Tolerances

Tolerance Stack-Up

One-dimensional tolerance stack-up of a dimension chain: each dimension enters with its nominal, its plus and minus tolerances, its direction along the loop, its distribution (normal, uniform or triangular) and the ratio of tolerance to process sigma. The gap is analyzed four ways: worst case (every dimension at its extreme), root-sum-square (the statistical band of the gap from the variances, with the ±3σ limits and the tolerance-equivalent √Σt²), modified RSS with Bender's factor 1.5 or an entered factor, and the mean-shift model of Mansoor, Greenwood and Chase in which a fraction of each tolerance is a shift of the process mean stacked arithmetically toward the worst side and the rest stacks statistically. Against an optional gap specification the page reports Cp, Cpk, the expected fraction out of limits in ppm and the yield, the share of each dimension in the worst-case sum and in the RSS variance, and a seeded Monte Carlo of 20,000 assemblies with the chosen distributions, its percentiles, observed yield and histogram; a loop diagram draws the chain. Lengths are in inches or millimetres through the unit selector. The default is a five-part shaft-and-housing chain with a 0.002–0.040 in gap requirement that worst case fails and RSS passes; the test script checks the library against closed forms, the factors of Scholz (1995) and an independent numpy Monte Carlo.

1 worked example reproduced, listed on the tool page.

Limits, Fits and Tolerances

The ISO system of limits and fits computed from the published formulas of ISO 286-1: the standard tolerance factor i = 0.45 ∛D + 0.001 D of the basic size step, the IT grades IT01 to IT18 (7i for IT5, 10i for IT6, 16i for IT7 and the geometric progression above, the small-grade formulas below) with the standard's rounding rules, the fundamental deviations of shafts a to zc from the Annex A formulas (d = 16 D^0.44, g = 2.5 D^0.34, k = 0.6 ∛D, n = 5 D^0.34, s = IT7 + 0.4 D, u = IT7 + D and the rest) with the standard's rounding, and the holes A to ZC by the symmetry rule, the Δ = ITn − IT(n−1) rule for K, M, N up to IT8 and P to ZC up to IT7, and the N and K grade rules. A fit calculator takes the basic size and the hole and shaft classes (any designation such as H7/g6, K7/h6, H8/js7) and gives the limits of each part, the maximum and minimum clearance or interference, the fit type, a tolerance-zone diagram, the IT progression at that size, the statistical (RSS) distribution of the clearance, the position-tolerance bonus and virtual condition of each part when a position tolerance at MMC is entered, and the Taylor-principle and surface-finish notes. Inch fits are analyzed from the entered limits with the ANSI B4.1 class named. Default: 50 mm H7/g6 (ISO 286-2: hole +25/0, shaft −9/−25, clearance 9 to 50 µm).

1 worked example reproduced, listed on the tool page.

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