Contact Surface Pressure Check: VDI 2230 Step R10

1. Purpose and Basic Principle

After bolt tightening, the bolt head (or nut) and washers transmit a high preload to the clamped part surface. If the surface pressure exceeds the material's承受极限 of the clamped part, crushing, plastic deformation, or creep can occur, leading to preload loss, joint loosening, or even failure of the clamped parts.

VDI 2230‑1 Step R10 prevents this failure by checking that the maximum surface pressure $p_{Bmax}$ does not exceed the allowable surface pressure $p_G$.

Core formula:

Where: - $p_{Bmax}$ — Maximum surface pressure (MPa) - $F_{Mmax}$ — Maximum assembly preload (N), calculated in Step R6 (including tightening scatter) - $A_p$ — Bearing area (mm²), i.e., the actual contact area between the bolt head/nut or washer and the clamped part - $p_G$ — Allowable surface pressure (MPa), determined by the clamped part material

Basic principle: Even if the bolt strength is sufficient, if the clamped part surface is crushed, the joint still fails. Therefore, this check must be performed independently.

2. Determining the Allowable Surface Pressure $p_G$

2.1 User-Provided Relationship

• $R_m$ — Tensile strength of the clamped part material (MPa)

This formula applies to ductile metallic materials (e.g., steel, aluminum alloys). The factor 0.85 originates from VDI 2230's empirical recommendation for steel clamped parts, essentially equating to the material's yield strength ($R_{p0.2} \approx 0.85 R_m$ for steel) to prevent macroscopic yielding of the surface.

2.2 Complete VDI 2230 Recommendation Values

Note: If the clamped part has been heat-treated or surface-strengthened, the actual surface strength should be used, not the base material $R_m$.

3. Calculation of Bearing Area $A_p$

depends on the geometry of the pressure-transmitting part. Common cases:

3.1 Direct Bearing by Bolt Head or Nut (No Washer)

For standard hexagon head bolts/nuts, the bearing surface is an annular area:

• $d_w$ — Outer diameter of the bearing surface, typically the minimum bearing circle diameter of the bolt head or nut. Can be obtained from standards or approximated as $d_w \approx 0.95s$ ($s$ is the width across flats)
• $d_h$ — Bolt hole diameter (or inner diameter, usually the through-hole diameter)

3.2 Using Flat Washers

The bearing area is the effective bearing area of the washer:

Washers increase the bearing area, effectively reducing surface pressure, and are a common method for protecting soft materials.

3.3 Bearing Characteristics of DIN 25201 Wedge-Lock Washers

Wedge-lock washers have radial interlocking teeth. The actual contact area is much smaller than the geometric annular area, and the tooth tip pressure is extremely high. VDI 2230 recommends checking such toothed contact surfaces based on the tooth projection area or empirical allowable pressure separately. Typically, the maximum allowable preload specified by the washer manufacturer should be used, rather than directly applying $p_G \approx 0.85 R_m$.

Simplified approach: A conservative approach is to calculate the nominal annular area using the root circle diameter and the hole diameter, but the allowable pressure must be significantly reduced, or the manufacturer's data should be used directly.

4. Calculation Procedure and Example

Procedure:

1. Obtain $F_{Mmax}$ from Step R6
2. Determine the geometry of the bearing part and calculate $A_p$
3. Look up the clamped part material $R_m$ and determine $p_G$
4. Calculate $p_{Bmax} = F_{Mmax} / A_p$
5. Check $p_{Bmax} \le p_G$

Example

Connection parameters: - M10×1.5 bolt, grade 8.8, Step R6 yields $F_{Mmax} = 12\,880\ \text{N}$ - Direct hexagon head bearing (no washer): bearing surface outer diameter $d_w = 13\ \text{mm}$, bolt hole $d_h = 11\ \text{mm}$ - Clamped part material: S235 structural steel, $R_m = 360\ \text{MPa}$

Bearing area:

Maximum surface pressure:

Allowable surface pressure:

Check: $341.6\ \text{MPa} > 306\ \text{MPa}$ → Fail! Corrective measures are needed (e.g., using a flat washer to increase the bearing area).

If a flat washer is added, with outer diameter 20 mm and inner hole 11 mm, then:

5. Important Notes

1. Multi-Interface Check
   If the joint contains multiple clamped parts (e.g., a sandwich structure), each contact surface should be checked for surface pressure, using the actual contact area corresponding to $A_p$.

2. Eccentric Loading and Bending
   When eccentric loads or bending moments are present, the surface pressure is no longer uniform, and edge high pressure may occur. In such cases, more complex pressure distribution models or finite element analysis are required; simply using $F_{Mmax}/A_p$ is insufficient.

3. Washer Selection

4. Soft material clamped parts (aluminum, magnesium) must be used with large outer diameter washers or flange-head bolts/nuts.

5. For wedge-lock washers, special attention must be paid to tooth crushing; it is recommended to follow the manufacturer's pressure limits.

6. Temperature Effects
   Material strength decreases at high temperatures. $R_m$ should be taken at the operating temperature.

7. Multiple Assemblies
   Repeated tightening may gradually flatten the surface, increasing $A_p$ and decreasing surface pressure. However, the initial assembly must pass the check.

8. Safety Factor
   The formula $p_G \approx 0.85 R_m$ already incorporates a safety consideration (relative to ultimate strength). An additional safety factor is usually not required. If the material is brittle or the consequences are severe, a more conservative factor can be used.

Summary: R10 surface pressure check is a critical step to prevent crushing of the clamped parts. The simple check $p_{Bmax} = F_{Mmax}/A_p \le p_G$ is effective for evaluation. When it fails, solutions include increasing the washer size, improving material strength, or reducing the preload.