DIN 2093 Friction Correction: Influence of Interleaf Friction and Guide Friction on Disc Spring Load

1. Ideal Load and Sources of Friction

Under the frictionless assumption, the force‑deflection relationship of a disc spring follows the Almen‑Laszlo theory (see previous sections). However, in practical engineering, when multiple disc springs are stacked in parallel (same direction) or stacked in series and installed via a guide mandrel/sleeve, the following two types of friction significantly alter the load‑stroke characteristics:

• Interleaf friction ($\mu_f$): Microscopic slip between adjacent conical surfaces of parallel disc springs.
• Guide friction ($\mu_g$): Friction between the disc spring inner diameter and the guide mandrel, or between the outer diameter and the guide sleeve.

These two types of friction lead to:

• During loading: The external force must overcome the elastic force + friction → actual load is 5 %~ 15 % higher than the theoretical value.
• During unloading: Friction opposes the return stroke → actual load is 5 %~ 15 % lower than the theoretical value.
• Cyclic loading/unloading forms a hysteresis loop, the area of which represents the energy dissipated by friction.

2. Ideal Almen‑Laszlo Load (Review)

The theoretical force of a single disc spring at compression $s$ is:

For a parallel stack, the theoretical total force is $n \cdot F_{theory}(s)$; for a series stack, the stroke is additive, and the force is the same as for a single disc.

3. General Method for Friction Correction

In engineering, a friction correction factor $k_f$ is used to convert the theoretical load to the actual load:

• During loading: $k_{f,load} > 1$, typically 1.05 ~ 1.15.
• During unloading: $k_{f,unload} < 1$, typically 0.85 ~ 0.95.

The factor $k_f$ depends on the interleaf friction coefficient $\mu_f$, the guide friction coefficient $\mu_g$, the stacking method, and the disc spring geometry.

3.1 Friction Correction for Parallel Stacks

For $n$ discs stacked in parallel in the same direction, interleaf friction increases the load approximately by:

• $\mu_f$ — Interleaf friction coefficient, generally 0.03 ~ 0.08 (phosphated + oil can be ≤ 0.03).
• $t$, $D_e$ — Disc spring thickness and outer diameter.
• $\zeta$ — Geometric correction factor, typically 0.8 ~ 1.5, can be taken as 1.0 for initial estimation.
• During unloading: $k_{f,unload} \approx 2 - k_{f,load}$ (approximated by hysteresis symmetry).

3.2 Additional Guide Friction

If a guide mandrel (or sleeve) is used, the additional friction torque causes an extra increase in axial force. DIN 2093 suggests replacing $\mu_f$ in the parallel formula with an equivalent friction coefficient $\mu_{eff} = \mu_f + \mu_g \cdot \frac{D_m}{D_e}$, where $D_m$ is the disc spring mean diameter $(D_e+D_i)/2$, and $\mu_g$ is the guide friction coefficient (typically 0.05 ~ 0.10). The actual load can also be determined directly through experimental calibration.

4. Hysteresis Loop and Energy Dissipation

Friction causes the load‑stroke curve to form a closed hysteresis loop.

The loop area $\Delta W$ represents the energy dissipated by friction in one cycle and can be approximated as:

Or more accurately obtained by integration. $\Delta W$ is used to evaluate the damping characteristics and heat generation of the disc spring.

5. Typical Friction Coefficients and Surface Treatments

Phosphating effectively reduces and stabilizes the friction coefficient and is the standard protective lubrication measure recommended by DIN 2093.

6. Design Recommendations

1. Load Setting: When using torque control or force control, the loading curve should be used as the preload target, accounting for a +5 %~ 15 % friction increment.
2. Return Springs: If the disc spring is used for return action, the unloading curve must be used to calculate the return force to ensure adequacy.
3. Experimental Calibration: For critical applications, the force‑stroke curve of the stacked disc spring should be measured to obtain the actual $k_f$ value.
4. Number of Discs Limit: DIN 2093 recommends a maximum of ≤ 4 discs in parallel to control friction non-uniformity and load scatter.
5. Guide Clearance: Strictly select the guide clearance according to the standard. Excessive clearance increases uneven wear and friction scatter, while insufficient clearance introduces additional friction.

Summary: DIN 2093 friction correction uses the factor $k_f$ to reflect the amplification (loading) and reduction (unloading) of the ideal load due to interleaf friction $\mu_f$ and guide friction $\mu_g$, forming hysteresis energy dissipation. During design, the friction effect must be reasonably estimated based on the surface treatment and stacking method, or the actual characteristics must be obtained directly through testing, to ensure preload accuracy and spring functionality.