Understanding Limits and Tolerance

In manufacturing and engineering, a limit system is used to ensure that mating parts fit together correctly. Each dimension is given a nominal size, along with upper and lower deviations, which define the acceptable range of variation for that dimension. This range is known as the tolerance.

For any part, the tolerance is the difference between its maximum permissible size (upper limit) and its minimum permissible size (lower limit). Mathematically, it can be expressed as:

$$ \text{Tolerance} = \text{Maximum Size} - \text{Minimum Size} $$

or, using deviations:

$$ \text{Tolerance} = \text{Upper Deviation} - \text{Lower Deviation} $$

Calculating Tolerance on a Shaft

The question provides the limits specified for a shaft in a clearance fit system. The notation for the shaft is given as \(shaft = 25_{ - 0.02}^{ - 0.004}\;mm\).

From this notation, we can identify the following:

• Nominal Size = 25 mm
• Upper Deviation = -0.004 mm
• Lower Deviation = -0.02 mm

Using these values, we can calculate the maximum and minimum permissible sizes for the shaft:

• Maximum Shaft Size = Nominal Size + Upper Deviation = \(25\;mm + (-0.004)\;mm = 24.996\;mm\)
• Minimum Shaft Size = Nominal Size + Lower Deviation = \(25\;mm + (-0.02)\;mm = 24.98\;mm\)

Now, we can determine the tolerance on the shaft using the formula:

$$ \text{Shaft Tolerance} = \text{Maximum Shaft Size} - \text{Minimum Shaft Size} $$

Substituting the calculated values:

$$ \text{Shaft Tolerance} = 24.996\;mm - 24.98\;mm $$

$$ \text{Shaft Tolerance} = 0.016\;mm $$

Alternatively, using the deviations directly:

$$ \text{Shaft Tolerance} = \text{Upper Deviation} - \text{Lower Deviation} $$

$$ \text{Shaft Tolerance} = (-0.004\;mm) - (-0.02\;mm) $$

$$ \text{Shaft Tolerance} = -0.004\;mm + 0.02\;mm $$

$$ \text{Shaft Tolerance} = 0.016\;mm $$

Result of Shaft Tolerance Calculation

The tolerance calculated for the shaft is 0.016 mm.

Comparing this value with the given options:

• 0.012 mm
• 0.016 mm
• 0.018 mm
• 0.014 mm

The calculated tolerance matches the second option.