Limits, fits and tolerances; limit gauge design

Why it matters

No machine can make two parts exactly the same size, so every drawing must say how much a dimension may vary and how mating parts should go together. Limits, fits and tolerances make mass-produced parts interchangeable: any shaft from one batch assembles with any hole from another and still gives the intended running, locating or press fit. Limit gauges then let an inspector accept or reject thousands of parts quickly without measuring the actual size.

Key ideas

Basic (nominal) size is the size from which limits are worked out; both hole and shaft of a fit share it.

Limits are the two extreme permissible sizes: the upper (maximum) limit and the lower (minimum) limit.

Deviation is a limit minus the basic size. Upper deviation is ES for a hole and es for a shaft; lower deviation is EI for a hole and ei for a shaft. Capital letters always mean holes, small letters shafts.

Tolerance is the permitted variation: upper limit − lower limit (always positive). A tolerance is unilateral when both limits are on one side of the basic size (e.g. 30 +0.05/+0.00) and bilateral when they lie on both sides (e.g. 30 ± 0.02).

Fundamental deviation is the deviation nearest the zero line; it fixes the position of the tolerance zone and is denoted by a letter (A–ZC for holes, a–zc for shafts). The tolerance grade (IT01, IT0, IT1 … IT16 in the ISO/IS 919 system) fixes the size of the zone. So 25 H7 means basic size 25 mm, hole position H (EI = 0), grade IT7.

Fits describe how a hole and shaft go together:

• Clearance fit — the smallest hole is larger than the largest shaft, so there is always a gap (e.g. H7/g6, H8/f7). Used for running and sliding parts.
• Interference fit — the largest hole is smaller than the smallest shaft, so there is always interference (e.g. H7/p6, H7/s6). Parts are pressed or shrunk together.
• Transition fit — the tolerance zones overlap, so a given pair may have a small clearance or a small interference (e.g. H7/k6, H7/n6). Used for accurate location such as gears and couplings on shafts.

Allowance is the intentional difference between the maximum material limits of mating parts: minimum hole − maximum shaft. It equals the minimum clearance (positive) in a clearance fit and the maximum interference (negative allowance) in an interference fit. Allowance is a property of the fit; tolerance is a property of one part.

Hole-basis and shaft-basis systems. In the hole-basis system the hole is always H (lower deviation zero) and different fits are obtained by changing the shaft; it is preferred because holes are made with fixed-size tools (drills, reamers) and checked with fixed plug gauges. The shaft-basis system (shaft always h) is used when one bright-drawn bar must carry several parts with different fits.

Maximum and minimum material condition. MMC is the state with most material: the largest shaft or the smallest hole. LMC is the smallest shaft or the largest hole.

Limit (GO / NO-GO) gauges and Taylor's principle. A limit gauge does not measure size; it only tells whether the part lies within its limits.

• The GO gauge is made to the MMC limit (smallest hole size for a plug gauge, largest shaft size for a ring/snap gauge). It must be a full-form gauge that checks the whole length and all features together, so it detects form errors that would prevent assembly.
• The NO-GO gauge is made to the LMC limit (largest hole, smallest shaft) and should check one dimension at a time (short or pin-type), so that it enters where any single dimension is oversize. That is Taylor's principle. A good part accepts GO and rejects NO-GO.

Gauge tolerance and wear allowance. Gauges must themselves be made to a tolerance; a common textbook rule is gauge tolerance ≈ 10 % of the work tolerance. The GO gauge wears because it enters every good part, so a wear allowance (commonly about 10 % of the gauge tolerance) is added to it in the direction that moves it into the work tolerance zone. In the unilateral system (older IS practice) both gauge tolerance zones are placed inside the work tolerance zone so that a gauge can never accept a bad part. These percentages are conventions; use the values your code or the question gives.

Formulas

T = UL − LL (tolerance of one part)

• T, UL, LL in mm; T > 0.

ES = UL_hole − basic size, EI = LL_hole − basic size, es = UL_shaft − basic size, ei = LL_shaft − basic size

Maximum clearance = UL_hole − LL_shaft Minimum clearance (allowance) = LL_hole − UL_shaft

• If both are positive: clearance fit. If both are negative: interference fit (the negatives are interferences). If the maximum is positive and the minimum negative: transition fit.

i = 0.45·∛D + 0.001·D (standard tolerance unit, i in µm)

• D in mm is the geometric mean of the diameter step, D = √(D1·D2); valid for sizes up to 500 mm.
• Grades IT5 to IT16 are multiples of i: IT6 = 10i, IT7 = 16i, IT8 = 25i, IT9 = 40i, IT10 = 64i, IT11 = 100i (the multiplier rises by about 1.6 per grade). Values are rounded as in the IS 919 / ISO 286 table; take finer grades and fundamental deviations from your data book.

Gauge tolerance ≈ 0.1 × work tolerance; Wear allowance ≈ 0.1 × gauge tolerance (conventions; use the stated values).

Worked examples

Example 1 (standard): classify the fit 25 H7/g6.

Given: basic size 25 mm (diameter step 18–30 mm); H hole EI = 0; g shaft fundamental deviation es = −2.5·D^0.34 µm.

1. D = √(18 × 30) = 23.24 mm.
2. i = 0.45·∛23.24 + 0.001 × 23.24 = 1.284 + 0.023 = 1.307 µm.
3. IT7 = 16i = 20.9 ≈ 21 µm; IT6 = 10i = 13.1 ≈ 13 µm.
4. Hole: EI = 0, ES = +21 µm → 25.000 to 25.021 mm.
5. Shaft: es = −2.5 × 23.24^0.34 = −7.3 ≈ −7 µm; ei = es − IT6 = −7 − 13 = −20 µm → 24.980 to 24.993 mm.
6. Maximum clearance = 25.021 − 24.980 = 0.041 mm.
7. Minimum clearance = 25.000 − 24.993 = 0.007 mm.

Both positive: clearance fit, clearance 0.007 mm to 0.041 mm (allowance 0.007 mm).

Example 2 (GATE level): design a GO/NO-GO plug gauge.

Given: hole 30.000 to 30.050 mm (work tolerance 0.050 mm); gauge tolerance = 10 % of work tolerance; wear allowance = 10 % of gauge tolerance on the GO gauge; unilateral system (gauge zones inside the work zone).

1. Gauge tolerance = 0.1 × 0.050 = 0.005 mm.
2. Wear allowance = 0.1 × 0.005 = 0.0005 mm.
3. GO gauge (MMC = smallest hole 30.000 mm), moved inward by the wear allowance: lower size 30.000 + 0.0005 = 30.0005 mm, upper size 30.0005 + 0.005 = 30.0055 mm.
4. NO-GO gauge (LMC = largest hole 30.050 mm), zone inside the work tolerance: upper size 30.050 mm, lower size 30.050 − 0.005 = 30.045 mm.

GO plug: 30.0005 to 30.0055 mm; NO-GO plug: 30.045 to 30.050 mm.

Common mistakes

• Defining allowance as "basic size − hole size". Allowance is minimum hole − maximum shaft, a property of the fit.
• Mixing up the capital (hole) and small (shaft) deviation symbols, or the sign of a shaft's upper deviation for letters a–h (negative).
• Deciding the fit from one clearance only. You need both maximum and minimum clearance; one positive and one negative means a transition fit, not an interference fit.
• Making the GO gauge to the LMC limit. GO always corresponds to maximum material: smallest hole, largest shaft.
• Applying the wear allowance to the NO-GO gauge, or moving it outside the work tolerance.
• Using the actual diameter instead of the geometric mean of the diameter step when computing i.

For GATE PI

Expect numericals that ask for maximum/minimum clearance or interference and the type of fit from given limits or deviations, IT-grade calculations from the tolerance unit formula, and the limits of GO and NO-GO plug or snap gauges with given gauge tolerance and wear allowance. Conceptual questions test Taylor's principle, hole-basis versus shaft-basis, and MMC/LMC. Practise drawing the zero line and tolerance zones before calculating; it prevents sign errors.

Quick check

1. A hole is 40.000/40.039 mm and a shaft 40.034/40.050 mm. What type of fit is it?
2. Which limit does a GO plug gauge correspond to?
3. Why is the hole-basis system preferred?
4. If the tolerance unit i = 1.5 µm, what is the IT8 tolerance?

Answers: 1. Transition fit (maximum clearance +0.005 mm, maximum interference 0.050 mm). 2. The minimum hole size (maximum material condition). 3. Holes are made and gauged with fixed-size tools, so varying the shaft is cheaper. 4. 25i = 37.5 µm.