Question:hard
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
Show Solution
Correct Answer: 0.006
Solution and Explanation
Step 1: Understanding the Concept:
We need to calculate the clearance between a specific mating condition of a hole and a shaft. Clearance is the empty space between them, given by (Hole size minus Shaft size).
Step 2: Key Definitions:
Minimum Material Condition (LMC) is the size limit that contains the least amount of material. For a shaft, this is its smallest allowed diameter.
Maximum Material Condition (MMC) is the size limit that contains the most amount of material. For a hole, this is its smallest allowed diameter, since adding more material shrinks the hole.
Step 3: Detailed Explanation:
Identify the limits for the shaft:
Maximum Shaft = $ 22 + 0.075 = 22.075 $ mm.
Minimum Shaft = $ 22 + 0.004 = 22.004 $ mm.
The Shaft at LMC (least material) is its smallest size, $ 22.004 $ mm.
Identify the limits for the hole:
Maximum Hole = $ 22 + 0.018 = 22.018 $ mm.
Minimum Hole = $ 22 + 0.010 = 22.010 $ mm.
The Hole at MMC (most material) is its smallest size, $ 22.010 $ mm.
Calculate the specific clearance under these conditions:
\[ \text{Clearance} = \text{Hole Size (MMC)} - \text{Shaft Size (LMC)} \]
\[ \text{Clearance} = 22.010 - 22.004 = 0.006 \text{ mm} \]
Final Answer:
The magnitude of the clearance is 0.006 mm. For a hole, MMC is the minimum diameter and LMC is the maximum diameter, while for a shaft it is the opposite: MMC is the maximum diameter and LMC is the minimum diameter. \[ \boxed{\text{Clearance} = 0.006 \text{ mm}} \]
We need to calculate the clearance between a specific mating condition of a hole and a shaft. Clearance is the empty space between them, given by (Hole size minus Shaft size).
Step 2: Key Definitions:
Minimum Material Condition (LMC) is the size limit that contains the least amount of material. For a shaft, this is its smallest allowed diameter.
Maximum Material Condition (MMC) is the size limit that contains the most amount of material. For a hole, this is its smallest allowed diameter, since adding more material shrinks the hole.
Step 3: Detailed Explanation:
Identify the limits for the shaft:
Maximum Shaft = $ 22 + 0.075 = 22.075 $ mm.
Minimum Shaft = $ 22 + 0.004 = 22.004 $ mm.
The Shaft at LMC (least material) is its smallest size, $ 22.004 $ mm.
Identify the limits for the hole:
Maximum Hole = $ 22 + 0.018 = 22.018 $ mm.
Minimum Hole = $ 22 + 0.010 = 22.010 $ mm.
The Hole at MMC (most material) is its smallest size, $ 22.010 $ mm.
Calculate the specific clearance under these conditions:
\[ \text{Clearance} = \text{Hole Size (MMC)} - \text{Shaft Size (LMC)} \]
\[ \text{Clearance} = 22.010 - 22.004 = 0.006 \text{ mm} \]
Final Answer:
The magnitude of the clearance is 0.006 mm. For a hole, MMC is the minimum diameter and LMC is the maximum diameter, while for a shaft it is the opposite: MMC is the maximum diameter and LMC is the minimum diameter. \[ \boxed{\text{Clearance} = 0.006 \text{ mm}} \]
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