Gearsmith user guide

Getting started in two minutes

Gearsmith is a set of machine-element calculators that share one screen: pick a module on the left, edit the inputs in the middle, and read the results on the right. Everything recalculates as you type.

• Choose a module from the left rail (or press Alt + 1 to Alt + 9).
• Choose SI (mm, N, MPa) or US (in, lbf, psi) at the top. Switching converts the current design, including inactive modules and table columns. Reset module explicitly loads the SI example converted to your display units.
• Replace the example numbers with yours. Fields tagged "chart" need a value you read from a chart or standard table (see Chart-based inputs).
• Read the Targets list: each bar shows the computed safety factor or margin, a tick at your target, and green when the target is met or red when it is not.
• Open Report for a printable sheet, or use Export CSV for a spreadsheet-friendly file. Save keeps all modules in one document.

The screen, panel by panel

• Header: Calculate, Guide and Verify views, and a light/dark toggle.
• Toolbar: unit system, Calculate/Report view, Undo, Redo, Reset module (restores the example inputs of the current module), Open, Save, Export CSV and the shortcut list.
• Module rail: nine modules. The highlighted one is current.
• Inputs: grouped fields. Up and Down arrows step a number (Shift for ten times, Alt for a tenth). A red border means the text is not a number. Tables (weld segments, shaft loads, bolt layers) have Add row and a delete button per row.
• Results: Targets (safety factors against your targets), Warnings (range or validity problems found), plots where relevant (shaft deflection, press-fit stresses), a weld layout drawing, and the full results table with symbols and units.

Units and conventions

• SI: lengths mm, forces N, stress and modulus MPa, torque and moments N·m (weld torque and moments N·mm), speeds rpm, bearing loads kN.
• Display switching uses a single SI calculation convention for empirical fits and gravity (9810 mm/s²). Thread standard family is explicit and does not change with display units. Version 2 files store the canonical SI model; opening a version 1 file preserves both old datasets as selectable Legacy SI and Legacy US designs. Undo/redo includes unit and design selection.
• US: lengths in, forces lbf, stress and modulus psi (shaft strengths in kpsi), torque and moments lbf·in, speeds rpm, bearing loads lbf.
• Gears take the normal module (SI) or normal diametral pitch (US). Helical gears use the normal module and the helix angle ψ; transverse values are derived.
• Shaft fatigue treats the section moments as the resultant bending moment and torque at the point studied; Kf, Kfs are fatigue stress-concentration factors (not Kt).
• Weld coordinates are in the plane of the weld group; torque is positive counter-clockwise about z, and the load point is where the force acts. Out-of-plane force Fz and moments Mx, My act on the weld group as a bending problem.
• Deflection loads act downward (positive F) between the supports; the shaft is simply supported with uniform diameter.

Chart-based inputs (what you must supply)

Gearsmith does not reproduce proprietary standard tables or charts. Where a factor normally comes from one, the field is tagged "chart" and you enter the value from your standard, handbook or supplier data. Where a published curve-fit equation exists in Shigley’s Mechanical Engineering Design, the equation is implemented and cited instead.

Spur and helical gears

Geometry follows Shigley Chapter 13: pitch, base, outside and root diameters, centre distance, base pitch, length of the line of action Z, transverse contact ratio mp = Z/pb, axial contact ratio mF = F tan ψ/pt for helical gears, and total contact ratio. Warnings flag tip interference, contact ratio below 1.2 and tooth counts below the undercut limit.

Two strength methods are provided. "AGMA 2001 structure" uses the AGMA stress equations with every factor formula taken from Shigley Chapter 14: bending stress σ = Wt·Ko·Kv·Ks·(1/(F·mt))·(Km·KB/J), contact stress σc = Cp·√(Wt·Ko·Kv·Ks·Km·Cf/(d1·F·I)), the dynamic factor Kv from the Qv curve fit, the load-distribution factor Km from the Cpf and Cma curve fits, the elastic coefficient Cp, the surface geometry factor I (with the helical load-sharing ratio mN = pN/(0.95 Z)), and the safety factors SF = St·YN/(KT·KR·σ) and SH = Sc·ZN·CH/(KT·KR·σc).

"Lewis bending + Hertz contact" is labelled as such: Lewis σ = Kv·Wt/(F·m·Y) with the Barth velocity factor, and the Hertz line-contact pressure at the pitch point. It is a screening method for spur gears; helical gears use the transverse load as an approximation.

• Outputs: geometry, contact ratios, Wt, Wr, Wa, pitch-line velocity, power, factors, stresses and four safety factors (pinion and gear, bending and contact).
• Limits: external gears only; no internal gears, no scoring or thermal rating, no gear-rim or case-depth checks.

Shaft stress and fatigue

The endurance limit is Se = ka·kb·kc·kd·ke·kf·Se′ with the Shigley Chapter 6 curve fits: surface factor ka = a·Sut^b (ground, machined or cold-drawn, hot-rolled, as-forged), size factor kb for rotating round shafts, load factor kc, the temperature polynomial kd, reliability factor ke from the tabulated values, and Se′ = 0.5 Sut up to 1400 MPa (200 kpsi) and 700 MPa (100 kpsi) above. Select "Combined" for bending plus torsion: the von Mises combination handles the mix and kc = 1.

Alternating and mean stresses use σ = 32·Kf·M/(π d³) and τ = 16·Kfs·T/(π d³) and combine as σ′ = (σ² + 3τ²)^½. Four fatigue criteria are reported with the load line through the origin: Goodman, Gerber, ASME-elliptic and Soderberg, plus a first-cycle yield check σ′a + σ′m against Sy. "Diameter for target n" solves for the section diameter that meets your target with the size factor recomputed at every trial.

• Limits: single section, constant diameter at that section; no keyseat or shoulder geometry (you supply Kf and Kfs); rotating-beam test basis for kb.

Shaft deflection and critical speed

A uniform simply supported shaft carries point loads. Deflection uses the standard single-load formulas by superposition; the maximum is found on a 100-point scan. End slopes are exact for the loads given.

The first critical speed is estimated by Rayleigh’s method (ω = √(g ΣWy/ΣWy²)) with the static deflections caused by the weights and by the shaft’s own weight (40 lumped elements), and by Dunkerley’s method (1/ω² = Σ1/ωi²), which is a lower bound. The margin check uses the Dunkerley value, which is the conservative one.

• Limits: simply supported ends, uniform diameter, one plane; gyroscopic effects and bearing stiffness are not modelled; stepped shafts need an equivalent diameter you choose.

Rolling bearings

Basic rating life follows the ISO 281 formula L10 = (C/P)^p with p = 3 for ball and 10/3 for roller bearings, in million revolutions, and L10h = 10⁶·L10/(60 n) in hours. The equivalent dynamic load is P = V·Fr when Fa/(V·Fr) ≤ e, otherwise P = X·V·Fr + Y·Fa; the application factor multiplies P.

Modified life Lnm = a1·aISO·L10 uses the ISO 281 reliability factors a1 (90 % to 99 %). The life modification factor aISO depends on lubrication and cleanliness charts and must come from the standard or your supplier. The required rating is reported both by inverting the life equation and by the Weibull catalogue-load form in Shigley section 11-3.

• Limits: no dynamic equivalent load for combined angular-contact preload, no variable-load cycles, no thermal or grease-life checks.

Helical compression springs

Rate k = d⁴G/(8 D³ Na) with active coils Na from the end type; solid length from the end type; stress τ = K·8FD/(πd³) with the direct-shear factor Ks = 1 + 0.5/C, the Wahl factor Kw = (4C−1)/(4C−4) + 0.615/C and the Bergsträsser factor KB = (4C+2)/(4C−3). Static checks use Ks at solid height and assume local yielding/stress redistribution. For an unpreset spring requiring an elastic peak-stress check, include curvature (Kw or KB); this simplified static check does not establish that elastic peak limit. Fatigue uses the curvature factor you choose.

Buckling uses the critical deflection ycr = L0·C′1·[1 − √(1 − C′2/λeff²)] with C′1 = E/(2(E−G)), C′2 = 2π²(E−G)/(2G+E) and λeff = αL0/D. Surge uses f = ½√(k g/W) with W the weight of the active coils, compared with your forcing frequency. Fatigue is a Goodman line in shear using the endurance strength you supply.

• Limits: round wire, constant pitch; no extension, torsion or conical springs; no relaxation or heat-treat effects.

Bolted joints

Member stiffness uses the frustum method: two 30° pressure cones, one from each washer face to the mid-grip, split at every layer boundary and summed in series, each frustum with k = π E d tan α / ln[(2 t tan α + D − d)(D + d)/((2 t tan α + D + d)(D − d))]. For one material and a 1.5 d washer face this reduces to the closed form in Shigley (Member Stiffness section form, evaluated here with tan 30°). Bolt stiffness is kb = Ad·At·E/(Ad·lt + At·ld) with the thread length from the standard rule; At is computed from the pitch with the ISO and UN definitions or entered.

Outputs: joint constant C = kb/(kb + km), preload (0.75 or 0.90 of proof load, or direct), tightening torque T = K·Fi·d, proof load factor using Fb = max(Fi + C·P, P), separation factor n0 = Fi/((1−C)·P), and Goodman and Gerber fatigue factors for a load that varies between Pmin and Pmax. Member force cannot become tensile: after separation Fb = P. Fatigue factors scale both load extrema and re-evaluate separation at every trial load.

• Limits: concentric tension joint; no prying, no eccentric loading, no embedment or thermal loss of preload, no gasketed-joint pressure vessels. The cone does not shrink at the member outer diameter, so thin flanges overstate stiffness.

Fillet weld groups

The group is described by straight line segments (use many short segments to approximate arcs). Throat t = 0.707 h. About the group centroid the tool computes the unit second moments Iux, Iuy, Iuxy and Ju = Iux + Iuy of the line group, the area A = t·L and J = t·Ju. Loads are moved to the centroid: primary shear τ′ = V/A, secondary shear τ″ = M·r/J, and for out-of-plane loading the bending of the line group. The resultant is evaluated at nine points on every segment and the maximum is reported with its location.

• Limits: static strength only; no fatigue category checks, no end returns, no mixed weld sizes; the allowable stress is yours to choose from the governing code.

Press fits (Lamé) and keys

The interface pressure for a radial interference δ is p = δ / ( r [ (1/Eo)((ro²+r²)/(ro²−r²) + νo) + (1/Ei)((r²+ri²)/(r²−ri²) − νi) ] ), with ri = 0 for a solid shaft. Stresses follow Lamé: the hub bore sees σt = p(ro²+r²)/(ro²−r²) and σr = −p; the shaft surface sees σt = −p(r²+ri²)/(r²−ri²). Torque capacity is T = 2π f p r² l and axial capacity F = 2π f p r l; von Mises safety factors compare with the yield strengths.

A parallel key sees F = T/(d/2), shear τ = F/(w l) and bearing stress σ = 2F/(h l). Shear strength uses distortion energy, rounded to 0.577 Sy (Tresca would use 0.5 Sy). The minimum length for each mode at your target is reported.

• Limits: plane stress, elastic, uniform temperature; surface roughness smoothing, centrifugal loosening and fretting are not modelled. Friction coefficient is your input.

Files and exports

Save writes a .gearsmith.json JSON document containing both unit systems’ inputs for all modules, the current module and system, a copyright and terms notice field, and the footer text. Open reads the same format. Your work is also autosaved in this browser (localStorage); nothing is sent to any server.

Export CSV writes one module: comment header lines (title, footer, terms notice, unit system), then Input, result, Check and Warning rows as section,item,symbol,value,unit,note. The Report view prints through the browser (Print / save as PDF) and carries the footer "Made with Gearsmith · simulations4all.com" on every printed page.

Keyboard shortcuts

What this tool does not do

• It is not a substitute for the governing standard. The AGMA module follows the equation structure and curve fits published in Shigley; chart factors are yours. It does not reproduce AGMA, ISO or bearing-maker tables.
• No finite-element analysis, no dynamic simulation, no CAD export, no database of materials or bearing designations.
• No variable-amplitude fatigue (cycle counting or Miner’s rule) and no fracture mechanics.
• Results are only as good as the inputs: check units, tagged chart values and the warnings list.

Troubleshooting

How we verify this tool

The separate Python generator includes same-formula recomputations of Kv, Km, Marin, beam and spring fits. These check implementation agreement and are not independent validation. Independent routes include integrated frustum compliance and weld properties, displacement compatibility for press fits, hand-derived boundary cases and bisection of fatigue intersections. Confirmed manufacturer values are identified by source. Unconfirmed tables and worked examples remain PENDING SOURCE with no reference value.

The Verify page runs the same case list the automated test suite runs, in your browser, and shows for every case what is checked, the source, the reference, the computed value, the difference, the tolerance and PASS or FAIL. Worked examples from Shigley, Norton and Juvinall & Marshek whose printed answers are not in hand are listed as PENDING SOURCE: they carry no number, are never counted as passes and are never invented.

Sources

• Budynas & Nisbett, Shigley’s Mechanical Engineering Design, 10th ed., McGraw-Hill, 2015 (descriptive section citations; exact equation numbers are not asserted without legitimate edition confirmation).
• ISO 281:2007, Rolling bearings: dynamic load ratings and rating life (formula and a1 factors).
• Norton, Machine Design: An Integrated Approach; Juvinall & Marshek, Fundamentals of Machine Component Design (worked examples pending).