# GEOMETRIC DIMENSIONING AND TOLERANCING

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GEOMETRIC DIMENSIONING AND TOLERANCING

Some surprises  10 0.2  10.2  9.8

Coordinate Tolerancing System
Shortcomings: - Square or rectangular zones Fixed-size tolerance zones Ambiguous instructions for inspection

Comparison of Tolerance Zone
15 0.2 10 0.2 10 0.2 20 0.2 57 % more clearance in a round zone compared to square zone 0.4 square 0.16 excess 0.4 This hole axis is allowed to be the further than this hole

Geometric Dimensioning and Tolerancing
4 Holes  5  0.5 O  0.56 15 20 10 10 20

Method of Inspection X X SURFACE PLATE SURFACE PLATE OR
This method for part measurement? This method for part measurement?

Geometric Dimensioning and Tolerancing
Geometric Dimensioning and Tolerance (GD&T) is an international language that is used on engineering drawings to accurately describe a part. It basically consists of well-defined set of symbols, rules, definitions and conventions. GD&T is a precise mathematical language that can be used to describe the size, form, orientation and location of part features. GD&T is also a design philosophy on how to design and dimension parts. It encourages a dimensioning philosophy called “Functional Dimensioning”, that defines a part based on how it functions in the final product.

Comparison between geometric and coordinate tolerancing
Drawing Concept Coordinate Tolerance Geometric Tolerance TOLERANCE ZONE SHAPE CONDITION Square or rectangular zones for hole locations Can use diameter symbol to allow round tolerance zone RESULTS Less tolerance available for hole Higher manufacturing cost 57% more tolerance Lower manufacturing costs TOLERANCE ZONE FLEXIBILITY Tolerance zone fixed in size Use of MMC modifier allows tolerance zone to increase under certain conditions Functional parts scrapped Higher operating costs Functional parts used Lower operating costs

Comparison between geometric and coordinate tolerance
Drawing Concept Coordinate Tolerance Geometric Tolerance EASE OF INSPECTION CONDITION Implied datum allows choices for set up when inspecting the part The datum system communicates one set up for inspection RESULTS Multiple inspectors may get different results Good parts scrapped Bad parts accepted Clear instructions for inspection Eliminates disputes over part acceptance

Roundness (Circularity)
Tolerance Symbols Characteristics Symbol Type Flatness Form Straightness Roundness (Circularity) Cylindricity Line Profile Profile Surface Profile Perpendicularity Orientation Angularity Parallelism Circular Runout Runout Total Runout Position Location Concentricity Symmetry

Tolerance Frame Tolerance Frame – A boxed expression containing the geometric characteristics symbol, the tolerance shape zone where applicable and tolerance; plus any other datum reference and modifiers for the features or datums: 0.1 0.1 A 0.1 M A B C Tolerance Symbol Tertiary Datum Tolerance Zone Shape and value Secondary Datum Primary Datum Modifier

GD&T Definitions A Feature – It is a general term applied to physical portion of a part, such as a surface, hole, or slot. In short a feature is a part surface Basic Dimension – It is a theoretical value used to describe the exact size or location. A tolerance is always required with a basic dimension to show the permissible variation. A basic dimension is symbolized by boxing e,g., 10

GD&T Definitions - Datum
A Datum is a theoretically exact plane, point or axis from which a dimensional measurement is made. A datum feature is a part feature that contacts a datum A planar datum is the true geometric counterpart of palanar datum feature Datum features and surfaces are actual part features and surfaces including all of their feature or surface inaccuracies. A true geometric counterpart is the theoretical perfect boundary or best fit tangent plane of a specified datum feature

Datum Tertiary datum (Minimum one points of contact) Secondary datum
(Minimum two points of contact) Primary datum (Minimum three points of contact)

Datums A A On the outline of the feature or an extension line A A
On the extension line when datum feature is the axis or median plane A On the axis or median plane when datum feature is the common axis or plane formed by two feature

Tolerance to axis or median plane of common features
Toleranced Feature Tolerance to line or Surface Tolerance to axis or median plane Tolerance to axis or median plane of common features

Datum Terminology A 10.6 – 0.4 Drawing Actual part
Simulated datum feature A (Considered as true geometric counterpart) Gauge element for establishing Datum Axis Datum feature Datum feature simulator (gauge element) Simulated datum axis A (Considered as datum axis A) When a diameter is designated as a datum feature, the datum axis is derived from placing the part in a datum feature simulator (gauge elements). The datum feature is the surface of the part. The gauge element that holds the part datum feature is the datum feature simulator; it is considered the true geometric counter part of the datum feature. The axis of the gauge element that holds the part datum feature is the simulated datum axis and is considered as the datum axis.the datum axis becomes the origin of measurement for dimensions that are related to the datum.

GD&T Definitions – Mating Size
Mating size for an external feature: The dimension of the smallest perfect feature which can be circumscribed about the feature so that it just contacts the surface at the highest points. Mating size for an internal feature: The dimension of the largest perfect feature which an be inscribed within the feature so that it just contacts the surface at the highest points

GD&T Definitions – MMC and LMC
Maximum Material Condition (MMC) - The state of the considered feature in which the feature is everywhere at that limit of size where the material of the feature is at its maximum e.g. minimum hole diameter and maximum shaft diameter Least Material Condition (LMC) - The state of the considered feature in which the feature is everywhere at that limit of size where the material of the feature is at its minimum e.g. maximum hole diameter and minimum shaft diameter

GD&T Definitions - Virtual Condition
Virtual condition (VC) is the limiting boundary of perfect form permitted by the drawing data for the feature; the condition is generated by the collective effect of the maximum material size and the geometrical tolerances. The VC of a feature of size includes effects of the size, orientation, and location for the feature. When the maximum material principle is applied, only those geometrical tolerances followed by the symbol shall be taken into account when determining the virtual condition M Virtual Size is the dimension defining the virtual condition of a feature

GD&T Definitions – Example
 0.5 M A  150–0.3 Mating size ` Virtual size  Virtual condition Actual local size Maximum material condition Perpendicularity tolerance zone dia. 0.05 A

Virtual Condition A A  12.6 –0.4  12.9 at VC Datum plane A
 0.3 Tol at MMC  0.3 M A A VC = MMC +Tol 12.9 = Virtual Condition  12.9 at VC  0.3 Tol at MMC Datum plane A A  0.3 M VC = MMC -Tol 12.9 = Virtual Condition

Multiple Virtual Condition
20 B C A  0.2 M  0.1 Size tolerance as per Rule #1 The Dia must pass thru a 10.2 envelope as per Rule #1 & must be > 9.8 10.3  0.1 A M Virtual condition boundary to datum A 10.4 Virtual condition boundary relative to datum A,B,C  0.2 A M B C

Rules of GD&T Rule #1 – Where only a tolerance of size is specified , the limits of size of an individual feature prescribe the extent to which variations in its form - as well as in its size – are allowed. It is referred to as the “perfect form at MMC” or “envelope rule.” It is a key concept it GD&T. It ensures that features of size will assemble with one another. It is the Taylor Principle. This means: No element of the actual feature of size shall extend beyond a boundary of perfect form at MMC. The actual measured size at any cross section of the feature shall within the LMC limit for size. 3. This rule does not apply to non-rigid parts or commercial stock, such as bar stock, plates tunings, etc.

Rules of GD&T Rule #2 – For all applicable geometric tolerances, Regard Less of Feature (RFS) applies with respect to the individual tolerance, datum reference or both, where no modifying symbol is specified.

Rule #1 Boundary 10.8-0.6 10.8 Rule #1 boundary 10.2 LMC part
Part Height Amount of Form Error Allowed 10.8 (MMC) 10.7 0.1 10.6 0.2 10.5 0.3 10.4 0.4 10.3 0.5 10.2 (LMC) 0.6

Go Gauge and No-Go Gauge : Shaft
10.8 40.8 MIN Go Gauge Verifies part diameter does not exceed MMC size and Rule #1 boundary Part must pass thru the gauge Part (Verifies that any two-point check is equal to or greater than LMC) 10.2 No-Go Gauge Multiple checks are required

Go Gauge and No-Go Gauge : Hole
Go Gauge Verifies part diameter does not violate MMC size and Rule #1 boundary 30.6 MIN Part 9.2 No-Go Gauge Verifies that any two-point check is equal to or less than LMC Part 9.4 The No-Go gauge could be used at both ends of the hole. If a check inside the part is needed , a variable two-point measurement can be made

Bonus Tolerance due to MMC
 1.0 A M  12.6 –0.6 Gauge Datum axis A  12.6 Part Gauge element for establishing datum axis A Size of toleranced part Bonus tolerance  8.4 (MMC) 1.0  8.5 1.1  8.6 1.2  8.7 1.3  8.8 (LMC) 1.4

Zero Tolerance at MMC  1.0 A M  12.6 –0.6 Zero tolerancing at MMC allows more size tolerances with out changing MMC concept. It allows machinist a wide range of tools sizes to choose from. Not to be applied to tapped holes. Adds weight and not be used where weight at premium.  0 A M

Position Tolerance zone dia
Bonus Tolerance at LMC A  0.2 L Toleranced dia AME Position Tolerance zone dia 24.2 0.2 24.4 0.4 24.6 0.6 24.8 0.8 Minimum Wall Thickness ? [(24.2 – 0.2) –20.8]%2 = 1.6

Datum Shift - Definition
Datum shift is the allowable movement, or looseness, between the part datum feature and the gauge. Datum shift may result in additional tolerance for the part

Datum Shift-Perfect Datum
 8.8 –0.4  1.0 A M  12.6 –0.6 Gauge Datum axis A  12.6 Part Gauge element for establishing datum axis A Actual mating size of datum feature A Diametral datum shift possible  (MMC) 0.0  12.4 0.2  12.2 0.4  (LMC) 0.6

10 – 0.3 5– 0.3  0.1 A M A Datum Feature Size Controlled Feature Size Datum Shift Tolerance 10 5 0.1 4.9 0.2 4.8 0.3 4.7 0.4 9.9 9.8 0.5 9.7 0.7

Datum Shift With Datum Tolerance
 1.0 A M  12.6 –0.6  0.2 Datum axis A Gauge  12.8 Part Simulated datum Actual mating size of datum feature A Diametral datum shift possible  12.8 0.0  (MMC) 0.2  12.4 0.4  12.2 0.6  (LMC) 0.8 Datum shift = Gauge size – Actual mating size

Straightness Tolerance - Surface
0.1 0.1 0.1 wide tolerance zone for each line element of the surface

Straightness Tolerance - Axis
0.1 Tolerance zone of 0.1mm wide  0.1 Cylindrical tolerance zone of diameter 0.1mm

Cylindricity Tolerance
0.5 0.5 All element of the surface must lie within two concentric cylinders 0.5mm apart parallel to the axis

Tolerance of Position B  6.0 +0.4 A 12.2  0.2 A B C C 16.2 16.2 12.2
 0.2 tol. zone Datum plane A Datum plane B Datum plane C

Tolerance of Position to Non-parallel Hole
6 B 4x30o 4x   0.4 C M Hole AME  Tol. Dia. Bonus Tol. Total Tol. Dia 6.0 0.4 6.1 0.1 0.5 6.2 0.2 0.6

Perpendicularity - definition
Perpendicularity is the condition that results when a surface, axis, or centerplane is exactly 90 degrees to a datum. A perpendicularity control is a geometric tolerance that limits the amount a surface, axis, or centerplane is permitted to vary from being perpendicular to the datum The two common tolerance zones for a perpendicularity are: Two parallel planes - A cylinder

Perpendicularity of Surface
24.8 – 0.4 B 0.2 Datum plane B Datum plane A Part contacts datum plane A first and datum plane B second Tolerance zone two parallel planes 0.2 apart, perpendicular to A All elements of the part surface must be within the tolerance zone

Perpendicularity to Axis
Tol. Zone dia. 50.2 – 0.2  0.2 A M Dia Perpendicularity tol Bonus tol. Tolerance Zone  50.2 0.05 0.0 50.1 0.1 0.15 50.0 0.2 0.25

Parallelism of Surface
0.1 A A Datum plane A All elements of the part surface must be within the tolerance zone Tolerance zone is two parallel planes 0.1 apart & parallel to datum plane A 21.8 22.8

Parallelism To A Diameter
 0.1 A M 22.2 – 0.4 A Tolerance zone 0.1 dia . cylinder Axis of diameter must be within tolerance zone Datum plane A  10.1 Adjustable to accommodate hole location tolerance Datum plane A Gauge for verifying parallelism of hole

Symmetry A 28.4 – 0.4 22.4 – 0.2 0.6 Datum centreplane A
Tolerance zone – 2 parallel planes 0.6 apart Median points of toleranced feature lie within the tolerance zone

Concentricity A  30.6–0.4  0.3  12.2 –0.2 Chuck or collet
X = Distance from datum axis to part surface Y = Distance from datum axis to part surface X – Y = Distance of two point measurement W = Midpoint = (X+Y)/2 Z = Distance between midpoint and datum axis Z = X - W X = 15.4 Y= 15.2 Z Midpoint 15.3 Chuck or collet Daum axis Median points of the toleranced dia. must be within the tolerance zone Each distance Z must be within the cylindrical tolerance zone

Circular Runout A  30.6–0.4 1  12.2 –0.2 Chuck or collet
Daum axis Part surface Two co-axial circles originate from the datum axis Radial distances between circles equal to the runout tolerance value

Circular Runout to a Surface
 12.2 –0.2 0.2 Chuck or collet Datum axis Rotated 360 degrees. The gauge is moved along consecutive vertical circles Maximum indicator reading 0.2 Angle of surface not controlled with circular runout

Total Runout A  30.6–0.4 1 A  12.2 –0.2 Chuck or collet Datum axis
Dial indicator reading is the runout tolerance value Rotated 360 degrees. The gauge is moved along the axis Gauge covers a helix of the surface of the diameter

Comparison of Concentricity, Runout and Tolerance of Position
CONCEPT GEOMETRIC CONTROL CONCENTRICITY TOTAL RUNOUT TOP Tolerance zone Cylinder Two co-axial cylinders Tolerance zone applies to … Median points of toleranced diameter Surface elements of a toleranced diameter Axis of AME of the tolerances diameter Relative cost to produce CC CCC C Relative cost to inspect Part characteristics being controlled Location and orientation Location, orientation and form

Functional Gauge-Shaft
 12.6 –0.4  0.3 Tol at MMC  0.3 M A  12.9 at VC A Virtual Condition Datum plane A Functional Gauge  12.9

Functional Gauge-Hole
 0.3 A M  12.9 at VC  0.3 Tol at MMC Datum plane A Virtual Condition  12.9 Functional Gauge

Functional Gauge A functional gauge verifies functional requirements of part features as defined by the geometric tolerances A functional gauge does not provide a numerical reading of a part parameter. When compared to variable gauge, a functional gauge offers several benefits:. The gauge represents the worst-case mating part. Part can be verified quickly A functional gauge is economical to produce No special skills are required to ‘read’ the gauge or interpret the result A functional gauge can check several part characteristics simultaneously

Advantages of Geometric Dimensioning & Tolerance
Improved communication and clear understanding between the designer, manufacturer and inspector, and vendor Ensures uniform drawings and minimises written specifications and instructions. Provides uniform interpretation. Eliminates implied datums and dictates the method of gauging rather than relying on an individual’s interpretation. Provides a clear understanding of how the part functions. Identifies product problems early in the design stage. Provides greater tolerances for manufacturing in the design stage, and later in form of “bonus tolerancing”. Ensures assembly of components. Provides savings in time and money.

Thank you

Geometric Dimensioning and Tolerance
4 Holes  5  0.5 O  0.56 15 20 10 10 20

Geometric Dimensioning and Tolerance
4 Holes  5  0.5 O  0.56 15 20 10 10 20

Worst Case Boundary  0.3 A  12.6 –0.4  12.9 Outer Boundary
Datum plane A  0.3 Tol at MMC Outer Boundary WCB = OB = MMC + Tol 12.9 =  0.3 A  12.9 Inner Boundary  0.3 Tol at MMC Datum plane A Inner Boundary WCB = IB = MMC - Tol 12.9 =

GD&T Definitions – Datum (Contd)
Depending upon the type of datum feature, true geometric counterpart may be: - A tangent plane contacting the high points of a surface - A maximum material condition boundary - A least material condition boundary - A virtual condition boundary - An actual mating envelope - A worst-case boundary