Preload Loss Due to Embedding Settlement (NFE 25-511 Single-Face Serrated Conical Spring Washer)

1. Mechanism of Embedding Settlement's Effect on Preload

In connections using NFE 25-511 single-face serrated conical spring washers, the preload loss caused by embedding settlement shares the same fundamental principles as standard bolted joints, yet also exhibits unique characteristics.

Common Principle:
After assembly, microscopic roughness peaks on the contact surfaces of components undergo plastic flattening under high pressure, leading to a reduction in clamping length → preload decrease.

Specificity of the Spring Washer:
The conical spring washer itself acts as a spring element. When embedding occurs, the washer can release part of its compression to compensate for the axial displacement, thereby mitigating the preload loss. Consequently, connections incorporating NFE 25-511 washers typically experience less preload loss compared to connections using rigid washers under identical conditions.

2. Basic Calculation Model

2.1 Standard VDI 2230 Embedding Loss Formula (Review)

For standard rigid connections, the embedding loss is:

Where: - $f_{Z,total}$ — Total embedding amount (sum of microscopic settlements across all contact surfaces) - $\delta_S$ — Bolt compliance - $\delta_P$ — Clamped part compliance

2.2 Correction After Introducing the Spring Washer

When the system includes an NFE 25-511 spring washer (compliance $\delta_W = 1/k_W$), the total system compliance changes, and the preload loss formula is corrected to:

Or equivalently expressed using stiffness:

Where: - $k_W$ — Working stiffness of the spring washer (N/mm), determined by the tangent slope of the force‑deflection curve at the operating point - $k_S = 1/\delta_S$ — Bolt stiffness - $k_P = 1/\delta_P$ — Clamped part stiffness

Key Conclusion:
The addition of the spring washer increases the total system compliance (reduces total stiffness). Therefore, the same embedding amount $f_{Z,total}$ results in a smaller preload loss $F_Z$. This is the fundamental mechanism by which the spring washer compensates for embedding loss.

3. Determining Spring Washer Stiffness $k_W$

3.1 Obtained from the Force‑Deflection Curve

The force‑deflection relationship for NFE 25-511 washers is given by the modified Almen‑Laszlo formula (see previous section "Force‑Deflection Characteristics"):

The tangent stiffness of the washer at the working compression $s_0$ (corresponding to the working preload $F_M$) is:

3.2 Stiffness Magnitude

Typical stiffness ranges for NFE 25-511 Z/M/L type washers:

Compared to the bolt's own stiffness (M10 approx. 30 000 – 50 000 N/mm), the washer stiffness is significantly lower, effectively "buffering" the embedding loss.

4. Determining the Embedding Amount $f_{Z,total}$

In an NFE 25-511 washer system, the embedding contact surfaces include:

1. Bolt head/nut and the upper surface of the washer (serrated face)
2. Serration tips on the lower washer surface and the clamped part
3. Interface between clamped parts
4. Thread pair

The embedding amount per surface depends on surface roughness, material hardness, and the presence of coatings. The embedding amount for serrated contact surfaces differs slightly:

The total embedding amount $f_{Z,total}$ is the sum of the embedding amounts from each surface.

5. Calculation Example

Given: - M10 bolt, grade 8.8 - NFE 25-511 M type washer, working point stiffness $k_W = 7\,500$ N/mm - Bolt compliance $\delta_S = 1.2 \times 10^{-6}$ mm/N → $k_S \approx 833\,000$ N/mm - Clamped part compliance $\delta_P = 0.8 \times 10^{-6}$ mm/N → $k_P \approx 1\,250\,000$ N/mm - 4 embedding surfaces, average embedding amount per surface 4 μm → $f_{Z,total} = 16$ μm = 0.016 mm

Loss without spring washer:

System compliance $\delta_S + \delta_P = (1.2 + 0.8) \times 10^{-6} = 2.0 \times 10^{-6}$ mm/N

Loss with spring washer:

Washer compliance $\delta_W = 1/k_W = 1/7\,500 = 1.33 \times 10^{-4}$ mm/N

Total system compliance:

Comparison:
Loss without spring washer: 8 000 N; loss with NFE 25-511 washer: only 119 N, a reduction of approximately 98%! This fully demonstrates the remarkable compensation capability of the spring washer against embedding settlement.

6. Design Application Points

1. Selection of Washer Operating Point
   The washer should operate in the approximately linear region of its force‑deflection curve under the working preload (typically $s/h \approx 0.3 \sim 0.7$) to achieve stable low stiffness and effective compensation.

2. Stiffness Matching
   The washer stiffness should be significantly lower than the bolt and clamped part stiffness to effectively absorb embedding displacement. A general requirement is $k_W \le 0.2\,k_{bolt}$.

3. Multiple Washers in Series
   If a single washer cannot provide sufficient elastic compensation deformation, multiple washers can be stacked in opposition (parallel stiffness) according to NFE 25-511 specifications to increase the total compression stroke.

4. Integration with VDI 2230 Procedure

5. R3: Include washer compliance $\delta_W$ in the compliance calculation
6. R4: Calculate $F_Z$ using the corrected total compliance

7. R5: $F_{Mmin} = F_{Kerf} + (1-\Phi^*)F_A + F_Z$

8. Verification
   After theoretical calculation, it is recommended to verify the loss amount through actual assembly and preload monitoring, especially for critical connections.

Summary:
The NFE 25-511 single-face serrated conical spring washer significantly reduces preload loss caused by embedding settlement by introducing additional elastic compliance. The corrected formula $F_Z = f_{Z,total} / (\delta_S + \delta_P + \delta_W)$ quantifies this compensation effect. During design, the working stiffness of the washer should be correctly determined, and this loss should be included in the minimum preload calculation per VDI 2230.