Wedge Self-Locking Condition Determination: DIN 25201 Locking Principle

1. Core Locking Concept

The wedge-locking washers specified by DIN 25201 achieve locking through radial wedge surface engagement. The fundamental principle is:

Any contact surface within the connection that could potentially undergo rotational motion must possess a "self-locking" characteristic, meaning the equivalent friction angle of that contact surface is strictly greater than its driving angle, thereby preventing spontaneous loosening under vibration or load fluctuations.

In bolted connections, the traditional difficulty in preventing loosening lies in the relatively small helix angle of the thread pair. Although the thread itself has a certain degree of self-locking (equivalent friction angle greater than the helix angle), the friction coefficient can drop significantly under transverse vibration, leading to self-locking failure. Wedge washers transfer the locking task from "relying on thread friction" to "forcing wedge surface self-locking," using a large-angle wedge surface to replace the thread helix angle as the potentially dangerous sliding inclined plane.

2. Wedge Self-Locking Condition Formula

For a pair of wedge washers, the locking function is determined by the relative relationship between the wedge surface angle $\alpha_{cam}$ and the thread helix angle $\varphi_{thread}$. The self-locking condition is:

Where:

• $\alpha_{cam}$ — The rise angle of the wedge washer cam surface (wedge surface), typically designed between 6° – 8°
• $\varphi_{thread}$ — The helix angle of the thread, typically between 2° – 4° for standard metric threads

Satisfying this condition means: When the bolt has a tendency to rotate and loosen, the torque required for the relative rotation "lifting" between the inner and outer wedge washers is significantly greater than the torque required for the relative rotation of the thread. Therefore, the connection will not loosen via rotation at the wedge surface; instead, it may continue to tighten at the thread, achieving wedge surface self-locking.

3. Physical Mechanism and Breakdown

3.1 Traditional Thread Self-Locking Condition (Review)

The self-locking condition for a standard thread is that the equivalent friction angle $\rho'$ is greater than the helix angle $\varphi$:

Where $\rho'$ is related to the thread friction coefficient $\mu_G$ and the thread profile angle $\alpha$: $\tan \rho' = \mu_G / \cos(\alpha/2)$.
When transverse vibration causes $\mu_G$ to drop instantaneously, this condition may be violated, leading to spontaneous thread loosening.

3.2 How Wedge Washers Change the "Weakest Self-Locking Link"

DIN 25201 washers are used in pairs. The inner side features a radial cam wedge surface (multi-tooth wedge shape), as illustrated below:

Component || Bolt Head/Nut || [Outer Washer] ← Outer radial teeth bite into bolt head/nut (no relative rotation) || [Inner Washer] ← Inner radial teeth bite into the component (no relative rotation) || Wedge surface contact between inner and outer washers (wedge angle α_cam)

Key Design:

• The upper surface of the outer washer (or the lower surface of the inner washer) has radial locking teeth. After clamping, these teeth mechanically lock with the clamped surface or the bolt head/nut, preventing relative rotation.
• The contact surface between the inner and outer washers is a large-rise-angle wedge surface, whose rise angle $\alpha_{cam}$ is significantly larger than the thread helix angle $\varphi_{thread}$.

The only kinematic path for loosening the bolt must include: relative sliding occurring at the wedge surface between the inner and outer washers (since other contact surfaces are mechanically locked). The geometric obstacle to overcome for this relative sliding is the wedge angle $\alpha_{cam}$.

At this point, for the wedge surface, the "self-locking condition" is also that the wedge surface friction angle $\rho_{cam}$ is greater than the wedge angle $\alpha_{cam}$, i.e.:

However, in actual design, engineers do not rely on friction to prevent wedge surface sliding. Instead, they utilize the kinematic conflict between the thread and the wedge surface to lock the system.

4. The Contest Between Wedge Angle and Thread Helix Angle: Kinematic Self-Locking

When the bolt attempts to rotate and loosen (e.g., the nut rotates counterclockwise), because the washer's outer teeth are embedded, the nut and outer washer become one unit, and the inner washer and the component become another unit. At this point:

• Thread Relative Motion: Nut rotation causes axial movement of the bolt. The rotational speed is $\omega$, and the axial relative speed depends on the thread helix angle $\varphi_{thread}$.
• Wedge Surface Relative Motion: For the nut to rotate, the outer washer must rotate relative to the inner washer (wedge surface sliding). This causes the outer washer to "climb" along the wedge surface, increasing the total washer thickness, i.e., further stretching the bolt.

These two motions are geometrically strongly coupled: When the bolt is stretched and elongated, the preload increases; the wedge surface climbing requires a greater separating force to overcome the preload. In most cases, because $\alpha_{cam} > \varphi_{thread}$, rotational loosening leads to an increase in bolt preload rather than a decrease, creating a self-locking effect of "the more it turns, the tighter it gets."

Restatement of the Judgment Condition:

When satisfied, the lifting efficiency of the wedge surface is much higher than that of the thread. The axial stretching amount converted from loosening rotation is greater than the retraction amount produced by direct thread loosening. The system cannot loosen smoothly, achieving geometric self-locking.

5. Typical Parameter Calculations

5.1 Thread Helix Angle $\varphi_{thread}$ Range

The helix angle for standard metric threads (ISO 68‑1) is calculated based on the pitch diameter:

Conclusion: The helix angle for coarse metric threads is approximately 2.5° – 3.5°; for fine threads, it is smaller (< 2°). Therefore, the order of magnitude for $\tan \varphi_{thread}$ is 0.04 – 0.06.

5.2 Wedge Surface Angle $\alpha_{cam}$ Design Values

The cam wedge surface angle for DIN 25201 washers is typically:

• Standard series: $\alpha_{cam} = 6°$
• Some heavy-duty series: $\alpha_{cam} = 7° \sim 8°$

Corresponding $\tan \alpha_{cam}$ values:

• $\tan 6° \approx 0.105$
• $\tan 7° \approx 0.123$
• $\tan 8° \approx 0.140$

5.3 Self-Locking Judgment Example

Take an M10 bolt ($\varphi \approx 3.03°$, $\tan \varphi \approx 0.053$) and a 6° wedge washer ($\tan \alpha_{cam} \approx 0.105$):

Even if the thread friction coefficient is completely lost (e.g., oil immersion with vibration), as long as the wedge surface geometry exists, the loosening motion is still geometrically forcibly prevented.

6. Engineering Verification and Standard Basis

• DIN 25201 The standard itself verifies this wedge surface self-locking principle through vibration tests (e.g., Junker tests per ISO 16130 or DIN 65151). Tests show that the preload retention rate under transverse vibration is significantly higher than that of standard washers and thread-locking adhesives.
• VDI 2230 Although it does not directly specify the self-locking condition, it states that locking design should ensure at least one separation surface in the connection has reliable self-locking or anti-rotation capability. Wedge washers meet this requirement through large-angle mechanical interference.
• It is important to note that the locking principle of wedge washers does not depend on friction but on geometric forced synchronization, making it equally effective in high-temperature and oily environments.

7. Precautions and Limitations

1. Hardness Matching: The hardness of the wedge washer must match the component and the bolt head/nut to ensure the teeth can effectively bite in without crushing the base material.
2. Single Use: After disassembly, the locking teeth and wedge surface of the wedge washer may undergo plastic deformation, reducing locking effectiveness upon reuse. Replacement is generally recommended.
3. Surface Damage: The teeth biting will leave indentations on the surface of the component. For parts sensitive to surface quality, it is necessary to evaluate whether this is acceptable.
4. Installation Direction: Must be used in pairs with the wedge surfaces facing each other. Incorrect installation will result in loss of locking function.
5. Extreme Temperatures: Although the locking principle is independent of friction, material strength changes at extreme temperatures may affect biting performance. The temperature range of the washer material must be confirmed.

8. Conclusion

The core locking mechanism of DIN 25201 wedge washers lies in the wedge surface rise angle being strictly greater than the thread helix angle:

This converts loosening rotation into an increase in axial tensile force, creating a self-locking loop of "the more it turns, the tighter it gets," unaffected by changes in the friction coefficient. During design, it is only necessary to verify the geometric relationship between the thread helix angle and the washer wedge surface angle to determine if the self-locking condition is met.

Recommended Design Steps:

1. Calculate the thread helix angle $\varphi = \arctan(P / \pi d_2)$
2. Confirm the wedge surface angle $\alpha_{cam}$ of the selected DIN 25201 washer (typically 6° or 7°)
3. Compare $\tan(\alpha_{cam}) > \tan(\varphi)$
4. If satisfied, the geometric self-locking for locking is established; simultaneously check surface pressure and bite depth to ensure mechanical compatibility.