ISO 3040:2016

Overview

ISO 3040:2016 - "Geometrical product specifications (GPS) - Dimensioning and tolerancing - Cones" specifies how to graphically indicate, dimension and tolerances right‑angle circular cones (any section perpendicular to the axis is a circle). The standard covers symbols, dimensioning methods (e.g., rate of taper, cone angle, diameters and lengths), and approaches to tolerancing conical features used on technical drawings and in GPS/GD&T practice. Truncated cones are illustrated for simplicity, but the rules apply to any right‑angle circular cone.

Key topics and technical requirements

• Scope: Applies only to right‑angle circular cones; other methods remain allowed (NOTE 2).
• Graphical symbol for rate of taper: A standardized symbol centered on a reference line aligned with the cone axis; leader line connects to the cone outline. Symbol size/line thickness per ISO 81714‑1.
• Rate of taper (C): Defined as the ratio of diameter difference to axial distance (relation to cone angle α is given in the standard). Common notation examples: 1:5, 0,2:1 or coded series (e.g., Morse).
• Dimensioning options: Preferred and optional dimensions include rate of taper, cone angle (α), larger/smaller end diameters (D, d), and axial lengths (L, L′, Lx). Use no more dimensions than necessary; auxiliary dimensions allowed.
• Tolerancing principles: A cone is intrinsically defined by its angle; tolerancing can control angle deviation, form (surface/profile), location (X, Y, Z) and orientation (β, γ). Tolerance zones are typically coaxial conical surfaces (examples in the standard show form-only zones and zones with datum constraints). Example tolerance zone given in ISO text: two coaxial conical surfaces 0.3 mm apart.
• Datum and TEDs: When gauge planes, datums or datum systems locate tolerance zones, related linear/angular dimensions must be defined as TEDs (tolerance explictly declared).
• Normative references: ISO 1119 (series of conical tapers and taper angles) and ISO 81714‑1 (graphical symbol design).

Practical applications

• Use ISO 3040:2016 for consistent dimensioning and tolerancing of conical parts in:
  • Machine tooling (spindle tapers, chucks, mandrels)
  • Fastener and mating taper fits (e.g., Morse/metric tapers)
  • Shaft and housing tapers, mold and die components
  • CAD model annotation, engineering drawings and manufacturing drawings
  • Inspection planning and CMM metrology (defining tolerance zones and datums)
• It helps avoid ambiguity in drawings, supports interoperability between design, manufacturing and quality departments, and improves supplier/contractor communication.

Who should use this standard

• Mechanical designers and draughtspersons
• CAD/GD&T practitioners and PLM modelers
• Manufacturing and machining engineers
• Quality, metrology and inspection engineers
• Technical authors and standards writers creating drawing conventions

Related standards

• ISO 1119 - series and codification of conical tapers (e.g., Morse numbers)
• ISO 81714‑1 - graphical symbol sizing and basic rules
• ISO GPS family references (ISO 14638, ISO 8015, ISO 14253) for GPS system context

Keywords: ISO 3040:2016, cones, geometrical product specifications, GPS, dimensioning, tolerancing, rate of taper, cone angle, ISO 1119, ISO 81714-1, cone tolerancing, GD&T.