kW
rpm
mm
mm
teeth
teeth
Material (both gears)
Gear quality
Driven machine (shock)
hours
Bending stress at the tooth root (Lewis with AGMA factors) and surface contact stress (Hertz) for a spur gear pair, with safety factors for pinion and gear, the power the set can carry and the smallest module that will do the job.
Stresses and limits for each wheel. The pinion turns more often, so its life factor is lower.
| Pinion | Gear |
|---|
| Module | Face b | Pinion Ø | SF bend | SH contact |
|---|
A gear tooth fails in two ways: it breaks off at the root because it bends like a short cantilever (bending fatigue), or its flank pits and flakes because of the contact pressure where the teeth roll on each other (surface fatigue). Both are checked for the pinion and the gear.
Allowable stresses St and Sc for steel follow the AGMA grade 1 hardness curves (St = 0.533·HB + 88.3 MPa, Sc = 2.22·HB + 200 MPa); case-carburized steel uses St 380 MPa and Sc 1240 MPa. Ka is the overload factor for a uniform driver (electric motor); Km is the load distribution factor for accurately mounted gears, rising with face width. Aim for SF ≥ 1.5 and SH ≥ 1.2 for industrial drives. The method follows Shigley's Mechanical Engineering Design, chapters 14, and ANSI/AGMA 2001; for certification use the full AGMA or ISO 6336 rating with the geometry factor J.
This calculator checks whether a pair of spur gears is strong enough for the power it has to carry. Enter the power and pinion speed, module (or diametral pitch), face width, tooth counts, material, gear quality, the type of driven machine and the required life. It returns the tooth force, pitch line speed and dynamic factor, the root bending stress of pinion and gear by the Lewis equation with AGMA factors, the Hertz contact stress on the flanks, safety factors against tooth breakage and pitting, the power the set can carry, and a table of modules so you can pick the smallest that works.
The teeth will not break (bending SF 1.83), but the pinion flanks are at the pitting limit (SH 0.98) for 20,000 hours. Case-hardening the pinion, using a 3 mm module or a 40 mm face width brings SH comfortably above 1.2.
Lewis treated a gear tooth as a cantilever beam of uniform strength, shaped like a parabola inside the tooth. The root bending stress is σ = Ft / (b·m·Y), where Ft is the tangential force, b the face width, m the module and Y the Lewis form factor, which depends on the number of teeth and the pressure angle. AGMA multiplies the force by dynamic, overload and load distribution factors.
Bending stress is at the root of the tooth and causes the tooth to crack and break off. Contact stress is on the flank where the teeth roll against each other and causes pitting: small craters that grow until the gear becomes noisy and fails. Bending is controlled mainly by module and face width; contact by pinion diameter, face width and surface hardness.
For industrial gear drives a bending safety factor of at least 1.5 and a contact safety factor of 1.2 or more are common. Bending failure is sudden and dangerous, so it gets the larger margin; pitting develops slowly and can be monitored.
Start from the torque and the pinion tooth count, then pick the smallest module where the bending safety factor and the contact safety factor are both above your target with a face width of about 8 to 16 times the module. The module table in this calculator does exactly that for the standard module series.
Errors in tooth spacing and profile cause small impacts each time a tooth enters the mesh, adding dynamic load. AGMA's dynamic factor Kv captures this: the rougher the gear and the faster the pitch line speed, the larger the extra load. Each quality grade also has a maximum recommended pitch line speed.
Yes, for bending. Choose acetal (POM): the Lewis method with an allowable stress of about 40 MPa is the usual approach for plastic gears. Contact stress is not rated for plastics; their limit is heat and wear, so keep the speed low and check the maker's data.
What you need to build, measure or check the result.
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