Dimensional Tolerancing

Dimensional tolerances are the tolerances that govern the dimensions (size) of a given part (length, radius, angle, etc.). There is another, complementary method of tolerancing – Geometric Dimensioning and Tolerancing – that governs the geometry (shape) of a given part (flatness, parallelism, symmetry, etc.). Read more about Geometric Dimensioning and Tolerancing here.

The dimensions that a part is specified to have are known as the nominal values. These are the 40 mm, 50 mm, and 100 mm values in Figure 1. If no tolerances are added, the actual dimensions on the final part will be completely dependent on, among other factors, the standard tolerances of the manufacturing company, machinery, and machinist capability.

There are three different types of dimensional tolerances:

  1. Lower deviation - this communicates the smallest value a dimension can have on the final part. This is noted by the “-” sign next to the 100 mm dimension in Figure 1. This means that the dimension can acceptably be as small as 99.8 mm but cannot be larger than 100 mm.
  2. Upper deviation - the exact opposite of a lower deviation. An upper deviation communicates the largest value a dimension can have on the final part. This is noted by the “+” sign next to the 40 mm dimension in Figure 1. This means that the dimension can acceptably be as large as 40.1 mm but cannot be smaller than 40 mm.
  3. Bilateral deviation - this communicates the total room for error that a dimension has on the final part. This is noted by the “±” sign next to the 50 mm dimension in Figure 1. This means that the dimension can acceptably be as small as 49.85 mm and as large as 50.15 mm.

Dimensional tolerances

Figure 1: Dimensional tolerances.

A question that arises here is – “is there a difference between a nominal value of 99.5 mm and an upper deviation of +0.5 mm and a nominal value of 100 mm and a lower deviation of -0.5 mm?” The answer is yes. The reason for this is that the manufacturer will strive for the dimension’s nominal value. So, if the intention is for a part’s dimension to be 99.5 mm, this should be specified as the nominal dimension, not 100 mm.

General Tolerances

When each of a part’s dimensions follow the same class of tolerances, general tolerances will be applied. This can either be done by adding a table to the technical drawing, as shown in Table 1, or by adding a note saying, “ISO 2768-m” or “ISO 3302-E1” – where the “-m” and “-E1” are the tolerance classes of “ISO 2768” and “ISO 3302” standards. Table 1 shows the E3 tolerance class of the ISO 3302 standard.

Table 1: ISO 3302-E3 tolerances.

Nominal Dimension (mm) Tolerence, ± (mm)
Greater than Less than or equal to
0.00 1.50 0.40
1.50 2.50 0.50
2.50 4.00 0.70
4.00 6.30 0.80
6.30 10.00 1.00
10.00 16.00 1.30
16.00 25.00 1.60
25.00 40.00 2.00
40.00 63.00 2.50
63.00 100.00 3.20
100.00
3.20%

General tolerances can be applied to linear dimensions, angular dimensions, external radii, chamfer heights, etc. The ISO 2768 and ISO 3302 mentioned above are examples of commonly used general tolerances that have been specified by the International Standards Organisation. ISO 2768 is applied to machined parts and ISO 3302 is applied to rubber parts that have been extruded or moulded.

Fits

In engineering, a “Fit” refers to the clearance between two mating parts and the international standard ISO 286 has been defined to govern tolerances for engineering fits. The choice of fit depends on the application – “is a fit needed that enables rotation of the parts?” or “should there be zero movement between the parts?” – are two questions to consider.

  1. Clearance fit - this type of fit requires a shaft diameter to be smaller than that of the hole. Meaning that there will always be a gap between the two. If the engineering solution needs the two to be able to slide or rotate independently of each other, this is the way to go. So, in this case both the shaft and the hole have tolerances that will ensure no overlapping.
  2. Transition fit - the maximum shaft size is bigger than the minimum size of the hole. At the same time, the minimum shaft size is also smaller than the maximum size of the hole. So, it is neither a clearance fit, nor an interference one. Depending on the final measurements, the tolerances allow for both scenarios to happen while not going into the extremes.
  3. Interference fit - the shaft diameter size is always bigger than the hole. Even when the shaft is at its minimum diameter and the hole at its largest. An interference fit ensures there is no movement between the two parts. Application of force is necessary during the physical fitting. Heating of the hole, freezing of the shaft and using a lubricant can all help to ease the process.

There are two systems to choose from – “Hole Basis” and “Shaft Basis”. These systems communicate which part has a constant measurement and which part is manufactured based off the other. In short, the hole basis system uses a constant measurement for the hole and the diameter of the shaft is made according to that to achieve the required fit. The shaft basis system works in the opposite way.

Engineers tend to follow the hole basis system because of simplicity – drilling does not allow for much precision, as the tooling comes in certain measurements.

Table 2 shows common notation for different fitting scenarios. Each of notation pair corresponds to a set of dimensional tolerances for the hole and shaft being designed. An upper-case letter signifies the hole, a lower-case letter signifies the shaft, the actual letter itself signified the start point of the tolerance zone, and the accompanying number indicates the international tolerance (IT) grade.

Table 2: Limits and fits.

Type of Fit Description Hole Basis Shaft Basis
Clearance Fits Loose Running H11/c11 C11/h11
Free Running H9/d9 D9/h9
Close Running H8/f8 F8/h8
Sliding H7/g6 G7/h6
Locational Clearance H7/h6 -
Transition Fits Similar H7/k6 K7/h6
Fixed H7/n6 N7/h6
Interference Fits Press H7/p6 P7/h6
Driving H7/s6 S7/h6
Forced H7/u6 U7/h6

An example will pull all this together and make it clearer. Say we want to design a hole and a shaft with nominal dimensions of 25 mm, and we want a sliding fit following the hole basis system – we would select the H7/g6 notation from Table 2. First, let’s consider the H7 notation. The upper-case nature of the “H” means that we are dealing with the hole, the actual letter “H” indicates that the tolerance zone starts at nominal value plus 0 µm, and the number 7 corresponds to the IT7 tolerance range in Figure 2 which is 21 µm. So, we now know that the hole’s actual dimensions can vary between 25.000 mm and 25.021 mm. If instead of H7 it were F7, the tolerance zone would start at nominal value plus 20 µm, so the hole’s actual dimensions would vary between 25.020 mm and 25.041 mm. Now let’s consider the g6 part of the notation. The lower-case nature of the “g” means that we are dealing with the shaft, the actual letter “g” indicates that the tolerance zone starts at nominal value minus 7 µm, and the number 6 corresponds to the IT6 tolerance range which is 13 µm. So, we know that the shaft’s actual dimensions will vary between 24.993 mm and 24.980 mm.

Values of standard tolerance grades

Figure 2: Values of standard tolerance grades.

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