DIN 6796 Permissible Maximum Load: Flattening Load Verification Based on Material Yield Strength

1. Definition and Strength Criterion

Permissible maximum load $F_{zul}$ refers to the maximum axial force that a DIN 6796 disc spring washer can safely withstand within the elastic range. Exceeding this value will cause undesirable plastic deformation of the washer, leading to a reduction in free cone height and loss or impairment of elastic compensation capability.

The basic criterion for strength verification is:

Where: - $F_{Mmax}$ — Maximum assembly preload (including tightening scatter, determined by VDI 2230 R6) - $F_{zul}$ — Permissible maximum load of the washer

2. Relationship Between Permissible Load and Flattening Force

The theoretical flattening force $F_{flat}$ (load at $s = h_0$) is the external force required to completely flatten the washer. However, the internal stress in the washer typically reaches the material's yield limit well before this value. Therefore, the permissible load must be derived from stress limits, rather than directly using the flattening force.

When a disc spring washer is axially compressed, the maximum stress occurs at the OM point on the upper surface inner edge (see NFE 25-511, washer body combined stress section). The compressive stress $\sigma_{OM}$ at this point increases monotonically with the compression amount.

3. Derivation of Permissible Load Based on OM Point Stress

3.1 OM Point Stress Formula

According to the Almen‑Laszlo stress theory, the stress at the OM point (upper surface inner edge) is:

Where:

, , , is the shape factor.

3.2 Stress Limitation Condition

To ensure elastic operation (no permanent deformation), the absolute value of the OM point stress must satisfy:

• $R_{p0.2}$ — 0.2% offset yield strength of the washer material (MPa)
• $\nu$ — Utilization factor, recommended as 0.9 for elastic washers (same as VDI 2230 assembly stress verification)

3.3 Permissible Load Formula

By combining the stress limitation condition with the force‑deflection relationship, the allowable maximum compression $s_{zul}$ can be solved, and then the permissible load can be obtained via the force formula. However, for engineering use, this can be simplified to a safety factor reduction based on the flattening force:

Where: - $F_{flat} = \dfrac{4E}{1-\nu^2} \cdot \dfrac{t^3 h_0}{K_1 D_e^2}$ — Theoretical flattening force - $S_{flat}$ — Anti-flattening safety factor, which integrates stress limitations and force‑deflection nonlinearity

4. Determination of Safety Factor $S_{flat}$

The value of the safety factor depends on the material, load type, and consequences of failure:

Standard Recommendation: For most DIN 6796 washer applications, use $S_{flat} = 1.3$. This implicitly satisfies the requirement of limiting OM point stress to approximately $0.9 R_{p0.2}$ and covers manufacturing tolerances.

5. Direct Stress Verification Method (Precise)

For precise evaluation, the OM point stress under the target load can be calculated directly:

1. Solve for the corresponding compression $s_{work}$ from the target preload $F_{Mmax}$ (see force‑deflection equation).
2. Calculate the OM point stress $\sigma_{OM}$ at this compression.
3. Verify: $|\sigma_{OM}| \le 0.9 R_{p0.2}$.

If the verification fails, reduce $F_{Mmax}$ or switch to a larger washer model. This method is more accurate than the simple safety factor approach and is suitable for parameter optimization.

6. Calculation Example

Given: DIN 6796 washer for M10 (parameters as before)

mm, mm, mm, mm
Material: 50CrV4, $R_{p0.2} = 1500$ MPa, $E = 206\,000$ MPa, $\nu = 0.3$

Step 1: Theoretical Flattening Force
Previously calculated $F_{flat} = 10\,998$ N.

Step 2: Permissible Load (Safety Factor Method)
Take $S_{flat} = 1.3$:

Step 3: Verify Bolt Preload
If $F_{Mmax} = 7\,500$ N, then $7\,500 \le 8\,460$ → Pass.

Step 4: OM Point Stress Verification (Optional)
Calculate the compression $s$ corresponding to $F_{Mmax}=7\,500$ N (solved from force‑deflection data or equation, approximately $s \approx 0.62$ mm).
Calculate the OM point stress at this $s$ (see relevant section). If $|\sigma_{OM}| \approx 1350 \le 0.9 \times 1500 = 1350$ MPa → Just meets the requirement. This confirms that the choice of $S_{flat}=1.3$ is reasonable, effectively controlling the stress near the elastic limit.

7. Temperature and Material Corrections

• High-temperature operation: The material yield strength $R_{p0.2}$ and elastic modulus $E$ decrease with increasing temperature. The permissible load must be recalculated based on the mechanical properties at the operating temperature. For example, for 50CrV4 at 150°C, $R_{p0.2}$ may drop to approximately 1300 MPa, resulting in a corresponding decrease in $F_{zul}$ of about 13%.
• Stainless steel washers: If stainless steel (e.g., 1.4310) is used, $R_{p0.2}$ is typically 1000–1200 MPa, and the permissible load is significantly lower than for spring steel. Pay attention to material differences during selection.

8. Integration with Other Verifications

The permissible load of the DIN 6796 washer is one link in the bolt connection design chain and must be coordinated with the following verifications: - VDI 2230 R6: $F_{Mmax}$ is derived from tightening scatter analysis. - VDI 2230 R10: Surface pressure verification at the mating interface (force transmitted from the washer to the connected parts). - Washer stress verification: Combined stress at critical locations such as the OM point and uM point. - Flattening safety: $F_{Mmax} \le F_{zul}$ ensures the washer is not flattened.

If any item fails, iteratively increase the washer size or adjust the bolt preload.

Summary:
The permissible maximum load for a DIN 6796 washer is typically obtained by dividing the flattening force by a safety factor $S_{flat} \ge 1.3$. This method is simple and implicitly satisfies the OM point stress limit. For critical applications, further verification using the direct stress method is recommended. Correctly setting the permissible load is a prerequisite for ensuring the washer provides reliable elastic compensation throughout its service life.