Preload Scatter by Tightening Method
Preload Scatter by Tightening Method
Formula Expression
Parameters
| Symbol | Name | Unit |
|---|---|---|
| bolt_grade | bolt_grade | — |
| nominal_dia | nominal_dia | — |
| tightening_method | tightening_method | — |
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DIN 9250 Preload Scatter: Tightening Coefficient α_A and Method Selection
1. Preload Scatter and Definition of Tightening Coefficient
In bolted joint assembly, due to tool accuracy, friction fluctuations, and operational variations, the actual preload scatters between $F_{Mmin}$ and $F_{Mmax}$. The tightening coefficient α_A is used to derive the maximum possible preload from the minimum required preload, serving as the basis for strength verification:
- $F_{Mmin}$ — Minimum assembly preload required to fulfill function (including embedding and thermal loss compensation, VDI 2230 R5)
- $F_{Mmax}$ — Maximum preload that may occur under the given tightening method
- $\alpha_A$ — Tightening coefficient (≥1); smaller values indicate higher tightening method precision and lower scatter
When using DIN 9250 serrated lock washers, due to the mechanical interlocking effect of the teeth, the sensitivity of the bearing surface friction coefficient $\mu_{serr}$ to lubrication and micro-motion is lower than for smooth surfaces. Therefore, preload scatter is typically 10%–20% smaller than for ordinary flat washer connections under the same tightening method. In design, a slightly lower $\alpha_A$ may be selected at discretion, or the conservative recommended values from VDI 2230 may be used directly.
2. α_A Values for Five Typical Tightening Methods
The table below combines VDI 2230 Table A8 and the surface characteristics of DIN 9250, providing reference α_A ranges for common tightening methods.
| Tightening Method | Method Description | α_A Range (General) | Recommended Value with DIN 9250 | Characteristics |
|---|---|---|---|---|
| ① Torque Control Method | Set tightening torque to indirectly control preload. Preload is highly sensitive to friction coefficient. | 1.6 – 2.5 | 1.5 – 2.0 | Serrated surface stabilizes μ_serr, reducing scatter; mid-to-low range can be selected |
| ② Torque‑Angle Method (Elastic Region) | Tighten to threshold torque, then rotate by a specified angle. Preload is proportional to angle, with low sensitivity to friction. | 1.3 – 1.6 | 1.3 – 1.5 | Serrated surface has minimal effect on angle method; α_A close to conventional |
| ③ Torque‑Angle Method (Yield Point Control / Partial Plastic) | Tighten until the bolt enters plasticity or a clear yield plateau, using material yield point to control preload. | 1.0 – 1.3 | 1.0 – 1.2 | High precision; serrated surface friction has almost no influence |
| ④ Hydraulic Tensioning Method | Hydraulic tensioner axially stretches the bolt; nut is tightened and tension released. Preload controlled by oil pressure. | 1.1 – 1.5 | 1.1 – 1.3 | Washer teeth do not affect axial tension; scatter slightly reduced |
| ⑤ Thermal Preloading / Mechanical Stretching | Heat or mechanical means elongate the bolt; nut is tightened. Preload controlled by elongation. | 1.0 – 1.3 | 1.0 – 1.2 | Unaffected by washer friction; high precision |
3. Influence Mechanism of DIN 9250 Washers on α_A
3.1 Advantages in Torque Method
Scatter in the torque method primarily originates from friction coefficient fluctuations in the torque-preload conversion relationship. The $\mu_{serr}$ of serrated washers is dominated by mechanical interlocking, making it far less sensitive to oil contamination and coating variations than pure friction. Thus, even under inconsistent lubrication conditions in industrial settings, the scatter band of $\mu_{serr}$ remains narrow. Experimental results (e.g., ISO 16047) show that for the same batch of serrated washers, the coefficient of variation (COV) of the K-factor can be reduced to 5%–8%, whereas for smooth washers it is typically 10%–15%. This allows reducing α_A for the torque method from the conventional 1.7–2.0 to 1.5–1.8.
3.2 Angle Method and Yield Point Method
These methods directly control bolt elongation and have minimal dependence on bearing surface friction. Therefore, α_A is almost unaffected by washer type. DIN 9250 washers serve only as locking elements and do not alter the slope of the tightening curve or the accuracy of yield point detection.
3.3 Hydraulic Tensioning and Thermal Preloading
Preload is achieved directly through external loading, independent of the washer. α_A depends solely on the accuracy of the loading equipment and the angular loss during nut tightening.
4. Procedure for Calculating $F_{Mmax}$ Based on α_A
- Determine the required minimum preload $F_{Mmin}$ (VDI 2230 R5).
- Select the tightening method and, considering whether DIN 9250 washers are used, choose the appropriate α_A from the table above.
- For the torque method with verified stable serrated surface friction, α_A = 1.6 may be used; otherwise, conservatively take 1.8.
-
Calculate the maximum assembly preload:
$$F_{Mmax} = \alpha_A \cdot F_{Mmin}$$ -
Perform strength verification (VDI 2230 R7, R8) and washer flattening force verification using $F_{Mmax}$.
- For the torque method: Use $\mu_{serr}$ to calculate the required tightening torque, ensuring the actual preload falls within the envelope $[F_{Mmin}, F_{Mmax}]$.
5. Example
M10 bolted connection requiring minimum preload $F_{Mmin} = 15\,000\ \text{N}$.
Select torque control method + DIN 9250 serrated lock washer. Based on on-site friction control level, take α_A = 1.7.
Subsequent steps: - Verify bolt stress: Use 25.5 kN for R7/R8 verification. - Calculate tightening torque: Based on $\mu_{serr}=0.24$, target $F_M$ can be taken as the midpoint value of 20 kN; calculated torque approximately 53 N·m. - Verify washer: The permissible load of the serrated washer (considering flattening force reduction) must exceed 25.5 kN.
Summary:
Preload scatter is characterized by the tightening coefficient α_A. DIN 9250 serrated lock washers, by providing more stable bearing surface friction, can moderately reduce the α_A value for the torque method (recommended 1.5–2.0). Selecting an appropriate tightening method and a reasonable α_A ensures connection safety while optimizing bolt utilization and avoiding overdesign.