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KINEMATICS AND MAIN DIMENSIONS OF SPUR GEAR CYLINDRICAL GEARS
Tovashov Rustam Xo‘jaxmat ugli
Doctor of Philosophy in technical Sciences, docent, Karshi State Technical University
Abstract:
This article presents theoretical information on the kinematics of spur gear cylindrical
gears, their main dimensions, and the forces acting on them, which are commonly used in the field
of mechanics.
Keywords:
gear wheel, gear, parameters, diameter, forces, kinematics, speed, tooth module,
number of teeth, outer, inner circle.
Introduction.
Nowadays, in the field of mechanical engineering, in particular in the
mechanization of agriculture, the use of gear mechanisms in many agricultural machines is of
great importance. The importance of gear mechanisms in this is that they convert the rotational
motion coming from the tractor's power take-off shaft into the working part of the machine [1-2].
When adapting the rotational motion to the movement of the working part, it is necessary that the
materials and dimensions of the parts of this mechanism can withstand the stresses generated in
the environment during movement and ensure smooth movement. For this reason, it is necessary
to study the movement of gear transmissions, their parameters and the forces acting on them [3-6].
Research method.
Permanently attached couplings can be fixed or movable. Fixed couplings
connect the shafts so that they do not slide relative to each other. Movable couplings connect the
shafts in a way that allows them to move in different directions [7-10].
Research results and discussions.
A gear wheel with a cylindrical gear and a pitch cylinder of
the side surfaces of the teeth parallel to the sides of the wheel is called a spur gear [11-13].
Cylindrical gears (Figure 1) belong to direct contact gears.
Figure 1. Cylindrical spur gear
These gears are used at speeds
≤ 2 / .
We determine the geometric parameters [ 14-15] of spur gear cylindrical gears depending on the
module and number of teeth (
t
and
z
).
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Fig. 2. Main geometric parameters of gear drives with tooth profiles
Tooth tip diameter
�
�
= � + 2ℎ
�
(1)
Tooth socket diameter
�
�
= � − 2ℎ
�
(2)
From the equation
=
, the diameter of the division is:
� = (
�
�
�
)�
yoki
� = ��
(3)
According to the standard, the height of the tooth head is
h = m
; the height of the tooth root is ℎ
= 1.25 ;
The height of the tooth is
h = h
a
+ h
f
= m + 1.25m = 2.25m
.
From here the diameter of the tooth tip
�
�
= �� + 2� = �(� + 2)
(4)
Tooth socket diameter
�
�
= �� − 2.5� = �(� − 2.5)
(5)
The difference between the height of the tip of one wheel and the height of the tread of the other
creates radial clearance.
c = ℎ
�
− ℎ
�
= 1.25� − � = 0.25�
(6)
The distance between the axes =
w
�
�
=
�
1
+�
2
2
=
�(�
1
+�
2
)
2
(7)
In a gear, the width of the tooth is equal to the pitch length: =
m
− tooth length coefficient (tooth width) modulus
The forces arising from the meshing of the teeth are applied to the teeth of the wheels, and then
these are transmitted to the joints in which the wheels are mounted, from the shafts to the bearings
and other parts [16-19]. To calculate the details listed above, it is necessary to know the
magnitude and direction of these forces [20-23].
As shown in the figure, a pair of teeth participate in the connection, and we assume that the
connection point coincides with the line N. The load in the tension distributed along the length of
the line NN is replaced by the resultant force, which is directed along the connection line NN and
is normal to the contours of the teeth at the connection point. Frictional forces in the connection
are not taken into account, since they are small [24-28].
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For practical purposes, not only the force is of interest, but also its components - the
circumferential force
F
t
, tangent to the dividing circles, and the radial force
F
r
, directed along the
line connecting the centers of the wheels.
Figure 3. Determining the forces acting on the meshing of gears
F
n
is the total force perpendicular to the tooth surface along the meshing line.
From this,
(8)
(9)
Here
T
1
,
T
2
are the torques on the gear and wheel, respectively;
d
1
,
d
2
- diameters of the gear and wheel pitch of the circle, respectively;
u
– number of transmissions.
The direction of force on the driven wheel is in the direction of rotation, and on the leading wheel
it is opposite [29-30].
Conclusion.
According to the analysis of the theoretical data considered above, the forces acting
on the gear mechanisms have a significant impact on the smooth movement of the mechanism, its
kinematics. At the same time, the provision of the required torque due to the rotational force
acting on the mechanism depends on the main dimensions of the gears, that is, it varies depending
on the diameter of their pitch circle.
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