Mechanical design and verification of a helical gearbox developed as part of the Fundamentals of Machine Design course at Politecnico di Torino.
The project covers the mechanical verification workflow of the gearbox, including gear-force calculations, shaft loading, static and fatigue verification, gear-tooth strength analysis, and rolling-bearing life assessment.
The objective of this project was to evaluate the structural integrity and mechanical performance of the main components of a helical gearbox.
The analysis includes:
- Gear torque and force calculations
- Shaft support reactions
- Internal forces and bending moments
- Torsional loading
- Shaft static stress verification
- Shaft fatigue verification
- Stress concentration effects
- Fatigue-limit correction factors
- Haigh-diagram fatigue assessment
- Gear-tooth bending verification
- Gear contact and pitting verification
- Rolling-bearing equivalent loads
- Bearing fatigue-life estimation
- Bearing static safety verification
The complete derivations and detailed calculations are available in the final project report and the supporting handwritten calculation notes.
Input Power and Speed
│
▼
Torque Calculation
│
▼
Gear Forces
│
▼
Shaft Support Reactions
│
▼
Internal Forces and Moments
│
▼
Shaft Stress Analysis
│
├──────────────► Static Verification
│
└──────────────► Fatigue Verification
│
▼
Haigh Diagrams
Gear Loads ───────────► Gear Tooth Verification
│
├── Bending
└── Contact / Pitting
Shaft Reactions ──────► Bearing Analysis
│
├── Rating Life
└── Static Safety
The mechanical analysis starts from the transmitted power and rotational speed.
| Parameter | Value |
|---|---|
| Input power | 36 kW |
| Input torque | 229.18 N·m |
| Output torque | 2062.64 N·m |
| Gear pair 1 tangential force | 9223.9 N |
| Gear pair 1 radial force | 3475.66 N |
| Gear pair 1 axial force | 2471.53 N |
| Gear pair 2 tangential force | 15812.75 N |
| Gear pair 2 radial force | 5956.23 N |
| Gear pair 2 axial force | 4237 N |
The tangential, radial, and axial gear forces were used to determine the bearing reactions and internal shaft loading.
Shaft A2 was selected as the critical shaft for detailed structural verification.
The shaft analysis includes:
- Support reaction forces
- Internal axial forces
- Bending moments about the principal axes
- Resultant bending moment
- Torsional moment
- Normal stress
- Bending stress
- Torsional shear stress
- Equivalent stress
- Static safety factor
For the static verification, four relevant shaft cross-sections were evaluated: V1, V2, V3, and V4.
Section V4 was identified as the most critical section for static loading.
| Cross-section | Equivalent stress | Static safety factor |
|---|---|---|
| V1 | 28.04 MPa | ≈ 33.16 |
| V2 | 46.93 MPa | ≈ 19.81 |
| V3 | 60.31 MPa | ≈ 15.42 |
| V4 | 75.93 MPa | ≈ 12.24 |
The minimum calculated static safety factor was therefore approximately 12.24.
Fatigue verification was performed by separating the mean and alternating stress components and accounting for geometric stress concentration effects.
The fatigue analysis includes:
- Mean and alternating stresses
- Stress concentration factors
- Fatigue notch factors
- Surface-finish correction
- Size correction
- Equivalent mean stress
- Equivalent alternating stress
- Haigh-diagram verification
The surface-finish correction factor used in the analysis was:
CF = 0.955
The calculated fatigue safety factors were:
| Cross-section | Fatigue safety factor |
|---|---|
| V1 | ≈ 13.59 |
| V2 | ≈ 5.10 |
| V3 | ≈ 3.97 |
| V4 | ≈ 5.18 |
The most critical section for fatigue was V3, with a minimum fatigue safety factor of approximately 3.97.
The gear-tooth verification focused on pinion G3, which was selected as the most critical gear for the analysis.
Two principal failure mechanisms were investigated:
- Tooth-root bending fatigue
- Surface contact and pitting fatigue
The bending analysis considered:
- Face width
- Overload factor
- Rim-thickness factor
- Dynamic factor
- Load-distribution factor
- Size factor
- Bending-strength geometry factor
- Stress-cycle life factor
- Temperature factor
- Reliability factor
Some of the main calculated parameters are:
| Parameter | Value |
|---|---|
| Face width | 56 mm |
| Overload factor K0 | 1 |
| Rim-thickness factor KB | 1 |
| Dynamic factor Kv | 1.17 |
| Load-distribution factor KH | 1.205 |
| Size factor KS | 1.095 |
| Bending geometry factor YJ | 0.4743 |
The calculated maximum tooth bending stress was approximately:
221.95 MPa
with a corresponding bending safety factor of approximately:
3.78
A contact-stress verification was performed to evaluate the resistance of the gear teeth to surface fatigue and pitting.
The calculated maximum contact stress was approximately:
70.25 MPa
The corresponding wear/contact safety factor was approximately:
19.83
The gearbox contains six analyzed bearing positions:
A, B, C, D, E, and F
The bearing analysis includes:
- Radial bearing loads
- Axial bearing loads
- Equivalent dynamic load
- Equivalent static load
- Dynamic load rating
- Static load rating
- Lubricant selection
- Viscosity ratio
- Life-correction factors
- Corrected rating life
- Static safety verification
| Position | Bearing |
|---|---|
| A | NU 206 ECP |
| B | 30206 DF |
| C | NU 209 ECP |
| D | 32011 X/DF |
| E | NU 2210 ECP |
| F | 32011 X/DF |
For the analyzed operating conditions, the study identified ISO VG 220 lubricant.
The bearing analysis evaluates the selected bearings in terms of equivalent loading, corrected rating life, and static safety under the considered operating conditions.
| Bearing position | Static safety factor |
|---|---|
| A | ≈ 24.96 |
| B | ≈ 7.71 |
| C | ≈ 19.35 |
| D | ≈ 14.98 |
| E | ≈ 17.40 |
| F | ≈ 8.50 |
| Analysis | Result |
|---|---|
| Input power | 36 kW |
| Input torque | 229.18 N·m |
| Output torque | 2062.64 N·m |
| Critical shaft | A2 |
| Critical static section | V4 |
| Maximum equivalent shaft stress | ≈ 75.93 MPa |
| Minimum shaft static safety factor | ≈ 12.24 |
| Critical fatigue section | V3 |
| Minimum shaft fatigue safety factor | ≈ 3.97 |
| Critical gear | G3 |
| Maximum gear bending stress | ≈ 221.95 MPa |
| Gear bending safety factor | ≈ 3.78 |
| Maximum gear contact stress | ≈ 70.25 MPa |
| Gear contact safety factor | ≈ 19.83 |
The project applies fundamental machine-design methods including:
- Static equilibrium
- Free-body diagrams
- Shaft reaction calculations
- Internal force and moment diagrams
- Normal stress analysis
- Bending stress analysis
- Torsional stress analysis
- Equivalent stress calculation
- Static safety-factor calculation
- Fatigue stress decomposition
- Stress concentration analysis
- Fatigue-strength correction
- Haigh-diagram analysis
- Gear-tooth bending verification
- Hertzian contact verification
- Rolling-bearing life calculations
- Bearing static-load verification
gearbox-machine-design-analysis/
│
├── README.md
│
├── report/
│ ├── README.md
│ └── gearbox_machine_design_report.pdf
│
├── calculations/
│ ├── README.md
│ └── handwritten_engineering_calculations.pdf
│
└── figures/
├── README.md
├── shaft_A2_internal_loads.png
├── shaft_fatigue_haigh_diagrams.png
├── gear_tooth_bending_verification.png
└── bearing_life_summary.png
The complete final project report contains the detailed calculations, verification procedures, diagrams, tables, and final engineering results.
View the Final Gearbox Design Report
The handwritten calculation notes document the intermediate engineering derivations performed during the development of the project.
View the Handwritten Engineering Calculations
Note: The final project report should be considered the authoritative source for final numerical results. The handwritten notes are included as supporting working material and may contain intermediate calculations or values that were later revised.
- Mohammad Nour Edeen
Course: Fundamentals of Machine Design
Course Code: 02SXJJM
Academic Year: 2023/2024
Institution: Politecnico di Torino
Professor: Nicola Bosso
Teaching Staff: Matteo Magelli and Francesco Mocera
Project Date: January 2024
machine-design gearbox helical-gears shaft-design fatigue-analysis stress-analysis gear-design bearing-life mechanical-engineering politecnico-di-torino