Machine Design · MCTE4102 · Fall 2025

Speed Reduction Gearbox Design

SOLIDWORKSFusion 360DE-GoodmanAGMAFatigueBearings

Brief

Couple a 2.4 hp engine at 3800 rpm to a 1.6 hp compressor at 1500 rpm.

The compressor sets the load, so the gearbox is a 2.53:1 reduction (3800 → 1500 rpm). The project sizes the full drivetrain — two shafts, a spur-gear set, the bearings, and the compressor head bolts — as one coherent machine rather than four disconnected homework problems, and every component targets a design factor of safety of 2.5 for infinite life.

Gearbox schematic: engine couples to the input shaft and pinion (Gear 1), which meshes with the larger output gear (Gear 2) on the output shaft to the compressor, both shafts carried on ball bearings in a mounted housing. — System layout — engine → input shaft & pinion → output gear & shaft → compressor, on ball bearings in a mounted housing.

The Load

A reciprocating compressor delivers a brutal, fluctuating torque.

The torque cycle (max 585, min −175 lb-in) gives a mean of 205 and an alternating component of 380 lb-in. That alternating load — not the peak — is what governs fatigue, so the shafts are sized against fully reversed bending plus fluctuating torsion, not a single static worst case.

Compressor torque versus crank angle for one cycle: a large positive peak near 575 lb-in, a negative dip near -175 lb-in, and a smaller secondary peak. — Compressor torque over one cycle — the alternating load that drives the fatigue design (Tmax 585, Tmin −175 lb-in).

Shafts

DE-Goodman fatigue sizing in SAE 1020 cold-drawn steel.

Each shaft is modelled as a simply supported beam with the gear load at mid-span, then sized with the DE-Goodman criterion using Marin-corrected endurance limits (surface, size, and 99.9% reliability factors). A second iteration adds the real shoulder-fillet stress-concentration factors and shaft self-weight.

Shaft	Diameter	Method	Resulting FOS
Input (engine side)	1.125 in	DE-Goodman	≈ 4.6
Output (compressor side)	1.1875 in	DE-Goodman	≈ 4.4

Gears

AGMA bending and contact checks on a 32 : 81 spur set.

A Pd 8, 20° spur set (32-tooth pinion, 81-tooth gear, 1.25 in face) in AISI 4140 nitrided steel (230 HB) gives the 2.53 ratio while clearing interference. Both members are checked for AGMA bending and contact (pitting) strength at a ~3980 ft/min pitch-line velocity, Quality Index 10.

Member	Teeth	Bending SF	Contact SF
Pinion	32	≈ 5.4	≈ 2.1
Gear	81	≈ 6.7	≈ 3.3

Bearings & Fasteners

Standardized bearings and a fatigue-safe head-bolt joint.

Bearings — single-row deep-groove 02-35 ball bearings on both shafts (sized for a 20,000-hour life with an application factor); standardizing on one bearing simplifies spares and assembly.
Head bolts — six 1/4"-20 UNC Grade 5 screws clamp the compressor head with a confined gasket to keep joint stiffness high; a 75%-proof preload (~2027 lb) gives a fatigue factor of ≈ 1.68 and a separation factor of ≈ 20 against the 0–1000 lb pressure load.

Outcome

An integrated drivetrain, every component above the 2.5 target.

The result is a complete, manufacturable gearbox: standard shaft and bearing sizes, a single well-characterized gear pair, and a sealed compressor joint — each verified against the same infinite-life design factor. The components were modelled in SOLIDWORKS and Fusion 360 to confirm fit and assembly.