Maximum Assembly Preload Calculation: VDI 2230 Step R6

1. Purpose and Core Formula

After obtaining the minimum assembly preload $F_{Mmin}$ via Step R5, the actual tightening scatter during assembly must be considered to determine the maximum possible axial preload that may occur in the bolt after assembly. This maximum force serves as the basis for bolt strength verification (R7), surface pressure verification (R8), and other checks.

VDI 2230‑1 (2015) Step R6 provides the following calculation formula:

Where: - $F_{Mmax}$ — Maximum assembly preload (N), corresponding to the maximum axial force experienced by the bolt after assembly - $F_{Mmin}$ — Minimum assembly preload (N), calculated in Step R5 - $\alpha_A$ — Tightening factor (dimensionless), reflecting the preload amplification ratio due to tightening method and tool accuracy, $\alpha_A \geq 1$

Engineering significance: Actual tightening cannot precisely achieve $F_{Mmin}$ every time, so the target value must be artificially amplified to ensure that, in the worst case, the actual preload is still not less than $F_{Mmin}$. $F_{Mmax}$ corresponds to the maximum possible force that must be sustained without bolt failure.

2. Physical Meaning of the Tightening Factor $\alpha_A$

is defined as the ratio of the maximum possible preload to the required minimum preload. It comprehensively reflects scatter caused by the following factors:

• Tightening method principle: Different methods (torque, angle, yield control, etc.) have varying sensitivity to friction and geometric variations.
• Tool accuracy and calibration: Indication error, repeatability, etc., of the tool itself.
• Friction coefficient scatter: Especially for torque-controlled methods, the uncertainty in converting torque to preload primarily originates from friction.
• Operator/automation level: Manual operation has larger scatter; automated systems are more stable.
• Joint stiffness, embedding, etc.: These also affect the preload build-up process.

The larger the tightening factor, the greater the tightening scatter, requiring a higher $F_{Mmax}$ for strength verification, thus reducing bolt utilization. Therefore, selecting a low-scatter tightening method is a core strategy for optimizing joint design.

3. Guideline Values of $\alpha_A$ for Different Tightening Methods

According to VDI 2230 and related engineering practice, typical $\alpha_A$ ranges for common tightening methods are as follows (note: specific projects should use the latest standards or measured data):

VDI 2230 recommended reference values: - Conventional torque method (no special control): take $\alpha_A = 1.7$ as a conservative design value. - Torque method with friction coefficient control or reliable $\mu$ measured in the lab: can be reduced to $\alpha_A = 1.4$. - Angle method or yield point control method: recommend $\alpha_A \leq 1.2$.

4. Refined Selection Logic for $\alpha_A$ (Torque Method Example)

For torque-controlled methods, $\alpha_A$ can be further decomposed:

• $\alpha_{A,1}$ — Scatter in the torque-preload conversion relationship (mainly from friction coefficient fluctuations)
• $\alpha_{A,2}$ — Accuracy and repeatability of the torque tool itself (e.g., ±3% to ±10% set torque error)

When the upper and lower limits of the friction coefficient $\mu_{min}, \mu_{max}$ are known, the corresponding $F_{M,max}$ and $F_{M,min}$ can be back-calculated using the R13 formula, directly yielding $\alpha_A = F_{M,max} / F_{M,min}$. This is the approach that explicitly incorporates friction coefficient effects into the design.

5. Application Example

Continuing from the previous R5 example, we have obtained:

• $F_{Mmin} = 8050\text{ N}$

Assume the torque-controlled method is used. Based on production conditions (good lubrication, torque wrench accuracy ±5%, controllable friction coefficient scatter), select $\alpha_A = 1.6$.

Then:

This $F_{Mmax}$ will be used for: - R7: Bolt stress verification, requiring $\sigma_{red} \leq R_{p0.2min}/k$ or $\sigma_{zul}$. - R8: Surface pressure verification of the jointed parts to avoid crushing. - R9: Fatigue strength assessment (using $F_{Mmax}$ as the mean value, superimposed with working loads).

6. Important Notes

• $F_{Mmax}$ is the maximum possible preload, not the preload directly corresponding to the process target torque. The process target torque typically corresponds to an intermediate nominal preload $F_{Mnom} = F_{Mmin} \cdot \sqrt{\alpha_A}$? Not exactly; sometimes approximated as $F_{Mnom} = F_{Mmax} / \alpha_A$? In practice, after selecting the tightening method, process parameters (target torque or angle) should be set with $F_{Mmin}$ as the lower limit, while ensuring that the probability of exceeding $F_{Mmax}$ is within an acceptable range. In the standard design process, $F_{Mmax}$ is often taken as the verification force, and the process nominal preload $F_{M,goal}$ can be chosen between $F_{Mmin}$ and $F_{Mmax}$, but must ensure that the preload in the worst case is still not less than $F_{Mmin}$.
• For the torque-controlled method, the ratio of $F_{Mmax}$ to $F_{Mmin}$ can be directly calculated from the R13 formula based on the upper and lower limits of the friction coefficient. This ratio is $\alpha_A$, eliminating the need for separate selection and providing a more direct approach.
• For the angle method or yield point method, $\alpha_A$ should also be determined based on experimental data and production statistics.

VDI 2230 systematic workflow: R5 Minimum preload → R6 Maximum preload → R7 Stress verification → R8 Surface pressure → R9 Fatigue safety → Finally determine tightening torque (R13).