Langford Analytic · Knowledge Base
Contact Mechanics, Bearings & Tribology
How normal load, geometry and material combine to create a contact patch, a pressure distribution and a subsurface stress field — and how friction, slip, lubrication, wear and fatigue determine the durability of the interface. From contact mechanics fundamentals and Hertzian theory through subsurface stress and contact fatigue, friction, wear and lubrication, then into rolling-element bearing life and operating state, bearing arrangements and misalignment, gear tooth contact and root bending, gear-mesh load distribution, splines, shafts, keys, couplings, springs, press fits, contact FEA and the complete chain from interface load to defensible machine-element substantiation.
Contact Fundamentals
Contact Mechanics FundamentalsWhen two structural bodies are pressed together, the load is transmitted through a finite contact region whose size, shape and pressure distribution depend on geometry, material stiffness and applied force. This article establishes the governing principles of contact mechanics — the foundation for every subsequent article on bearings, gears, splines, interference fits and surface durability.Hertzian Contact TheoryHertzian contact theory provides the classical analytical framework for non-conformal elastic contacts — spheres, cylinders and curved bodies pressed together under normal load. This flagship article explains the Hertzian assumptions, the equivalent radius and modulus concepts, the pressure distribution within the contact patch, and the limits of the theory — without drowning in derivations.Contact Pressure, Contact Patch & Elastic DeformationHow does the contact patch change as load increases? How does conformal contact differ from non-conformal? And why can nominal projected area be deeply misleading? This article explains the relationship between load, patch size, peak pressure and elastic indentation — and the practical implications for structural design.Subsurface Stress & Contact FatigueThe most critical contact stress is not always located at the surface. Under Hertzian pressure, the maximum shear stress occurs beneath the surface — at a depth typically 0.3 to 0.5 times the contact half-width. This subsurface stress drives rolling contact fatigue, pitting and spalling — the failure modes that govern bearing and gear life.Friction FundamentalsFriction is the tangential force that resists relative sliding between two contacting surfaces. The simplified Coulomb model — Ff = μN — is a useful engineering approximation, but the coefficient of friction is not an immutable material constant. It depends on surface condition, contact pressure, temperature, sliding speed and lubrication. This article explains the engineering use and the limits of the friction model.Stick, Slip & Partial SlipWhen a tangential load is applied to a contacting interface, part of the contact may stick while part slips. This partial-slip condition — where the interface is globally stuck but locally slipping near the edge of contact — is the mechanism behind fretting, microslip and the onset of gross sliding. This article explains the Mindlin partial-slip theory and its engineering implications.
Damage & Surface Behaviour
Fretting & Fretting FatigueFretting is the surface damage caused by small-amplitude oscillatory relative movement between two contacting surfaces under normal pressure. It occurs at bolted interfaces, spline teeth, bearing seats, blade attachments and bushes — and it can reduce fatigue life by more than half. This major article explains the mechanism, the applications, the factors that worsen it and the design strategies that mitigate it.Wear Mechanisms & Surface DamageWear is the progressive removal of material from a surface due to mechanical interaction with a mating surface or particles. This article covers the principal wear mechanisms — adhesive, abrasive, surface fatigue and erosive — and explains how wear changes geometry and load distribution over time, and why there is no simple universal wear law.Lubrication FundamentalsLubrication is not simply "adding oil to reduce friction". It changes the contact condition fundamentally — from dry solid-solid contact to fluid-film separation, with a range of intermediate regimes. This article explains the boundary, mixed, hydrodynamic and elastohydrodynamic lubrication regimes and the factors that determine which regime an interface operates in.
Bearings & Torque Interfaces
Rolling-Element Bearing FundamentalsRolling-element bearings — ball and roller — transmit load between a shaft and a housing through rolling elements that minimise sliding friction. This article explains the internal geometry, the load transfer mechanism, radial and axial loading, preload and clearance — conceptually, without relying on catalogue ratings as universal engineering values.Bearing Load Distribution & Internal Load SharingNot all rolling elements in a bearing carry equal load. The load distribution depends on the bearing clearance, the preload, the housing stiffness, the shaft stiffness and the misalignment. This substantial article explains the loaded zone, the load-sharing mechanism and why bearing load distribution depends on the complete shaft-bearing-housing system — not just the bearing itself.Plain Bearings, Bushes & Journal InterfacesPlain bearings and bushes carry load through sliding contact between a journal (shaft) and a bearing surface. Unlike rolling-element bearings, the contact is conformal — the surfaces mate over a large area. This article explains bearing pressure, sliding speed, alignment, edge loading, clearance and lubrication, and why the nominal bearing pressure does not describe the true local contact-pressure distribution.Gear Tooth Contact & Local Tooth LoadingGear teeth transmit torque through rolling-sliding contact at the tooth flank. The contact is Hertzian (line contact), but the load, the sliding and the contact position change as the teeth mesh. This article explains tooth contact, mesh position, the distinction between tooth-root bending and flank contact, load sharing and misalignment — at the engineering level, without becoming a gearbox design handbook.Splines, Serrations & Torque-Transfer InterfacesSplines and serrations transmit torque through multiple teeth that engage simultaneously. In principle, the teeth share the torque equally; in practice, manufacturing tolerances produce unequal engagement that concentrates load on a few teeth. This article explains the contact mechanics, the load sharing, the fretting risk and the effect of misalignment.Press Fits & Interference FitsAn interference fit assembly creates contact pressure between the shaft and the hub before any external load is applied. This flagship article explains the interference, the contact pressure, the assembly force, the hoop stress, the thermal assembly and the tolerance sensitivity — and why an interference fit is not a zero-load assembly state.
Modelling & Life
Contact FEA & Numerical Modelling StrategyContact FEA is the numerical tool for interfaces that exceed the Hertzian assumptions — conformal contacts, rough surfaces, plasticity, friction, complex geometry. This flagship article explains contact pair definition, surface-to-surface contact, friction, normal stiffness, penetration tolerance, mesh refinement, non-linear convergence, contact opening and closing, and the critical distinction between solver convergence and contact-pressure accuracy.Surface Condition, Manufacturing & Contact DurabilityThe nominal CAD surface is not the physical interface. Surface finish, hardness, coating, residual stress, manufacturing marks, roundness, waviness and alignment all affect the contact mechanics and the durability. This article explains why the real surface differs from the drawing and how these differences change the contact behaviour.From Interface Load to Defensible Contact-Life AssessmentThe complete chain from interface load to contact-life assessment. This concluding article walks through the entire process — interface load, geometry, material, contact patch, pressure, subsurface stress, slip/friction, lubrication/environment, fatigue/wear, test/inspection and engineering decision — and finishes with the principle that contact must be assessed as an interface system, not as a single stress value.
Bearings & Life
Rolling-Element Bearing Rating Life, Static Capacity & ReliabilityHow bearing catalogue ratings become defensible life and static-capacity assessments once load spectra, reliability, contamination, lubrication, oscillation and system-level load distribution are included.Bearing Internal Clearance, Preload, Fits & Thermal Operating StateHow manufacturing fits, internal clearance, preload and differential thermal growth determine the installed bearing state, contact load distribution, stiffness, friction and life.Bearing Arrangements, Misalignment & Support-System StiffnessHow shaft, bearing and housing stiffness combine to distribute reaction loads, control alignment and create edge loading in real bearing systems.
Gears & Torque Transmission
Gear Tooth Bending, Root Stress & Bending FatigueHow transmitted torque, tooth-root geometry, load sharing, dynamic factors and material condition combine to determine gear-tooth bending stress and fatigue margin.Gear Mesh Load Distribution, Misalignment & System DeflectionHow shaft bending, bearing compliance, housing deformation, manufacturing error and tooth modifications control face-load distribution, mesh alignment and local gear durability.
Shafts & Torque-Carrying Components
Shaft Strength, Deflection & FatigueHow combined bending, torsion, axial load, stress concentrations, fits and duty cycles are converted into defensible shaft strength, stiffness and fatigue assessments.Keys, Keyways & Torque-Transfer FeaturesHow keys and keyed shaft-hub connections transfer torque, create local bearing/shear stress and introduce shaft fatigue concentrations that must be assessed together.Mechanical Couplings — Misalignment, Torsional Flexibility & Structural IntegrityHow rigid, flexible and compliant shaft couplings transfer torque while accommodating alignment error, axial motion and torsional dynamics without creating unacceptable hub, bolt, element or shaft loads.