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newSchoolWorks.com › VoTechWorks › Manufacturing & Marine › CNC Machining › Blueprint Reading and GD&T for CNC Machining › Lesson 4
MFG-CNC14-02 · Lesson 4 · 14 clock hours · theory

Dimensions, Tolerances, and Fits

Objective. Students calculate maximum material condition (MMC), least material condition (LMC), and allowable variation for linear, angular, and diametral dimensions, and classify fits using ANSI/ASME B4.1 or B4.2 standards.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed engineer or certified journey-level tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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Why Tolerances Matter in CNC Machining

No cutting tool produces a perfect dimension every time. Temperature, tool wear, vibration, and material variation all shift the actual size of a feature away from the designer's target. Tolerances define the permissible band of variation so that parts still assemble and function correctly. Understanding tolerances is essential for reading blueprints, setting up a CNC machine, and inspecting finished work — and it is directly tested in NIMS Machining credentials and Haas Certification.

Basic Tolerance Vocabulary

A nominal size (also called the basic size) is the theoretical target dimension stated on the drawing — for example, 1.500 in. The limits are the two extreme permissible sizes: the upper limit (largest acceptable) and the lower limit (smallest acceptable). The tolerance is the arithmetic difference between those two limits.

Tolerance = Upper Limit − Lower Limit

Maximum Material Condition (MMC)

MMC is the condition in which a feature contains the most material it is allowed to contain. For an external feature such as a shaft or pin, MMC is the largest permissible size. For an internal feature such as a bore or slot, MMC is the smallest permissible size. Think of it this way: more material means the feature is heavier and tighter.

Least Material Condition (LMC)

LMC is the opposite — the condition in which the feature contains the least material. For an external feature, LMC is the smallest permissible size. For an internal feature, LMC is the largest permissible size.

Methods of Stating Tolerances

Limit dimensioning states both limits directly on the drawing, one above the other. The upper limit is placed on top.

Example: 1.505 / 1.495 means the shaft must measure between 1.495 in. and 1.505 in.

Plus/minus (±) tolerancing states a nominal size with a single equal variation in both directions. A bilateral tolerance allows variation in both directions from nominal; a unilateral tolerance allows variation in only one direction.

Angular dimensions follow the same rules — an angle callout of 30° ± 0°30′ means the actual angle may range from 29°30′ to 30°30′.

ANSI/ASME Fit Systems: B4.1 and B4.2

When two mating parts must fit together — a shaft into a bore — the designer selects a fit class that controls how much clearance or interference exists at assembly.

ASME B4.1 covers inch fits and defines three broad categories:

ASME B4.2 covers the ISO metric preferred hole system (hole-basis) and shaft-basis system using tolerance grades (IT grades) and deviation letters. Common callouts such as H7/g6 indicate the tolerance grade and position for each mating feature.

To use a fit table, you need: (1) the basic size, (2) the fit class desired, and (3) the table column for upper and lower deviations. Apply those deviations to the basic size to get the actual limits, then verify with a tolerance stack — confirming that at MMC of both features, the correct condition (maximum interference or minimum clearance) is within specification.

Measuring Parts with a Micrometer

An outside micrometer measures external dimensions such as shaft diameters. Common ranges in the shop are 0–1 in. and 1–2 in. Safe and accurate measurement procedure:

1. Clean the part and anvil faces — chips or oil cause false readings.

2. Zero the micrometer using the standard or by closing on a clean gauge block.

3. Bring the spindle into light contact with the part; use the thimble ratchet or friction stop — never force the spindle.

4. Read the sleeve (main scale), then the thimble graduation, then the vernier line if present. Add the values.

5. PPE reminder: Burrs on machined parts can cut. Wear safety glasses at all times on the shop floor. Handle sample parts carefully; deburr before measuring if sharp edges are present.

6. Record the reading to the nearest 0.0001 in. and compare to the drawing limits to accept or reject the part.

A part is in tolerance when its actual size falls on or between the two limits (including the limits themselves). A part is out of tolerance when its actual size exceeds either limit, even by 0.0001 in. When in doubt, re-measure and, if still out, quarantine the part — never pass a borderline reading by guessing.

Key terms10

Nominal size (basic size)The theoretical target dimension from which limits and deviations are calculated; not itself a permissible size.
ToleranceThe total permissible variation in a dimension; equal to the upper limit minus the lower limit.
Maximum Material Condition (MMC)The condition where a feature contains the greatest amount of material: largest size for external features, smallest size for internal features.
Least Material Condition (LMC)The condition where a feature contains the least amount of material: smallest size for external features, largest size for internal features.
Bilateral toleranceA plus/minus tolerance that allows variation in both directions from the nominal size.
Unilateral toleranceA tolerance that allows variation in only one direction from the nominal size.
Clearance fitA fit in which the shaft is always smaller than the bore, guaranteeing a gap at all permissible sizes.
Interference fitA fit in which the shaft is always larger than the bore, requiring force or thermal methods to assemble.
Transition fitA fit whose tolerance zones overlap, so the assembly may result in either clearance or interference depending on actual sizes.
Tolerance stackA calculation that combines the limits of two or more mating features to find the extreme conditions of clearance or interference at assembly.

Worked examples4

1. A drawing calls out a shaft diameter as 1.750 +0.000/−0.008 in. Find (a) the upper limit, (b) the lower limit, (c) MMC, (d) LMC, and (e) the total tolerance.
  1. Identify the nominal size: 1.750 in.
  2. Apply the plus deviation: 1.750 + 0.000 = 1.750 in. → upper limit.
  3. Apply the minus deviation: 1.750 − 0.008 = 1.742 in. → lower limit.
  4. The shaft is an external feature. MMC = largest permissible size = 1.750 in.
  5. LMC = smallest permissible size = 1.742 in.
  6. Total tolerance = upper limit − lower limit = 1.750 − 1.742 = 0.008 in.
Answer: Upper limit = 1.750 in., lower limit = 1.742 in., MMC = 1.750 in., LMC = 1.742 in., tolerance = 0.008 in.
2. A bore is dimensioned 2.005/1.995 in. Find (a) MMC, (b) LMC, and (c) total tolerance.
  1. From limit dimensioning, upper limit = 2.005 in., lower limit = 1.995 in.
  2. The bore is an internal feature. MMC = smallest permissible size = 1.995 in. (least space inside = most material).
  3. LMC = largest permissible size = 2.005 in. (most space inside = least material).
  4. Total tolerance = 2.005 − 1.995 = 0.010 in.
Answer: MMC = 1.995 in., LMC = 2.005 in., total tolerance = 0.010 in.
3. A shaft has limits 1.7480–1.7490 in. and its mating bore has limits 1.7500–1.7515 in. Classify the fit (clearance, interference, or transition) and calculate the maximum and minimum clearance.
  1. Determine shaft MMC (largest shaft): 1.7490 in. Determine bore MMC (smallest bore): 1.7500 in.
  2. Check minimum clearance (tightest condition): smallest bore − largest shaft = 1.7500 − 1.7490 = 0.0010 in. Positive value → always a gap.
  3. Check maximum clearance (loosest condition): largest bore − smallest shaft = 1.7515 − 1.7480 = 0.0035 in.
  4. Because the minimum clearance is positive (no interference possible at any combination), this is a clearance fit.
  5. Minimum clearance = 0.0010 in., maximum clearance = 0.0035 in.
Answer: Clearance fit; minimum clearance = 0.0010 in., maximum clearance = 0.0035 in.
4. A drawing calls an angle of 45° ± 1°30′. What are the upper and lower angular limits?
  1. Convert the tolerance to a consistent unit. 1°30′ = 1.5°.
  2. Upper limit = 45° + 1°30′ = 46°30′.
  3. Lower limit = 45° − 1°30′ = 43°30′.
  4. Total angular tolerance = 46°30′ − 43°30′ = 3°00′.
Answer: Upper limit = 46°30′, lower limit = 43°30′, total angular tolerance = 3°00′.

The math in this lesson2

Learners compute clearance between shaft and bore limits to classify the fit.
7.NS.1N-Q.3
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor explains limit dimensioning, plus/minus tolerancing, and bilateral versus unilateral tolerances; students calculate MMC, LMC, and tolerance range for 15 dimension callouts. · Students use an ANSI fit table to determine clearance, interference, or transition fit class for a shaft-and-bore pair given basic size and tolerance grade, then verify with a tolerance stack calculation. · Students examine a set of sample turned shafts measured with a micrometer and determine which are in tolerance and which are out of tolerance for a given drawing callout.
Materials: ASME B4.1/B4.2 fit table handout, tolerance calculation worksheet, outside micrometer (0–1 in. and 1–2 in.), sample turned shafts (in- and out-of-tolerance set), calculator
Check: Tolerance calculation quiz (20 problems): minimum 16 of 20 correct (80%); shaft accept/reject exercise: all 6 accept/reject decisions must be correct.

Practice check9

Answer each question, then check it. Nothing is recorded; this is your own practice.

NIMS Machining L1 — Blueprint Reading
1. A shaft is dimensioned 0.875 ± 0.005 in. What is the MMC of the shaft?
NIMS Machining L1 — Blueprint Reading
2. A bore is called out as 1.2510/1.2490 in. What is the total tolerance?
NIMS Machining L1 — GD&T Fundamentals
3. For an internal feature (bore), the Least Material Condition (LMC) corresponds to which size?
NIMS Machining L1 — Measurement and Inspection
4. A shaft measures 1.4988 in. The drawing limits are 1.4990/1.4975 in. What is the correct inspection decision?
NIMS Machining L1 — Measurement and Inspection
5. A shaft measures 1.4988 in. The drawing limits are 1.4985/1.4975 in. What is the correct inspection decision?
NIMS Machining L1 — Blueprint Reading
6. Which type of tolerance allows variation in both directions from the nominal dimension?
NIMS Machining L2 — Tolerancing and Fits
7. Using ASME B4.1, if the tightest possible assembly of a shaft-and-bore pair always produces a gap (never interference), the fit is classified as:
NIMS Machining L2 — Tolerancing and Fits
8. A shaft has limits 2.0015–2.0020 in. and its mating bore has limits 2.0000–2.0010 in. At MMC of both features, what is the interference?
NIMS Machining L1 — Measurement and Inspection
9. When reading an outside micrometer, which practice ensures the most accurate measurement?
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