Question:
In a hole-shaft assembly, the following are the dimensions and tolerances (all in mm) provided for the hole and shaft:
Hole: \( 22^{+0.018}_{+0.010} \)
Shaft: \( 22^{+0.075}_{+0.004} \)
The magnitude of the clearance when the shaft is at the minimum material condition and hole is at the maximum material condition is ______ mm (to three decimal places).
In a hole-shaft assembly, the following are the dimensions and tolerances (all in mm) provided for the hole and shaft:
Hole: \( 22^{+0.018}_{+0.010} \)
Shaft: \( 22^{+0.075}_{+0.004} \)
The magnitude of the clearance when the shaft is at the minimum material condition and hole is at the maximum material condition is ______ mm (to three decimal places).
Hole: \( 22^{+0.018}_{+0.010} \)
Shaft: \( 22^{+0.075}_{+0.004} \)
The magnitude of the clearance when the shaft is at the minimum material condition and hole is at the maximum material condition is ______ mm (to three decimal places).
Show Hint
MMC hole is the smallest hole size; LMC shaft is the smallest shaft size. Clearance is the difference between them.
Updated On: Aug 5, 2026
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Verified By Collegedunia
Correct Answer: 0.006
Solution and Explanation
Step 1: Understanding the Concept:
In limits and fits, every dimension is written as a basic size plus an upper and a lower deviation.
Maximum Material Condition (MMC) is the limit that leaves the most material in the part, and Minimum Material Condition (LMC) is the limit that leaves the least material.
For a hole, more material means a smaller opening, so MMC of a hole is its smallest allowed size. For a shaft, more material means a larger diameter, so LMC of a shaft is its smallest allowed size.
Step 2: Key Formula or Approach:
Since both the hole and the shaft share the same basic size of 22 mm, that common 22 mm cancels out when we subtract one dimension from the other. So instead of writing out full sizes, we can work directly with the deviation values:
\[ \text{Clearance} = (\text{Lower deviation of hole}) - (\text{Lower deviation of shaft}) \]
This works because the smallest hole size uses its lower deviation, and the smallest shaft size also uses its lower deviation.
Step 3: Detailed Explanation:
From the hole tolerance \( 22^{+0.018}_{+0.010} \), the lower deviation is \( +0.010 \) mm, which corresponds to the smallest (MMC) hole size.
From the shaft tolerance \( 22^{+0.075}_{+0.004} \), the lower deviation is \( +0.004 \) mm, which corresponds to the smallest (LMC) shaft size.
Subtracting the deviations directly:
\[ \text{Clearance} = 0.010 - 0.004 = 0.006 \text{ mm} \]
Final Answer:
The magnitude of the clearance between the MMC hole and the LMC shaft comes out the same whether we subtract full sizes or just the deviations. \[ \boxed{\text{Clearance} = 0.006 \text{ mm}} \]
In limits and fits, every dimension is written as a basic size plus an upper and a lower deviation.
Maximum Material Condition (MMC) is the limit that leaves the most material in the part, and Minimum Material Condition (LMC) is the limit that leaves the least material.
For a hole, more material means a smaller opening, so MMC of a hole is its smallest allowed size. For a shaft, more material means a larger diameter, so LMC of a shaft is its smallest allowed size.
Step 2: Key Formula or Approach:
Since both the hole and the shaft share the same basic size of 22 mm, that common 22 mm cancels out when we subtract one dimension from the other. So instead of writing out full sizes, we can work directly with the deviation values:
\[ \text{Clearance} = (\text{Lower deviation of hole}) - (\text{Lower deviation of shaft}) \]
This works because the smallest hole size uses its lower deviation, and the smallest shaft size also uses its lower deviation.
Step 3: Detailed Explanation:
From the hole tolerance \( 22^{+0.018}_{+0.010} \), the lower deviation is \( +0.010 \) mm, which corresponds to the smallest (MMC) hole size.
From the shaft tolerance \( 22^{+0.075}_{+0.004} \), the lower deviation is \( +0.004 \) mm, which corresponds to the smallest (LMC) shaft size.
Subtracting the deviations directly:
\[ \text{Clearance} = 0.010 - 0.004 = 0.006 \text{ mm} \]
Final Answer:
The magnitude of the clearance between the MMC hole and the LMC shaft comes out the same whether we subtract full sizes or just the deviations. \[ \boxed{\text{Clearance} = 0.006 \text{ mm}} \]
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