DIN 6796 Series Assembly: Opposing Arrangement Increases Total Travel

1. Principle of Series Assembly

Series assembly (opposing stacking) refers to arranging $i$ pieces of DIN 6796 disc springs alternately in opposite directions (adjacent springs with cone surfaces facing toward or away from each other), which deform together under bolt preload. Its mechanical characteristics are:

• Total compression travel is the sum of the travel of each piece: $s_{total} = i \cdot s_{single}$
• Total axial force is the same as that of a single spring: $F_{total}(s_{total}) = F_{single}(s_{single})$, where $s_{single} = s_{total} / i$
• Total stiffness is $1/i$ of the single spring stiffness: $k_{total} = k_{single} / i$

The core advantage of series assembly is significantly increased elastic deformation capacity under the same preload, used to compensate for large axial settlements (e.g., embedding of thick gaskets, severe thermal expansion differences, creep of soft connections).

2. Core Calculation Formulas

2.1 Total Travel-Load Relationship

If the force of a single spring at compression $s$ is $F_{single}(s)$, then for $i$ pieces in series with total compression $s_{total}$:

That is, after series assembly, the preload is determined by the force corresponding to the compression equally shared by each spring. When the total travel equals $i \times h_0$, the series assembly reaches full flattening (total flattening force still equals the single spring flattening force).

2.2 Total Stiffness and Flexibility

The tangent stiffness of the series assembly at the operating point:

The introduced flexibility is:

This flexibility is directly substituted into the VDI 2230 system flexibility chain for calculating preload loss and load distribution factor.

2.3 Stress State

In a series assembly, the compression of each spring is only $1/i$ of the total travel, so the stress in each piece is significantly lower than when a single spring bears the full compression. OM point stress and fatigue stress amplitude are both substantially reduced, which is beneficial for strength and service life.

3. Design Advantage for Compensating Larger Settlements

When the connection is expected to undergo a large axial settlement $f_{total}$ (e.g., crushing of thick coatings, embedding of multi-layer interfaces, high-temperature creep of aluminum/magnesium parts), the spring must retain sufficient elastic travel to absorb this displacement without being flattened.

Assuming the required compensation displacement is $\Delta f$, the required number of series pieces $i$ must satisfy:

where $\eta_{util}$ is the allowable travel utilization factor of the spring (recommended 0.75 to avoid excessive stress). The minimum number of series pieces can be back-calculated from this.

Typical applications: - Compensation for large embedding of long bolts + soft connected parts - High-temperature connections where the thermal expansion of the connected parts is greater than that of the bolt - Vibration-isolating connections requiring low-stiffness elastic support

4. Series Assembly Design Procedure

1. Determine the required elastic compensation travel $\Delta f$ (estimated from settlement).
2. Select a single spring specification and obtain its $h_0$.
3. Calculate the minimum number of series pieces $i_{min} = \lceil \Delta f / (0.75\,h_0) \rceil$.
4. Verify preload: Ensure the allowable load of a single spring $F_{zul,single}$ is greater than the maximum assembly preload $F_{Mmax}$ (since series assembly does not increase total force, a single spring must be able to bear the entire preload).
5. Calculate the total series thickness $i \times t$ (axial space), ensuring sufficient bolt thread length.
6. Update system flexibility $\delta_{W,total} = i \cdot \delta_{W,single}$ and substitute into VDI 2230 to calculate preload loss and residual force.
7. Verify spring stress (calculate based on single spring compression $s = s_{total}/i$; stress is usually low and easily passes).

5. Calculation Example

Conditions: - Expected total settlement requiring elastic compensation $\Delta f = 2.0\ \text{mm}$.
- Selected DIN 6796 spring for M10: $h_0 = 0.6\ \text{mm}$, $t = 1.2\ \text{mm}$, allowable load $F_{zul,single} = 8\,460\ \text{N}$.
- Maximum bolt preload $F_{Mmax} = 7\,500\ \text{N}$ (less than spring allowable load, single spring usable).

Required minimum number of series pieces:

Verification: - Total elastic travel of 5 pieces in series: $5 \times 0.6 = 3.0\ \text{mm}$; usable travel (0.75 factor) = 2.25 mm > 2.0 mm, satisfied. - Force on a single spring remains 7 500 N; compression $s = s_{total}/5$. If total travel after compensation is 2.0 mm, then $s = 0.4\ \text{mm}$, much less than $h_0$, stress is low. - Total thickness: $5 \times 1.2 = 6.0\ \text{mm}$; bolt must be lengthened accordingly. - System flexibility increases by a factor of 5; preload loss due to embedding is smaller.

Conclusion: Using 5 pieces in opposing series can safely compensate for 2 mm settlement, with spring stress well below the allowable value.

6. Precautions

1. Axial space: Series assembly significantly increases the total spring height; ensure sufficient effective bolt thread length and structural space.
2. Centering and guidance: For multiple pieces in series, use a guide sleeve or ensure a small clearance between the bolt and hole to prevent lateral instability or misalignment of the springs.
3. Load assurance: Series assembly does not increase the maximum load capacity; a single spring must still be able to bear the entire preload. If the preload exceeds the allowable value of a single spring, first use parallel assembly to increase load capacity, then use series assembly to increase travel (i.e., mixed assembly).
4. Friction and hysteresis: Friction between springs may cause the actual loading curve to deviate slightly from theory, with hysteresis during unloading. For precision applications, lubricate the spring contact surfaces to stabilize characteristics.
5. Single-use recommendation: After disassembly of multiple pieces in series, the deformation of each piece may be uneven; reuse is not recommended.
6. Assembly identification: Clearly indicate the opposing arrangement and number of pieces on installation drawings to avoid incorrect assembly.

Summary:
The opposing series arrangement of DIN 6796 springs, characterized by travel superposition and constant force, can significantly increase elastic compensation capacity, making it an effective means for connections with large settlements. During design, determine the minimum number of pieces based on the required compensation travel, ensure sufficient load capacity of a single spring, and pay attention to axial space and installation centering.