Using DOE to Balance Gear Hardness and Case Depth in Mixed Fatigue
A geared aircraft engine gearbox must survive several forms of fatigue at once. The tooth flank sees repeated rolling and sliding contact, while the tooth root experiences bending loads. Subsurface shear, micropitting, scuffing and impact from transient torque can all develop within the same component. Hardening the surface may improve one failure mode while moving the risk into the core.
Design of experiments (DOE) gives engineers a disciplined way to study that trade-off. Instead of changing hardness or carburised case depth one test at a time, a DOE model varies the important factors together and measures their interactions. This is valuable for aerospace gearsets, where a small change in material condition can affect durability, mass, manufacturing yield and power density.
The OPTIMIZE project’s focus on power reduction gearboxes makes this question especially important. Higher rotational speeds and compact layouts increase thermal and contact stresses, while lubrication quality and geometric tolerances can influence how those stresses are distributed. A practical design must therefore balance surface strength with core toughness rather than chase the highest possible hardness.
For Australian aerospace manufacturers, the setting adds further considerations. Components may be produced in Melbourne or Adelaide, tested near Brisbane, and supplied into remote operations where maintenance access is limited. Heat, dust, long logistics chains and strict CASA expectations make a robust process window more useful than a nominally perfect result that is difficult to reproduce.
| Design choice | Main benefit | Main risk | DOE response |
|---|---|---|---|
| Higher surface hardness | Better pitting and wear resistance | Lower toughness, grinding sensitivity | Test hardness with load and lubricant factors |
| Deeper carburised case | Greater subsurface fatigue margin | More distortion, cost and cycle time | Include depth and retained-austenite effects |
| Softer, tougher core | Better root and impact resistance | Reduced flank load capacity | Measure bending and contact fatigue together |
| Narrow process window | Potentially strong peak performance | Poor manufacturing robustness | Add tolerances and confirmation runs |
Why Mixed Fatigue Modes Need A Joint Study
Gear tooth surface fatigue and root bending fatigue are governed by different stress fields. Contact fatigue responds strongly to flank hardness, residual compressive stress, roughness, lubricant film thickness and subsurface material support. Root fatigue depends more heavily on tooth geometry, fillet condition, core strength, inclusions and the local tensile stress produced during meshing.
Case depth connects these mechanisms. A shallow case can leave the maximum orthogonal shear stress below the hardened layer, allowing cracks to initiate in a softer transition region. An excessively deep case may increase distortion and reduce the ability of the core to arrest a crack. Hardness gradients, retained austenite and compressive residual stress should therefore be treated as response variables, rather than reduced to one surface hardness value.
The design space also includes local stress raisers. A useful companion to the DOE is the research on tooth stress-relieving grooves, which examines how a geometric feature can alter root stress concentration. If a groove, fillet radius or lead modification is present, the experiment should account for it because geometry may interact with material hardness. A harder tooth does not automatically deliver better root life when its local stress concentration remains high.
Building A Useful Gearbox DOE
A screening experiment should begin with controllable factors that have a plausible physical effect. Candidate inputs include surface hardness, effective case depth, carburising potential, tempering condition, retained-austenite content, shot-peening intensity, grinding allowance and surface roughness. Operating factors can include torque, speed, oil temperature, lubricant viscosity and duty-cycle severity.
The first design should be large enough to identify curvature and interactions, but focused enough to be manufactured consistently. A fractional factorial design can screen many inputs, followed by a response-surface design around the promising region. For a high-consequence aerospace gearbox, centre points and replicated runs are important because they reveal process drift and experimental noise.
Measurement quality needs the same attention as factor selection. Hardness should be recorded by depth, with a defined test method and location. Metallographic sections can confirm the effective case depth, transition profile and microstructural condition. Bending fatigue, pitting life, micropitting, scuffing onset, dimensional distortion and residual stress should be tracked as separate responses.
Automated inspection can strengthen this workflow, especially when production volume makes manual checks inconsistent. The discussion of machine vision methods is presented in a solar context, yet its principles are relevant to gear inspection: controlled lighting, repeatable image capture and algorithmic detection can help identify grinding burns, surface marks or edge defects before endurance testing.
Reading The Trade-Offs In Hardness And Depth
A response surface can show where hardness and case depth reinforce each other and where they begin to conflict. For example, increasing surface hardness may raise pitting resistance until roughness, brittle microstructure or grinding damage becomes dominant. Increasing effective case depth may improve subsurface support until distortion affects contact alignment or the core becomes insufficiently tough.
The right target is usually a constrained operating region rather than a single optimum point. A multi-response desirability function can maximise contact fatigue life and bending life while placing limits on mass, distortion, manufacturing cost and allowable temperature. Engineers should also use confidence intervals, because a predicted life advantage is of little value if the uncertainty band crosses the acceptance threshold.
A useful analysis separates material effects from system effects. If pitting improves after a hardness increase, the result may reflect a stronger surface, a changed residual-stress profile or a different finishing response. If root life falls, the cause may be reduced toughness, altered fillet geometry after heat treatment or a lubrication change that raises torque variation. Microscopy, hardness traverses and finite-element stress maps help explain the statistical pattern.
The analysis should include tolerance propagation. Case depth varies with furnace position, load arrangement, quench response and section thickness. Hardness also varies with chemistry, tempering and local cooling. Monte Carlo simulation can combine these distributions with gear geometry and duty-cycle variation, revealing whether a design remains safe when manufactured at the edges of its normal process window.
Connecting Material Results With Lubrication
Hardness and case depth cannot be selected separately from lubrication. A high-speed geared aircraft engine may experience changes in film thickness as oil temperature, viscosity, flow rate and gear speed vary. Thin-film conditions increase asperity interaction and can turn a marginal surface-finish issue into micropitting or scuffing.
Oil delivery consistency is particularly important in compact reduction gearboxes. The OPTIMIZE project’s analysis of oil jet pulsation shows why pump outlet behaviour can influence local cooling and film formation. A DOE that tests hardness under steady laboratory lubrication may overstate the benefit of a harder case if real operation includes pulsating flow or intermittent jet coverage.
Lubrication should therefore be included as a blocking factor or experimental factor where feasible. Test conditions might combine low and high oil temperature with representative jet pressure, duty cycle and speed. The resulting model can identify whether a deeper case provides meaningful protection under poor film conditions, or whether improving oil delivery produces a larger and more reliable gain.
Australian operating conditions make this especially practical. A gearbox supporting mining, surveillance or regional transport may face large temperature swings between a cool start in Tasmania and hot, dry work near Alice Springs. Dust does not belong inside a sealed aviation gearbox, yet maintenance environments, transport delays and contamination-control practices still affect reliability. Validation should reflect the actual service and support model rather than an idealised laboratory cycle.
Turning The DOE Into A Production Specification
A successful experiment ends with a manufacturing rule that suppliers can hold. That rule may define a hardness band at the flank, a minimum effective case depth, a maximum hardness gradient, a retained-austenite range and limits for distortion or residual tensile stress. It should also identify which measurements are release tests and which belong to periodic process audits.
The specification should distinguish capability from compliance. A batch can meet the nominal case-depth requirement while showing excessive variation across teeth or around the gear circumference. Statistical process control, furnace mapping and calibrated hardness testing help demonstrate that the process is centred rather than merely passing inspection by chance.
For Australian supply chains, this matters when specialist heat treatment is performed by a subcontractor several states away. Shipping between Adelaide, Sydney and Brisbane can add schedule pressure, while a remote operator may not be able to replace a gearbox quickly. Clear acceptance data, traceability and digital records reduce the risk of discovering a material trend after parts have entered service.
The project’s technical documentation provides a useful reference point for connecting modelling, tolerance analysis and physical testing. A comparable gear-development record should preserve the DOE matrix, material certificates, test conditions, failed-part examinations and model assumptions. That evidence supports design reviews and makes later changes easier to assess.
A practical verification programme should include confirmation gears manufactured at the selected settings, followed by endurance tests at nominal and boundary conditions. The final decision should consider life, damage progression, dimensional stability, inspectability and cost. Engineers can then choose a slightly less aggressive hardness-depth combination if it delivers a wider, more dependable process window.
Checks That Keep The Experiment Grounded
Before releasing the design, the team should confirm that:
- Surface hardness and effective case depth are measured at defined locations and depths.
- Contact fatigue and bending fatigue are evaluated as separate responses.
- Retained austenite, residual stress, roughness and grinding damage are recorded.
- Lubrication temperature, flow stability and oil condition match intended service.
- Confirmation parts are made using normal production equipment and operators.
During analysis, the most useful warning signs include:
- A strong peak response paired with poor repeatability between batches.
- Improved pitting life accompanied by a fall in root fatigue performance.
- Model predictions that change sharply with small measurement errors.
- Case-depth variation that is larger than the design margin.
- Failure locations that do not match the stresses used in the original simulation.
The strongest DOE outcome is not simply a hardness number or a case-depth target. It is an evidence-based relationship between material condition, geometry, lubrication, manufacturing variation and fatigue life. That relationship lets gearbox designers make sensible trade-offs when speed, weight and power density are all rising.
For teams developing geared aircraft engines in Australia, the next step is to convert this framework into a controlled trial: define the response measures, select representative operating conditions, manufacture the matrix and compare the predicted failure modes with physical evidence. Build the resulting limits into the drawing, supplier process and verification plan so the gearbox is ready for service rather than merely impressive in simulation.