The Simplified Torque Formula
The primary purpose of a bolted joint is to create a large clamping force, or **Preload ($\mathbf{F}$)**, between the components. **Torque ($T$)** is applied to the nut or bolt head to achieve this desired preload. The simplified model, often called the $K d F$ method, is the most common estimation used in workshops and field maintenance.
The Relationship
The required torque is calculated using the following linear relationship:
$$\mathbf{T = K F d}$$
The Critical Parameter: Nut Factor ($\mathbf{K}$)
The **Nut Factor ($K$)** is a dimensionless coefficient that accounts for the combined friction losses occurring between the threads and under the fastener head/nut face. Since a significant portion (often 80-90%) of the applied torque is consumed by friction, the choice of $K$ is the most critical factor for accuracy.
| Condition / Lubricant | Typical $\mathbf{K}$ Value | Notes |
|---|---|---|
| Dry, unplated bolt | 0.20 - 0.30 | High friction, high variability. |
| Lightly oiled/Zinc Plated | 0.17 - 0.20 | Common industrial condition. |
| Copper/Molybdenum disulfide anti-seize | 0.10 - 0.15 | Low friction, high consistency. |
Note on Accuracy:
The torque method using the $K d F$ formula has an inherent inaccuracy often cited to be $\pm 25\%$. For critical joints, methods like **Turn-of-Nut** or **Hydraulic Tensioning** should be used for higher precision.