Tools › Mechanical Design › Tolerances › Limits, Fits and Tolerances › Example

50 mm H7/g6 sliding fit and 25 mm H7/p6 interference fit from the ISO 286-1 formulas, checked against the printed tables

ToolLimits, Fits and Tolerances
SourceInternational Organization for Standardization (1988). ISO System of Limits and Fits, Part 1: Bases of Tolerances, Deviations and Fits. ISO 286-1:1988, Annex A (Table 4 size steps, A.3.2.2 tolerance factor, Table 7 multipliers, Table 8 rounding, Table 9 deviation formulae, Table 10 rounding, A.4.2 hole rules), as printed in the identical IS 919 (Part 1):1993; International Organization for Standardization (1988). ISO System of Limits and Fits, Part 2: Tables of Standard Tolerance Grades and Limit Deviations for Holes and Shafts. ISO 286-2:1988, Tables 6, 10, 21 and 26, as printed in IS 919 (Part 2):1993.
LevelUndergraduate

Problem

Find the limits of a 50 mm H7/g6 sliding fit and of a 25 mm H7/p6 locational interference fit from the formulas of the ISO system: the standard tolerance factor of the size step, the IT6 and IT7 tolerances with the rounding rule, the fundamental deviations g and p, the limits of each part, the clearance or interference extremes and the fit type; give the statistical (RSS) clearance band of the sliding fit for centred processes with tolerance = 3 sigma.

Inputs to Enter

  • ISO 286 designation, basic size 50 mm, preferred fit H7/g6 (hole basis), k = 3; no overrides
  • Second case: basic size 25 mm, preferred fit H7/p6
Open the Limits, Fits and Tolerances tool (loaded with this example)

Answers

  • 30 to 50 mm step: D = sqrt(30 x 50) = 38.73 mm, i = 0.45 D^(1/3) + 0.001 D = 1.561 um; IT7 = 16 i = 24.98 -> 25 um, IT6 = 10 i = 15.61 -> 16 um (ISO 286-1 Table 1: 25 and 16)
  • g: es = -2.5 D^0.34 = -8.67 -> -9 um, ei = -9 - 16 = -25 um; H: EI = 0, ES = +25 um (ISO 286-2 Table 21: -9/-25; Table 6: +25/0)
  • Limits 50.025 / 50.000 mm and 49.991 / 49.975 mm; clearance 9 to 50 um (mean 29.5 um, fit tolerance 41 um): clearance fit; RSS band sigma_C = sqrt(25^2 + 16^2)/6 = 4.95 um, 14.7 to 44.3 um at 3 sigma, interference probability 1.2e-9
  • 25 mm H7/p6: 18 to 30 mm step, i = 1.308 um, IT7 = 21, IT6 = 13 um; p = IT7 + 1 = +22 um (the increment of ISO 286-1 Table 2 in the range IT7 + 0 to 5), es = +35 um; limits 25.021 / 25.000 and 25.035 / 25.022 mm; interference 1 to 35 um (ISO 286-2 Table 26: +35/+22); the hole-basis rule gives P7/h6 as -14/-35 against 0/-13 (Delta = IT7 - IT6 = 8, the standard's own example), the same interference

Notes

The tool's default inputs are the 50 mm H7/g6 case; press Submit, then enter 25 mm and H7/p6 for the second. test_limits_and_fits.php checks IT5 to IT11 at every size step, the deviations of g, h, k, p, s, u at ten sizes, the holes K, M, N, P, S, J by the A.4.2 rules, these fits and the preferred fits at 25 mm against the printed tables of the standard, the rounding rules, the hole-basis / shaft-basis equivalence and an independent numpy implementation (References/Limits-Fits/checks/). The IT and deviation values are computed from the published formulas with the standard's rounding rules; the standard's own note that its tables depart from the formulas in places is printed, and such a cell is entered in the override fields (the two fits of this example are formula values that agree with the printed tables).