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Dimensioning and Tolerancing Design representation: enough information to manufacture the part precisely inspect the manufactured part [geomtery, dimensions, tolerances]

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Projections Theoretical technique to map 3D objects to 2D Dimensions To assist machinist: e.g. distance between centers of holes Tolerances imprecision in machining must specify the tolerance range,

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What is a ‘good level of tolerance’? Designer: tight tolerance is better (less vibration, less wear, less noise) Machinist: large tolerances is better (easier to machine, faster to produce, easier to assemble) Tolerances interchangeability

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Tolerance and Concurrent Engineering Why ? Tolerance specification needs knowledge of accuracy, repeatability of machines process capability …

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Part 1. Projections. 3D models: expensive, difficult to make => need 2D representaitons Images must convey feasible 3D objects

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Albrecht Durer’s machine [14??AD] (perspective map)

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1. Renaissance architects 2. Modern CAD systems (a) 3D rendering, image processing (b) Mathematics of free-form surfaces (NURBS) Importance of perspective maps

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Why perspective maps ? larger, farther same image size same size, farther smaller image Human sight and perception

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parallel lines converge to a point The vanishing point (or station point)

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Effect of vanishing point on perspective map Image on the ‘picture plane’ is a perspective of the 3D object [Is the object behind in perspective view ?]

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Perspectives and vanishing points Perspectives in mechanical draftingNot good ! (1) parallel lines converge misinterpreted by the machinist (2) Views have too many lines

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Orthographic views A mapping where parallel lines remain parallel How ? Set the vanishing point at infinity Another problem: Back, Sides of object not visible (hidden surfaces) Solution: Multiple views

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Orthographic views: Language of engineering communication

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View direction selection in orthographics Maximize true-size view of most faces

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Isometric view: gives a ‘3D image’

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Different types of projections All engineering drawings must be made to scale

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Datum: A theoretical geometric object (point, line, axis, or plane) derived from a specific part/feature of a datum feature on the part. Uses: (1) specify distance of a feature from the datum (2) specify a geometric characteristic (e.g. straightness) of a feature Part 2. ANSI dimensioning

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Basic Dimension: The theoretically exact size of a feature or datum Feature: A geometric entity on the part, (hole, axis, plane, edge) Datum feature: An actual feature of a part, that is used to establish a datum.

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Limits: The max/min allowable sizes Largest allowable size: upper limit Least allowable size: lower limit. LMC (Least Material Condition) MMC (Maximum material Condition)

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Conventions for dimensioning (a) Specify tolerance for all dimensions (b) All necessary, sufficient dimensions X over-dimensioned X X under-dimensioned X Reference dimensions: Redundant dimensions, in ( …) (c) Dimensions should be (i) marked off the datum feature (ii) shown in true-size view (iii) shown in visible view

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(a) Size of a feature Specified by a basic size, and tolerance: 2.50±0.03 upper limit = lower limit = No of digits after decimal precision Part 3. Mechanical Tolerancing Conventional Tolerancing:

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Unilateral and Bilateral Tolerances:

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(b) The type of fit between mating features Designer needs to specify basic dia, tol of shaft: S±s/2 basic dia, tol of hole: H±h/2 Allowance: a = D hmin – D smax. Conventional Tolerancing..

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Standard fits

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The hole-basic specification convention [Holes are made by drills]

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Generalization of hole-basic/shaft-basic MMC: Maximum material condition LMC: Least material condition Hole at MMC at the lower limit Hole at LMC at the upper limit

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Geometric Tolerancing Problems in Conventional tolerancing: (a) Assumes perfect surfaces (b) No use of Datums (c) No specification of form tolerances (d) X±t/2, Y±t/2 rectangular tolerance zone (cylindrical preferred)

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Datums A theoretical feature (e.g. plane, line) Serves as a global coordinate frame for the part during different activities such as design, manufacturing and inspection. Each design must specify the datum planes (or other datums)

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Datum feature The actual plane on the part (imperfect) corresponding to a (perfect) datum plane Sequence of establishing datums: PRIMARY (3 points) SECONDARY (2 points) TERTIARY (1 point)

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ANSI symbols for geometric tolerancing

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Different allowed notations (ANSI)

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Location tolerances: Conventional system: rectangular tolerance zones True Position Tolerancing circular (cylindrical) tolerance zone

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Form Tolerances

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Geometric Dimensioning and Tolerancing (GD&T)

Geometric Dimensioning and Tolerancing (GD&T)

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