Symbol	Name	Unit
De	De	mm
Di	Di	mm
bolt_grade	bolt_grade	—
bolt_size	bolt_size	—
h0	h0	mm
t	t	mm

DIN 6796 Bolt Preload: Specification‑Strength Matching and Washer Flattening Force Adaptation

1. Design Objective and Matching Logic

DIN 6796 disc spring washers act as elastic elements in bolted joints. Their safe operation requires:

Bolt preload remains within the washer's elastic range and does not exceed the washer's permissible load;
Washer provides sufficient elastic restoring force to compensate for expected embedding, thermal losses, etc.
The washer must neither be overloaded (flattened or yielded) nor have negligible compression at minimum preload (losing elasticity).

Therefore, the design must achieve a bidirectional match of "bolt → preload → washer selection/verification".

2. Calculation of Permissible Bolt Preload (VDI 2230 Basis)

2.1 Maximum Allowable Assembly Preload $F_{Mmax}$

During elastic tightening, the assembly stress must not exceed the material yield strength, considering torsional superposition. VDI 2230 R7 gives:

\sigma_{red,M} = \sqrt{\sigma_M^2 + 3\tau_M^2} \le \nu \cdot R_{p0.2}

Common simplification: directly relate maximum preload to yield strength. In engineering practice, for elastic tightening (torque method), the maximum permissible preload can be estimated by:

\boxed{F_{Mmax} \approx \frac{0.9 \cdot R_{p0.2} \cdot A_S}{\sqrt{1 + 3 \left( \frac{2 d_2}{d_S} \cdot \frac{0.16P + 0.58 d_2 \mu_G}{d_S} \right)^2}}}

However, the more general VDI 2230 R0 initial selection and standard tables provide direct recommended values. The maximum permissible preload for common bolts at a utilization factor of 0.9 can be found in tables. To simplify matching, the bolt proof load (ISO 898‑1) can be used as a reference:

F_{Mmax} \le 0.9 \cdot F_{0.2}

Where $F_{0.2}$ is the bolt proof load (i.e., the minimum tensile load at 0.2% yield strength, N), given by standards (e.g., M10 grade 8.8 $F_{0.2} \approx 37\,400$ N, 0.9 times ≈ 33 700 N). However, in actual design, considering tightening scatter, the maximum preload $F_{Mmax}$ is typically taken as 70%–80% of the bolt proof load as a target value, depending on the tightening coefficient $\alpha_A$ .

Recommended preload $F_{M,rec}$ can be taken as:

F_{M,rec} \approx (0.6 \sim 0.8) \cdot F_{0.2} \quad \text{or} \quad F_{M,rec} \approx 0.7 \cdot R_{p0.2} \cdot A_S

2.2 Reference Preloads for Common Bolts

The table below shows recommended preload ranges (in kN) for coarse threads, elastic tightening (torque method), based on 0.7 times the proof load.

Bolt Size	Grade	$F_{0.2}$ (kN)	Recommended Preload $F_{M,rec}$ (kN)
M8	8.8	21.6	15 ～ 17
M10	8.8	37.4	26 ～ 30
M10	10.9	52.5	37 ～ 42
M12	8.8	54.5	38 ～ 44
M12	10.9	76.5	54 ～ 61
M16	8.8	98.5	69 ～ 79
M16	10.9	138	97 ～ 110

These values already include a safety margin for tightening scatter and can be used as input for matching with the washer flattening force.

3. Review of DIN 6796 Washer Flattening Force

The force when the washer is fully flattened ( $$s=h_0$$ ) is:

F_{flat} = \frac{4E}{1-\nu^2} \cdot \frac{t^3 h_0}{K_1 D_e^2}

The maximum permissible load (elastic safety) of the washer is:

F_{zul} = \frac{F_{flat}}{S_{flat}}, \quad S_{flat} = 1.2 \sim 1.5

The permissible load can be considered the maximum preload the washer can withstand. To ensure elastic compensation, the requirement is:

F_{Mmax} \le F_{zul} \quad \text{(i.e., } F_{Mmax} \le F_{flat}/S_{flat}\text{)}

At the same time, the minimum preload $F_{Mmin}$ should ensure sufficient initial compression of the washer (typically $s \ge 0.1h_0$ ), otherwise the washer cannot function elastically.

4. Matching Procedure

Determine the bolt size and grade from the joint requirements, obtaining $F_{Mmax}$ (from design or standard recommended values).
Preliminarily select a DIN 6796 washer (according to the standard outer diameter series for the nominal bolt diameter).
Calculate the washer flattening force $F_{flat}$ and permissible load $F_{zul} = F_{flat} / S_{flat}$ .
Verify:
If $F_{Mmax} \le F_{zul}$ , the washer is elastically safe.
If $F_{Mmax} > F_{zul}$ , select a larger size (increase $$D_e$$ , $$t$$ , or $$h_0$$ ), or reduce the bolt preload.
Reverse verify the minimum preload: Calculate the compression $s_{min} = f(F_{Mmin})$ at minimum preload, ensuring $s_{min} \ge 0.1h_0$ .
Check contact surface pressure (especially for soft clamped parts): Calculate the contact pressure at maximum preload to ensure no crushing.

5. Matching Example

5.1 Bolt Side

M10 × 1.5, grade 8.8, VDI 2230 calculation yields a maximum assembly preload $F_{Mmax} = 25\,000\ \text{N}$ (target maximum force considering tightening coefficient $\alpha_A=1.7$ ). Recommended preload is 25 kN.

5.2 Washer Side

Select a DIN 6796 washer for M10 (parameters as before: $$D_e=20$$ mm, $$D_i=10.2$$ mm, $$t=1.5$$ mm, $$h_0=1.0$$ mm).
The theoretical flattening force is calculated as $F_{flat} = 11\,000\ \text{N}$ .

Taking a safety factor $S_{flat} = 1.3$ , the permissible load is:

F_{zul} = \frac{11\,000}{1.3} \approx 8\,460\ \text{N}

5.3 Matching Assessment

F_{Mmax} = 25\,000\ \text{N} \gg 8\,460\ \text{N}

Mismatch: This washer cannot withstand a 25 kN preload. Solutions: - Switch to an L-type large washer (outer diameter 25 mm, thickness 1.8 mm, cone height 1.2 mm), with a flattening force of approximately 16 kN and permissible load of 12.3 kN, still insufficient. - Further increase size: Use an M12 washer (outer diameter 30 mm, thickness 2.0 mm, cone height 1.4 mm) with an M10 bolt (requires an adapter washer or checking inner diameter compatibility). This occupies more space. - Or reduce the bolt preload to below 8 kN, which may compromise joint function.

This example shows that standard DIN 6796 washers have limited load capacity. High preload bolts often require multiple washers in stack (parallel) or series (nested) arrangements, or the use of higher-strength disc spring washers. If a single DIN 6796 washer must be used, the bolt preload should be limited to approximately 0.4  $F_{flat}$ to ensure elasticity and strength safety.

6. Matching with Multiple Washer Combinations

If a single washer's load capacity is insufficient, combinations can be used:

Stack (parallel): $$n$$ washers stacked in the same direction, total flattening force $= n \times F_{flat}$ , but the allowable compression stroke remains $$h_0$$ .
For example, 2 washers in parallel can achieve a permissible load of $2 \times 8.46 = 16.9\ \text{kN}$ .
Nested (series): $$m$$ washers nested in alternating directions, total compression stroke $= m \times h_0$ , flattening force same as a single washer.
If greater relaxation compensation is needed, series arrangement increases elastic travel.

In matching, parallel combinations increase load capacity, while series combinations increase compensation capability. The design must be determined based on both bolt preload and expected relaxation.

7. Conclusion

The recommended bolt preload $F_{M,rec}$ is selected as 60%–80% of the bolt proof load, ensuring elastic tightening safety.
The permissible load of a DIN 6796 washer is $F_{zul} = F_{flat}/S_{flat}$ ( $S_{flat} \ge 1.3$ ).
Matching condition: $F_{Mmax} \le F_{zul}$ , and the washer has sufficient initial compression at minimum preload.
Standard washers have limited load capacity; for high preloads, combinations or larger sizes are often required.
After matching, contact surface pressure and washer stress must be verified to ensure full-life joint safety.

Bolt Preload Force

Formula Expression

Parameters

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Detailed Calculation Guide