DIN 6796 Tightening Torque Calculation: $T = K \cdot F_M \cdot d$

1. Basic Formula

For all bolted connections, the relationship between the assembly tightening torque $T$ (often denoted as $M_A$) and the resulting preload $F_M$ can be simplified using the torque coefficient $K$:

• $T$ — Tightening torque (N·mm or N·m)
• $F_M$ — Target preload (N)
• $d$ — Nominal bolt diameter (mm)
• $K$ — Torque coefficient (dimensionless)

This formula consolidates the effects of thread friction, bearing surface friction, and the helix angle into a single parameter $K$. When using DIN 6796 disc spring washers, the $K$ value changes due to the washer's geometric characteristics and tribological behavior.

2. Composition of the K Factor and the Influence of DIN 6796

The composition of $K$ can be derived from the precise torque formula in VDI 2230 R13:

Where: - First term — Useful work of the helix angle (contribution <5%) - Second term — Thread friction contribution - Third term — Bearing surface friction contribution, directly influenced by the washer

The use of DIN 6796 washers alters the third term in two ways:

2.1 Equivalent Friction Diameter $D_{km}$

During compression, the washer's bearing surface transitions from conical to flat. For full contact conditions, $D_{km}$ is approximately the mean diameter of the washer's annular area:

Where $D_e$ is the washer outer diameter and $D_i$ is the washer inner diameter (equal to the bolt hole or nut bearing surface inner diameter).

2.2 Equivalent Friction Coefficient $\mu_K$

Two friction pairs exist between the washer and the bolt head/nut, and between the washer and the clamped part. If the materials and lubrication are the same for both interfaces, a uniform $\mu_K$ can be used. DIN 6796 washers are typically made of spring steel. When in contact with steel bolt heads/nuts and steel clamped parts, the friction coefficient $\mu_K$ is comparable to standard steel-on-steel friction, depending on surface treatment and lubrication:

Unlike serrated washers (e.g., NFE 25-511), DIN 6796 washers have no locking teeth, so $\mu_K$ does not increase significantly and remains within the conventional friction range.

3. Typical K Value Ranges and Recommended Values

Considering that DIN 6796 washers are commonly used with standard steel bolts, the K factor typically falls within the following ranges based on test statistics:

Note: Because the contact area of the disc spring washer changes slightly during compression, the actual K value can vary slightly with the preload level. The values above are statistical averages for the assembled state.

For higher accuracy, it is strongly recommended to perform torque-clamp force tests according to ISO 16047 to directly measure the K factor for the specific washer combination or to determine $\mu_G$ and $\mu_K$ separately.

4. Calculation Example

Conditions:
- Bolt: M10 × 1.5, Grade 8.8
- Target preload $F_M = 20\,000\ \text{N}$
- Using DIN 6796 washer (for M10), light oil film, assume $K = 0.18$

Tightening Torque:

If good lubrication is used ($K=0.14$), the torque would be $0.14 \times 20\,000 \times 10 = 28\ \text{N·m}$. This shows that small changes in K lead to significant torque differences, making friction control critical.

5. Connection to the VDI 2230 R13 Precise Calculation

For designs requiring higher precision, the R13 formula can be used directly:

Where: - Thread portion: $\mu_G$ is the measured thread friction coefficient
- Bearing surface portion: $\mu_K$ is the friction coefficient of the washer mating surfaces, $D_{km} = (D_e + D_i)/2$

This method avoids the roughness of a single "lumped" K factor and allows separate control and adjustment of each friction interface.

6. Important Considerations

1. K is not a constant: It is sensitive to surface condition, temperature, and assembly speed. In torque control methods, preload scatter primarily originates from K value fluctuations.
2. Washer spring-back effect: DIN 6796 washers exhibit slight elastic spring-back after tightening, but this has a negligible effect on the final preload and is implicitly included in the K value within the torque formula.
3. Combined use: If the washer is used in combination with a flat washer, the number of friction interfaces increases, potentially increasing the K value. Testing is recommended.
4. High-temperature environments: A decrease in the elastic modulus can reduce the washer's flattening force, but the effect on the friction coefficient is relatively small. The K value from room temperature data can still be used, but the preload loss must be checked considering the temperature.

Summary:
When using DIN 6796 disc spring washers, the tightening torque can still be calculated using $T = K F_M d$. The K factor is primarily governed by thread and bearing surface friction, with typical values between 0.12 and 0.25. Since the washer has no serrations to amplify friction, the K value is similar to that of a standard flat washer connection. During design, K should be selected appropriately based on surface treatment and lubrication, and should be verified through testing whenever possible to control preload accuracy.