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EngrCAD

Fits & tolerance stackups

Iso286 answers the question every mating pair raises — what limits do I put on this bore and this shaft? — from the ISO 286-1 tables: standard tolerance grades IT5–IT12 and the fundamental deviations of shaft letters a through h, js, k, m, n, p and r through z, plus the holes of both systems — the basic hole H and JS, and the shaft-basis holes A–G — for sizes over 1 up to 500 mm. That covers the whole preferred-fit range, from H11/c11 loose running to H7/u6 force. The tables are transcriptions carrying the ⚠ verify-against-datasheet flag (StandardHoles’ convention): they are stored in the standard’s own micrometres — the form a human checks against the printed chart — and converted to model millimetres at the API.

// The classic sliding fit at Ø40: H7 bore +25/0 µm, g6 shaft −9/−25 µm.
var bore  = Iso286.Limits(40, "H7");
var shaft = Iso286.Limits(40, "g6");
if (Math.Abs(bore.Upper - 0.025) > 1e-12 || bore.Lower != 0)
    throw new Exception("H7 at 40 is +0.025/0");
if (Math.Abs(shaft.Upper - -0.009) > 1e-12 || Math.Abs(shaft.Lower - -0.025) > 1e-12)
    throw new Exception("g6 at 40 is -0.009/-0.025");


// A fit derives its kind from the clearance EXTREMES, never from the letter.
var sliding = Iso286.Fit(40, "H7", "g6");
if (sliding.Kind != FitKind.Clearance)
    throw new Exception("H7/g6 always clears");
if (Math.Abs(sliding.MinClearance - 0.009) > 1e-12 || Math.Abs(sliding.MaxClearance - 0.050) > 1e-12)
    throw new Exception("the handbook numbers: 9 to 50 µm");


var press = Iso286.Fit(40, "H7", "p6");
if (press.Kind != FitKind.Interference)
    throw new Exception("H7/p6 always binds");
var locational = Iso286.Fit(40, "H7", "k6");
if (locational.Kind != FitKind.Transition)
    throw new Exception("H7/k6 can do either");

The wide-clearance and interference letters

Letters a–c (large clearance) and r–z (interference) carry their deviations on the standard’s own finer size steps — c changes at 40 inside the 30–50 range the grades use, and t, u, v, x, y, z each take a new value there too — so they read from a 25-row table rather than the grades’ 13. Which letters split where is not uniform: r and s carry one value across 30–50 while their neighbours do not.

// H11/c11 — the loose running fit: at Ø40 the shaft sits 120 µm below the bore at
// its closest and 440 µm at its loosest.
var loose = Iso286.Fit(40, "H11", "c11");
if (loose.Kind != FitKind.Clearance)
    throw new Exception("H11/c11 always clears");
if (Math.Abs(loose.MinClearance - 0.120) > 1e-12 || Math.Abs(loose.MaxClearance - 0.440) > 1e-12)
    throw new Exception("the chart row: 120 to 440 microns");


// H7/s6 — the medium drive fit: ALWAYS interference, 18 to 59 microns of it.
var drive = Iso286.Fit(40, "H7", "s6");
if (drive.Kind != FitKind.Interference)
    throw new Exception("H7/s6 always binds");
if (Math.Abs(drive.MinClearance - -0.059) > 1e-12 || Math.Abs(drive.MaxClearance - -0.018) > 1e-12)
    throw new Exception("the chart row: 18 to 59 microns of interference");


// The three interference letters ORDER as the standard intends at one size.
var press = Iso286.Fit(40, "H7", "r6");   // light press
var force = Iso286.Fit(40, "H7", "u6");   // force fit
if (!(force.MaxClearance < drive.MaxClearance && drive.MaxClearance < press.MaxClearance))
    throw new Exception("r lighter than s lighter than u");


// The finer steps are visible: c takes a new cell at 40, s does not.
if (Math.Abs(Iso286.Limits(45, "c11").Upper - -0.130) > 1e-12)
    throw new Exception("c changes inside the 30-50 grade range");
if (Iso286.Limits(45, "s6").Lower != Iso286.Limits(40, "s6").Lower)
    throw new Exception("s carries one value across 30-50");

Shaft basis

Where a bought-in ground shaft is the fixed member, the fit is cut into the hole instead: the shaft is the basic h and the hole takes the letter. Iso286 reads the shaft-basis holes A–G by the standard’s own mirror rule — EI = −es of the same-letter shaft, with no correction at any grade — and that rule has a consequence worth checking rather than asserting: G7/h6 carries exactly H7/g6’s clearances, because the two IT widths are the same two numbers added in the other order.

// The same joint, described from either side.
var holeBasis  = Iso286.Fit(40, "H7", "g6");
var shaftBasis = Iso286.Fit(40, "G7", "h6");
if (holeBasis.MinClearance != shaftBasis.MinClearance ||
    holeBasis.MaxClearance != shaftBasis.MaxClearance)
    throw new Exception("the IT widths commute, so the two systems agree exactly");


// G7 at Diameter 40 is +34/+9 microns — g6's -9 mirrored, plus IT7.
var g7 = Iso286.Limits(40, "G7");
if (Math.Abs(g7.Upper - 0.034) > 1e-12 || Math.Abs(g7.Lower - 0.009) > 1e-12)
    throw new Exception("G7 at 40 is +0.034/+0.009");

What stays refused by name: the holes J and K–ZC, because those carry the Δ = IT(n) − IT(n−1) correction for fine grades — with tabulated exceptions and an IT3/IT4 dependence the grade table does not hold — and half-transcribing it is exactly the plausible-wrong-row failure the ⚠ flag exists to prevent; the hole-basis spelling of the same fit (H7/s6 for S7/h6) is supported. Also refused: the intermediate letters cd, ef, fg and j, the extreme za–zc, sizes outside the 1–500 mm table, and t, v and y below 24, 14 and 18 mm — the standard’s own empty cells, named as such rather than interpolated. A refusal that names its reason beats a plausible number from the wrong row.

Stackups

ToleranceStackup sums a chain of toleranced dimensions worst-case and root-sum-square. The chain is the caller’s design statement — which dimensions contribute, in which direction — because nothing in the model carries it: mates constrain poses and hold no toleranced dimensions, so a stackup derived from the mate graph would be a guess about intent.

Asymmetric tolerances are handled the textbook way, stated rather than implied: worst-case uses each contribution’s own signed band ends, while RSS re-centres each contribution on its mid value and root-sum-squares the half-widths — so the RSS mean shifts away from the nominal exactly when a band is asymmetric.

// A housing pocket 50 ±0.1 holds a bearing 20 +0/−0.05 and a spacer 10 ±0.02.
// How much gap is left, and how bad can it get?
var gap = new ToleranceStackup()
    .Add("pocket", 50, 0.1, 0.1)
    .Subtract("bearing", 20, 0, 0.05)
    .Subtract("spacer", 10, 0.02, 0.02)
    .Evaluate();


if (Math.Abs(gap.Nominal - 20.0) > 1e-12)
    throw new Exception("50 - 20 - 10");
if (Math.Abs(gap.WorstCaseMin - 19.88) > 1e-12 || Math.Abs(gap.WorstCaseMax - 20.17) > 1e-12)
    throw new Exception("every dimension at its worst end");
// RSS lands strictly inside worst case — the whole reason the method exists —
// and its mean carries the bearing's asymmetric band (+0.025 off the nominal).
if (gap.RssMin <= gap.WorstCaseMin || gap.RssMax >= gap.WorstCaseMax)
    throw new Exception("RSS inside worst case");
if (Math.Abs(gap.RssMean - 20.025) > 1e-12)
    throw new Exception("the asymmetric band shifts the statistical centre");


// A fit's clearance enters a chain like any other dimension: the pin's float.
var withPin = new ToleranceStackup()
    .Add("pin float", Iso286.Fit(40, "H7", "g6"))
    .Evaluate();
if (Math.Abs(withPin.WorstCaseMax - 0.050) > 1e-12)
    throw new Exception("the fit's own extremes carry through");

The units are model millimetres throughout, like everything else in the kernel; the µm figures in the prose are the standard’s own spelling of the same numbers.