11.3 Engineering Drawing, Limits, Fits, Tolerances & GD&T

11.3 Engineering Drawing, Limits, Fits, Tolerances & GD&T

Engineering drawings serve as the authoritative legal and technical specification for manufacturing mechanical components. Precise control of dimensional tolerances, fits, and geometric boundary conditions ensures part interchangeability, assembly functionality, and quality control. This section details engineering projection standards, limit dimensions, fit classifications, hole/shaft basis systems, and Geometric Dimensioning and Tolerancing (GD&T) per ISO and ASME Y14.5 standards for the PRC Mechanical Engineering Licensure Examination.

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1. Engineering Drawing Standards & Projections

Engineering drawings present three-dimensional objects on two-dimensional media using standardized orthographic projections.

1st Angle vs. 3rd Angle Orthographic Projection

• 1st Angle Projection (ISO / European Standard): The object is positioned between the observer and the projection plane. The top/plan view is projected below the front view, and the right-side view is projected to the left of the front view.
• 3rd Angle Projection (ASME / North American Standard): The projection plane is positioned between the observer and the object. The top/plan view is drawn above the front view, and the right-side view is drawn to the right of the front view.

Projection Symbols:
1st Angle Symbol: [ (O) | -|-- ]  (Truncated cone with circle on RIGHT)
3rd Angle Symbol: [ -|-- | (O) ]  (Truncated cone with circle on LEFT)

Sectional Views & Dimensioning Principles

Sectional views expose internal geometry by passing an imaginary cutting plane through the object:

• Full Section: Cutting plane extends completely through the object.
• Half Section: Cutting plane passes halfway through, showing one half in section and one half in exterior view.
• Revolved / Removed Section: Cross-section rotated $90^\circ$ onto the view or placed adjacent.

Key dimensioning rules require dimensions to be placed outside object outlines, referenced from functional datums, and specified without redundant (over-constrained) dimensions.

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2. Limits, Fits & Tolerance Systems

No manufacturing process can produce exact nominal dimensions. A tolerance ($IT$) is the total permissible variation in a feature's size ($IT = \text{Upper Limit} - \text{Lower Limit}$).

Definitions

• Basic Size ($D$): The theoretical nominal size from which limits are derived.
• Upper Limit of Size ($UL$): The maximum allowable size of a feature.
• Lower Limit of Size ($LL$): The minimum allowable size of a feature.
• Allowance: The intentional difference between maximum material limits of mating parts (minimum clearance or maximum interference).

Standard Classes of Fits

Fits define the tightness or looseness between mating parts (such as a shaft inside a hole):

1. Clearance Fit: The hole diameter is always larger than the shaft diameter ($LL_{\text{hole}} > UL_{\text{shaft}}$), ensuring positive operating clearance.

   • Max Clearance = $UL_{\text{hole}} - LL_{\text{shaft}}$
   • Min Clearance = $LL_{\text{hole}} - UL_{\text{shaft}}$
   • Examples: ISO H7/f7 (running/sliding fit), H8/e8 (free running fit).

2. Transition Fit: The tolerance zones of the hole and shaft overlap. Assembly may result in either a slight clearance or a slight interference.

   • Examples: ISO H7/k6 (push fit), H7/n6 (drive fit).

3. Interference Fit: The shaft diameter is always larger than the hole diameter ($LL_{\text{shaft}} > UL_{\text{hole}}$), requiring force or thermal expansion/contraction for assembly.

   • Max Interference = $UL_{\text{shaft}} - LL_{\text{hole}}$
   • Min Interference = $LL_{\text{shaft}} - UL_{\text{hole}}$
   • Examples: ISO H7/p6 (press fit), H7/s6 (heavy press fit).

Fit Classifications:
Clearance Fit:     [  Hole Zone  ] 
                                   [ Shaft Zone ]
Transition Fit:    [  Hole Zone  ]
                        [ Shaft Zone ]
Interference Fit:                 [ Hole Zone ]
                   [ Shaft Zone ]

Hole-Basis vs. Shaft-Basis System

• Hole-Basis System: The basic size is taken as the lower limit of the hole (fundamental deviation symbol H, where lower deviation $EI = 0$). Shaft dimensions are varied to achieve the required fit. This is the preferred industrial system because standard cutting tools (drills, reamers) create fixed hole sizes, while shaft diameters are easily adjusted on lathes or grinders.
• Shaft-Basis System: The basic size is taken as the upper limit of the shaft (fundamental deviation symbol h, upper deviation $es = 0$). Hole dimensions are varied to suit.

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Worked Step-by-Step Calculation: Hole-Basis Clearance Fit

Problem: A $40 \text{ mm}$ basic diameter shaft and hole assembly is specified as an ISO 40 H7/f7 clearance fit. From ISO tolerance tables:

• For Hole 40 H7: Upper deviation $EI = +0.025 \text{ mm}$, Lower deviation $EI = 0.000 \text{ mm}$.
• For Shaft 40 f7: Upper deviation $es = -0.025 \text{ mm}$, Lower deviation $ei = -0.050 \text{ mm}$.

Calculate:

1. The upper and lower limits of the hole.
2. The upper and lower limits of the shaft.
3. The maximum and minimum clearances of the assembly.

Step 1: Calculate Hole Limits

$$UL_{\text{hole}} = 40.000 + 0.025 = 40.025 \text{ mm}$$ $$LL_{\text{hole}} = 40.000 + 0.000 = 40.000 \text{ mm}$$ $$\text{Hole Tolerance } IT_{\text{hole}} = 40.025 - 40.000 = 0.025 \text{ mm}$$

Step 2: Calculate Shaft Limits

$$UL_{\text{shaft}} = 40.000 + (-0.025) = 39.975 \text{ mm}$$ $$LL_{\text{shaft}} = 40.000 + (-0.050) = 39.950 \text{ mm}$$ $$\text{Shaft Tolerance } IT_{\text{shaft}} = 39.975 - 39.950 = 0.025 \text{ mm}$$

Step 3: Calculate Clearances

$$\text{Max Clearance} = UL_{\text{hole}} - LL_{\text{shaft}} = 40.025 - 39.950 = 0.075 \text{ mm} \quad (75 \> \mu\text{m})$$ $$\text{Min Clearance} = LL_{\text{hole}} - UL_{\text{shaft}} = 40.000 - 39.975 = 0.025 \text{ mm} \quad (25 \> \mu\text{m})$$

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3. Geometric Dimensioning and Tolerancing (GD&T)

GD&T (ASME Y14.5-2018 / ISO 1101) is a symbolic language that defines the permissible variation of geometric form, orientation, location, and runout of feature surfaces.

The 5 GD&T Tolerance Categories (14 Symbols)

Datum Reference Frame (DRF) & The 3-2-1 Rule

A Datum Reference Frame establishes a 3D Cartesian coordinate system using three mutually perpendicular planes to lock all 6 degrees of freedom (3 translations $X,Y,Z$ and 3 rotations $R_x, R_y, R_z$):

1. Primary Datum (A): Contacts at least 3 points on the part surface, constraining 3 degrees of freedom (1 translation, 2 rotations).
2. Secondary Datum (B): Contacts at least 2 points, constraining 2 degrees of freedom (1 translation, 1 rotation).
3. Tertiary Datum (C): Contacts at least 1 point, constraining the final 1 degree of freedom (1 translation).

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4. Material Condition Modifiers & Bonus Tolerance

Material condition modifiers define how geometric tolerances interact with feature-of-size dimensions:

• Maximum Material Condition (MMC - ⴟ): The condition where a feature contains the maximum amount of material within specified limits (e.g., smallest hole diameter or largest shaft diameter).
• Least Material Condition (LMC - Ⰼ): The condition where a feature contains the minimum amount of material (e.g., largest hole diameter or smallest shaft diameter).
• Regardless of Feature Size (RFS): Geometric tolerance remains constant regardless of actual feature size (default rule under ASME Y14.5).

Bonus Tolerance Concept

When a geometric tolerance (such as Position) is specified at MMC, the stated tolerance applies when the feature is produced at its MMC size. If the actual produced feature departs from MMC toward LMC, an additional bonus tolerance is gained:

$$\text{Bonus Tolerance} = | \text{Actual Feature Size} - \text{MMC Feature Size} |$$ $$\text{Total Permissible Geometric Tolerance} = \text{Specified Tolerance} + \text{Bonus Tolerance}$$

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Worked Step-by-Step Calculation: Position Tolerance at MMC

Problem: A pin hole drawing specifies a diameter of $\varnothing 10.00 \pm 0.10 \text{ mm}$ with a position tolerance of $\varnothing 0.05 \text{ mm}$ at MMC relative to Datums A, B, and C. Calculate:

1. The MMC size of the hole.
2. The total allowable position tolerance if the manufactured hole measures $\varnothing 10.08 \text{ mm}$.

Step 1: Determine MMC Size of Internal Hole For an internal hole, Maximum Material Condition occurs at the minimum allowable hole diameter:

$$\text{MMC Size} = 10.00 - 0.10 = 9.90 \text{ mm}$$

Step 2: Calculate Bonus Tolerance

$$\text{Bonus Tolerance} = | \text{Actual Size} - \text{MMC Size} | = 10.08 \text{ mm} - 9.90 \text{ mm} = 0.18 \text{ mm}$$

Step 3: Calculate Total Allowable Position Tolerance

$$\text{Total Position Tolerance} = \text{Specified Tolerance} + \text{Bonus Tolerance} = 0.05 + 0.18 = 0.23 \text{ mm}$$

Thus, the manufactured hole is allowed a position tolerance zone of $\varnothing 0.23 \text{ mm}$.