Design and Calculation of Solar Tracking System Gearbox

This article discusses the design and calculation of gearbox for a solar tracking system. It covers gear calculations, forces on gears, speed and number of teeth on gears, bending stress on gears, and references. The article is relevant for students studying solar energy, mechanical engineering, and related courses. Course code, course name, and college/university are not mentioned.

The solar tracking system can be shown as-
The gear box system for the motor can be designed as-
Gear calculations
Calculations for gear A-
Ft(A) = 2τ A / Dp
Dp=Z p∗m
¿ 18∗3
¿ 54 mm
= 2 x 49.75 Nm
0.053m
= 1845.6 N
ϕn= 20 ̊ normal pressure angle
Ψ = 15 ̊ helix angle
ϕt = tan−1 (tan ϕn¿¿ cos Ψ )¿
= tan−1 ( tan 20 ¿̊  /cos 15̊  )¿
= 20.65 ̊ transverse pitch angle
1

Fr(A) = Ft(A) tan ϕt
= 1842 tan 20.65
= 695 N
Fa(A) = Ft(A) tan Ψ
= 1842 tan15
= 494 N
Forces on gear B-
Ft(B) = 2τ B / Dg
Dg=ZB∗m=45∗3=135 mm
= 2 x 151.43 Nm
0.135 m
= 2244 N
Fr(B) = Ft(B) tan ϕt
= 2244 tan 20.65
= 846 N
Fa(B) = Ft(B) tan Ψ
= 2244 tan15
= 602 N
Forces on gear C-
Ft(C) = 2τC / Dp
2

Dp=Z p∗m=18∗3=54 mm
= 2 x 151.43 Nm
0.054 m
= 5608 N
Fr(C) = Ft(C) tanϕt
= 5608 tan 20.65
= 2114 N
Fa(C) = Ft(C) tan Ψ
= 5608 tan15
= 1503 N
Forces on gear D-
Ft(D) = 2τ D / Dg
Dg=ZD∗m=52∗3=156 mm
= 2 x 357.99 Nm
0.156 m
= 4589 N
Fr(D) = Ft(D) tan ϕt
= 4589 tan 20.65
= 1730 N
Fa(D) = Ft(D) tan Ψ
= 4589 tan15
= 1230 N
3

Calculations regarding the speed and number of teeth on the gears
Uh = U
Ul
U = 1460
156.16
U = 9.34
Where:
Ul =¿ Reduction ratio for second or low speed stage
This is also given as:
Ul =0.88 √ U
So high speed stage reduction ratio becomes
Uh = U
0.88 √U
¿ 12.98
0.88 √12.98
¿ 4.094
Given the gear ratio the number of teeth for gear 1 and 2 can be determined. The pinion, gear 1,
should have its number of teeth minimized to reduce the overall size of the gearbox. The number
of teeth is assumed to be 18 as it is the minimum number required to avoid undercutting for spur
gears. If helical gears are selected then with further calculations the minimum number of teeth
may be reduced.
Z1 =¿ Number of teeth in gear 1
¿ 18
Z2 =¿ Number of teeth in gear 2
¿ Z1 Uh ¿ 18 × 4.094 ¿ 73.69 ¿ 74
4

Altered high speed reduction ratio
Uh =74
18 ¿ 4.11
High Speed Uh = U
Ul
= 9.34
2.362 = 3.95
Low Speed Ul = 0.88 √U = 0.88 √9.34 = 2.68
Input Shaft Speed-
np = nA = 1460 rpm
Intermediate Shaft Speed-
nBC = nA
U AB
= nA
Uh
= 1460
3.95 = 369.62 rpm
Output Shaft Speed-
nD = nBC
UCD
= nBC
Ul
= 369.62
2.68 = 137.91 rpm
Input Shaft Speed-
ω A = 1460 π
30 = 152.81 rad/s
Intermediate Shaft Speed-
5

ωBC = 369.62 π
30 = 38.68 rad/s
Output Shaft Speed-
ωD = 137.91 π
30 = 14.43 rad/s
Input Shaft Torque-
τ A = Pn 1
ω A
=
7500 W
152.81 rad
s
= 49.08 Nm
Intermediate Shaft Torque-
τ BC = Pn 1
ωBC
=
7500 W
49.08 rad
s
= 152.81 Nm
Output Shaft Torque-
τ D = Pn 1
ωD
=
7500 W
14.43 rad
s
= 519.75 Nm
Calculations for the bending stress on the gear
 vt = πDnp / (60 x 1000)
= π x 54 x 1460 / 60000
= 4.125 m/s
Kv = 50 / [50 + √ 137.91∗vt ]
6

= 50/ [50 + √137.91× 4.125 ]
= 0.677
C pf = F
10 d - 0.038 + 0.0005d where F = face width
= 40
10× 52.20 - 0.038 + 0.0005(52.20) d = diametrical pitch
= 0.070
Km = 1 + C pf + Cma
= 1 + 0.070 + 0.164
= 1.32
St = (Ft. Pd / b. J).Ko.Ks.Km.K B.Kv
where Ft = 1845 N
Pd = 0.35
b = 40 mm
J = 0.5
Ko = 1.5
Ks = 1.0
Km = 1.25
K B = 1.0
Kv = 0.65
St = (Ft. Pd / b. J).Ko.Ks.Km.K B.Kv
= ((1843×0.35)/(40×0.5))×1.5×1×1.25×1×0.677
= 40.94 MPa
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References
Kalogirou, S. A. (1996). Design and construction of a one-axis sun-tracking system. Solar
Energy, 57(6), 465-469.
Ponniran, A., Hashim, A., & Joret, A. (2011). A design of low power single axis solar tracking
system regardless of motor speed. International Journal of Integrated Engineering, 3(2).
Khan, M. T. A., Tanzil, S. S., Rahman, R., & Alam, S. S. (2010, December). Design and
construction of an automatic solar tracking system. In Electrical and Computer Engineering
(ICECE), 2010 International Conference on (pp. 326-329). IEEE.
Tudorache, T., & Kreindler, L. (2010). Design of a solar tracker system for PV power
plants. Acta Polytechnica Hungarica, 7(1), 23-39.
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