=0,23402 kg/sm2; 3-Ao'20=0,38402 kg/sm2; to -Aff20=0,11402 kg/sm2
Figure 2. Regularities of change on belt tension in the slack side of belt transmission on Fig.3 shows the dependence of the change olmax max increase o20 with variation M0
The graphs shown that with increasing o20 tension increased in linear regularity. So, while increasing of the value o20 from 0,082-10 2 kg/sm 2 to 0,75-102 kg/sm 2 the maximum value of the tension o1max in slack side of belt transmission is increased 0,145-10 2 kg/sm 2 to 0,58-10 2 kg/sm 2 at M(=30 Nm. Where in M0=50 Nm, the maximum value of the tension in the slack side of belt transmission increases to 1,29-10 2 kg/sm 2Wherein reduce the belt tension in the slack side of belt o1max considered appropriate reduction on resistance in form of driven pulley, as a preliminary tension of a belt.
Tolerant range of change on parameters for a belt transmission with the reviewed initial value of parameters are M0< (40...45) Nm, ff20< (0,30...0,45)40 2kg/sm 2 The amplitude of the oscillations of tension in the slack side of belt transmission are based on depends from the amplitude resistance to moment and the moment of inertia pulleys (see. Fig. 3b)
Based on the dependent of graphical analysis in Fig. 3 b identified the recommended values of the moments inertia pulleys and M0, amplitude, which correspond to the results and graphs in Fig. 3 a:
a
b
Where, 1-M =30 Nm; 2-M=40 Nm; 3-M=50 Nm
Where, 1-to Ii = 0,050 kgm2; I2 = 0,075 kgm2; 2-to I1= 0,035 kgm2; I2 = 0,055 kgm2; 3-to I1 = 0,02 kgm2; I2 = 0,035 kgm2
Figure 3. Laws of the maximum value change in the slack side of belt transmission from changes in the pre-tension in slack side of belt (a) and the amplitude of the oscillations voltage in slack side of belt transmission from variation Мo
I1= (0,035^0,046) kgm2, I2= (0,057^0,068) kgm2; M0<(40...45) Nm.
On Fig. 4 shows the laws of oscillations voltage in the slack side of belt transmission from variation the value of rang amplitude Ao^ and changed frequency moment w and j lead and driven pulleys.
According to analysis laws of changes on o as shown on Fig. 4 shows that with increasing frequency difference moving moment on the wave to the drive pulley j, and frequency oscillation of resistance to the moment on the wave to the drive pulley w leads to a phase shift, which may lead to negative result.
That's why it considered appropriate to change moment closely to each other (see. Fig. 4). That's why It recommended limits of variation frequencies ^ = (30 ... 40) s-1 and j= (40 .„45) s-1.In addition amplitude change Aa does not affect the character of oscillating voltage in the slack side of belt transmission (see. Fig. 4).
Where, a, b: 1-^=40 s-1; j=50 s-1; Ao-^0,24-102 kg/sm2;
2-^=40 s-1; j=55 s-1; AO20 =0,125T02 kg/sm2;
3-^=40 s-1; j=60 s-1; AO20 =0,130T02 kg/sm2;
in: to=j=40 s-1; 1-AO20 =0,28^102 kg/sm2; 2-AO20 =0,25T02 kg/sm2; 3-AO20 =0,14T02 kg/sm2 Figure 4. Laws of change tension in the slack side of belt transmission from variation amplitude Ao20 and frequency moments on the drive and driven pulleys
Conclusions. Formulaic for the calculation of tension in the tions voltage in the slack side of belt transmission. Justify the paslack side of belt transmission with tensioning device. On the ba- rameters of transmission. sis of numerical solution on the problem defined laws of oscilla-
References:
1. Juraev A., MirakhmedovJ. and etc. Patent Uzbekistan. Belting. FAP00734. Bull. - № 6, - Tashkent - 2012.
2. Juraev A., Turdaliev V. M., and Maksudov R.Kh, "Kinematic and dynamic analysis of belt transmissions with variable gear" Monograph, Ed. - Tashkent, - Uzbekistan: Fan vatexnologiya, - P. 168, - 2013.
3. Vorobyov I. I., "Belt Transmission" - M. Engineering, Ed. - Moscow, - Russia, - P. 168, - 1979.
