Tools
Engineering Calculators
The working calculators from the original site, ported to run in any modern browser. The computation is a literal port of the original JavaScript and is checked against the legacy output before a calculator is marked validated.
Gas & aerostatic bearings
Aerostatic thrust bearing — simple orifice restrictorLoad capacity, stiffness, mass flow and orifice sizing for an aerostatic thrust bearing with a simple orifice restrictor. Unlocked from the legacy demo gate; general in its geometry.Aerostatic shallow-pocket thrust bearingLoad capacity, stiffness and flow for an aerostatic shallow-pocket thrust bearing, from the pocket and land pressure profiles. Unlocked from the legacy demo gate; general in its geometry.Aerostatic bearing — grouped inherent orificesDesign pressure ratio and load capacity for an aerostatic thrust bearing fed through grouped inherent orifices.Self-acting plain cylindrical journal bearingCompressibility number, dimensionless stiffness and attitude angle for a self-acting (aerodynamic) plain cylindrical journal bearing — a specialist gas-bearing calculation with essentially no free equivalent anywhere.Simple orifice restrictor sizingCross-section area and diameter of a simple orifice restrictor for a gas bearing, from the required flow rate and supply/restrictor/ambient pressures.Aerostatic thrust bearing, simple orifice restrictor — fixed reference geometry (A)Reference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 pressure ratio — fixed, matching the original) for an aerostatic thrust bearing with a simple orifice restrictor. Vary feed diameter, pressures and discharge coefficient.Aerostatic thrust bearing, simple orifice restrictor with slot-flow check — fixed reference geometry (B)Reference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 — fixed) for an aerostatic thrust bearing with a simple orifice restrictor, including a supply-slot vs. choked-flow area check (A3/A3c).Air bearing, porous surface feed — fixed reference geometryReference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 — fixed) for an aerostatic thrust bearing fed through a porous surface (permeability-coefficient restriction).Air bearing, slot feeding — fixed reference geometryReference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 — fixed) for an aerostatic thrust bearing fed through an annular slot with nr discrete orifices.Thrust-collar air bearing, orifice/slot — fixed reference geometry (A)Reference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 — fixed) for a thrust-collar aerostatic bearing with an outer feed zone and an inner vacuum/exhaust zone.Thrust-collar air bearing, orifice/slot — fixed reference geometry (B)Reference-geometry calculator (Ø40mm outer diameter, 5µm film, β=0.6 — fixed) for a thrust-collar aerostatic bearing fed through a slot of nr discrete orifices, with an inner vacuum/exhaust zone and a supply choked-flow check.Vacuum-preloaded air bearing, porous ring feed — fixed reference geometryReference-geometry calculator (76mm outer diameter, 5µm film, 0.5MPa supply — fixed, matching the original) for a vacuum-preloaded aerostatic thrust collar bearing fed through a porous ring. Vary the remaining diameters and pressures.Vacuum-preloaded air bearing, simple orifice feed — fixed reference geometryReference-geometry calculator (76mm outer diameter, 5µm film, 0.28MPa supply — fixed, matching the original) for a vacuum-preloaded aerostatic thrust collar bearing fed through discrete simple orifices. Vary the remaining diameters and pressures.Externally pressurized gas bearing — shallow pocket (design chart)Dimensionless pressure ratio, load, stiffness and load-change (at ε=0.5) design formula for an externally pressurized gas bearing with a shallow-pocket (constant-flow) restrictor.Externally pressurized gas bearing — partially grooved surface (design chart)Dimensionless pressure ratio, load, stiffness and load-change (at ε=0.5) design formula for an externally pressurized gas bearing with a partially grooved feed surface.Aerostatic slim air bearing — groove-compensated circular thrust bearingLoad capacity, stiffness, mass flow and volume flow for a circular groove-compensated aerostatic thrust bearing (modeled on the slimairbearings.eu product family).Aerostatic radial bearing — partially porous surfaceLoad, stiffness, restrictor gap and gas flow for a radial (journal) aerostatic bearing fed through a partially porous sleeve surface.Aerostatic radial gas bearing — design and calculationLoad, stiffness, restrictor gap and gas flow for an aerostatic radial (journal) gas bearing, using the porous/groove-feed design correlation for L/D ratios from ~0.25 up.Aerostatic radial bearing — partially grooved surfaceEccentric load capacity and gas mass flow for a partially grooved (symmetric) radial aerostatic bearing, integrated over the groove pattern around the bearing.New Way porous air bearing — flat roundCatalog performance data (load, stiffness, flow, mass) for New Way flat round porous-carbon air bearings, by diameter, at the vendor-fixed 60 psi supply and 5 µm fly height.New Way porous air bearing — bushing (sleeve)Catalog performance data (max load, radial stiffness, flow, mass, dimensions) for New Way porous-carbon air bearing bushings (radial sleeves), by bore diameter, at the vendor-fixed 60 psi supply and 4 µm air gap.Externally pressurized (udv) gas thrust bearing — porous surfaceLoad, stiffness, restrictor gap and gas flow for an externally pressurized aerostatic thrust bearing fed through a porous annular ring.Flow resistance of a compressed-air supply hosePressure drop along a compressed-air supply hose/line for a given flow rate, length and inner diameter — for sizing the air supply feeding an aerostatic bearing.
Spiral-groove bearings
Spiral-groove bearing (axial)Axial load capacity, stiffness, friction torque and power loss for a spiral-groove thrust bearing — a specialist calculation with essentially no free equivalent anywhere.Spiral-groove thrust bearing (design)Operating speed, friction torque and power loss for an axial spiral-groove thrust bearing carrying a given load, from the groove geometry and film thickness.Self-acting spiral-groove journal bearingCompressibility number, dimensionless stiffness and attitude angle for a self-acting (aerodynamic) spiral-groove journal bearing — a specialist gas-bearing calculation with essentially no free equivalent anywhere.Herringbone thrust bearing (design)Operating speed, friction torque and power loss for a herringbone-profile spiral-groove thrust bearing carrying a given load.
Hydrostatic bearings
Hydrostatic circular thrust pad with restrictor choiceLoad capacity, stiffness, flow rate and pump power for a circular hydrostatic thrust pad, with a choice of capillary, orifice or fixed-flow restrictor — after the hydrostatic bearings of the Prins Willem-Alexander locks in Amsterdam.Hydrostatic bearing — wedge-film thrust padDimensionless load, stiffness and load-sensitivity for a wedge-film hydrostatic thrust pad, from the film-thickness ratio h1/h0.Hydrostatic bearing — shallow-recess thrust padDimensionless load, stiffness and load-sensitivity for a shallow-recess hydrostatic thrust pad, from the recess-area and film-thickness ratios.Hydrostatic 4-chamber thrust bearingLoad, stiffness, flow and power for a hydrostatic 4-chamber thrust bearing, with a choice of capillary, orifice, or fixed-flow restrictor.Hydrostatic journal bearing, externally pressurizedLoad, stiffness, flow and power for an externally pressurized hydrostatic journal bearing — separated or connected recess elements, with a choice of restrictor.Partially grooved hydrostatic journal bearingLoad and flow for a partially grooved, externally pressurized hydrostatic journal bearing with k grooves, by numerical summation around the circumference.Hydrostatic shallow-pocket liquid thrust bearing — fixed reference geometryReference-geometry calculator (Ø40mm bearing, 5µm film — fixed, matching the original) for a hydrostatic shallow-pocket liquid thrust bearing fed through a small central inlet hole. Vary pocket/inlet diameter, pressures and viscosity.Hydrostatic thrust bearing, central pocket, capillary restrictor — fixed reference geometryReference-geometry calculator (60mm bearing radius — fixed, matching the original) for a circular hydrostatic thrust bearing with a central pocket fed through a capillary restrictor. Vary pocket radius, film thickness, pressure and fluid properties.Orifice-compensated hydrostatic thrust bearing, central pocket — fixed reference geometryReference-geometry calculator (60mm bearing radius — fixed, matching the original) for a circular hydrostatic thrust bearing with a central pocket fed through a sharp-edged orifice. Vary pocket radius, film thickness, pressure and fluid properties.Orifice-compensated hydrostatic thrust bearing, central pocket (lock-gate scale) — fixed reference geometryReference-geometry calculator (650mm bearing diameter, 0.1mm film thickness, 0.7 pressure factor — all fixed, matching the original) for the alternative single-pocket design to the 4-pocket hydrostatic lock-gate bearings of the Prins Willem Alexander Lock in Amsterdam.Hydrostatic journal bearing, multi-recess — fixed reference geometryReference-geometry calculator (60mm shaft diameter, L/D=1, 50 bar supply pressure — all fixed, matching the original) for an externally pressurized journal bearing with 4 or 5 pockets and a choice of capillary, orifice or fixed-flow restrictor.Hydrostatic collar bearing, slot feed through orifices — fixed reference geometryReference-geometry calculator (40mm outer diameter — fixed, matching the original) for a hydrostatic thrust collar bearing fed via a circumferential groove supplied by discrete orifices. Vary groove/inner diameter, film thickness, pressures and fluid properties.Hydrostatic thrust bearing, single center pocket — fixed reference geometryReference-geometry calculator (650mm bearing diameter, 0.1mm film, β=0.7 — fixed, matching the original) for a single-pocket, multi-orifice hydrostatic thrust bearing. Vary pocket diameter, supply pressure and fluid properties.
EHL & film thickness
EHL line contact — film thicknessCentral film thickness of an elastohydrodynamic line contact from the Moes dimensionless load/lubrication groups, with contact half-width and Hertzian pressures.EHL film thickness in wire drawingLubricant film thickness and drawing stress between wire and die, from area reduction, die angle, speed and lubricant properties.EHL film thickness in sheet rollingLubricant film thickness, contact length and roll force between the work rolls and the sheet, from the reduction ratio and lubricant properties.EHL film thickness in a grooved ball bearingElastohydrodynamic film thickness, contact ellipse and pressure for a grooved ball bearing, using the Hamrock-Dowson regression.EHL film thickness in a point contact (direct load/speed)Elastohydrodynamic film thickness, contact ellipse and pressure for a general elliptical point contact, from directly specified load and entrainment speed.
Bearings (general)
Rolling bearing basic rating life (L10)Basic (L10) rating life of a rolling bearing, in millions of revolutions and in operating hours, from the catalogue dynamic load rating, equivalent bearing load and rotational speed.Equivalent dynamic bearing loadEquivalent dynamic bearing load P for a single-row deep-groove ball bearing under combined radial and axial load, from the SKF e/X/Y factor tables for Normal/C3/C4 radial clearance.Water-lubricated journal bearingPV-value, side-leakage flow, power loss and frictional temperature rise of a water-lubricated journal bearing operating at near-full eccentricity, assuming adiabatic conditions.Pivot bearing — contact pressure and friction torqueContact pressure (Hertz, with interpolation to a plastic/Brinell regime at high loads) and friction torque/power for a pivot bearing ("boltaats").Tilting-pad (Michell) bearing — rectangular padLoad capacity, friction coefficient and film-thickness/eccentricity numbers for a rectangular Michell tilting-pad bearing, sized as a compromise between minimum friction and maximum film thickness.Hydrodynamic journal bearingSommerfeld number, attitude angle, friction, load capacity, stiffness, side leakage and frictional heating for a finite-length hydrodynamic journal bearing. Unlocked from the legacy demo gate; general in shaft diameter, clearance and film thickness.Hydrodynamic bearing under shock (impulsive) loadDimensionless and dimensional impulse capacity of a finite-length hydrodynamic journal bearing (π-film boundary condition) subjected to a shock/impact load.Design of a hydrodynamically lubricated plain bearingSommerfeld number, attitude angle, friction and flow numbers, plus load capacity, friction coefficient and lubricant flow for a hydrodynamically lubricated plain (journal) bearing, from length ratio, eccentricity, clearance ratio, radius, speed and viscosity.Journal bearing — oil flow / pressure dropPressure drop across a journal bearing film needed to produce a prescribed axial (cooling) flow rate, from shaft diameter, bearing length, radial clearance, eccentricity and viscosity.Static load capacity of polymer (thermoplastic) bearingsElastic indentation, contact geometry, load capacity and stiffness of a thermoplastic sliding bearing bush from shaft diameter, bearing length, wall thickness, modulus of elasticity, radial clearance and allowable contact pressure.Load capacity and stiffness of guide ringsContact geometry, load capacity and stiffness of a resilient thermoplastic guide (wear) ring supporting a piston/rod, from piston diameter, ring width/thickness, elastic indentation, radial clearance and modulus of elasticity. Unlocked from the legacy demo gate; general in shaft diameter and indentation.Static load rating of a deep-groove ball bearing (Hertz)Elliptical (Hertzian) contact pressure for a prescribed bearing load, and the ISO 76:1987 basic static load rating C0 for a prescribed maximum contact pressure, from ball and raceway elastic properties and curvatures.Friction in a ball-cage linear guideHertzian contact stiffness and pressure of a single ball in a ball-cage linear guide (loaded at 45° to the guide axis), plus the resulting sliding friction force and coefficient.
Wear
Journal bearing specific wear rateAverage contact pressure, worn volume and specific wear rate of a journal bearing, from the shaft/bearing dimensions, load, wear depth and sliding distance.Specific wear rate (pin-on-disk)Specific wear rate from a pin-on-disk test, derived from the worn volume, normal load and sliding distance (Archard-type wear coefficient).Specific wear rate (ball-on-disk, nominal point contact)Specific wear rate from a ball-on-disk test, derived from the worn spherical-cap volume (from the measured wear scar radius on a ball of known radius), normal load and sliding distance.Specific wear rate (nominal line contact)Specific wear rate for a nominal line-contact wear scar, derived from the worn circular-segment cross-section (counter-body radius and scar half-width) times the contact length, normal load and sliding distance.Plain (journal) bearing wear and service lifeProjected pressure, PV value, wear volume and service life of a plain bearing from shaft/bearing geometry, load, sliding speed and specific wear rate. Unlocked from the legacy demo gate; general in shaft diameter.Allowable load / LPV value of plastic (or sintered) plain bearingsTwo independent checks for a plastic or sintered-bronze plain bearing: the contact temperature rise for a given load and sliding speed, and the maximum allowable load for a given permissible temperature rise (limiting pressure-velocity, LPV).Specific wear rate, nominal point contact (three methods)Archard specific wear rate for a point-contact (pin-on-disk) wear scar, computed three independent ways: from scar diameter+depth, from wear depth+pressure+velocity+time, or from mass loss+density.Specific wear rate, nominal line contact — from ring radius and scar widthArchard specific wear rate for a line-contact (pin-on-ring) wear scar, computed from the ring radius and semi scar width, deriving the scar depth from circular-segment geometry.Specific wear rate, nominal line contact — from scar depth and widthArchard specific wear rate for a line-contact (pin-on-ring) wear scar, computed from the scar depth and semi scar width, deriving the ring radius algebraically.Contact (flash) temperature, pin-on-diskBulk and flash frictional contact temperature rise for a pin-on-disk sliding contact, from normal load, sliding velocity, friction coefficient, pin geometry (radius, length) and material properties.Contact (flash) temperature, ball-on-disk point contact (Ashby T-maps)Bulk and flash frictional contact temperature rise for a ball-on-disk (point) contact via the Ashby T-maps method, from normal load, sliding velocity, friction coefficient, contact radius and material properties — no separate pin-length input.
Contact mechanics (Hertz)
Hertz point contactContact radius, elastic approach, mean and maximum contact pressure, and contact stiffness for two bodies in point contact (Hertz theory).Hertz elliptical contactContact semi-axes, mean and maximum contact pressure for two bodies in elliptical (general curved) contact, with independent radii of curvature in two perpendicular planes (Hertz theory).Hertz elliptical contact (full precision)Contact semi-axes, mean and maximum contact pressure for two bodies in elliptical contact — same formula as the "Hertz elliptical contact" calculator, but returning unrounded, full-precision results as the original e2_7 page does.Hertz line contactSemi contact width, mean and maximum contact pressure for two parallel cylindrical bodies (or a cylinder on a flat) in line contact under a prescribed load per unit length (Hertz theory).Hertz line contact, contact pressure and dimensionsSemi contact width, mean and maximum contact pressure for a cylindrical body in line contact (optionally against a concave/conforming counter-surface), under a prescribed load per unit length (Hertz theory).Hertz initial point contact — load from prescribed contact pressureFor a ball on a flat, computes the effective modulus, effective radius, initial contact diameter, indentation and contact load corresponding to a prescribed mean contact pressure (e.g. the onset of yield, pmc = Rp0.2).Traction rollers, point contact (Hertz)Increase in maximum subsurface stress and matching decrease in allowable normal load for Hertzian POINT-contact rollers (crowned/ball-like contact) under a given traction coefficient Ftan/F.Traction rollers, line contact (Hertz)Increase in maximum subsurface stress and matching decrease in allowable normal load for Hertzian LINE-contact rollers (parallel cylinders) under a given traction coefficient Ftan/F.
Bolts, threads & fasteners
Bolt preload torqueTightening torque to reach the preload of a metric bolt, with the induced torsional/equivalent stress and the bolt-force reserve — from ISO thread geometry and the strength class.Maximum dynamic load on a preloaded metric boltMaximum fatigue (dynamic) load capacity of a preloaded metric bolted joint, from thread size, property class and joint stiffness.Maximum tightening torque to preload a metric boltTightening torque (thread + head friction), resulting preload and stress relaxation for a metric bolted joint tightened to a prescribed equivalent stress.Thread (stripping) shear strengthShear (stripping) strength of a metric thread engagement, from the effective thread length and allowable shear stress.Flat belt drive — shaft loadBelt length, wrap angle, belt tensions and resulting shaft load for a flat belt drive.Maximum tensile force in a metric boltPreload and load reserve for a metric bolt tightened to a prescribed tensile stress (fraction of yield strength).UNC fastener in tensionThread geometry, SAE proof strength and initial preload for a UNC fastener under tension.Tightening torque to preload a UNC boltTightening torque (thread + head friction), preload and equivalent stress for a UNC bolt (SAE grade system, US customary units).UNF fastener in tensionThread geometry, SAE proof strength and initial preload for a UNF fastener under tension.Tightening torque to preload a UNF boltTightening torque (thread + head friction), preload and equivalent stress for a UNF bolt (SAE grade system, US customary units).Flat (parallel) key designStandard key cross-section for a given shaft diameter, and the resulting shear stress, bearing pressure and shaft torsional stress.
Mechanical joints
Bolted joint fatigue (dynamic load) strength — fixed M12 geometryLoad-fatigue limit of a bolted joint (M12 thread — fixed, matching the original locked demo) from property class, joint stiffness factor and minimum clamping force.Bolted joint under operating load — maximum operating loadPreload, stiffness-based load split and maximum permissible operating load for a preloaded metric bolted joint, from thread size, property class, preload fraction and joint stiffness factor.Bolted joint stiffness ratio (joint stiffness factor)Bolt stiffness, an assumed pressure-cone stiffness of the clamped material, and the resulting joint stiffness factor Cₘ=kᵦ/(kᵦ+kₘ) used elsewhere in bolted-joint load-sharing calculations.Adhesive slip-fit joint (shaft in a bore)Maximum shear force and transmissible torque for an adhesive slip-fit joint of a shaft in a bore, from bond diameter, length and adhesive shear strength.Clamping bushing (collar) on a shaftMean contact pressure, friction force and maximum transmissible torque for a clamping bushing on a shaft, from bore diameter, clamped length, clamping force and coefficient of friction.Pinned joint (shaft with a cylindrical transverse pin)Shear force, shear stress, bearing pressure and torsional stress for a shaft-and-hub joint secured by a cylindrical transverse pin, from shaft/pin diameter, hub thickness and applied torque.Adhesive lap joint — shear stress distribution (Goland & Reissner)Minimum and maximum adhesive shear stress across a bonded lap joint (Goland & Reissner model), from plate thickness/stiffness, adhesive thickness/shear modulus, load per unit width and overlap length.
Press & interference fits
Interference fit — probability of falling short of a targetProbability that the actual (normally-distributed) interference of a hole/shaft fit falls below a chosen minimum threshold, from the hole and shaft tolerance bands.Interference fit of a thin-walled hollow shaft (min/max tolerances)Deterministic (worst-case) and probabilistic (±1.96σ) contact pressure, mounting force and transmissible torque for an interference fit of a thin-walled hollow shaft in a bore, stressed into the plastic regime, from the min/max tolerance bands of every dimension.Press fit (interference fit)Contact pressure, transmissible force and torque, and the tangential/radial/equivalent stresses in an interference fit, from Lamé’s equations in the elastic regime.Press-fit tolerance calculator (probabilistic interference)Deterministic (worst-case) and probabilistic interference for a press fit from the bore and shaft tolerance bands, using an inverse-normal-CDF approximation for the chosen reliability interval.Interference fit — pressure, force, torque and assembly temperatureContact pressure, friction force/torque and stresses for an interference fit (Lame equations), plus the cooling/heating temperature needed for expansion/shrink-fit assembly.Press fit calculation — fixed 23mm interface diameterContact pressure, friction force/torque and stresses for an interference fit (Lame equations), with the interface diameter fixed at 23mm as in the original locked demo page.Press fit of a thin-walled tubeContact pressure, mounting/friction force and transmission torque for a press fit of a thin-walled tube, from the tube’s hoop (tensile) stress at assembly.Cone-type shaft-hub interference fit — fixed 20mm mean diameterInterference, contact pressure, friction force, axial force and transmission torque for a cone-type shaft-hub connection (Lame equations), with the mean diameter fixed at 20mm as in the original locked demo page.
Shaft & axle fatigue
Fatigue life of welded structuresS-N curve slope and fatigue life for a welded structure, from the fatigue strength parameter and applied stress amplitude (Eurocode 3 / NEN 2063 weld-detail categories).Drive shaft fatigue strength in torsion (with notch factor)Maximum static and dynamic (fatigue) torque for a drive shaft loaded in torsion at a critical, notched cross-section.Drive shaft fatigue strength in bendingMaximum static and cyclic bending moment for a drive shaft at a critical, notched cross-section, from tensile strength and stress concentration factor.Drive shaft torsional stress and stiffnessTorsional stress, angle of twist and torsional stiffness of a solid or hollow drive shaft under a static torque.Idler / support axle bendingBending stress, deflection and end slope of a solid or hollow support axle, for an applied moment and (separately) an end force.Drive shaft under combined bending and torsionBending stress, torsional stress and von Mises equivalent stress for a solid or hollow drive shaft loaded simultaneously in bending and torsion.Drive shaft fatigue strength with a keywayStandard key cross-section for a given shaft diameter, and the fatigue strength (static and cyclic torque limit) of the shaft at the keyway root.Splined shaft connection — torsional stressTorsional (shear) stress in a splined shaft connection, based on the root/minor diameter, under a static torque.
Stress concentration
Shaft diameter for a grooved shaft in bending (given Kt)Sizes the diameters of a grooved/shouldered shaft in bending from the applied bending moment, yield strength, target endurance ratio and a prescribed geometric stress concentration factor Kt.Geometric stress concentration for a shaft with shoulder fillet in torsionGeometric stress concentration factor Kt = A(r/d)^b for a stepped shaft with a shoulder fillet loaded in torsion, from chart-fit coefficients A, b keyed on the D/d ratio.Geometric stress concentration for a shaft with shoulder fillet in bendingGeometric stress concentration factor Kt = A(r/d)^b for a stepped shaft with a shoulder fillet loaded in bending, from chart-fit coefficients A, b keyed on the D/d ratio.Geometric stress concentration for a shaft with a transverse hole in torsionGeometric stress concentration factors for a shaft with a transverse (drilled) hole loaded in torsion — on the shaft surface at the hole (KtA) and below the surface inside the hole (KtB) — from independent polynomial fits in the hole/shaft diameter ratio d/D.Geometric stress concentration for a shaft with a transverse hole in bendingGeometric stress concentration factor on the surface of a shaft with a transverse (drilled) hole loaded in bending, from a log10 curve fit in the hole/shaft diameter ratio d/D.Geometric stress concentration for a grooved shaft in tensionGeometric stress concentration factor Kt = A(r/d)^b for a grooved shaft loaded in tension, from chart-fit coefficients A, b keyed on the D/d ratio (r/d clamped to 0.1 above its 0.3 validity limit, as in the legacy page).Geometric stress concentration for a grooved shaft in bendingGeometric stress concentration factor Kt = A(r/d)^b for a grooved shaft loaded in bending, from chart-fit coefficients A, b keyed on the D/d ratio (r/d clamped to 0.1 above its 0.3 validity limit, as in the legacy page).Geometric stress concentration for a grooved shaft in torsionGeometric stress concentration factor Kt = A(r/d)^b for a grooved shaft loaded in torsion, from chart-fit coefficients A, b keyed on the D/d ratio (r/d clamped to 0.1 above its 0.3 validity limit, as in the legacy page).
Gears (ISO 6336)
Gear tooth flank (pitting) strength — ISO 6336-1/-2Maximum tangential force and drive torque for a spur/helical gear pair from permissible flank (contact) stress, per ISO 6336-1/-2.Gear tooth-root bending strength — ISO 6336-1/-3Maximum tangential force and drive torque for a spur/helical gear pair from permissible tooth-root bending stress, per ISO 6336-1/-3.Gear flank load factor, K_H,tot — ISO 6336-2Total load factor σ_H/σ_H0 = (K_A·K_v·K_Hα·K_Hβ)^½ used in the ISO 6336-2 flank (pitting) strength calculation.Gear flank permissible-stress factor, K_C,tot — ISO 6336-2Total correction factor σ_HP/σ_H,lim = (Z_NT·Z_L·Z_v·Z_R·Z_w·Z_x)/S_H for the permissible flank (contact) stress in the ISO 6336-2 pitting calculation.Gear tooth-root load factor, K_F,tot — ISO 6336-3Total load factor σ_F/σ_F0 = K_A·K_v·K_Fα·K_Fβ used in the ISO 6336-3 tooth-root bending strength calculation.Gear tooth-root permissible-stress factor, K_S,tot — ISO 6336-3Total correction factor σ_FP/σ_F,lim = (Y_ST·Y_NT·Y_δ·Y_R·Y_X)/S_F for the permissible tooth-root bending stress in the ISO 6336-3 calculation.
Flexure & springs
Hole (notch) flexure hingeNormal and rotational stiffness, and maximum rotation angle, of a circular-hole (notch) flexure hinge in a flat plate.Cross (leaf-spring) flexure hingeTorsional stiffness of a cross-spring (leaf-spring) flexure hinge from plate-spring geometry and the crossing-angle ratio.Compression / tension spring (A)Deflection, stiffness, shear stress and stored energy of a helical compression/tension spring, from wire diameter, coil diameter, number of coils and shear modulus.Compression / tension spring (B)Deflection, stiffness and shear stress of a helical compression/tension spring, using an alternative coefficient set to compression-tension-spring-a.Conical springDeflection, stiffness and shear stress of a helical conical (tapered-coil) spring, from wire diameter and top/bottom mean coil diameters.Torsion spring (coiled)Bending stress, angular deflection, stiffness and stored energy of a coiled helical torsion spring, loaded by a force at a lever arm.Torsion spring (bar)Bending stress, angular deflection and stiffness of a straight torsion-bar spring, from wire diameter, lever arm and effective spring length.Disc (Belleville washer) springStress, deflection and stiffness of a Belleville disc spring, from outer/inner diameter, thickness and material properties.Torsion bar (solid, round)Polar moment of inertia, shear stress, angular deflection and torsional stiffness of a solid round torsion bar.Torsion bar (hollow, round)Polar moment of inertia, shear stress, angular deflection and torsional stiffness of a hollow round torsion bar.Leaf spring (cantilever)Bending moment, stress, deflection, end slope and stiffness of a cantilever leaf spring under an end load.Tension bar (rod spring)Cross-section area, tensile stress, axial deflection and stiffness of a cylindrical bar loaded in tension, acting as a simple rod spring.
Lubricant & viscosity
Shell four-ball tester — contact temperature from frictionBulk and flash contact temperature rise in a Shell four-ball lubricant/EP-additive tester, from load, speed, ball size, friction coefficient and material properties.Rotating concentric-cylinder viscometerShear rate, shear stress and torque (or, given a measured torque, the dynamic viscosity) for a rotating concentric-cylinder viscometer, from spindle and reservoir geometry.Cone-on-plate viscometerShear rate, shear stress and torque (or, given a measured torque, the dynamic viscosity) for a cone-on-plate viscometer, from cone angle, radius and rotational speed.Viscosity-temperature relation — Reynolds & Vogel-Cameron (reference case)Reynolds and Vogel & Cameron viscosity-temperature interpolation for one worked reference oil (T1=40°C/68 mPa·s, T2=100°C/8.6 mPa·s, interpolated to T3=60°C). The original site never ships the interpolation formula client-side — only this login-gated worked example.Viscosity-temperature relation — ASTM D341 (reference case)ASTM D341 (Ubbelohde-Walther) kinematic viscosity-temperature interpolation for one worked reference oil (40°C/68 cSt, 100°C/8.6 cSt, interpolated to 60°C). The original page never ships the interpolation formula client-side — only this login-gated worked example.Viscosity Index — ISO 2909 / ASTM D2270 (reference case)Viscosity Index (VI) and its two inverse forms (kinematic viscosity at 100°C, or at 40°C) for one worked reference oil (40°C/68 cSt, 100°C/8.6 cSt, VI=97). The original page never ships the VI formula client-side — only this login-gated worked example, in three directions.Viscosity at temperature T from VI — ISO 2909/ASTM D2270 + ASTM D341 (reference case)Kinematic viscosity at an arbitrary temperature T, derived from the Viscosity Index (ISO 2909/ASTM D2270) and interpolated per ASTM D341, for one worked reference oil (40°C/68 cSt, VI=97, evaluated at T=100°C). The original page never ships the combined formula client-side — only this login-gated worked example.Kinematic viscosity of a base-oil mixture (reference case)Kinematic viscosity of a blend of two base oils by weight percentage, for one worked reference case (40 mm²/s and 20 mm²/s oils, 50% by weight, at 40°C). The original site never ships the blending formula client-side — only this login-gated worked example.Viscosity-pressure dependence — Barus & Roelands (reference case)Barus and Roelands piezoviscosity ratios η/η₀ for one worked reference lubricant (η₀=60 mPa·s, pressure-viscosity coefficient α=20×10⁻⁹ 1/Pa, at p=100 MPa). The original site never ships the Barus/Roelands equations client-side — only this login-gated worked example.
Vibration & damping
Viscous damping, solid piston in a cylindrical boreDamping constant of a solid (bore-less) piston sliding in a viscous-fluid-filled cylinder, given both as pressure-driven (Poiseuille) squeeze flow and as pure Couette drag flow across the radial gap.Viscous damping, capillary-tube (suspension / shock absorber) damperDamping constant and normalised impulse of a piston damper that forces fluid through a thin capillary tube (Hagen-Poiseuille flow), as used in suspension and shock absorbers.Viscous damping, annular (bored) pistonDamping constant and normalised impulse of an annular piston (outer radius R₀ over an inner bore/rod R₁) sliding concentrically through a viscous-fluid-filled radial gap.Viscous annular damper, impact (shock) responseStopping stroke, peak piston force and peak hydrostatic pressure of an annular viscous damper (outer radius R₀, inner radius R₁, gap h₀) when a mass enters at a given impact velocity, including a relative-eccentricity correction.Viscous damper, steady-state harmonic (sinusoidal) responseSteady-state sinusoidal force/velocity/displacement amplitudes of a pure viscous damper of known damping constant C at a given frequency f — either from a known displacement amplitude or from a known force amplitude.
Power transmission
Band brakeBelt tensions, shaft load, actuating force and peak contact pressure for a simple lever-actuated band brake, from the brake torque, drum radius, wrap angle and friction coefficient.Differential band brakeBelt tensions, shaft load and actuating force for a differential (two-lever) band brake, which can be configured bi-directional, self-energising, or as a one-way clutch.Trapezoidal thread power screw — fixed nut lengthTightening/loosening torque, thread efficiency, contact pressure and sliding-wear service life of a trapezoidal-thread power screw (nut length fixed at 44 mm, matching the original locked demo).Power screw — torque, safety factor and service lifeForward/back-drive friction torque, screw efficiency, thread contact pressure, safety factor and sliding-wear service life of a trapezoidal power screw, from thread size, material grade, axial load, friction and nut geometry.Van Doorne's metal push-belt (CVT) driveTransmission ratio, belt speed/length, wrap angle, drive torque and force, belt-strand tensions and resulting shaft load for a metal V-belt (Van Doorne push-belt / CVT) drive between two pulleys.V-belt drive: length, wrap angle, tensions and shaft loadTransmission ratio, belt speed and length, wrap angle, drive force, belt tensions T1/T2 and resulting shaft load for a V-belt drive, from power, speed, pulley diameters, center distance and groove angle.
Structural
Fillet weld under static loadResultant forces, weld-throat shear/normal stresses and the equivalent stress for a statically loaded fillet weld under an eccentric, angled load (single- or double-sided weld).Stresses in cylinders, vessels and pipes (Lame)Tangential (hoop) and von Mises equivalent stresses at the inner and outer surfaces, and diametric expansion, of an open-ended thick-walled cylinder under internal pressure only, from Lame's equations.Weld fatigue life, dynamically loaded (Eurocode 3, prEN 1993-1-9)Constant-amplitude fatigue limit, cut-off limit, S-N slope exponent and fatigue life of a dynamically loaded weld detail, from its Eurocode 3 detail category (FAT class) and applied stress range.Buckling limit of compression-loaded columnsEuler buckling load, axial stiffness, cross-section area and second moment of area for a hollow circular column, for four standard end-condition (buckling mode) cases.Buckling limit of S-shaped beams (wire springs)Longitudinal and lateral stiffness, bending stress and buckling load for an S-shaped (reinforced mid-section) wire spring/beam, for two beam-type configurations.
Seals
Mechanical seal bearing capacity — tapered filmLoad capacity, flow rate and axial stiffness for a mechanical seal with a tapered (converging) film, treated as an annular hydrostatic collar bearing.Mechanical shaft seal contact pressure, leakage and frictionContact pressure on the seal face, leakage flow, friction coefficient and heat generation for an axial (mechanical) shaft seal with a thin parallel lubricating film.Dynamic O-ring seal groove sizing (piston and rod)Sizes the piston-bore and rod-bore groove geometry (bore/shaft tolerances, groove width, squeeze) for a dynamic O-ring seal from O-ring cross-section, stretch and squeeze.
Reliability & tolerances
Normal distribution: value for a given failure probabilityGiven a mean, standard deviation and target failure probability F(t) = p, returns the corresponding value t.Probabilistic radial clearance of a hydraulic cylinder wear ringProbabilistic (1% percentile) and worst-case deterministic radial clearance of a hydraulic cylinder wear ring, from the piston, groove and ring-thickness tolerance ranges.Probability interval from measured dataMean, standard deviation and a probability (tolerance) interval derived from up to 10 measured data points.Probability interval of shaft diameter tolerancesConverts a uniform manufacturing tolerance field into an equivalent normal-distribution tolerance interval at a chosen confidence level.System reliability — series and parallel combinationCombined system reliability for two components, both in series and in parallel.Reliability data conversion — μ, σ → R(t)Converts a mean and standard deviation (normal life distribution) plus a service life into a reliability R(t), by numerical integration of the standard normal density.Motor reliability with two bearingsWeibull-based reliability of each bearing at a given service life (from its L10 life), combined into overall motor reliability.Tolerance chain dimensioningWorst-case, root-sum-square and probabilistic combination of a three-link tolerance chain (B, C, D) at a chosen reliability R.MTBF to R(t) conversionMean time between failure from a test of n specimens over duration T with r failures, and the corresponding reference reliability values.Fault tree analysisSystem reliability from a fault tree of three series blocks (A, B, C) followed by two redundant pairs (D+E, F+G).Operating reliability of a ball bearingEstimated operating reliability of a ball bearing at a given service life, from its L10 life (in revolutions) and rotational speed.Reliability factor for fatigue strengthReliability correction factor for fatigue strength, from the coefficient of variation of the strength and a target reliability.Estimation of system reliability — two parts in seriesReliability of two parts, each with its own normal life distribution (mean, standard deviation), connected in series, at a common service life.Normal distribution percentile calculatorOne-sided or two-sided probability (area under the standard normal curve) for a given t-value.Probability distribution of a tolerance intervalConverts a ±3σ tolerance range into mean, standard deviation, and a probability interval at a chosen reliability.Probability of bearing housing radial clearance toleranceDeterministic (worst-case) and probabilistic bush wall-thickness and radial bearing clearance, from housing bore, bush and shaft tolerances.Estimation of service interval for timing belt replacementBack-calculates the mileage service interval at two prescribed reliability levels from a normally distributed failure mileage (mean and standard deviation), for timing belt replacement scheduling.
Unit & scale conversion
Temperature scale conversion (Celsius / Kelvin / Fahrenheit)Converts a temperature value between the Celsius, Kelvin and Fahrenheit scales.Rotational speed unit converter (rpm, m/s, rad/s)Converts a rotational speed between rpm, surface speed (m/s) and angular velocity (rad/s), using the shaft/pulley diameter to relate the angular and linear representations.General unit converterConverts a value between any two units within one of 21 engineering unit categories (length, mass, force, pressure, energy, power, temperature, viscosity, volume flow, etc.), using the legacy JSUC conversion-factor tables.Hardness conversion of metals (ASTM E 140-97)Converts a hardness value between Vickers, Brinell, Knoop, Rockwell (A/B/C/D), Rockwell superficial (15N/30N/45N) and Scleroscope scales for non-austenitic steels, per ASTM E 140-97 Table 1.
General engineering
Hydraulic diameterHydraulic diameter Dh = 4A/S for a rectangular duct (sides a, b) and, independently, for the annular gap between two concentric round tubes (outer/inner diameter).Pressure drop in pipe flow (Darcy-Weisbach)Reynolds number, Darcy friction factor (laminar f=64/Re or Colebrook for turbulent flow) and Darcy-Weisbach pressure drop for flow of a Newtonian fluid through a circular pipe.