Equivalent Serration Friction Coefficient
Equivalent Serration Friction Coefficient
Formula Expression
Parameters
| Symbol | Name | Unit |
|---|---|---|
| mating_material | mating_material | — |
| mu_flat | mu_flat | — |
| n_teeth | n_teeth | — |
| washer_material | washer_material | — |
Need to compute this formula?
Contact us for design calculations with your actual parameters and a complete technical report.
Contact Engineering TeamDetailed Calculation Guide
DIN 9250 Equivalent Friction Coefficient μ_serr: Tooth Count and Material Correction
1. Definition and Purpose
In bolted joints using DIN 9250 serrated lock washers, the frictional behavior of the washer bearing surface is significantly enhanced due to radial tooth indentation and plowing effects. To facilitate the use of the Coulomb friction model in classical torque‑preload formulas, the equivalent friction coefficient μ_serr is introduced, which combines pure friction and the mechanical interlocking contribution of the teeth.
- $\mu_{flat}$ — Friction coefficient of a smooth flat surface (reference value) for the same material and surface treatment
- $k_{serr}$ — Serration amplification factor, reflecting the enhancement effect of tooth geometry, tooth count, and material hardness matching ($k_{serr} \ge 1$)
This $\mu_{serr}$ directly replaces the bearing surface friction coefficient $\mu_K$ in the VDI 2230 R13 torque formula or the K-factor method for calculating tightening torque.
2. Physical Model of the Amplification Factor $k_{serr}$
$k_{serr}$can be considered as the superposition of two contributions:
where $\Delta k_{mech}$ is the mechanical interlocking additional term of the teeth, depending on:
- Tooth count $z$: More teeth result in a longer total engagement edge and higher shear resistance;
- Tooth geometry parameters: Tooth height, tooth tip angle, tooth crest width;
- Material hardness matching: The difference between washer hardness $H_w$ and mating part hardness $H_p$ determines the tooth penetration depth, thus affecting the engagement area;
- Normal pressure: The preload level influences the saturation of penetration.
Based on a simplified indentation hardness model, $\Delta k_{mech}$ can be expressed as:
However, since obtaining all parameters is difficult in practice, empirical data is commonly used in engineering.
3. Correction Effect of Tooth Count $z$
For the same washer diameter and thickness, a higher tooth count $z$ (i.e., smaller tooth spacing) increases the engagement line density, raising the equivalent friction coefficient. However, beyond a certain limit, the enhancement effect tends to saturate due to reduced individual tooth penetration depth.
The table below provides reference values for $k_{serr}$ based on test statistics, classified by tooth density (tooth count range) and considering material matching.
| Tooth Density | Tooth Count (approx.) | Steel Washer + Steel Mating Part | Steel Washer + Aluminum Alloy Mating Part | Steel Washer + Cast Iron |
|---|---|---|---|---|
| Coarse teeth (low density) | 6 – 9 | 1.3 – 1.6 | 1.8 – 2.2 | 1.4 – 1.7 |
| Standard teeth (common for DIN 9250) | 10 – 16 | 1.5 – 2.0 | 2.2 – 2.8 | 1.7 – 2.2 |
| Fine teeth (high density) | ≥ 18 | 1.8 – 2.5 | 2.5 – 3.2 | 2.0 – 2.5 |
Material influence rules: - Soft mating parts (e.g., aluminum alloy, magnesium alloy): Teeth easily penetrate, $\Delta k_{mech}$ is large, use the upper limit of $k_{serr}$. - Hard mating parts (hardened steel, case-hardened): Teeth penetrate with difficulty, $k_{serr}$ approaches 1.0, mechanical contribution is very low; carefully evaluate whether alternative locking methods are needed. - Insufficient washer hardness: Teeth will yield first, causing a significant drop in $k_{serr}$; therefore, washer hardness ≥ mating part hardness + 30 HV is required.
4. Selection of the Base Friction Coefficient $\mu_{flat}$
$\mu_{flat}$is the friction coefficient of the same material pair without serrations and should be taken as the lower limit value for the actual surface treatment condition (to obtain a conservative tightening torque).
| Surface Condition | Smooth Flat $\mu_{flat}$ |
|---|---|
| Dry, oil-free (slight oxidation) | 0.18 – 0.25 |
| Phosphated + oil | 0.10 – 0.15 |
| Dacromet/ZnNi coating (without additional lubrication) | 0.10 – 0.16 |
| Good oil/grease lubrication | 0.08 – 0.14 |
Note: If the washer has a coating, use the $\mu_{flat}$ value for that specific coating system.
5. Application in Torque‑Preload Calculation
After obtaining $\mu_{serr}$, substitute it into the torque coefficient $K$ or the VDI 2230 precise formula:
or
where $D_{km}$ is the mean diameter of the washer annular bearing surface ($(D_e + D_i)/2$).
Important: Due to the higher $\mu_{serr}$ values (up to 0.3～0.5), the tightening torque will be 30%～80% higher than for a joint with a plain washer. The tool torque setting must be increased accordingly in the design.
6. Calculation Example
Conditions: - Bolt M10, grade 8.8, target preload $F_M = 20\,000$ N - Serrated washer DIN 9250: outer diameter 20 mm, inner diameter 10.5 mm → $D_{km} \approx 15.25$ mm - Thread friction coefficient $\mu_G = 0.12$ - Smooth flat friction coefficient (with oil) $\mu_{flat} = 0.14$ - Standard tooth profile, steel‑steel joint, from table take $k_{serr} = 1.7$ (medium density teeth)
Calculation:
If the serration effect were ignored and $\mu_{flat}=0.14$ used directly, the torque would be approximately 38.8 N·m, leading to a significant preload deficiency.
7. Design Recommendations and Experimental Verification
- Prefer actual measurement: Conduct torque‑clamp force tests per ISO 16047 to determine the $K$-factor or directly back-calculate $\mu_{serr}$ for the specific washer‑mating part combination, replacing table values.
- Safe torque setting: If testing is not possible, calculate torque using the upper limit of $k_{serr}$ from the table to ensure preload is not below the design minimum.
- Consider reuse: Teeth may be partially flattened after the first tightening; $k_{serr}$ may decrease by approximately 10%～20% upon reuse. Adjust torque accordingly or replace the washer.
- Surface pressure check: High $\mu_{serr}$ may be accompanied by high local surface pressure. Verify that the mating part is not crushed per VDI 2230 R10.
Summary:
The equivalent friction coefficient for DIN 9250 washers, $\mu_{serr} = k_{serr} \cdot \mu_{flat}$, incorporates the mechanical interlocking effect of the teeth into the friction model via the tooth count‑material correction factor $k_{serr}$. A higher tooth count and a softer mating part result in a higher $k_{serr}$. Correctly determining $\mu_{serr}$ is essential for accurate tightening torque setting and achieving the required preload.