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Juraev Anvar Dzhuraevich, Academician of the international Academy of engineering and academician of the international Informatization Academy, Doctor of technical Sciences, Professor Tashkent Institute of textile and light industry E-mail: anvardjuraev1948@mail.ru Mamaxanov Azam Abdumajitovich, Candidate of technical sciences, docent, Namangan engineering-technological Institute E-mail: Azamat83@mail.ru
ANALYSIS OF THE UNEVEN GEAR RATIO CHAIN TRANSMISSION WITH ELASTIC ROLLER SLEEVE
Abstract: The article describes the scheme and operation of the recommended design of the chain transmission with elastic roller sleeve. Provides an analytical method for the determination of the coefficient of uneven gear ratio chain transmission with flexible roller chain including an elastic rubber sleeve, substantiates the values of the recommended parameters.
Keywords: Chain drive, compound roller, an elastic sleeve, the unevenness, gear ratio, sprocket, link, teeth, and deformation of rubber.
Introduction
In the existing design of the chain transmission contains driving and driven sprocket, and a flexible elementa chain transmitting motion from the drive sprocket to the driven one [1; 2]. The disadvantage of this chain transmission is in operation, the reduction angle of wrap of the chain sprockets, a significant slack in the driven (idle) branch of circuit that conducts to decrease in efficiency, and in some cases tearing or snagging of the chain with the sprockets. Additionally, when transmitting heavy loads at high speed modes of movement there appears noise due to the shock interaction of the teeth with the surfaces of the rollers of the chain, increases friction, and thus wear and tear, as rollers of the chain and the teeth of the sprockets.
The development of construction. We recommended a new design of chain transmission (see Fig.1) [3; 4].
In the process, this chain transmits rotational motion from the sprocket 1 to the driven sprocket 2 via the chain 3. Further movement of the sprocket 2 is transmitted to the base 6 to the output shaft 7 via an elastic annular bushing 5. the change in angular displacement of the driven sprocket 2, arising because of the gaps be-
tween the chain 3 and the sprocket teeth 2, and also due to changes in friction and wear and gearing etc. to some extent aligned (damped) elastic annular bushing 5. Where in rotation of the base 6 to the output shaft 7 sprocket 2 becomes more uniform and smoother. In the interaction of the teeth of the sprockets 1 and 2 with the roller 12 due to the deformation of the rubber sleeve 15 significantly reduced the wear sleeve 13 and the teeth of the sprockets 1 and 2. It also reduces the friction between the bushing 11 and the roller 10. This leads to increased durability and reliable operation of the chain transmission. In the process, by performing the outer surface 16 of the rubber bushing 15 when interacting with the teeth of the sprockets 1 and 2 is the required deformation of the sleeve 15, particularly at its edges is provided by a kind of centering the pressure of the roller 12 from the teeth of the sprockets 1 and 2. This leads to uniform distribution of load over the entire length of the roller 12, which allows increasing the reliability, thereby increasing the resource chain 3 assists.
The analysis of the operation of the chain transmission shows that the gear ratio is changed continuously. Meanwhile, the average value of the ratio will be constant [5]:
U = ®L = Zl
11
Z
where fflj, ffl2 is the angular velocity of driving and driven sprockets Zl, Z2 the number of teeth of the driving and driven sprockets.
Figurel.Diagram of the chain transmission
Definition of uneven gear ratios. In technological machines an important thing is the determination of the uneven gear ratio chain transmission with flexible roller chain due to deformation of the elastic sleeve. This provides the ability to control the unevenness of the angular velocity of driven sprocket directly connected with the working body of the machine.
In (Fig. 2) presents the scheme ofthe chain oftransmis-sion at different positions of the chain and sprockets with account of deformation of the elastic bushing roller chain.
If we consider that the length of the leading branches of the multiples of a whole number of links in a chain, the distance between the axes of the sprockets will be:
A = (2)
cosa
Where k is the number of whole links in the leading branch of the chain; t is the step between the teeth of the sprockets.
According to this we have:
a = arctg— 2k
sin
V V
sin
n
V Z
(3)
JJ
Where A^, A$>2 are the offset angles of the axes of the rollers of the chain due to deformation of the elastic rubber bushings in engagement with the teeth of the driving and driven sprockets. In this case, the angular speed of the driven sprocket at first gear (the chain shown in solid line) taking into consideration [5]:
®2i =-
R2 cos
Then we have:
coR
cos
n
v Z
n
v Z2
+ A^2
R
cos
n
v Z2
+ A^2
tg
ox, = c
n
v Z2
+ A^2
tg
n
vZi
+ A^i
(5)
(4)
For this position the chain in engagement with the sprockets the gear ratio will be:
U = Q =
w 21
tg
n
v Z
tg
n
v Z2
+ A^2
(6)
In this case, the angular speed of the driven sprocket after rotating it to the corner (chain and sprockets shown in (Fig. 2) a by dash-dotted line):
Ri
cc = ( — = (
22 i R 1
sin
n
v Z2
+ A^2
sin
n
vZi
+ Aq>x
(7)
The gear ratio of chain transfer in this moment would be:
sin
w i2
n
y Z
sin
n
y Z2
+ A^2
(8)
a)
b)
Figure 2. Scheme chain transmissions with elastic elements of the roller chain; where - a) is the length of the leading branches equal to the length of the integer member number of the links; - b) is the length of the leading branches equal to the length of the whole number of links plus the half link
Comparison of expression ratios (6) and (8) are different and depend mainly on the number of teeth of the sprockets. In this case the angular speed of the driven sprocket also varies.
Important is to define actual values of transfer numbers with a glance of the deformation of the elastic rubber bushings roller chain transmission. In (Fig. 2 b) the transfer length of the drive chain is determined from the expression.
The angular speed of the driven sprocket in this moment is:
Rl
CC = c —- cos
23 1R
í \ n A
Z+A©
v 7 i
sin
= c
tg
í \ n A
— + A© 7
f \ n A 7 + A©i
v 71 J
(10)
Taking into account (10) the gear ratio will be: tg
U =
13
sin
f \ n A
7+A©
V 71_y
í \ n A
— + A©. 7
V^ 2 y
(11)
In the second point of the gearing (chain and sprockets shown in (Fig. 2 b), by the dash-dotted line) the angular velocity of driven sprocket is determined from the following expression:
tg
=
R2 cos
i \ n A
— + A® 7
v 7 2 y
sin
f \ n A
7 + A®
V 71
f \ n A
— + A® 7
V 7 2 y
(12)
At the time of engagement of the chain with sprockets the gear ratio will be:
tg
U13 =
sin
f \ n A 7 + Am
V 71__
f \ n A
— + Am 7
V7 2 _
(13)
In our case, we have:
U13 > ^3 , ^24 >©23^ > Uis (14)
Then the coefficient of unevenness ratio of the chain transmission will be:
s = 2 (U is-U is)
" Uis + Uis
Substituting (11) and (13) to (15) we obtain:
(15)
S =
sin f \ n A 7 + A$1 V 71 - sin2 f \ n A 7 + AK V 71 cos f \ n A 7 + a$2 V 7 2 y
sin f \ n A 7 + A$1 V 71 + sin2 r \ n A 7 + A^1 v 71 y cos f \ n A 7 + a$2 V 7 2 y
(16)
The solution of the task and analysis of the results.
Analysis (16) shows that the coefficient of unevenness of gear ratios recommended chain depend on the number of sprocket teeth and magnitudes of deformation of the elastic bushings of the chain at engagement with the sprocket. In (Figure 3 a) presented the patterns of change of the coefficient of uneven gear ratio chain transmission from variations in the number of teeth of the sprockets.
With the increase of the average value of the transmission ratio Z /Z coefficient is increased Su with non-2 1 u
linear patterns.
When the value of the deformation A^ and A^2 is equal to 0.15% from the step value ofthe transmission and Z2/Z1 changed from 1.4 to 3.2 coefficient ofunevenness in-
creases from 1.1 • 10-2 to 9.2 • 10-2, and at an angular deformation of the elastic rubber bushings to 0,225% from the value of the step coefficient Su increases to 12,31 • 10-2.
a) b)
Figure 3 Graphic dependences of change of coefficient of uneven gear ratio chain transmission from changes in the number of teeth of the sprockets (a) and values of angular deformation of the elastic rubber bushings of roller chain in the process of gearing with the sprocket; Where 1 at A^ and A^2 equals to 0,15t, 2 at A^ and Ap2 equals to 0.225t and t is step value of the transmission; Where 1-1 -
Su equals to f (A^); 2 - 5u equals to f (Ap2)
It should be noted that the increase of the uneven rota- When changing A^ from 0,5 0.5 10-2 rad to
tion ofthe driven sprocket is deemed necessary for the in- 2.6-10-2 rad Su increases from 3.25-10-2to 9.8-10-2, and
tensification of technological processes in machines (particularly in cotton cleaners and machines for soil treatment). But, a significant increase of Su could lead to a breach of the gearing in the transmission.
Therefore, the recommended values of Su for ginning machines are (3.4...6.5) ■ 10-2. In (Fig. 3 b) shows a graphical dependence of change of coefficient of uneven gear ratio chain transmission from changes in angular strain of the elastic bushings ofthe chain rollers with meshing teeth ofsprocket. The increase of A^1 and A^2 strain leads to increase of Su by non-linear patterns. The difference between A^1 and A^2 influence to change 5u is insignificant.
with the increase of A^2 in the specified limits, the coefficient Su of uneven gear ratio chain transmission is increased to 11.92 ■ 10-2. The difference 5u for changes A^1 and Ap2 comes to 0.89 -10-2.
Conclusion
Practically in the transmission chain with an elastic rubber sleeve roller chain in many cases, A^1 = A^2. Therefore, the recommended values of Su (3.4...6.5) ■ 10-2 A^1 and A^2 should be taken in the range of (0.6...1.4) ■ 10-2 number. These values of deformation of the elastic bushings provided by rubber stamps 7B-4 MBC.
References:
1. Gotovtsev A. A., Kitten I. P. Design of chain drives: a Reference book. - 2nd ed. Rev. And extra - M.: Mashi-nostroenie, - 1982. - 336 p.
2. N. In. Sparrows Chain transmission: - Moscow: Mashinostroenie, - 1968. - 132 p.
3. Djuraev A. Dr. kinematic and dynamic analysis of a chain of devices with an elastic element and a tensioning mechanism, Monograph: - T: Navruz, - 2014. - 140 p.
4. Juraev A., Mamaxonov A., Yunusov S. Development of the design of the circuit with the elastic bushing of a chain drive for drives of technological machines. III- International scientific-practical conference "Mathematical modeling of mechanical systems and physical processes", devoted to 25-anniversary of independence of the Republic of Kazakhstan on November 18-19. - 2016. - P. 32-34.
