Gearbox Design

Objective: Engineered a three-stage spur gear transmission to reduce input speed from 3000 rpm to 360 rpm while transmitting 65 kW of power. I was responsible for the design, analysis, and component selection of the input shaft subsystem (Shaft 1).

Requirements: The gearbox was required to operate with 99% reliability over a 5-year continuous duty cycle. Key constraints included ensuring infinite fatigue life for the shafts using the Goodman criterion, verifying gear teeth against AGMA bending and contact stress standards, and selecting bearings with sufficient dynamic load ratings (L10 life)

Top Skills: Mechanical Design (Shaft & Gear Sizing in Siemens NX), Failure Analysis (Modified Goodman, distortion energy theory), MATLAB (Shear/Moment Diagrams), Component Selection (SKF Bearings), AGMA Standard

Overview

As part of a three-person team in my Machine Elements Design course, we developed a compact gearbox to step down high-speed input power for industrial application. While the final assembly integrated three interacting shafts, my individual focus was on the complete engineering of Shaft 1 (the input shaft). This involved designing the input pinion, sizing the shaft to withstand combined belt tension and gear mesh forces, and selecting appropriate rolling-element bearings.

Design (Shaft 1 Subsystem)

• Gear Specifications: Designed Gear 1 as a 17-tooth steel pinion (Module = 6 mm, Pressure Angle = 20°) to transmit the full 206.9 Nm of input torque.

• Material Selection: Utilized High Strength Steel (Sut = 1300 MPa, Sy = 1000 MPa) to ensure durability under high-cycle fatigue.

• Bearing Selection: Selected SKF NJG 2308 VH Cylindrical Roller Bearings. These were chosen specifically to handle the substantial radial loads (over 7,000 N at Bearing C) resulting from the belt drive input, as there was no thrust load present in the spur gear arrangement.

Loading and Analysis

The critical challenge for Shaft 1 was handling the overhung load from the input belt drive, combined with the forces generated at the gear mesh.

• Force Analysis: Calculated a belt tension of ~6,280 N acting on the input pulley and a tangential gear force of ~4,057 N at the pinion.

• Critical Sections: Developed shear and moment diagrams (using MATLAB) to identify the most critical locations. The highest stress concentrations were found at Bearing C (due to the reaction force) and Point A (the gear location), where torque transmission occurs.

• Stress Calculation: At the critical gear section, the shaft experiences a maximum bending moment of 345.7 Nm. Using the Distortion Energy (Von Mises) theory, I calculated a combined stress state involving 55 MPa of bending stress and 16.5 MPa of torsional shear stress.

Results Summary

• Shaft Fatigue: Using the Modified Goodman Fatigue Safety Factor, Shaft 1 achieved a Factor of Safety (FOS) of 9.38, validating it for infinite life (>10^9 cycles).

• Static Yield: The Yield FOS was calculated at 16.1, ensuring no plastic deformation under peak loads.

• Gear Integrity: The pinion achieved an AGMA Bending FOS of 2.82 and a Contact Stress FOS of 1.26, successfully meeting the surface durability requirements.

• Bearing Life: The selected cylindrical roller bearings exceeded the design life requirement of 3.2 billion rotations with no scheduled changes needed over the 5-year service period.

Key Takeaways

This project highlighted the importance of analyzing components not just as static bodies, but as dynamic systems subject to fatigue. While the shaft design was highly successful in meeting reliability goals, the resulting Safety Factor of 9.38 indicates the design is likely over-engineered.

In a constrained environment, such as the aerospace applications I am interested in, this would represent an opportunity for weight optimization. I could have reduced the shaft diameter or selected a lighter grade of steel to lower the mass while still maintaining an acceptable safety margin (e.g., FOS ~1.5 to 2.0).

Additionally, coordinating the gear ratios with my teammates taught me the importance of clear interface definitions; changes to my pinion geometry immediately impacted the torque and speed requirements for Shaft 2, necessitating constant synchronization of our mathematical models.