With the advancement of globalization, the international division of labor and collaboration in manufacturing have continued to deepen. However, challenges persist regarding communication barriers and differing production habits between countries. How can we solve the dilemma of improving production precision while ensuring interchangeability to reduce costs? The unification of international standards for Geometric Dimensioning and Tolerancing (GD&T) became an urgent necessity.
→ 1950: Industrialized nations submitted the “ABC Proposal” to the ISO organization, aiming to unify the concepts and text-based representation of geometric tolerances.
→ 1969: The ISO officially released the geometric tolerancing standard ISO/R1101-I:1969, titled “Tolerances of Form and Position — Part I: Generalities, Symbols, Indications on Drawings.”
→ 1978 – 1980: The ISO recommended principles and methods for the inspection of geometric tolerances. During this period, China officially rejoined the ISO and promulgated its basic standards for form and position tolerances in 1980.
→1996: The ISO established the dedicated technical committee ISO/TC213 “Dimensional and Geometrical Product Specifications and Verification (GPS)”, responsible for the international unification of geometric tolerances and their drawing symbols.
Through the long-term collective efforts of many nations, the internationally unified 14 geometric characteristics and symbols were finally established, as shown in the table below.
01 Straightness
Straightness represents the condition where a line element on a part maintains an ideal straight shape. The straightness tolerance is the maximum allowable variation of the actual line from the ideal straight line.
- Example 1: In a given plane, the tolerance zone must lie within the area between two parallel lines spaced 0.1 mm apart.
- Example 2: If the symbol “Ø” is added before the tolerance value, the tolerance zone must lie within the region of a cylinder with a diameter of 0.08 mm.
02 Flatness
Flatness represents the condition where a planar element on a part maintains an ideal plane. The flatness tolerance is the maximum allowable variation of the actual surface from the ideal plane.
- Example: The tolerance zone is the area between two parallel planes spaced 0.08 mm apart.
03 Circularity
Roundness represents the condition where the elements of a circle on a part remain equidistant from its center. The roundness tolerance is the maximum allowable variation of the actual circle from the ideal circle within the same cross-section.
- Example: The tolerance zone must lie within the area between two concentric circles with a radial difference of 0.03 mm on the same normal cross-section.
04 Cylindricity
Cylindricity represents the condition where all points on the surface of a cylindrical feature are equidistant from its axis. The cylindricity tolerance is the maximum allowable variation of the actual cylindrical surface from the ideal cylindrical surface.
- Example: The tolerance zone is the region between two coaxial cylindrical surfaces with a radial difference of 0.1 mm.
05 Profile of a Line
Profile of a line represents the condition where a curve of any shape maintains its ideal form within a given plane of a part. The line profile tolerance refers to the allowable variation of the actual contour of a non-circular curve.
- Drawing Example: The tolerance zone is the area between two envelopes of a series of circles with a diameter of 0.04 mm. The centers of these circles are located on a line having the theoretically exact geometric shape.
06 Profile of a Surface
Profile of a surface represents the condition where a curved surface of any shape maintains its ideal form. The surface profile tolerance refers to the allowable variation of the actual contour of a non-circular surface from the ideal profile.
- Example: The tolerance zone is bounded by two envelopes of a series of spheres with a diameter of 0.02 mm. The centers of these spheres should theoretically be located on the surface of the theoretically exact geometric shape.
07 Parallelism
Parallelism represents the condition where the actual feature under measurement remains equidistant relative to a datum. The parallelism tolerance is the maximum allowable variation between the actual direction of the measured feature and the ideal direction parallel to the datum.
- Example: If the symbol “Ø” is added before the tolerance value, the tolerance zone is within a cylinder of diameter 0.03 mm that is parallel to the datum.
08 Perpendicularity
Perpendicularity represents the condition where the feature under measurement maintains a correct 90° angle relative to a datum. The perpendicularity tolerance is the maximum allowable variation between the actual direction of the measured feature and the ideal direction perpendicular to the datum.
- Example 1: If the symbol “Ø” is added, the tolerance zone is within a cylinder of diameter 0.1 mm perpendicular to the datum plane.
- Example 2: The tolerance zone must lie between two parallel planes spaced 0.08 mm apart and perpendicular to the datum line.
09 Angularity
Angularity represents the condition where the relative orientation of two features on a part maintains any given angle. The angularity tolerance is the maximum allowable variation between the actual direction of the measured feature and the ideal direction at a given angle relative to the datum.
10 Position
Position represents the accuracy of points, lines, or surfaces on a part relative to their ideal locations. The position tolerance is the maximum allowable variation of the actual position of the measured feature relative to its ideal position.
11 Concentricity
Concentricity represents the condition where the measured axis of a part remains on the same straight line relative to the datum axis. The concentricity tolerance is the allowable variation of the actual measured axis relative to the datum axis.
- Example: When a symbol is added to the tolerance value, the tolerance zone is the region within a cylinder of diameter 0.08 mm. The axis of this circular tolerance zone coincides with the datum.
12 Symmetry
Symmetry represents the condition where two symmetrical central features on a part remain within the same central plane. The symmetry tolerance is the allowable variation of the actual feature’s center plane (or center line/axis) from the ideal symmetry plane.
- Example: The tolerance zone is the region between two parallel planes or straight lines spaced 0.08 mm apart and arranged symmetrically with respect to the datum center plane or center line.
13 Circular Runout
Circular runout represents the condition where a surface of revolution maintains a fixed position relative to a datum axis within a limited measurement plane. The circular runout tolerance is the maximum allowable variation within a limited measurement range when the measured feature rotates one full revolution around the datum axis without axial movement.
- Example 1: The tolerance zone is the region between two concentric circles with a radial difference of 0.1 mm in any measurement plane perpendicular to the axis, centered on the same datum axis.
- Example 2: The tolerance zone is the region between two circles spaced 0.1 mm apart on a measurement cylinder at any radial position coaxial with the datum.
14 Total Runout
Total runout refers to the total variation along the entire measured surface as the part rotates continuously around the datum axis. The total runout tolerance is the maximum allowable runout when the actual feature rotates constantly around the datum axis while the indicator moves relatively along its ideal profile.
Example 1: The tolerance zone is the region between two concentric cylinders with a radial difference of 0.1 mm, which are coaxial with the datum.
Example 2: The tolerance zone is the region between two parallel planes spaced 0.1 mm apart and perpendicular to the datum.
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