Why Tooth Breakage Always Occurs at the Root and Pitting Preferentially Forms Below the Pitch Line

In-depth Investigation into Two Major Gear Fatigue Failures (Gear Column 08 · Part 1) Author: Chen Yaming (ANSV Transmission Engineering & Micro Actuator Laboratory) Specialties: Gear Transmission Engineering · Contact & Bending Fatigue · Fractographic Metallurgical Diagnosis · Drivetrain Dynamics

Case Background

Record of troubleshooting sudden tooth breakage and clustered surface pits during an 800-hour accelerated life bench test for a high-reduction-ratio gearbox.

Professionals working on mechanical transmission, on-board actuators, industrial reducers or precision robot joints have most likely experienced that heart-stopping moment in front of a reliability life bench.

A fully loaded continuously running test prototype, originally operating with a steady low meshing sound, is suddenly interrupted by a sharp, shrill metallic impact. Accompanied by violent shaking of the whole unit, the driving motor current spikes to the protection limit, triggering bench emergency shutdown.

When the heavy cast iron gearbox cover is lifted off, a pungent smell of high-temperature oxidized engine oil surges out. Shining a high-intensity flashlight into the dark lubricant sump, a layer of sparkling metallic debris is deposited at the bottom.

The main shaft is removed, placed on the workbench and cleaned of oil contamination. Every engineer on site frowns immediately: On the primary driving gear, two teeth are completely broken off flush at the root, with jagged fracture surfaces. On the remaining adjacent tooth flanks, dense clusters of sesame-seed-sized concave pits are distributed on the dedendum area below the pitch line, rough and sharp to the touch, just as if etched by strong acid.

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Why Tooth Breakage Always Occurs at the Root and Pitting Preferentially Forms Below the Pitch Line – Full Investigation Record of Two Major Gear Fatigue Failures

Then comes the supplier dispute: The gear manufacturer insists the teeth were snapped off by several-fold impact overload induced by an abrupt motor emergency stop. The motor supplier counters that the gearbox operating current remained stable, claiming the failure originates from poorly finished root fillets and excessively brittle carburizing & quenching which triggered fatigue fracture.

As for the dense pits on tooth flanks, some suspect abrasive wear caused by casting iron particles mixed into lubricating oil; others argue the tooth surface hardness failed to meet specification and yielded under compression.

Everyone holds a magnifying glass and sticks to their own opinion.

Among all gear damage modes, tooth breakage and tooth surface pitting are the two most frequent and catastrophic fatigue failure modes.

They are neither mysterious phenomena nor random accidents. Every fractured cross-section and every tiny spall pit strictly follows the physical laws of material mechanics, contact elasticity and fluid lubrication.

Setting aside dry textbook theories, we combine real bench test data and microscopic fracture surfaces from field practice to thoroughly clarify: Why more than 85% of tooth fractures occur at the root; why tooth surface pitting densely concentrates in the specific zone below the pitch line; and how lubricating oil acts like a "metal wedge" and forcibly creates pits inside steel.

The King of Catastrophic Damage: Tooth Breakage

Tooth breakage is the most destructive catastrophic failure inside gearboxes. Once one tooth partially or fully detaches, the fallen hardened steel fragment gets trapped between adjacent rotating tooth spaces, instantly triggering cascading tooth fracture, shaft bending-torsion vibration or even casing burst.

By carefully examining fracture surfaces with a flashlight, the metal microstructure itself can "reveal the cause of death".

Figure 1 · Cantilever beam bending force model of gear tooth, ISO 30° tangent critical section and vector analysis of three-stage mechanical partition on fracture surface

1. Why Over 85% of Fractures Occur at the Tooth Root

During meshing, each single gear tooth can be simplified as a cantilever beam subjected to alternating transverse load. When the mating tooth slides to the Highest Point of Single Tooth Contact (HPSTC), the entire normal load Fn of the gear pair is borne solely by this tooth. The bending moment at the tooth root M = Fn × h reaches its maximum value.

At this moment, opposite stress states exist on both sides of the tooth root: Tensile Side: subject to extremely high tensile stress; Compressive Side: subject to corresponding compressive stress.

An ironclad rule in mechanical material mechanics: the tensile fatigue strength of steel is far lower than its compressive limit.

More critically, the transition from involute tooth profile to root fillet features an abrupt cross-section change, creating inherent severe stress concentration.

In gear engineering, the ISO 30° Tangent Method is adopted to locate the weakest cross-section at the tooth root: Draw two tangents to the root transition curve, forming a 30° angle with the tooth centreline and intersecting each other; The connecting line sF between the two tangent points represents the geometrically critical cross-section with maximum stress concentration and minimum bending section modulus at the tooth root!

Under millions of cycles of fluctuating bending stress, even if the working stress is much lower than the material yield strength, a tiny machining tool mark, grinding burn microcrack or microscopic inclusion at the fillet on the tensile side of the tooth root will initiate micro-slip bands and open the first crack – the fatigue origin is born.

Figure 2 · Macro morphology of industrial gear tooth root fatigue crack initiation, crack propagation along the 30° critical section and full tooth fracture (with centimetre scale marker)

Look at this real industrial gear fatigue failure photo: on the left two teeth, a deep crack propagating transversely along the 30° critical section is clearly visible at the root fillet on the tensile side. The right two teeth completely fail to withstand bending load under subsequent alternating cycles and break off entirely at the root.

2. Identify the Three-Stage Failure Mechanism from Fracture Surfaces under Microscope

When inspecting fatigue fracture surfaces under stereoscopic and metallographic microscopes, they exhibit distinct textbook-like macroscopic morphology divided into three stages:

Fatigue Origin Zone It is always located on the root fillet surface of the tensile side. Macroscopically it appears as a flat, smooth, even faintly glossy dark tiny speck. This polish effect forms at the very beginning of crack initiation, as the two mating micro-fracture surfaces repeatedly open and close under alternating load.

Crack Propagation Zone (Beach Marks) Cracks grow gradually inward from the fatigue origin. Regular concentric circular ripple patterns form on the fracture surface, known as beach marks or fatigue striations in engineering. The centre of these ripples points precisely back to the fatigue origin, just like ripples spreading across water.

Fine and dense beach marks indicate a high number of alternating stress cycles, typical high-cycle fatigue. Widely spaced marks imply frequent heavy impact loading.

Final Fast Fracture Zone As the crack consumes most of the cross-section, the remaining intact metal area shrinks continuously. Until at one instant, the residual cross-section can no longer sustain a normal meshing load and sudden unstable tearing occurs. The fracture surface appears rough and dull; for carburized hardened tooth flanks, shiny metallic cleavage grains can be observed, while soft gears show dull grey shear lips.

If a single fatigue origin wrapped by fine beach marks is found on the fracture surface, the supplier’s claim of "sudden extreme overload" collapses immediately — this is 100% tooth root bending fatigue failure.

Figure 3 · Macro metallographic diagnosis of typical alternating bending fatigue fracture with three characteristic zones: ① Fatigue Origin Zone, ② Beach Mark Propagation Zone and ③ Final Unstable Fast Fracture Zone

We mark the typical bending fatigue fracture surface under stereoscopic microscope: The red box at the bottom marks ① the fatigue origin induced by stress concentration; The dark semi-elliptical area in the blue box in the middle is ② beach marks propagating outward like ripples. Each concentric ring records the microscopic propagation track of alternating load inside metal. The large rough whitish area at the top is ③ the final fast fracture after the effective load-bearing cross-section is exhausted. With these three zones identified, the truth behind the fracture is fully revealed.

3. Two Additional Tooth Breakage Modes: Overload Brittle Fracture & Edge Chipping

Not all tooth fractures originate from fatigue:

Overload Breakage: In cases of sudden mechanical seizure, emergency braking or multiple-fold impact, no beach marks can be found on the fracture. The whole surface shows rough crystalline brittle tearing morphology.

Edge Breakage & Tip Chipping: If instead of full tooth breakage, a triangular notch peels off at one end of the tooth face at roughly a 45° oblique angle, the root cause usually lies not in gear material itself but shaft stiffness and assembly alignment. Shaft bending deflection or excessive bearing clearance leads to poor full-width tooth contact. All load concentrates on a few millimetres at the tooth end (severe load distribution misalignment), resulting in local shear overload and edge chipping.

Lubricant Turns into Metal Wedge: Tooth Surface Fatigue Pitting

If tooth breakage is sudden fatal "acute cerebral haemorrhage", tooth surface pitting is the most common "chronic cancer" inside gearboxes.

In enclosed lubricated reducers, pitting starts with a few tiny pinholes. With continuous machine operation, pinholes rapidly connect into dense crater-like pits. Eventually large areas of hardened layer spall off, and noise rises from faint rustling to harsh roaring.

Figure 4 · Hertzian contact stress, subsurface shear stress peak at 0.78b and full micro-process vector analysis of hydraulic wedge splitting effect of lubricating oil

1. Why Cracks Initiate 0.78b Beneath the Surface

Many beginners assume contact wear creates cracks starting right at the outermost tooth surface. However, Hertzian elastic contact mechanics reveals a counterintuitive physical truth: When two involute curved surfaces press together under normal force, the actual contact zone is a narrow elliptical strip with half-width b. Elastic field stress integration shows: The outermost tooth surface bears triaxial compressive stress, and maximum Hertz compressive stress occurs at the surface centre. Yet lattice structures of metallic materials fear shear stress far more than compressive stress.

Calculations show the peak orthogonal maximum shear stress τ_max ≈ 0.304 σ_Hmax does NOT appear at the tooth surface, but lurks at subsurface depth z ≈ 0.78b.

This resembles "striking through the mountain" in martial arts novels. The tooth surface remains visually intact, yet dozens to hundreds of microns underneath, material lattices undergo repeated intense shear kneading over tens of millions of rolling cycles.

Grain boundary slip and micro-inclusion edges in the subsurface are torn first, generating invisible initial fatigue cracks. These cracks then grow toward the tooth surface at an oblique angle of 30°~45°, until they penetrate the surface and form tiny openings.

2. Century-Old Puzzle: Why Pitting Concentrates Below the Pitch Line

When inspecting pitted gears, engineers observe a distinctive pattern: Tooth tips rarely develop pitting, almost no pits appear exactly on the pitch circle node. All dense pits gather consistently in the dedendum zone right below the pitch line.

Three interwoven mechanical driving forces account for this strong preferential location:

Driving Force 1: Negative Sliding Opening Crack Mouth Involute gear meshing is not pure rolling. At the pitch line node, relative sliding velocity vs = 0, which represents pure rolling. In the dedendum zone under the pitch line, tangential sliding velocity is opposite to rolling direction, defined as the negative sliding zone.

Under negative sliding, friction force points away from the node toward the tooth root. This direction is extremely dangerous: it pries open the edge of oblique subsurface cracks, keeping crack openings continuously in tensile opening status.

Driving Force 2: Lubricant Becomes Hydraulic Wedge This is one of the most impressive damage mechanisms in contact tribology:

1. Oil infiltration: The moment negative sliding pries open crack openings, splashed thin lubricant flows into microcracks and fully fills the tiny voids.
2. Instant sealing: The mating tooth rolls over and seals the crack opening tightly from outside, forming a sealed dead cavity inside metal.
3. Ultra-high pressure wedge impact: As the Hertzian contact pressure peak (several GPa) rolls across the sealed opening, lubricant trapped inside the microcavity is severely compressed and forms an ultra-high pressure liquid hydraulic wedge.
4. Violent tearing and spalling: Liquids are nearly incompressible. Multi-GPa oil pressure propagates along crack tips and tears the material violently, generating tensile stress exceeding steel’s fracture resistance. A microscopic rupture occurs.

Tiny metallic fragments fall into the oil sump, leaving steep-walled pinhole pits on the tooth surface — this is the physical process of fatigue pitting.

Lubricating oil originally designed to protect gears from wear becomes the biggest culprit that shatters tooth flanks at microscopic scale, under specific geometric loading and negative sliding conditions.

Figure 5 · Macro morphology of severe fatigue macro-pitting on real gear meshing surface: dense spall pits concentrated on dedendum side below pitch line, with peeled hardened layers forming steep crater-like cavities, solid evidence of repeated hydraulic wedge explosion under multi-GPa pressure.

Before massive pitting propagation, foggy grey patches often emerge on tooth surfaces, which are micro-pitting observable only under microscope.

Figure 6 · Micro-pitting (grey staining) under microscope: dense microcrack band on involute sliding contact zone of dedendum

Three Evolution Forms of Pitting: Some Self-Heal, Others Require Gear Replacement

During on-site gear inspection, do not rush to scrap gears upon discovering a few pits. Pitting is strictly classified into three stages in engineering:

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End of Part 1: Fundamental Shift in Engineering Thinking

Many junior engineers immediately blame "poor material quality" once gears break, or suspect counterfeit lubricant once pits appear.

But once you observe beach marks on fracture surfaces under microscope, derive the shear stress peak at subsurface depth 0.78b, and understand the micro physical process of hydraulic wedge splitting induced by negative sliding, you will realize: All macroscopic damage is essentially inevitable outcome of microscopic mechanical imbalance accumulated under alternating load cycles.

Tooth root breakage and tooth surface pitting represent the physical end state of gears under two major fatigue mechanisms: alternating tensile stress and alternating shear stress.

With these two fatigue killers understood, another more challenging engineering question arises: Under high-speed heavy-load operating conditions, gears show neither tooth breakage nor pitting. Why do tooth flanks instantly weld together under transient high temperature of several hundred degrees Celsius the moment teeth mesh, then tear apart under relative sliding? How do sediment particles in open gearing cut away half the tooth thickness like cutting tools? What creates ridges and grooves near the pitch line under low-speed ultra-high torque, resembling marks rolled by a rolling pin?