Limits, Fits and Tolerance

   +  ------------------ upper limit
      |  tolerance zone |   (upper deviation)
      ------------------ lower limit
 0 ============================ zero line
      (basic size)                (lower deviation
   -                               if below the line)

Deviations are measured from the zero line: positive above, negative below.

Tolerance zone: the zone between the upper and lower limits, defined by the grade (size) and the fundamental deviation (position), as in $40\ \text{H7}$.

A fit is the relationship between a hole and a shaft that are assembled, resulting from the difference of their sizes before assembly.

Types

  Clearance    Transition    Interference
   |hole|       |hole|         |shaft|
   |    |       |    |         |     |
                |shaft|        |hole|
   |shaft|      |     |
   (hole zone   (zones         (shaft zone
    above shaft  overlap)       above hole)

1. Clearance fit: the shaft is always smaller than the hole, so there is always a gap (minimum clearance $\ge 0$). The parts can slide or rotate. Example: shaft in a plain bearing (H7/g6, H8/f7), sliding fit of a piston in a cylinder (running fits).
2. Interference (force/press) fit: the shaft is always larger than the hole, so the assembly needs force (pressing, or heating or cooling the parts) and they are fixed together by friction. Example: bush in a housing, gear on a shaft, wheel on an axle (H7/p6, H7/s6).
3. Transition fit: the sizes overlap, so, depending on the actual dimensions, there may be a small clearance or a small interference. It is used for accurate location without much load: pulley on shaft with a key, spigot location, coupling hub (H7/k6, H7/n6).

Hole basis and shaft basis

• Hole basis system: the hole has zero lower deviation (H); the fits are obtained by changing the shaft's fundamental deviation. Examples: H7/g6 (clearance), H7/k6 (transition), H7/p6 (interference).
• Shaft basis system: the shaft has zero upper deviation (h); the fits are obtained by changing the hole's deviation. Examples: G7/h6 (clearance), K7/h6 (transition), P7/h6 (interference).

The minimum clearance is the difference between the lower limit of hole and the upper limit of shaft; the maximum clearance is the difference between the upper limit of hole and the lower limit of shaft.

In the hole basis system the basic size is the minimum limit (lower limit) of the hole, so the lower deviation of the hole is zero (letter H). Different fits are obtained by varying the size of the shaft. In the shaft basis system the basic size is the maximum limit of the shaft, so the upper deviation of the shaft is zero (letter h). Different fits are obtained by varying the size of the hole.

Why hole basis is preferred

• Holes are made by drills, reamers, boring and broaches whose sizes are fixed; one reamer size of H7 covers all fits.
• Shafts are easily turned and ground to any size, so the changing member is the cheaper one to change.
• Fewer tools and gauges are needed, so the cost of production and inspection is lower.

The shaft basis is used when a single shaft carries several parts with different fits (for example a bar on which several bearings, collars, and pulleys are fitted) because cutting steps on a shaft would weaken it and cost more.

Conversion: the limits of $40.00 \pm 0.03$ are $39.97$ and $40.03$ mm; the total tolerance is $0.06$ mm. As a unilateral dimension with the same limits:

$$39.97^{+0.06}_{\ 0}\ \text{mm}$$

Type of $60^{+0.05}_{+0.02}$: both deviations are positive, so the limits are $60.02$ and $60.05$ mm and the basic size 60 mm lies outside the tolerance zone. It is a unilateral tolerance (both limits are on the same side of the basic size), with a tolerance of $0.05 - 0.02 = 0.03$ mm.

Step 1: diameter step

$$D = \sqrt{30 \times 50} = 38.73\ \text{mm}$$

Step 2: tolerance unit

$$i = 0.45\,(38.73)^{1/3} + 0.001(38.73) = 0.45(3.383) + 0.039 = 1.561\ \mu\text{m}$$

• IT7 $= 16i = 24.98\ \mu$m, standard value 25 $\mu$m
• IT6 $= 10i = 15.6\ \mu$m, standard value 16 $\mu$m

Step 3: fundamental deviation of shaft g

$$es = -2.5\,D^{0.34} = -2.5(38.73)^{0.34} = -2.5(3.468) = -8.67\ \mu\text{m} \approx -9\ \mu\text{m}$$

Step 4: limits

Hole 40 H7 (lower deviation zero):

• Lower limit $= 40.000$ mm
• Upper limit $= 40.000 + 0.025 = 40.025$ mm
• Tolerance $= 0.025$ mm

Shaft 40 g6 (upper deviation $-0.009$ mm):

• Upper limit $= 40 - 0.009 = 39.991$ mm
• Lower limit $= 39.991 - 0.016 = 39.975$ mm
• Tolerance $= 0.016$ mm

Step 5: clearances

$$C_{max} = \text{hole max} - \text{shaft min} = 40.025 - 39.975 = 0.050\ \text{mm}$$ $$C_{min} = \text{hole min} - \text{shaft max} = 40.000 - 39.991 = 0.009\ \text{mm}$$

Check: $C_{max} - C_{min} = 0.041 = 0.025 + 0.016$.

Both clearances are positive, so this is a clearance fit (close running or sliding fit).

Answer: hole 40.000 to 40.025 mm; shaft 39.975 to 39.991 mm; $C_{max}$ = 0.050 mm, $C_{min}$ = 0.009 mm; clearance fit.

Use: $C_{max} =$ hole max $-$ shaft min; $C_{min} =$ hole min $-$ shaft max. A negative value is interference.

Results

• (a) Clearance fit: the clearance is always between 0.020 mm and 0.054 mm. The shaft is always smaller than the hole, so it is a running fit (like H7/f7).
• (b) Transition fit: the maximum clearance is 0.023 mm and the maximum interference is 0.018 mm. Depending on actual sizes it may be a clearance or an interference. Used for accurate location (like H7/k6).
• (c) Interference fit: the minimum interference is 0.014 mm and the maximum is 0.048 mm. Always a press fit (like H7/s6).

The three pairs are on the hole basis, as the hole lower limit equals the basic size in all of them (lower deviation zero).

Answer: (a) clearance, 0.020 to 0.054 mm; (b) transition, +0.023 to -0.018 mm; (c) interference, 0.014 to 0.048 mm.