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

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,

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

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

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

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

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

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

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

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 ?]

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

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

Orthographic views: Language of engineering communication

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

Isometric view: gives a ‘3D image’

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

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

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.

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

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

(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:

Unilateral and Bilateral Tolerances:

(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..

Standard fits

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

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

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)

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)

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)

ANSI symbols for geometric tolerancing

Different allowed notations (ANSI)

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

Form Tolerances