DIN 6796 Static Safety Factor: Comprehensive Strength Verification

1. Definition of Static Safety Factor

The static safety factor $S$ is the ratio of the material's allowable stress to the actual working stress of the component. For DIN 6796 disc spring washers, the following four critical points must be satisfied: OM point, I point (outer edge of upper surface), cross-section shear, and contact surface:

Each item is evaluated independently, and the minimum safety factor is taken as the final criterion for the washer's static strength.

2. OM Point Compressive Stress Safety Factor

The OM point (inner edge of the upper surface) experiences the maximum compressive stress. Verification uses the allowable compressive stress:

• $\sigma_{OM}$ — Radial stress at the OM point calculated using the Almen‑Laszlo formula (MPa, absolute value of negative)
• $\sigma_{zul,c}$ — Allowable compressive stress of the material (MPa), for quenched and tempered spring steel can be taken as $1.4\sim1.6\,R_{p0.2}$

Example: 50CrV4 steel, $R_{p0.2}=1500$ MPa, take $\sigma_{zul,c}=2200$ MPa. If $|\sigma_{OM}|=1800$ MPa, then $S_{OM}=2200/1800=1.22$, which is acceptable.

3. I Point (OU Point) Tensile Stress Safety Factor

The I point (outer edge of the upper surface) may experience tensile stress. The stress formula for this point is:

If $\sigma_{OU} > 0$ (tensile stress), verification is mandatory:

If $\sigma_{OU} \le 0$ (compressive stress), it is treated using the allowable compressive stress value. In this case, the safety margin is typically more generous than at the OM point, and separate verification can be omitted.

Typical case: Due to the low $\eta$ of DIN 6796 washers, the OU point is mostly under compressive stress or very low tensile stress, so this check is often automatically satisfied.

4. Shear Stress Safety Factor

Transverse shear stress exists within the cross-section of the disc washer, with the maximum shear stress occurring near the inner edge on the upper or lower surface. The shear stress is approximated as:

However, a more precise disc spring theory gives the shear stress at the inner edge:

The allowable shear stress can be conservatively taken as:

Safety factor:

Note: For DIN 6796 washers, due to the relatively large thickness compared to the outer diameter, the shear stress is usually much smaller than the bending normal stress. This check rarely becomes a limiting condition, but it should still be verified for long strokes or high loads.

5. Contact Stress Safety Factor

The surface pressure between the washer and the bolt head/nut and the connected parts must prevent crushing (especially when the connected parts are softer). The contact stress is calculated according to VDI 2230 R10 method:

• $A_{nom} = \frac{\pi}{4}(D_e^2 - D_i^2)$ — Nominal annular area of the washer

The allowable surface pressure $p_G$ refers to the material limit of the connected part:

• Steel: $p_G \approx 0.85\,R_m$ (or $R_{p0.2}$)
• Aluminum alloy: $p_G \approx 0.5\,R_m$

Safety factor:

Note: If a single-sided toothed washer is used, the actual contact area is much smaller than the nominal area. The tooth projection area or equivalent friction coefficient correction is required. This applies to the smooth conical surface of DIN 6796.

6. Comprehensive Safety Factor Evaluation

The four safety factors above must be satisfied simultaneously. A safety factor matrix can be listed during design:

In practical design, for low-cone-angle DIN 6796 washers, OM point compressive stress and contact stress are usually the first two items to approach the limit and should be given priority attention.

7. Calculation Example

DIN 6796 washer for M10, parameters as before: - $F_{Mmax}=7500$ N, $s=0.5$ mm, $\delta=0.3333$ - OM stress $|\sigma_{OM}|=2266$ MPa, OU point $\sigma_{OU} \approx 532$ MPa (tensile stress), $\tau_{max} \approx 120$ MPa (estimated) - Washer area $A_{nom}=(\pi/4)(20^2-10.2^2) \approx 219\ \text{mm}^2$, $p_{Bmax}=7500/219 \approx 34$ MPa - Material 50CrV4: $R_{p0.2}=1500$ MPa, $\sigma_{zul,c}=2200$ MPa, $\tau_{zul}=900$ MPa - Connected part S355 steel: $R_m=550$ MPa, $p_G=0.85\times550=467$ MPa

Safety factors:

Conclusion: Only the OM point safety factor is insufficient. The preload must be reduced to $F_{Mmax} \le 6000$ N (corresponding to $|\sigma_{OM}| \le 1833$ MPa, then $S_{OM}=2200/1833=1.2$), or a larger washer model should be selected.

Summary:
The static strength verification of DIN 6796 washers is a comprehensive evaluation involving multiple locations and stress types. By calculating the OM point compressive stress, I point tensile stress, cross-section shear, and contact stress, and applying appropriate safety factors, it can be ensured that the washer does not experience any form of static failure under maximum preload. The low-cone-angle design typically provides ample margins for shear and I point tensile stress, so the design focus should be on controlling OM compressive stress and contact surface pressure.