Anti-Slip Safety Factor: VDI 2230 Step R12

1. Purpose and Principle of Verification

When a bolted joint is subjected to transverse load $F_Q$ (perpendicular to the bolt axis), the friction at the interface is the only barrier preventing relative slip between the clamped parts. Once slip occurs, it can lead to positioning failure, increased wear, and in severe cases, shear or bending failure of the bolt.

VDI 2230‑1:2015 Step R12 verifies the anti-slip safety factor $S_G$ to ensure that no macroscopic slip occurs at the interface under design loads.

Core formula:

Where: - $S_G$ — Anti-slip safety factor (dimensionless) - $\mu$ — Coefficient of friction at the interface (static or sliding friction, conservatively taken as sliding friction) - $F_{Mmin}$ — Minimum assembly preload (N), determined in Step R5 (residual preload after accounting for embedding and thermal losses) - $F_Q$ — Transverse working load (N), the maximum shear force acting on the interface

Criterion: A safety factor ≥ 1.2 indicates that, under the most unfavorable conditions (minimum preload, maximum transverse load, minimum friction coefficient), slip is reliably prevented.

2. Physical Meaning of the Formula

The maximum friction force that the interface can withstand is given by Coulomb's friction law:

As long as this friction force exceeds the transverse load $F_Q$ to be transmitted, no slip occurs. Introducing the safety factor gives:

provides approximately 20% margin to account for fluctuations in friction coefficient, load calculation deviations, and minor dynamic overloads.

3. Determination of Parameters

3.1 Interface Friction Coefficient $\mu$

The friction coefficient depends on the contact surface materials, roughness, lubrication state, and presence of coatings. VDI 2230 recommends taking the minimum value from tests. If no test data is available, refer to the table below (dry friction condition):

Conservative Design Principle: The smaller the friction coefficient, the lower the friction force and the safety factor. Calculations must use the smallest possible friction coefficient (e.g., under oily or wet conditions) to ensure safety.

Role of Washers:
Using washers with high friction coefficients (e.g., toothed washers, DIN 25201 wedge-lock washers with radial teeth that bite into the surface) can significantly increase the equivalent $\mu$, or even transition from pure friction resistance to mechanical interlocking. In such cases, the anti-slip mechanism goes beyond Coulomb friction, and calculations should use the equivalent friction coefficient provided by the washer manufacturer or directly use the anti-slip force data. Standard flat washers have limited effect on increasing $\mu$.

3.2 Minimum Preload $F_{Mmin}$

must be the lowest residual preload expected during service life, i.e., after deducting: - Embedding settlement loss $F_{Z,Setz}$ - Preload reduction due to thermal effects $\Delta F_{Vth}$ (heating loss) - Possible long-term relaxation, etc.

is calculated in Step R5; it is not the target assembly preload but the minimum clamping force under the most unfavorable conditions.

3.3 Transverse Load $F_Q$

should be the maximum resultant transverse force that the interface must transmit, including: - External transverse forces - Equivalent force from torque converted via radius - Dynamic load peaks from vibration or impact

If the interface is subjected to shear forces in multiple directions, the vector sum should be taken as the maximum resultant force. The safety factor is verified against this resultant.

4. Calculation Procedure and Example

Procedure:

1. Obtain the minimum residual preload $F_{Mmin}$ from Step R5
2. Determine the interface friction coefficient $\mu$ (take the smallest possible value)
3. Determine the maximum transverse load $F_Q$
4. Calculate the safety factor $S_G = \mu \cdot F_{Mmin} / F_Q$
5. Verify $S_G \ge 1.2$

Example

Given: - Steel-steel connection, dry friction, take $\mu = 0.20$ - Step R5 calculation gives $F_{Mmin} = 18\,000\ \text{N}$ - Maximum transverse load $F_Q = 2\,500\ \text{N}$

Calculation:

Verification: $1.44 \ge 1.2$ → Pass, anti-slip capacity is sufficient.

If oil contamination reduces $\mu$ to 0.10, then:

Corrective measures are needed: clean the surface, use high-friction washers, or increase preload.

5. Relationship with DIN 25201 Washers

In addition to their locking function, DIN 25201 wedge-lock washers have radial biting teeth that, when pressed into the clamped part surfaces, provide significantly higher anti-slip resistance than plain surfaces. In this case, the friction coefficient $\mu$ is replaced by a larger equivalent anti-slip coefficient, or resistance is directly provided by "tooth shear strength."

Two design approaches exist: 1. Conservatively ignore the friction-enhancing effect of the teeth, still calculate $S_G$ based on plane friction, and treat the washer as an additional safety measure. 2. Use manufacturer data: Apply the equivalent anti-slip load or equivalent $\mu$ value provided by the washer supplier; in this case, $S_G$ may far exceed 1.2.

6. Important Notes

1. Multiple Interfaces: If the joint has multiple interfaces (e.g., multiple clamped parts stacked), each interface must satisfy the anti-slip requirement. The preload $F_{Mmin}$ is transmitted to each interface, but the same bolt preload clamps all interfaces simultaneously, so the anti-slip capacity is the same for each interface (provided the friction coefficient of each interface is not lower than the assumed value).

2. Eccentric Transverse Load: If the transverse force does not pass through the center of the interface, it creates an overturning moment, leading to uneven pressure distribution and possible partial separation. A more detailed friction model (e.g., considering pressure distribution) or an increased $S_G$ is needed.

3. Dynamic/Impact Loads: The friction coefficient under impact loads may be lower than the static friction coefficient, and load peaks are higher. The $S_G$ value should be appropriately increased (e.g., ≥1.5).

4. Preload Scatter: $F_{Mmin}$ already accounts for the minimum value under tightening scatter, but the scatter of the friction coefficient $\mu$ is often larger and requires special attention.

5. Surface Coatings: Soft coatings such as paint or sealant can significantly reduce $\mu$; values must be based on the coated condition.

Summary: The anti-slip safety factor $S_G = \mu F_{Mmin} / F_Q$ is the core criterion for ensuring that no interface slip occurs in a bolted joint under transverse load. Correctly selecting the minimum friction coefficient and minimum residual preload, and satisfying $S_G \ge 1.2$, is a fundamental step in joint integrity design.