DIN 6796 Anti-Loosening Safety Assessment: Elastic Compensation Capability Under Vibration Conditions

1. Anti-Loosening Mechanism of DIN 6796 Washers

DIN 6796 disc spring washers do not rely on wedge geometry or tooth engagement for anti-loosening, but instead utilize their high elastic compliance to play a unique role in vibration environments:

• Compensation for fretting wear settlement: Transverse vibration causes fretting wear on contact surfaces, removing material and shortening the clamping length. The stored elastic energy in the washer is released, pushing the bolt head/nut to follow the settlement, thereby maintaining preload.
• Reducing the rate of preload loss: For the same wear depth $\Delta h$, the low stiffness of the washer results in a preload loss $\Delta F = k_W \cdot \Delta h$ that is significantly smaller than that of a rigid connection, thus extending the preload retention time.
• Dissipating vibration energy: The hysteresis loop of the washer during loading/unloading absorbs part of the vibration energy, converting it into heat and reducing the energy input to the thread pair.

Core criterion: After a specified number of vibration cycles, the residual preload remains higher than the minimum required to prevent joint slippage or separation.

2. Energy-Based Anti-Loosening Assessment

2.1 Releasable Elastic Recovery Energy of the Washer

The available elastic energy of a DIN 6796 washer at its working compression $s_{work}$ is the energy released when unloading from this point to $s=0$. This can be approximated as:

Where $F_{work}$ is the current preload and $s_{work}$ is the corresponding compression.

This energy is used to compensate for the "loosening work" induced by vibration—i.e., the energy required to overcome friction and maintain the thread pair position.

2.2 Vibration Input Energy and Loosening Criterion

Junker vibration tests show that loosening is primarily the result of accumulated transverse slip. A simplified criterion is: if the releasable elastic energy of the washer is greater than the frictional work consumed by interface slip within one vibration cycle, the joint will not continuously loosen.

• $W_{cycle}$ — Energy consumed by friction at the joint interface in a single vibration cycle
• $N$ — Design number of cycles

If this condition is met, the elastic reserve of the washer is sufficient to "absorb" the vibration energy, preventing cumulative rotation of the thread pair.

3. Preload Decay Model Based on Displacement Compensation

Vibration causes fretting wear on contact surfaces, resulting in an equivalent axial settlement $\Delta s_{vib}$. The reduction in washer preload is:

The residual preload is:

Design objective: Under the expected vibration intensity and duration, $F_{res}$ still meets the anti-slip/anti-separation requirements.

Estimation of fretting wear depth $\Delta s_{vib}$:

• $K_{wear}$ — Wear coefficient (depends on material pairing, lubrication)
• $p$ — Contact surface pressure (average value)
• $\delta$ — Transverse slip amplitude
• $N$ — Number of vibration cycles

Substituting $\Delta s_{vib}$ allows evaluation of the residual preload.

4. Definition of Safety Factors

Based on the above, two anti-loosening safety factors are defined:

4.1 Anti-Slip Safety Factor

• $\mu$ — Coefficient of friction at the joint interface (minimum value)
• $F_Q$ — Amplitude of transverse vibration load

4.2 Preload Retention Safety Factor (Energy Ratio)

This factor ensures that the washer has sufficient elastic energy to cope with vibration wear and prevent premature loss of preload.

5. Evaluation Procedure

1. Determine vibration conditions: Amplitude, frequency, number of cycles $N$, transverse load $F_Q$.
2. Calculate washer operating point: Preload $F_{work}$, compression $s_{work}$, stiffness $k_W$.
3. Estimate vibration wear settlement $\Delta s_{vib}$ (or directly use test data).
4. Calculate residual preload $F_{res}$, verify $S_{slip}$.
5. Calculate available elastic energy $U_{avl}$ and vibration cycle energy consumption, verify $S_{energy}$.
6. If not acceptable: Select a washer with larger $h_0$ or lower stiffness (increasing energy storage and compensation capability), or reduce vibration intensity.

6. Design Recommendations and Limitations

• DIN 6796 washers are suitable for moderate vibration: When the transverse load is less than the friction force at the joint interface, elastic compensation can effectively prevent loosening.
• For strong vibration or high safety requirements: Specialized anti-loosening washers (e.g., DIN 25201 wedge-locking washers) should be used, or combined with thread-locking adhesive.
• Final verification must be performed via Junker testing to ensure the residual preload ratio meets the standard (e.g., ≥ 70%).

Summary:
The anti-loosening capability of DIN 6796 disc spring washers stems from their elastic energy storage compensating for vibration wear. Residual preload can be estimated through energy balance and displacement compensation models, and quantified using anti-slip and energy safety factors. These washers can serve as an auxiliary anti-loosening measure but cannot replace dedicated geometric locking elements.