Technical Threads: ISO Metric, UNC/UNF and Trapezoidal

A — ISO Metric Thread

a) Thread Characteristics

The geometric characteristics of an ISO metric thread are presented in the following figure and table:

Calculation example: M10 × 1.5 screw

1) d₃ = 10 - 1.2269 × 1.5 = 8.160 mm

2) d₂ = 10 - 0.6495 × 1.5 = 9.026 mm

3) d₁ = 10 - 1.0825 × 1.5 = 8.376 mm

4) d_core = d₃ = 8.160 mm

5) H = 0.866 × 1.5 = 1.299 mm

Additional example: M20 × 2.5 screw

1) d₃ = 20 - 1.2269 × 2.5 = 16.933 mm

2) d₂ = 20 - 0.6495 × 2.5 = 18.376 mm

3) d₁ = 20 - 1.0825 × 2.5 = 17.294 mm

4) d_core = d₃ = 16.933 mm

5) H = 0.866 × 2.5 = 2.165 mm

Note: the same method applies to any ISO metric thread.

Addition: Tightening Torque

The tightening torque is evaluated by C ≈ K × F₀ × d, with F₀ = α × R_e × A_s.

For M8 × 60 class 8.8 screw: F₀ = 16396.8 N → C ≈ 25 N·m

For M20 × 60 class 8.8 screw: F₀ = 109760 N → C ≈ 420 N·m

Note: in the presence of lubrication, reduce the torque by 10 to 20%. For critical assemblies, refer to the VDI 2230 method.

b) Thread Tolerances

c) Thread Designation

The designation of a metric thread is written with the symbol M, followed by the nominal diameter and pitch, then the tolerance class.
Example: for a screw, M8 × 1.25 - 6g; for a nut, M8 × 1.25 - 6H.

B — Inspection Methods

a) Inspection with Thread Gauges

For routine inspection of medium-quality threads made on machine tools, threaded "go" and "no-go" gauges are used, as well as plain "go" and "no-go" gauges.

Reminder: threaded ring and plug gauges must be checked and calibrated periodically in accordance with applicable standards, particularly NF ISO 1502.

b) Inspection of Pitch Diameter d₂

The pitch diameter of a screw can be measured by two methods: direct measurement with a thread micrometer, or indirect measurement with calipers or an outside micrometer using wires.

b-1 Direct Measurement

Fig. B1: Thread micrometer — 60° cone and 60° V-anvil probes — 0.01 mm sensitivity

The thread micrometer has two removable probes. The first probe is a cone with the thread angle (60° for a metric thread). The second probe is a 60° V-anvil. This micrometer provides d₂ with a sensitivity of 0.01 mm.

Fig. B2: Removable probes — Thread micrometer — Inspection of pitch diameter d₂

b-2 Indirect Measurement (three-wire method)

Wires (three calibrated cylinders) of diameter d_p are used, then the measurement M is taken with calipers or an outside micrometer to calculate d₂.

Formula (60° metric thread): d₂ = M + 0.866 × P − 3 × d_p

Example — M10 × 1.5 screw: d_p = 0.866 mm, measured M = 10.459 mm
d₂ = 10.459 + 1.299 − 2.598 = 9.160 mm (theoretical value: 9.026 mm)

c) Inspection of Pitch P

The pitch P of the thread is inspected using a thread gauge or a special comparator equipped with two spherical contacts engaging in the threads, with a sensitivity of 0.001 mm.

Concrete example — M10 × 1.5 screw:
Nominal pitch: P = 1.5 mm | Measurement over 10 threads: L = 14.997 mm
Actual P = 14.997 / 10 = 1.4997 mm | ΔP = −0.0003 mm → Part compliant (class 6g)

d) Profile Inspection

The profile can be inspected using a profile projector. This allows determination of the pitch diameter d₂, the pitch P, and the profile angle.

Example — M12 × 1.75 screw — class 6g: Actual d₂ = 10.871 mm → ⚠️ Non-compliant — Excess +0.039 mm

C — Manufacturing by Rolling

Rolling is a manufacturing method by cold plastic deformation, without material removal.

D — Practical Case: Inconel 718 / M20 × 2.5 Rolling

Context: M20 × 2.5 Stud in Inconel 718 for chemical reactor at 650°C / 80 bar.

Specification: ASTM B637 + NACE MR0175.

• k_f = 1.5 × 1,380 = 2,070 MPa
• F_r = 49.7 kN/die → machine ≥ 200 kN
• Recommended torque: 750 N·m
• Speed: 10–30 rpm | Passes: 3–5
• Cooling: Sulfochlorinated oil 15–25 L/min at 8–12 bar
• Contact T° ≤ 120°C

E — FAI (First Article Inspection) — GJN-718-M20-001

Machine: 3-die 200 kN hydraulic thread rolling machine

Operator: A. Talal with technical assistance to operator and team leader | Date: 19/05/2026

SEM Micrograph — Axial section — Kalling's Etch N°2 — Rolled Inconel 718 — Scale: 100 µm

✅ PART VALIDATED — Production authorization granted
Signed: A. Talal | Approved: Quality Department | Date: 19/05/2026

F — Calculation Standards for Bolted Joints

F_M = α_A × (F_Kerf + F_Z + Φ × F_A) — VDI 2230

T = K × W × d — ASME PCC-1 — Sequence: 30% → 70% → 100% → 100% + hot retorque

G — UNC / UNF (Unified National) Thread

The American Unified thread is defined in inches with the pitch expressed in TPI (Threads Per Inch). The profile is identical to the ISO thread (60° angle) but the units and tolerance classes differ.

Fig. G1: Basic Profile of Unified National (UN/UNR) Thread — ASME B1.1 — 60° Angle, dimensions in fractions of pitch P

UNC/UNF Geometric Formulas

• Pitch: P = 25.4 / TPI (mm) | d₂ = d − 0.6495 × P | H = 0.866 × P
• Screw Tolerance: 2A / 3A | Nut Tolerance: 2B / 3B

UNC (Unified National Coarse) Table

UNF (Unified National Fine) Table

ISO vs UNC Comparison — Equivalences

H — Tr ISO Trapezoidal Thread (ISO 2904:2016)

The trapezoidal thread is used for motion transmission (jacks, presses, vices, lead screws). Its 30° trapezoidal profile allows for the transmission of significant axial forces with self-locking.

Symbols and Standardized Dimensions — ISO 2904:2016

Fig. H1: Basic Profile — Tr ISO Thread — ISO 2904:2016 — 30° Angle

Fig. H2: Nominal Profile — Figure 2 and Table 2 — NF ISO 2901:2016(F)

Table 2 — Nominal Profile Dimensions (NF ISO 2901:2016)

Tr ISO Designation

The designation is written as: Tr d × P — screw class / nut class
Examples: Tr 32 × 6 — 7e / 7H | Tr 20 × 4 — 8e / 8H (long lead)

Normative references: ISO 724, ISO 2904, ASME B1.1 (UNC/UNF), ASME B1.5 (ACME), VDI 2230, ASME PCC-1, EN 1591-1, ASME B16.5, ASTM A193/A193M, ASTM B637, NACE MR0175/ISO 15156, AMS 5664, AS9102, ASTM E3, ASTM E384, ASTM F606, ASTM F1941, ISO 3506, NF E25-030.