ECES 402
Machine Elements Design Project
Gear-box Design Project
Author Name:
Contents
Introduction ........................................................................................................................................................ 3
Analytical Analsis .............................................................................................................................................. 4
MILESTONE I ............................................................................................................................................. 4
Helical Angle (ψ)........................................................................................................................................ 5
Pinion Pitch Diameter (dp).......................................................................................................................... 5
Gear Pitch Diameter (dg) ............................................................................................................................ 5
Gear ratio (e): ............................................................................................................................................. 5
Diametral Pitch (transverse Pt and normal Pn)............................................................................................ 5
MILESTONE II: .......................................................................................................................................... 5
Transmitted Load (Wt)................................................................................................................................ 5
Required Engine HP (H) - Using Pitch Line Velocity (V) ......................................................................... 5
Power with 20% losses............................................................................................................................... 6
Engine Cruise RPM .................................................................................................................................... 6
Gear Tooth Bending Stress (σb) - Using Milled Velocity Factor (Kv) ........................................................ 6
Gear Contact Stress (σc) - Using Elastic Coefficient (Cp) and r1 and r2 ..................................................... 6
Max Moment (Ma) - Using R ..................................................................................................................... 6
Pinion Shaft Torque (Tm-pinion) and Gear Shaft Torque (Tm-gear) .................................................................. 7
Pinion Shaft Diameter (dpinion-shaft) - Using A and B for Pinion (K=1) ....................................................... 7
Gear Shaft Diameter (dgear-shaft) - Using A and B for Gear (K=1) ............................................................... 7
MILESTONE III: ......................................................................................................................................... 7
Chosen Standard Size Shaft Diameters (dpreferred size)................................................................................... 8
Line Shaft Diameter, ABS Formula, (D) .................................................................................................... 8
Critical Speed of Pinion Shaft, (ωcrit-p) - Using Max Deflection for Pinion Shaft (ymax) ............................ 8
Critical Speed of Gear Shaft, (ωcrit-g) - Using Max Deflection for Gear Shaft (ymax) ................................. 8
MILESTONE IV: ......................................................................................................................................... 8
Bearing Design Load (FD) .......................................................................................................................... 9
Bearing Catalog Load Rating (C10) - Using a for Roller Bearings ............................................................. 9
Technical Drawings ......................................................................................................................................... 11
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Gear-box Design Project
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Engine and Assembly Specification ................................................................................................................. 12
Engine Dimensions and Weight ................................................................................................................ 12
Engine Specifications ................................................................................................................................. 13
Conclusion ....................................................................................................................................................... 13
References: ....................................................................................................................................................... 14
Appendices: ...................................................................................................................................................... 15
Appendix A ................................................................................................................................................. 15
Drive bearing particulars. ......................................................................................................................... 15
Appendix B.................................................................................................................................................. 16
Pinion bearing particulars. ........................................................................................................................ 16
Appendix C ................................................................................................................................................. 17
Marine Engine Particulars ........................................................................................................................ 17
Table of Figures
Figure 1 Schematic of Engine- Gearbox Assembly .......................................................................................... 4
Figure 2: SEALMASTER Pillow Block Bearing: 4 7/16 in Bore, 4 Holes, 4 3/4 in Shaft................................ 9
Figure 3: MOLINE BEARING Pillow Block Bearing: 3 7/16 in Bore, 3 3/4 in Shaft .................................... 10
Figure 4: Gear Set Drawing ............................................................................................................................. 11
Figure 5: Gearbox Assembly Drawing ............................................................................................................ 11
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Introduction
Maritime vessels propel through water via a spinning shaft-mounted propeller. In larger vessels, the emphasis
shifts from speed to torque for the propeller shaft. However, the speed of the shaft from a medium-speed
engine is typically fast, lacking in torque. To address this, a reduction gear is employed. This gear transmits
force from the engine drive shaft to a larger gear connected to the propeller shaft, reducing speed while
increasing torque.
This project focuses on designing a reduction gear for a training ship, considering specific design factors
tailored to the ship's layout and functionality:
 The propeller must spin at 300 RPM with 270,000 in × lbf of torque at maximum speed.
 A single reduction gear set consists of helical gears mounted on a shaft rotating on bearings.
 A 20% horsepower loss from the engine to the propeller is assumed.
 The gearbox assembly, housing the reduction gear, is within a maximum dimension of 6 × 6 × 6 ft.
The project progresses through four milestones:
1) Initial Concept Design: Engineers estimate gear ratio, pitch, pressure angle, and engine horsepower
range. Research is conducted on potential engine candidates, accompanied by a preliminary sketch.
2) Load Calculation: Engineers determine transmitted load, required engine horsepower, bending
stress, contact stress, maximum alternating moment, minimum shaft diameter, minimum line
shafting, and lowest critical speed using an Excel spreadsheet.
3) Finalization of Shaft and Gear Parameters: Shaft and gear diameters and materials are finalized. An
assembly plan and technical drawings are created.
4) Bearing Selection and Engine Specification: Bearings are selected through appropriate calculations,
and the main engine specifications are finalized. These milestones lead to the final design plan for
the reduction gear.
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Figure 1 Schematic of Engine- Gearbox Assembly
Analytical Analysis:
This project was divided into four main milestones, each serving a distinct purpose in the design
process. The first milestone focused on initial dimension estimates. In the second milestone, we tested
these initial values and made necessary corrections. The third milestone involved finalizing the
gearbox designs. Lastly, in the fourth milestone, we determined the bearings to be used and calculated
the system's functionality from the engine to the gearbox and bearings. Here, we will discuss those
milestones one by one in detail.
MILESTONE I
In the first milestone, we drafted an initial design and made estimations regarding the dimensions and
properties required for the gears. These estimations were informed by research conducted on existing
propulsion engines. This gave us a starting point that we could work with in later milestones.
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Helical Angle (ψ)
ψ = 20 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
Pinion Pitch Diameter (dp)
𝑑𝑝 = 10𝑖𝑛
Gear Pitch Diameter (dg)
𝑑𝑔 = 60𝑖𝑛
Gear ratio (e):
𝑒=
𝑑𝑔
60 𝑖𝑛𝑐ℎ𝑒𝑠
=
=6
𝑑𝑝
10 𝑖𝑛𝑐ℎ𝑒𝑠
Diametral Pitch (transverse Pt and normal Pn)
𝑃𝑡 =
𝑁𝑝
18 𝑖𝑛𝑐ℎ𝑒𝑠
𝑡𝑒𝑒𝑡ℎ
=
= 1.8
𝑑𝑝
10 𝑖𝑛
𝑖𝑛
Pn = π(Pt ) = π(1.8) = 5.65
teeth
in
MILESTONE II:
For our second milestone, we dove into Excel to crunch some numbers. We ran various equations to see how
our initial values stacked up. This let us figure out what was working and what needed tweaking. We tackled
everything from transmitted load to minimum shaft diameter. Once we had all the data, we neatly laid it out in
a Word document for a thorough review.
Transmitted Load (Wt)
𝑇 −𝑝
𝑊𝑡 = ( 𝑚
𝑑𝑔 /2
)=
270,000 𝑖𝑛 × 𝑙𝑏𝑓
60
𝑖𝑛
2
= 9,000 𝑙𝑏𝑠
Required Engine HP (H) - Using Pitch Line Velocity (V)
V=
π× np ×dg
12
𝑊 ×𝑉
=
𝑡
𝐻 = 33000
=
π×300 rpm×60 inches
12
in
ft
9,000×4712.38898
33000
5
ft
= 4712.38898 min
= 1285.196995hp
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Power with 20% losses
𝐻𝑤𝑖𝑡ℎ−𝑙𝑜𝑠𝑠𝑒𝑠 = 𝐻 × 1.2 = 1285.19 × 1.2 =1542.236394hp
Engine Cruise RPM
𝑛𝐸𝑛𝑔𝑖𝑛𝑒 = 𝑛𝑃 × 𝑒 =300 𝑅𝑃𝑀 × 6 = 1800 𝑅𝑃𝑀
Gear Tooth Bending Stress (σb) - Using Milled Velocity Factor (Kv)
𝐾𝑣 =
𝜎𝑏 =
1200 + 𝑉
1200 + 4712.38898
=
= 4.93
1200
1200
𝐾𝑉 × 𝑊𝑡 × 𝑃𝑡 (4.93)(9,000)(1.8)
=
= 4957.59𝑝𝑠𝑖
(50)(0 ⋅ 322)
𝐹×𝑌
Gear Contact Stress (σc) - Using Elastic Coefficient (Cp) and r1 and r2
𝐶𝑝 = 2300√𝑝𝑠𝑖 𝑓𝑟𝑜𝑚 𝑇𝑎𝑏𝑙𝑒 18 − 4
𝑑𝑝 × sin 𝜓 (10)(sin 20)
=
= 1.71𝑖𝑛
2
2
𝑑𝑔 × sin 𝜓 (60)(sin 20)
𝑟2 =
=
= 10.26𝑖𝑛
2
2
𝑟1 =
1⁄
2
1
(4.93)(9000) 1
𝐾𝑉 × 𝑊𝑡 1 1 ⁄2
1
𝜎𝑐 = −𝐶𝑝 [
( + )] = −2300 [
(
+
)]
𝐹 𝑐𝑜𝑠 𝜃 𝑟1 𝑟2
50 𝑐𝑜𝑠(20) 1.71 10.26
Max Moment (Ma) - Using R
𝑅=
𝑀𝑎 =
𝑊𝑡
9000
=
= 9577.60𝑙𝑏𝑠
cos 𝜓 cos(20)
𝑅 × 𝐹 (9577.60)(50)
=
= 59860.00𝑝𝑠𝑖
8
8
6
= −58361.25𝑝𝑠𝑖
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Pinion Shaft Torque (Tm-pinion) and Gear Shaft Torque (Tm-gear)
𝑇𝑚−𝑝𝑖𝑛𝑖𝑜𝑛 = 𝑊𝑡 × 𝑟𝑝 = (9000)(5) = 45,000 𝑖𝑛 𝑙𝑏𝑠
𝑇𝑚−𝑔𝑒𝑎𝑟 = 𝑊𝑡 × 𝑟𝑔 = (9000)(3027) = 270000 𝑖𝑛 𝑙𝑏𝑠
Pinion Shaft Diameter (dpinion-shaft) - Using A and B for Pinion (K=1)
2
𝐴 = √4(𝐾𝑓 )(𝑀𝑎 ) = √4(1)(59860)2 = 119720.00
2
𝐵𝑝𝑖𝑛𝑖𝑜𝑛 = √3 (𝐾𝑓𝑠 𝑇𝑚−𝑝𝑖𝑛𝑖𝑜𝑛 ) = √3(1)(45000)2 = 77, 942. 29
1
16𝑛 𝐴 𝐵𝑝𝑖𝑛𝑖𝑜𝑛 3
𝑑𝑝𝑖𝑛𝑖𝑜𝑛 = ⌊
( +
)⌋
𝜋 𝑠𝑒
𝑠𝑢𝑡
1
16(3) 119720.00 77, 942. 2 3
𝑑𝑝𝑖𝑛𝑖𝑜𝑛 = ⌊
(
+
)⌋ = 2.97𝑖𝑛
𝜋
92,950
185,900
Gear Shaft Diameter (dgear-shaft) - Using A and B for Gear (K=1)
2
𝐴 = √4(𝐾𝑓 𝑀𝑎 ) = √4(1)(79813.33)2 = 119720.00
2
𝐵𝑔𝑒𝑎𝑟 = √3 (𝐾𝑓𝑠 𝑇𝑚−𝑔𝑒𝑎𝑟 ) = √3(1)(27000)2 = 467, 653. 718
1
16𝑛 𝐴 𝐵𝑔𝑒𝑎𝑟 3
𝑑𝑔𝑒𝑎𝑟 = ⌊
( +
)⌋
𝜋 𝑠𝑒
𝑠𝑢𝑡
1
16(3) 119720.00 467,653.72 3
𝑑𝑔𝑒𝑎𝑟 = ⌊
(
+
)⌋ = 3.87𝑖𝑛
𝜋
92,950
185,900
MILESTONE III:
In the third milestone, we utilized insights gained from milestone two to determine the ultimate shaft diameter
and select the material for our gearbox. Additionally, we outlined a comprehensive strategy for assembling all
requisite gearbox components. With our definitive plans in place, we proceeded to create a detailed technical
drawing to visually represent our design and ensure precise alignment of all dimensions.
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Chosen Standard Size Shaft Diameters (dpreferred size)
7
𝑖𝑛
16
7
𝑑𝑝𝑖𝑛𝑖𝑜𝑛−𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 = 4 𝑖𝑛
16
𝑑𝑝𝑖𝑛𝑖𝑜𝑛−𝑝𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 = 3
Line Shaft Diameter, ABS Formula, (D)
𝐻
𝐶1
1542.236394
3.695
𝐷 = 100𝐾√ (
) = (100)(1)√
(
) = 0. 95316 𝑖𝑛
𝑅 𝑈𝑇𝑆 + 𝐶
300
185,900 + 23,180
Critical Speed of Pinion Shaft, (ωcrit-p) - Using Max Deflection for Pinion Shaft (ymax)
5 × 𝑊𝑡 × 𝐹 3
𝑦𝑚𝑎𝑥 =
=
384 × 𝐸 × 𝐼
5 × 𝑊𝑡 × 𝐹 3
5 × 9000 × (50)3
=
= 0.1322𝑖𝑛
4
𝜋(2.97)4
𝜋 𝑑𝑝𝑖𝑛𝑖𝑜𝑛
(384)(29,000,000)
[
]
384 × 𝐸 × [ 64 ]
64
386 𝑖𝑛⁄ 2 60
60
𝑠 ) ( ) = 515.90𝑅𝑃𝑀
√
𝜔𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙−𝑝 = (√
)( ) = (
𝑦𝑚𝑎𝑥 2𝜋
0.1322𝑖𝑛 2𝜋
𝑔
Critical Speed of Gear Shaft, (ωcrit-g) - Using Max Deflection for Gear Shaft (ymax)
𝑦𝑚𝑎𝑥 =
5 × 𝑊𝑡 × 𝐹 3
=
384 × 𝐸 × 𝐼
5 × 𝑊𝑡 × 𝐹 3
5 × 10000 × (60)3
=
= 0. 04587 𝑖𝑛
𝜋(3.87)4
𝜋 𝑑𝑔4
(384)(29,000,000)
[ 64 ]
384 × 𝐸 × [
]
64
386 𝑖𝑛⁄ 2
𝑔
60
𝑠 ) (60 ) = 875.94 𝑅𝑃𝑀
𝜔𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙−𝑔 = (√
) ( ) = (√
𝑦𝑚𝑎𝑥 2𝜋
0.04587 𝑖𝑛 2𝜋
MILESTONE IV:
With the gearbox design complete, our attention turned to milestone 4, which focused on selecting the optimal
bearings and propulsion engine for our system. We began by calculating the radial load and catalog load rating
required for our bearings, considering the specific demands of our application. Next, we searched online
manufacturer catalogs to identify a suitable bearing that met our calculated requirements. Additionally, we
verified that our chosen engine met the necessary horsepower and rpm specifications. Finally, we performed
comprehensive
calculations
to
ensure
seamless
8
integration
and
functionality
across
all
Gear-box Design Project
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components of our design.
Bearing Design Load (FD)
𝐹𝐷 =
𝑅 9577.60 𝑙𝑏𝑠
=
= 4788.80𝑙𝑏𝑠
2
2
Bearing Catalog Load Rating (C10) - Using a for Roller Bearings
3
1
𝐿𝐷 × 𝑛𝐷 × 60 𝑎
10,000 ℎ𝑜𝑢𝑟𝑠 × 300 𝑅𝑃𝑀 × 60 10
𝐶 = 𝐹𝐷 (
)
=
4788.80
(
) = 22740.94𝑙𝑏𝑓
106
106
The drive shaft bearing selected for our design is the SEALMASTER tapered roller bearing, boasting
a robust set of specifications.
Figure 2: SEALMASTER Pillow Block Bearing: 4 7/16 in Bore, 4 Holes, 4 3/4 in Shaft
Bore diameter
4 7/16 inches (4.4375 inches)
Width
6.75in
Dynamic load capacities
25,750 lbf
Static radial load capacities
13,100 lbf
Material
high-strength steel alloy
Housing Material
Cast iron
Moreover, a comprehensive list of specifications can be found in Appendix A for reference.
The bearing chosen for the drive shaft was a MOLINE spherical roller bearing, boasting a robust set
of specifications.
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Figure 3: MOLINE BEARING Pillow Block Bearing: 3 7/16 in Bore, 3 3/4 in Shaft
Bore diameter
3 7/16 (3.4375) inches
Width
4.562in
Dynamic load capacities
56,900 lbf
Static radial load capacities
76,400 lbf
Material
high-strength steel alloy
Housing material
Cast iron
Moreover, a comprehensive list of specifications can be found in Appendix B for reference.
Factor of Safety:
𝐹𝑆 =
𝑈𝑇𝑆
𝜎𝑐𝑜𝑛𝑡𝑎𝑐𝑡
=
185,900
= 3.18
58361.25
Force on the shaft = 9577.60lbf
9577.60
= 319. 75 𝑝𝑠𝑖
4.4375 × 6.75
10,641.77772
𝜎𝑃𝑖𝑛𝑖𝑜𝑛 =
= 610.74 𝑝𝑠𝑖
3.4375 × 4.562
These yield stresses can be used to calculate the safety factor.
𝜎𝐷𝑟𝑖𝑣𝑒 =
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Technical Drawings
Figure 4: Gear Set Drawing
Figure 5: Gearbox Assembly Drawing
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Engine and Assembly Specification
● We've selected 4140 steel for both our gears and shafting, ensuring exceptional strength
and durability.
● Our drive shaft will have a diameter of 3 7/16 inches, while the propeller shaft will be
slightly larger at 4 7/16 inches.
● The bull gear will boast an impressive 54-inch diameter, paired with a 9-inch pinion gear
for efficient power transmission.
● To secure the gears to their respective shafts, we'll employ a shrink fit method. This
involves chilling the shafts in cold water for 10 minutes to reduce their diameter, allowing
the gear to slide on smoothly.
● Once the gears are in place, we'll add the bearings, which may require gentle heating to
ensure a snug fit.
● Next, we'll carefully align the gears and position them with the shafting and bearings,
ensuring seamless integration.
● With the gears properly aligned, we can connect the shafts to the engine and propeller,
ready to tackle oil spills with ease.
● Finally, we'll encase the entire assembly in a protective casing, safeguarding our bot's vital
components.
When selecting an engine for our training ship's gearbox, two crucial requirements emerged: power
and speed. The propeller needed to operate at 300 RPM and produce a torque of 270,000 in*lbs.
Using a gear ratio of 6, we determined that the engine would need to run at 1,800 RPM. Considering
a 20% loss from the engine to the propeller, our calculations revealed a final power requirement of
1,543 HP. To meet these specifications, we chose the Cummings KTA50-M2 engine, a robust V-16
cylinder, continuous, 4-stroke diesel engine capable of producing 1,600 BHP at 1,800 RPM. This
engine satisfies both power and speed requirements, and its dimensions and specifications are as
follows:
Engine Dimensions and Weight
Overall Length
104 inches
Overall Width
62 inches
Overall Height
89 inches
Overall Weight
11,389 lbs
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Engine Specifications
Configuration
V-16 cylinder, 4-stroke diesel
Aspiration
Turbocharged/Aftercooled
Displacement
3,068 in³
Bore & Stroke
6.25 x 6.25 in
kW
1,193
MHP
1,622
BHP
1,600
Speed
1,800
Conclusion
In this challenging project, we undertook the complex task of designing a robust and efficient gearbox
for a marine propulsion plant, a critical component that would enable vessels to navigate the open
waters with precision, reliability, and sustainability. Our mission was to create a seamless integration
of gears, propulsion engine, and shaft bearings, ensuring a harmonious operation that could withstand
the harsh marine environment, including corrosive seawater, intense pressures, and extreme
temperatures. Through meticulous calculations and rigorous analysis, we determined the forces that
would be exerted on our gears, considering the intense stresses and strains of continuous operation,
as well as the dynamic interactions between the gears, shafts, and bearings. With these calculations,
we precision-crafted the dimensions and materials of the gears, ensuring optimal performance,
durability, and resistance to fatigue and corrosion.
As we worked on this project, we gained valuable experience in using Excel for our calculations,
initially encountering errors and difficulties but eventually mastering its capabilities, making
calculations a breeze. Moreover, we developed our technical drawing skills, utilizing AutoCAD to
bring our final designs to life in stunning detail and precision. We created precise and detailed
drawings of our gearbox design, showcasing our creativity, innovation, and attention to detail. With
each milestone achieved, we gained confidence in our abilities, and our collective efforts culminated
in the successful design of a gearbox for a marine propulsion plant.
This project taught us technical skills, collaboration, perseverance, and creative problem-solving. We
learned to embrace challenges, think critically, and innovate solutions, producing a top-notch gearbox
design for marine propulsion. Through this journey, we grew as engineers and individuals, equipped
to tackle complex projects, and make a meaningful impact in marine engineering.
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References:
● CCEC K50-M2000 Marine Engine,
https://ccec-engine.com/k50-m2000-marine-engine/
●
Shigley’s Mechanical Engineering Design, 11th Edition
https://www.mheducation.co.uk/shigley-s-mechanical-engineering-design-11th-edition-siunits-9789813158986-emea-group
● SEALMASTER Pillow Block Bearing
https://www.grainger.com/product/SEALMASTER-Pillow-Block-Bearing-4-7-16-44A509
● MOLINE BEARING Pillow Block Bearing
https://www.grainger.com/product/MOLINE-BEARING-Pillow-Block-Bearing-3-7-1660JR02
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Appendices:
Appendix A
Drive bearing particulars.
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Appendix B
Pinion bearing particulars.
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Appendix C
Marine Engine Particulars
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