# ASME Y14.5.1-2019 pdf download

ASME Y14.5.1-2019 pdf download.Mathematical Definition of Dimensioning and Tolerancing Principles.

This paragraphestablishes thesurfaceinterpretationof bidirectional position tolerancing when applied in a rectangular coordinate system. (a) Definition. Forapatternofcylindrical features, each bidirectionalpositiontolerancespecifiesthateachsurface must not violate a tolerance boundary. For holes at MMC or RFS and shafts at LMC, each tolerance boundary is a cylinder of diameter equal to the collective effects of the limits ofsize, material condition basis, and applicable positiontolerance.bythebasicdimensionsofthepatternrelativetothespeci- fieddatumreferenceframeandbytheapplicabledirection of tolerance control, such that the axis of each boundary lies in the plane containing the true position axis of the corresponding feature and normal to the direction in which the tolerance applies. The orientation and position of the boundary axis within this plane is unconstrained. For holes at LMC and shafts at MMC or RFS, each toler- ance boundary is a pair of parallel planes separated by a distance equal to the collective effects ofthe limits ofsize, material condition basis, and applicable position toler- ance. The center plane of each boundary is that plane containing the axis of the corresponding feature and normal to the direction in which the tolerance applies. A position tolerance zone is a volume defined by all points P that satisfy the appropriate equation from Table 7-8, where b is a position tolerance zone size pa- rameter (radius or half-width). (b) Conformance. A cylindrical feature conforms to a bidirectional position tolerance t 0 at a specified material condition basis ifall points ofthe feature lie outside some position tolerance as defined above with b determined by the appropriate value from Table 7-9. Figure 7-9 shows an example ofbidirectional toleranc- ing of a hole at MMC. Each callout creates its own cylin- drical position tolerance zone. The tolerance zoneThis subsection provides definitions of concentricity and symmetry tolerances that control concentricity and symmetry of features.

Concentricity and symmetry controls are similar concepts and are treated together in this Section. Concentricity is that condition where the median points (centroids) of all diametrically opposedelementsofafigureofrevolution(orcorrespond- ingly located elements of two or more radially disposed features) are congruentwith a datum axis or center point. Symmetryis thatcondition where one or more features is equally disposed about a datum plane. A symmetry toler- ance is used for the mathematical concept of symmetry about a plane and a concentricity tolerance is used for the mathematical concept of symmetry about a point or symmetry about an axis. Concentricity and symmetry controls are applied to features on an RFS basis only. Datum references must also be RMB. (a) Definition. A concentricity or symmetry tolerance specifies that the centroid of corresponding point elements on the surfaces of the actual features must lie in the symmetry tolerance zone. The tolerance zone is bounded by a sphere, cylinder, or pair of parallel planes of size equal to the total allowable tolerance for the features. The tolerance zone is located and oriented by the basic dimensions of the feature(s) relative to the specified datum reference frame. The tolerance zone is a spherical, cylindrical, or parallel-plane volume defined by all points P that satisfy the equation ( ) P r b, where b is the radius or half-width of the tolerance zone. Corresponding point elements are obtained by inter- secting a pattern of symmetry rays with the actual feature. The rays of symmetry are determined per Table 7-12. If the feature is symmetric about a plane, a two-fold symmetry pattern is always used. For point and axis symmetry, the symmetry pattern is constructed using the lowest order of symmetry of the basic feature. One consequence ofthis is that surfaces ofrevolution use two-fold patter) Definition. Aprofile tolerance zone fora continuous true profile is constructed by sweeping a line segment of length t 0 , where t 0 is the specified tolerance, along each point on the true profile. The line segment is kept normal to the true profile at each point. Ifthe line segment inter- sects the true profile at another point, the line segment shall be truncated at that intersection. The profile toler- ance zone is the union ofline segments obtained from all points on the basic surface. A maximum material boundary (MMB) and a least material boundary (LMB) are created, each one a locus of endpoints of the line segments. The disposition of the generating line segment follows the disposition indicated by the tolerance specification. See Table 8-1 and Figures 8-1 through 8-4. (1) Forequallydisposedtolerances, theline segment is centered on the basic surface with equal extension in both directions. (2) For unilateral and unequally-disposed toler- ances, the line segment is disposed in the manner indi- cated by the unequally-disposed symbol Ⓤ or graphical indication. Several different dispositions are defined for a profile tolerance t 0 with a value t u following the unequally-disposed symbol. (b) Conformance. A feature conforms to a profile toler- ance t 0 if all points on the actual surface are within the tolerance zone described above.