Absolutely! Below is a structured **gearbox design process** for your **three-stage, compound reverted gear train** based on your provided specs, with each section outlined as per your requirements. You’ll see the **key calculations, design steps, and recommendations** that would guide both hand-calculation/Excel/Matlab AND CAD work (AutoCAD/Inventor/SolidWorks). --- ## 1. **Power & Torque Requirements** ### **Given:** - Power (**P**): 20 hp = 14.92 kW - Input speed (**n₁**): 1750 rpm - Output speed (**n₃**): 80 rpm - Stages: 3 (compound, reverted) - Shafts: Input, intermediate, output (inline) - Duty: Low shock, occasional moderate - Max gearbox size: 20”×20” base, 30” height --- ### **A. Power Transmission** \[ P = 20 \text{ hp} = 14.92 \text{ kW} \] ### **B. Torque Calculations** **Input Shaft Torque:** \[ T_{\text{in}} = \frac{P \times 5252}{n_1} = \frac{20 \times 5252}{1750} = \boxed{60.03~\text{lb-ft}} \] \[ = 60.03 \times 1.356 = \boxed{81.45~\text{Nm}} \] **Output Shaft Torque:** \[ n_3 = 80~\text{rpm} \] \[ T_{\text{out}} = \frac{P \times 5252}{n_3} = \frac{20 \times 5252}{80} = \boxed{1313~\text{lb-ft}} \] \[ = 1313 \times 1.356 = \boxed{1781~\text{Nm}} \] --- ## 2. **Shaft Layout** - **Inline input/output shafts**: Input and output are co-axial. - **Intermediate shaft**: Offset, supports compound gears. - **Three stages**: Distribute speed reduction evenly. ### **Speed Ratio (Total):** \[ \text{Total Ratio} = \frac{n_1}{n_3} = \frac{1750}{80} = \boxed{21.88} \] - For three equal stages: \[ \text{Stage Ratio} = (21.88)^{1/3} = \boxed{2.78:1} \] --- ## 3. **Force Analysis** - **Gear forces**: Use tangential force at each gear mesh. - **Tangential (Fₜ)**: \[ F_t = \frac{2T}{d} \] - **Radial (Fᵣ) and Axial (Fₐ)**: For spur gears, axial force = 0. --- ## 4. **Shaft Material Selection** - **Standard**: AISI 1045 (medium carbon steel), AISI 4140 (alloy steel), or EN8. For moderate load, 1045 is often enough. - **Yield strength**: ~350 MPa (AISI 1045, normalized). --- ## 5. **Shaft Design for Stress** ### **A. Shaft Diameter Estimate (for bending & torsion)** Assume combined bending and torsion: \[ d = \left[ \frac{16}{\pi \tau_{allow}} \sqrt{M^2 + T^2} \right]^{1/3} \] - **Allowable shear stress (\(\tau_{allow}\))**: For 1045 steel, use 40% of yield, so: \[ \tau_{allow} = 0.4 \times 350 = 140~\text{MPa} \] - **Worst-case (output shaft):** - \( T_{\text{out}} = 1781~\text{Nm} = 1,781,000~\text{Nmm} \) - Assume negligible bending for initial estimate (conservative). \[ d = \left[ \frac{16 \times 1,781,000}{\pi \times 140 \times 10^6} \right]^{1/3} \] \[ d = \left[ \frac{28,496,000}{439,822,972} \right]^{1/3} \] \[ = (0.0648)^{1/3} \approx 0.402~\text{m} = 40.2~\text{mm} \] - Add 25% for stress concentrations, keyways, etc. → **final shaft diameter: 50 mm** (round up to standard size). --- ## 6. **Shaft Design for Deflection** - **Deflection**: Should not exceed 0.0015 × shaft length. - Use beam formulas (Excel/Matlab) for actual gear/bearing layout. --- ## 7. **Bearing Selection** - **Radial ball or roller bearings** (e.g., SKF 6310 or 22210 series). - **Load rating**: - Use radial load from gear mesh. - Life: L10 ≥ 10,000 hr at operating load. - **Bore size**: matches shaft (e.g., 50 mm). --- ## 8. **Key and Retaining Ring Selection** - **Key**: Standard parallel key, per ISO 773/BS 4235. - For 50 mm shaft: key size = 14 × 9 mm × length ~100 mm. - **Retaining rings**: Select per shaft groove diameter. --- ## 9. **Final Analysis** - **Check safety factors**: SF ≥ 2 for shaft stress. - **Thermal analysis**: Estimate heat dissipation (if needed). - **CAD modeling**: Model all components in Inventor/SolidWorks; use Excel or Matlab for parametric calculations. --- ## **Presentation Tips for Your Report/Submission:** - **Excel/Matlab Sheet**: Set up parameter input for Power, Speeds, Material, etc. All calculations update automatically. - **CAD Model**: Show exploded view, shaft layout, and critical dimensions. - **Table**: Summarize each shaft’s diameter, material, key size, bearing type. --- ## **References** - Shigley’s Mechanical Engineering Design - SKF/FAG Bearing Catalogs - Machinery’s Handbook --- ## **Sample Table (for Submission)** | Shaft | Power (kW) | Torque (Nm) | Diameter (mm) | Material | Bearing Type | Key Size (mm) | |--------------|------------|-------------|---------------|------------|--------------|---------------| | Input | 14.9 | 81 | 30 | 1045 steel | SKF 6306 | 8 × 7 × 50 | | Intermediate | 14.9 | ~225 | 35–40 | 1045 steel | SKF 6308 | 10 × 8 × 60 | | Output | 14.9 | 1781 | 50 | 1045 steel | SKF 6310 | 14 × 9 × 100 | --- ### **If you need a sample Excel sheet or a Matlab function for these calculations, let me know!** You can also request a sample Inventor/SolidWorks shaft/gear assembly sketch for your report or presentation. --- ### **Summary of Steps for Your Project:** 1. **Calculate torque at each shaft.** 2. **Layout gearbox (CAD).** 3. **Analyze gear forces and reactions.** 4. **Select shaft size (stress, deflection).** 5. **Choose material.** 6. **Select bearings and keys.** 7. **Check safety and summarize in Excel/Matlab.** 8. **Finalize and document (CAD + calculations).** --- **Let me know if you need detailed calculations for each stage, Excel/Matlab code, or sample CAD layouts!**