The American Journal of Engineering and Technology
225
https://www.theamericanjournals.com/index.php/tajet
TYPE
Original Research
PAGE NO.
225-229
10.37547/tajet/Volume07Issue03-19
OPEN ACCESS
SUBMITED
14 January 2025
ACCEPTED
22 February 2025
PUBLISHED
20 March 2025
VOLUME
Vol.07 Issue03 2025
CITATION
D.M. Mukhammadiev, I.O. Ergashev, L.Y. Zhamolova, & M.S. Abdusalomov.
(2025). Strength Calculation Of Planetary Gear Of The Seed-Removing Pipe.
The American Journal of Engineering and Technology, 7(03), 225
–
229.
https://doi.org/10.37547/tajet/Volume07Issue03-19
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Strength Calculation Of
Planetary Gear Of The
Seed-Removing Pipe
D.M. Mukhammadiev
1,
I.O. Ergashev
2
, L.Y.
Zhamolova
3
, M.S. Abdusalomov
1
1
Institute of Mechanics and Seismic Stability of Structures named after
M.T. Urazbaev, Academy of Sciences of the Republic of Uzbekistan,
Tashkent, 100125, Uzbekistan
2
Fergana Polytechnic Institute, Fergana, 150107, Uzbekistan.
3
Tashkent State Agrarian University, Tashkent, 100140, Uzbekistan
Abstract:
In the article, a planetary gearbox is adopted to
ensure the efficiency and compactness of the vas
deferent drive. The number of teeth of the sun gear
Z
1
=12, satellite Z
2
=12 and main gear Z
3
=36 with a module
m=3 mm is checked for compliance with the condition of
assembly and proximity to the number of satellites equal
to K=4. Verification calculations of the sun gear teeth and
the satellite axis for bending are carried out, in which the
strength condition is met with a reserve of
F
=24.93
MPa
[
F
]= 465 MPa
–
18.5 times and
u
=20.26
MPa
[
u
]= 60 MPa
–
2.96 times. In addition, taking into
account the strength calculations, the dimensional
values of the planetary gearbox units of the vas deferent
tube are determined.
Introduction:
A planetary gearbox is one of the types of mechanical
gearboxes. This type of gearbox, widely used in many
industries, is based on a planetary gear. A planetary
gearbox is a gear mechanism, the characteristic feature
of which is that the axes of some gear wheels are
movable (Fig. 1) [1].
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The American Journal of Engineering and Technology
Fig. 1. Planetary gear diagram
The most popular type of planetary gear consists of the
following elements:
−
Sun gear
–
a small gear wheel with external teeth,
located in the center of the mechanism
−
Crown gear (epicycle)
–
a large gear wheel with
internal teeth
−
Planet carrier
–
this part of the planetary gear
mechanically connects all the satellites. It is on the
planet carrier that the rotation axes of the satellites
are mounted.
−
Satellites
–
small gear wheels with external teeth,
located between the sun and crown gear. The
satellites are in simultaneous engagement with
both the sun and crown gear.
Due to their efficiency and compactness, planetary
gearboxes have become widespread in mining
engineering. A gearbox, like any mechanism, has a
leading and a driven link. The leading link in a gearbox
is a shaft that receives power from the engine; in a
planetary gearbox, this is usually the central gear. The
driven link is the output shaft of the gearbox, which sets
some mechanism in motion. Considering the new
layout of the gearbox elements [2].
It is known that a planetary gearbox, when working
with high peripheral speeds, should take into account
that during rotation any mechanism creates vibrations
that negatively affect the operation of the mechanism
as a whole. In addition, each engagement in the
transmission, especially when it comes to multi-stage
transmissions, negatively affects its power, which in
turn depends on the efficiency. The efficiency of a
closed planetary transmission without taking into
account friction losses and oil mixing is within 0.96-0.98
[3].
Shaft misalignment of units is also a common problem
of the lifting and turning mechanisms of electric quarry
excavators equipped with planetary gearboxes. Signs of
misalignment of electric motors with gearboxes are
found on approximately 30% of objects from the
surveyed sample. In this case, the spectrum is usually
dominated by the second - third component of the
electric motor rotation frequency, and the amplitudes
of significant harmonics increase in those planes of the
spatial position of the unit, where the misalignment of
the shaft installation is more pronounced (the so-called
"horizontal" misalignment is quite widespread on
mining equipment units due to the low qualification of
service and repair personnel). Signs of misalignment of
the shafts of the first and second stages of planetary
gearboxes are much less common, which can be
explained by the rapid onset of emergency failure of
the units. Destruction and/or jamming of gears in the
case of shaft misalignment and general disruption of
the geometry of gear engagements in planetary
gearboxes develops very quickly, which often does not
allow for the timely detection and assessment of
diagnostic signs corresponding to this process [4, 5, 6].
The article by P.B. Guericke and A.G. Nikitin [7]
summarizes the results of studies of the parameters of
vibration generated during operation of planetary
gearboxes, widely used in mining equipment, and
applies the obtained results to solve the urgent
problem of creating a single diagnostic criterion
suitable for assessing the actual state and forecasting
the degradation processes of the technical condition of
planetary gearboxes, taking into account the features
of their design and the specifics of the methodology for
collecting diagnostic information. The obtained results
prove the fundamental effectiveness of the proposed
methodological approach for solving the problem of
creating algorithms for developing uniform diagnostic
criteria for assessing and forecasting the process of
changing the technical condition of planetary
gearboxes.
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In the work of A.M. Pashkevich [8], a new method of
engineering calculation of radial-plunger ball reducers
was developed, allowing to determine all radial and
axial dimensions of reducers, to get rid of undercutting
of the central wheel and, consequently, to increase the
load capacity of the transmission. The profile of the
central wheel after approximation by the simplest lines
was described by mathematical dependencies, which
formed the basis of the new method.
To ensure the efficiency and compactness of the seed-
transfer device drive, we adopt a planetary-type
reducer. Further, to ensure compactness and
efficiency, we perform a strength calculation of the
planetary reducer units.
Initial data of the seed-discharging device planetary gearbox: torque on the drive shaft (pipe) T
t
=77.95 N
m; rotation
speed of the driven shaft (auger) n
sh
=1440 rpm; rotation speed of the drive shaft (pipe) n
t
=360 rpm; service life of
the gearbox is 5 years, 240 working days per year, in three shifts of 8 hours.
1. Determine the gear ratio of the drive
1. Determine the gear ratio of the drive
4
360
1440
=
=
=
t
sh
n
n
i
.
(1)
2. The gear ratio of the planetary gearbox is determined by the following formula:
H
H
pl
U
U
U
13
3
1
1
−
=
=
hence
=
=
1
3
3
1
Z
Z
U
H
3
(2)
3. Select the number of teeth of the sun wheel Z
1
= 12.
4. Determine the number of teeth of the satellite using the formula
(
)
12
)
2
4
(
12
5
.
0
2
5
.
0
)
3
(
1
1
2
=
−
=
−
=
H
i
Z
Z
.
(3)
5. From the above number of teeth of the main gear
.
36
12
2
12
2
2
1
3
=
+
=
+
=
Z
Z
Z
(4)
6. We take the number of satellites (from the condition of balancing the forces in the engagement) K=4.
7. Check the number of satellites according to the neighborhood conditions:
=
K
180
sin
0.707
=
+
+
2
1
*
2
2
Z
Z
h
Z
a
0.5833
(5)
where h
a
*
=1.
8. We check the number of teeth of the wheel according to the conditions of collection B, since its value must be
an integer (natural) number:
=
+
=
)
1
(
1
1
K
p
K
U
Z
B
Н
9.
(6)
Here p=0. The condition is met.
9. To install the next satellite, it is necessary to turn the carrier to the following angle:
=
+
=
)
1
(
360
K
p
K
Н
90
(7)
here p=0 and K=4.
10. We select 40ХН steel for gear wheels, improved, average hardness HB 280; basic number of stress change cycles
[9]:
N
H0
=2.66
10
7
.
(8)
11. We determine the working number of voltage change cycles for the solar wheel for the entire service life
t=5•240•3•8=28.8•10
3
h using the formula
7
3
)
(
1
10
5
.
746
10
8
.
28
1080
4
60
60
=
=
=
t
n
K
N
H
Н
(9)
here
1080
360
1440
)
(
1
=
−
=
−
=
t
sh
H
n
n
n
rpm
12. Since
N
H
>
N
H0
,
we take the durability coefficient K
HL
=1 [9].
13. We determine the center distance between the sun wheel and the satellite [9]:
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The American Journal of Engineering and Technology
mm
u
n
K
T
u
K
a
ba
H
c
H
sh
a
w
68
.
35
5
.
0
1
550
3
.
3
2
.
1
10
487
.
19
)
1
1
(
5
.
49
]
[
)
1
(
3
2
2
3
3
2
2
'
=
+
=
+
(10)
where
К
а
=49.5
–
for
cylindrical
spur
gear
transmissions;
u=Z
2
/Z
1
=12/12=1
–
gear
ratio;
mm
i
T
T
H
t
sh
=
=
=
N
10
487
.
19
4
10
95
.
77
3
3
)
3
(
1
–
screw torque;
K
H
=1.2
–
load concentration factor;
п
с
’
=K
–
0.7=4
–
0.7=3.3
–
calculated number of satellites;
MPa
S
K
H
HL
b
H
H
550
15
.
1
1
630
]
[
]
[
lim
=
=
=
–
permissible contact stress;
MPa
HB
b
H
630
70
280
2
70
2
lim
=
+
=
+
=
–
limiting value of contact endurance; [
S
H
]=1.15
–
safety factor;
ba
=
0.5
–
satellite width factor.
We accept the center distance
–
a
w
=36 mm.
14. We determine the engagement module [9]:
mm
Z
Z
a
m
w
3
12
12
36
2
2
2
1
=
+
=
+
=
(11)
15. Determine the width of the wheels [9]:
mm
a
b
w
ba
18
36
5
.
0
=
=
=
(12)
16. We perform a verification calculation of the teeth for bending using the values of the coefficients according to
GOST 21354-75 [9]:
.
93
.
24
3
18
12
3
.
3
2
.
1
5
.
1
1
10
487
.
19
1
6
.
0
8
.
3
2
2
2
3
2
2
'
MPa
m
b
Z
n
K
K
K
T
Y
Y
Y
c
F
F
F
sh
F
F
=
=
(13)
17. Compare with the permissible stress:
.
465
8
.
1
5
.
1
1
555
]
[
]
[
lim
MPa
S
K
K
F
FC
FL
b
F
F
=
=
=
(14)
The strength condition
F
=24.93
MPa
<
[
F
]=465 MPa is met.
Calculation of planetary gear satellite axes for bending
The most loaded part in planetary gearboxes is the satellite axis, so special attention must be paid to their
calculation.
In general, the normal forces acting on the surface of the satellite teeth in the engagement pole of a
cylindrical transmission are divided into circumferential F
t
, radial F
r
and axial S forces. In a straight-toothed
cylindrical engagement [10, 11]:
,
2
:
;
;
2
2
2
Z
m
S
M
F
S
tg
F
F
Z
m
M
F
u
r
t
r
kr
t
=
=
=
=
(15)
where for our case
m
=3 mm is the tooth module; М
kr
=Т
sh
/К=19.48/4=4.87 N
m is the torque on the gear shaft;
Z
2
=12 is the number of satellite teeth;
=20
is the tooth profile angle in the normal section;
М
и
–
is the bending
moment created by the axial force S. Then the circumferential force F
t
= 270.65 N, the radial force F
r
=98.5 N, the
axial force S=98.5 N, and the bending moment
М
и
=1773.15 N
mm.
When calculating the bending stresses arising in the cross section of the axis,
𝜎
𝑢
=
𝑀
𝑢
𝑊
𝑢
=
1773.15
98.17
= 18.06 𝑀𝑃𝑎 ≤ [𝜎
𝑢
] = 60𝑀𝑃𝑎
.
(16)
where
[σ
u
]=60
–
70
MPa
is
the
permissible
bending
stress
for
carbon
steel
axles;
3
3
3
3
17
.
98
32
10
14159
.
3
32
mm
mm
d
W
u
=
=
=
–
is the moment of resistance of the satellite axle during bending;
d=10 mm is the diameter of the satellite axle.
The bending stability condition
u
=18,06
MPa < [
u
] =60 MPa is fulfilled.
CONCLUSIONS
For efficiency and compactness, a planetary gearbox of
a reverse scheme is provided in the drive of the seed-
removing pipe. In this case, the number of teeth of the
sun gear Z1=12, satellite Z2=12 and main gear Z3=36
with a module m=3 mm, are checked for the condition
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The American Journal of Engineering and Technology
of collection and proximity to the number of satellites
equal to K=4.
Verification calculations of the teeth of the sun gear
and the satellite axis for bending were carried out, in
which the strength condition with a reserve of F=24.93
MPa [ F]= 465 MPa
–
18.5 times and u=20.26
MPa [ u]= 60 MPa
–
2.96 times was met. In addition,
taking into account the strength calculations, the
dimensional values of the nodes of the planetary
gearbox of the seed-removing pipe were determined.
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