Spur Gears

Part of Gear Making

The simplest and most common gear type — parallel-shaft power transmission with straight teeth cut parallel to the shaft axis.

Why This Matters

Spur gears are the foundation of mechanical power transmission. Straight teeth, parallel shafts, simple geometry — they can be cut with basic tools, calculated without trigonometry tables, and understood from first principles. Every other gear type (helical, bevel, worm) adds complexity that spur gears avoid. When rebuilding machinery, start with spur gears: they’re easier to make, easier to repair, and easier to reason about.

Historical mills, clockwork, and early industrial machinery relied almost entirely on spur gears. With patience and a few tools, a skilled craftsperson can cut functional spur gears from wood, bronze, or mild steel without a dedicated gear-cutting machine. The involute tooth profile that makes modern gears work smoothly was described by Euler in 1754, but earlier approximations using circular arc teeth worked adequately for centuries of millwork.

The trade-offs are real: spur gears produce significant noise and vibration because teeth engage abruptly rather than gradually. They work only on parallel shafts. But for a post-collapse workshop, these disadvantages are far outweighed by their fabricability and repairability.

Gear Geometry Fundamentals

Every spur gear is defined by two numbers: number of teeth (N) and module (M, metric) or diametral pitch (P, imperial).

Module is the most fundamental parameter in metric gearing: it equals the pitch diameter divided by the number of teeth, in millimeters. A gear with module 4 and 24 teeth has a pitch diameter of 4 × 24 = 96 mm.

Diametral pitch (imperial) is the number of teeth per inch of pitch diameter. A 6 DP gear with 24 teeth has a pitch diameter of 24 ÷ 6 = 4 inches.

Two gears can only mesh if they have the same module (or same DP). This is the fundamental compatibility rule. Mixing modules gives gears that look similar but won’t mesh correctly.

Key dimensions for any spur gear:

• Pitch diameter (PD) = N × M (metric) or N ÷ P (imperial)
• Addendum (tooth height above pitch circle) = 1.0 × M
• Dedendum (tooth depth below pitch circle) = 1.25 × M
• Outside diameter = PD + 2 × Addendum = (N + 2) × M
• Root diameter = PD − 2 × Dedendum = (N − 2.5) × M
• Center distance between two meshing gears = (PD1 + PD2) ÷ 2

Minimum tooth count: Gears with fewer than 12-13 teeth suffer tooth undercutting — the base of the tooth gets cut away during generation, weakening it severely. A pinion (small gear) should have at least 14 teeth for standard proportions; this can be reduced to 12 with profile shift corrections.

Cutting Spur Gear Teeth

Form cutters are the most accessible method for a workshop without a hobbing machine. A milling cutter shaped to the exact tooth space profile removes one tooth space at a time; the blank is rotated by the gear tooth count between each cut using a dividing head.

Gear cutters come in sets of 8 (or sometimes 15) cutters per pitch, each correct for a range of tooth counts. A cutter for 14-16 teeth, another for 17-20, etc. Use the cutter appropriate for the tooth count being cut. Improvise a dividing head by indexing a plate with holes drilled at equal angular spacing (use a geometry layout to establish correct hole positions).

Step-by-step process:

1. Turn the gear blank to outside diameter on a lathe
2. Face both sides flat and parallel
3. Bore or drill the bore for the shaft
4. Mount on arbor in the milling machine
5. Set cutter height to center of gear blank
6. Make a test cut: plunge cutter to full tooth depth in one space
7. Check tooth form, then proceed around the blank

Gear tooth depth = 2.157 × Module (this is the standard full depth including addendum + dedendum + clearance).

Indexing: For a 24-tooth gear, you need to rotate the blank exactly 360° ÷ 24 = 15° between cuts. A simple indexing plate with 24 equally spaced holes handles this directly.

Wood and Soft Material Gears

Before cutting metal gears, consider wooden gears for low-speed, moderate-load applications. Historical mills used wooden gear wheels with the teeth (called cogs) made from hard wood like apple, hornbeam, or osage orange inserted individually into holes in the rim.

Cog-wheel construction:

1. Rim wheel: a large wooden disc or ring with holes drilled or mortised at equal spacing around the perimeter
2. Individual cogs: turned or carved from the hardest available wood, to fit tightly in the holes
3. Cogs are wedged, pegged, and if needed glued in place
4. They can be individually replaced when worn — no need to replace the entire wheel

The advantage of wooden cogs: they’re quieter than metal (wood absorbs shock), they run well on dry or water-lubricated bushings, and replacements can be made by any capable woodworker. The great millwrights of the pre-industrial era built surprisingly durable machinery this way.

Carved wooden spur gears: For smaller gears (under 12 inches diameter), cut teeth on a lathe-turned blank using chisels, files, and a tooth template. The profile doesn’t need to be mathematically perfect involute — a close approximation using circular arcs works adequately for low-speed applications.

Mounting, Alignment, and Maintenance

Shaft alignment: Spur gears require the two shafts to be exactly parallel. Misalignment by even 0.5° causes uneven tooth loading — one end of the teeth takes all the load, causing rapid wear and noise. Check alignment by placing a straight edge along both shafts and measuring the gap; or use a dial indicator mounted on one shaft to sweep the other.

Backlash: The small clearance between meshing teeth when loaded from one direction. Too little backlash: gears bind and overheat. Too much: noisy clatter and impact loading. Standard backlash is approximately 0.04 × Module. Check by holding one gear and rocking the other; feel for controlled, even play with no binding.

Center distance: Small errors in center distance dramatically affect gear behavior. Moving gears too far apart increases backlash excessively; too close causes binding and interference. Adjustable bearing housings (slotted mounting holes) allow center distance to be dialed in precisely when installing new gears.

Lubrication: For enclosed gearboxes, gear oil or grease splash lubrication. For open gears (exposed tooth mesh), heavy grease applied to the teeth. Graphite-based grease is traditional for open gear lubrication and works well. For wooden gears, tallow or animal fat applied to the teeth.

Inspect tooth surfaces monthly on working machinery: look for pitting (small fatigue craters), scoring (scratches from inadequate lubrication), and spalling (chunks breaking off). Pitting is progressive and will destroy the gear if not caught early. Scored teeth indicate dry running; increase lubrication immediately.