Gear Drives and Tooth Geometry

Spur teeth engage straight across; helical teeth engage progressively

Gears transmit rotation by direct tooth contact. They make a compact positive drive, but accurate mounting, tooth compatibility and lubrication matter. This page compares external spur and helical gears on parallel shafts.

Spur gear

Teeth run parallel to the shaft. It is comparatively simple to make and produces no axial thrust from the ideal tooth mesh. Engagement can be noisy at higher speed.

Helical gear

Teeth run at a helix angle around the gear. Contact enters progressively across the face and overlapping teeth share load. This generally gives smoother, quieter operation, with added manufacturing cost.

The inclined helical tooth force also pushes along the shaft. That axial thrust needs a suitable bearing arrangement. A spur gear still loads its bearings radially; “no axial thrust” does not mean “no bearing force.”

The driver supplies power. The pinion is the smaller gear in a pair; it can be the driver or the driven member. An idler passes motion between gears and still needs a shaft or other bearing support. Follow Gear Ratios for direction, tooth-count ratios and compound trains.

Tooth contact and shaft attachment are separate connections. Where a gear hub is keyed to its shaft, the key transfers torque at the hub. Check axial retention separately, especially when the tooth mesh produces thrust.

Measure teeth from the pitch circle

Pitch diameter, d

The diameter of the reference pitch circle. In a standard unshifted pair at its standard center distance, the pitch circles roll together without slipping.

Module, m

Metric tooth size: m = d/N, with d in millimeters and N teeth. Larger module means larger teeth.

Diametral pitch, P_d

Inch-based tooth size: P_d = N/d, with d in inches. More teeth per inch of pitch diameter means smaller teeth. Do not confuse it with circular pitch, the distance along the pitch circle between successive teeth.

Pressure angle, α

The angle between the line of action (the contact-force direction, neglecting friction) and the common tangent to the pitch circles at the pitch point. It describes tooth geometry, not the helix angle.

Addendum / dedendum

Radial tooth height from pitch circle to tip / radial depth from pitch circle to root. Neither is a diameter difference by itself.

Backlash

Clearance between mating tooth flanks. It allows clearance in the mesh but creates lost motion when the load reverses.

Check the size definitions with one gear

A spur gear with 30 teeth and 60 mm reference diameter has m = 60/30 = 2 mm. The diameter is 60/25.4 in, so its equivalent diametral pitch is 30/(60/25.4) = 12.7 teeth/in. In general, m = 25.4/P_d. Two gears can have different diameters and tooth counts while sharing the same tooth size.

Matching pitch is necessary, but not sufficient

Ordinary spur gears intended to mesh must share module or diametral pitch and pressure angle. Matching outside diameter or tooth count does not establish compatibility. Check the tooth system, center distance, clearance and manufacturer's mating information too.

For external helical gears on parallel shafts, match tooth size, pressure angle and helix angle. Use one right-hand and one left-hand gear (teeth slanting in opposite directions), and confirm the manufacturer's mating specification. Equal tooth counts are not required.

Normal and transverse measurements use different planes

The normal plane cuts across a tooth at right angles to its slant; the transverse plane cuts across the gear at right angles to its shaft. Module (tooth size) and pressure angle can be specified in either plane, so compare values measured in the same plane. For this helical pair, match normal module, normal pressure angle and helix-angle magnitude, with opposite helix hands.

A larger tooth size can support more load when other conditions are comparable, but pitch alone cannot determine capacity, backlash or achievable reduction. Material, face width, heat treatment, alignment and speed remain part of the design.

Primary references for the geometry and helical mesh

KHK, Calculation of Gear Dimensions, sections 4.1 and 4.3, distinguishes reference geometry, profile shifts, and normal/transverse helical dimensions. KHK, ABCs of Gearing, B, develops tooth terminology and spur/helical calculations. KHK's helical-gear catalog gives mating-series and bearing-thrust cautions. Use the mating table for the exact product.

Gear damage tells you where the load went

Choose gears for compact packaging, a positive ratio and a supported shaft arrangement. Choose helical teeth when smoothness and noise justify their cost and thrust bearings. Check tooth bending strength, surface durability, speed, lubricant, seals and bearing loads before approving a pair.

A symptom is a clue, not a unique diagnosis. Correct the cause before replacing parts. Most loaded metal gear sets need a controlled lubricant supply; some specially selected materials can run dry. Follow the product data and Equipment Operating Procedure for access.

Compare family trade-offs in Belt, Chain and Gear Drives, and follow Power and Efficiency for power losses. A positive drive is not automatically lossless.