The standard formula for bolt tightening torque is:

Where:

• T = Tightening torque (N·m)
• K = Friction coefficient (K-factor), typically 0.10–0.25
• F = Target preload force (N)
• d = Nominal bolt diameter (m)

This formula is based on the VDI 2230 standard and provides accurate results for standard bolted joints.

K-factor (also called torque coefficient or nut factor) is a dimensionless value that represents the combined friction characteristics of a bolted joint. It includes both thread friction (μth) and bearing surface friction (μb).

Typical K-factor values:

• Dry threads: 0.20 – 0.25
• Oiled threads: 0.14 – 0.18
• MoS₂ lubrication: 0.10 – 0.12
• PTFE coating: 0.08 – 0.10

Per ISO 16047, K-factor is determined at 75% of proof load (0.75 Fp) and is valid only for fasteners with identical friction conditions and diameter.

The recommended preload as a percentage of the selected strength basis depends on application:

• 50% — Light duty, vibration-prone assemblies
• 65% — Moderate duty applications
• 75% — Standard industrial practice (most common)
• 85% — High-performance joints
• 90% — Maximum, critical applications only

The preload force is calculated as: F = S × As × η, where S is Rp (yield strength) or Sp (proof stress) (MPa), As is tensile stress area (mm²), and η is the utilization factor (0.50–0.90).

ISO 16047:2005 (Fasteners — Torque/clamp force testing) specifies:

• Scope: Metric bolts M3–M39 per ISO 898-1/898-2
• Test equipment: ±2% measurement accuracy
• Tightening speeds: 10–40 rpm (M3–M16), 5–15 rpm (M16–M39)
• Substitute parts: HH (50–60 HRC) and HL (200–300 HV) types
• Formulas: K-factor, μtot, μth, μb calculations
• Test conditions: Temperature 10–35°C
• Kellermann-Klein equation for complete torque analysis

The standard ensures consistent and comparable torque/clamp force testing worldwide.

Lubrication significantly reduces the K-factor, meaning less torque is required to achieve the same preload force:

Warning: Using a dry K-factor for a lubricated bolt will result in severe over-tightening, potentially causing bolt failure. Always match K-factor to actual conditions.

Proper tightening sequence ensures even load distribution:

1. Hand-tighten all bolts until snug
2. Tighten to 30% of final torque (in pattern)
3. Tighten to 70% of final torque (in pattern)
4. Tighten to 100% final torque in smooth motion
5. Verify final torque on all bolts

Patterns:

• 4 bolts: Cross pattern (1-3-2-4)
• 6 bolts: Star pattern (1-4-2-5-3-6)
• 8+ bolts: Diametrically opposite, then 90° rotation

Property class selection per ISO 898-1:

Decoding: First digit × 100 = tensile strength (Rm) in MPa. First × second digit × 10 = yield strength (Rp) in MPa. Example: 8.8 → Rm=800 MPa, Rp=8×8×10=640 MPa.

Generally, no. High-strength bolts (class 10.9 and 12.9) should not be reused after being tightened to design preload because:

• Plastic deformation occurs during tightening
• Thread damage may not be visible
• Bolt strength is reduced after stretching
• Torque-to-yield bolts are single-use by design

Exceptions: Class 8.8 and below may be reused if no visible damage exists and application is non-critical. Per ISO 16047, substitute parts for testing are single-use only.

Torque tool accuracy:

• Click-type torque wrench: ±4–5%
• Beam-type torque wrench: ±3–4%
• Digital torque wrench: ±1–2%
• ISO 16047 test equipment: ±2%

However, torque-to-preload accuracy is limited by friction variations. Even with precise torque, actual preload can vary ±25–30% due to:

• Surface finish variations
• Lubrication inconsistency
• Thread quality differences

For critical applications, consider torque-angle method or hydraulic tensioning (±5% preload accuracy).

These standards serve different but complementary purposes:

ISO 16047 tells you how to measure friction coefficients; VDI 2230 tells you how to use them in bolted joint design.