Managing Friction in Parallel Disc Spring Stacks:
The Importance of Lubrication

Disc Springs are ideal functional components for achieving consistent and predictable spring forces within specified ranges of travel. Relative to their size, they provide larger spring forces over smaller deflection distances than can be achieved with helical springs. They are designed with both static and dynamic (oscillating) compression cycling in mind, and they can be stacked in various configurations to achieve spring load and deflection properties beyond what would be possible with single Disc Springs (Figure 1). The ability to stack Disc Springs makes them extremely versatile for a variety of different applications across global industry.

Figure 1
Disc Springs can be stacked in different configurations to achieve different force and deflection properties

General guidance in Disc Spring Stack design is that for every Disc added in a parallel set, the expected (calculated nominal) spring load for one Disc Spring is multiplied by the total quantity in parallel.

This is a simple way to begin the Stack design process, however in practice Disc Spring load/deflection behavior increasingly departs from the theoretical calculated curve as more Discs are stacked in parallel due to friction and geometric variation between the springs.

If friction between Disc Springs in parallel configuration is not properly accounted for, it may result in unexpected spring performance during real-world testing, and in some cases, it could even lead to premature component failure. In this White Paper, clarity is provided for this often-misunderstood aspect of Disc Stacking to enable end-users to achieve the best possible performance in their assemblies.

When Disc Springs are cycled individually or stacked in series configuration, friction occurs between the edge radii of the individual springs and their bearing surfaces (points I and III shown in Figure 2), but when stacking Disc Springs in parallel configuration, friction also acts between the conical contact surfaces of the individual springs.

When Discs stacked in parallel are loaded, frictional forces act in opposing directions on the conical surfaces of each Disc Spring (Figure 3). These frictional forces work against the applied load, increasing the required force to compress the Stack. Inversely, when the Stack is unloaded, these same frictional forces work in reverse, reducing the required load to hold the Stack at a specified deflection. When dynamically cycling a Disc Spring Stack and plotting the load/deflection data, this is observed as a “loop” (Figure 4), wherein the actual spring load output from the Disc Stack increases during loading and decreases during unloading

DIN EN 16983 divides Disc Springs into different “Series” based on their ratio of free cone height to thickness (h₀/t), which informs the shape of their theoretical load/deflection curves. As a result of these “Series” differences, DIN EN 16984 provides the following coefficient of friction values to be used for w_M and w_R when calculating F_gesR for each Series of Disc Spring:

Table 1
Coefficient of friction values for different Series of Disc Springs provided by DIN EN 16984

Calculating $\frac{n}{1\mp w_M\times (n-1)\mp w_R}$  for each DIN Series creates a “modifier” against which a Disc Spring’s nominal spring load (F) can be multiplied to estimate the range of potential spring loads in a parallel Disc Stack after allowances are made for friction. For clarity, these “modifier” values have been converted into percentages applying to the theoretical Disc Stack force, where “+” indicates loading and “—” indicates unloading.

Table 2
SPIROL converted DIN 16984 friction modifiers

While DIN EN 16984 provides this calculation and friction coefficients to estimate the friction effect between Disc Springs in a parallel set (Figure 5), in practical application there are a large number of factors which can influence friction in multi-part assemblies, and the actual load/deflection results are highly dependent on both surface finish and lubrication (which affect coefficient of friction between spring surfaces). So, while these tables derived from DIN EN 16984 are theoretically “correct”, a simpler friction modifier (Figure 6) has been derived through testing of ±2-3% per parallel spring (“+” applied to loading, “—” applied to unloading). The “maximum” friction modified curves between the two methods are roughly equivalent, but the “minimum” friction modified curve using the DIN derived figures barely deviates from the standard calculated curve.

---  -  --- Calc. Nominal Curve     _______ Max. Friction Modified Curve     _______ Min.  Friction Modified Curve

Since individual Disc Springs may have a greater or lesser curve amplitude than the theoretical curve calculated per DIN EN 16984, the amplitude of the force/deflection curve is not necessarily the most important factor when comparing Disc Spring Stack load curves in lubricated versus unlubricated conditions. A Disc Spring within a particular Stack may have a slightly higher load, which could lead the experimenter to mistakenly attribute the variation in performance to the Stack's lubrication state. Instead, the more meaningful measure is the reduction in the Area Under the Curve (AUC) between loading and unloading, which represents the energy dissipated in the assembly due to frictional hysteresis. SPIROL performed testing on Disc Springs from DIN Series A, B, and C. Each Disc Spring used for testing was preset to F = 2 × F_t (where F_t equals the DIN nominal force for the Disc at l_t = l₀ − (0.75 × h₀)). Two Stacks of four Disc Springs in parallel were assembled from each Series: one with lubricant and one without (Figure 7).

Each test consisted of ten total cycles where the Stacks were loaded to deflection s = 0.75 × (L₀ − L_C), and then unloaded to s = 0.0mm. This was intended to allow the lubricant to settle between the Discs, and to see how well each Disc Stack performed under dynamic loading conditions.

Breaking down the test results by DIN Series reveals a number of interesting findings. At the outset, it can be said that the trends observed between DIN Series largely do corroborate the figures derived from the F_gesR calculations in DIN EN 16984, showing that Series A Disc Springs experience the greatest frictional hysteresis when stacked in a parallel set, followed by Series B and Series C Discs. The DIN Series A graph (Figure 8) shows that while the lubricated Stack reached a higher force amplitude at maximum deflection s_ges than the unlubricated Stack (likely due to the Discs within it having higher spring forces), the lubrication had a demonstrable effect on energy dissipation, with an AUC reduction between loading and unloading cycles of 17.4% for the lubricated Stack vs 28.0% for the unlubricated Stack.

---  -  --- Calc. Nominal Curve     _______ No Lubrication     _______ Lubrication

The Series C Stack tests (Figure 9) showed the lowest frictional hysteresis of all the DIN Series in both lubrication states, with an AUC reduction between loading and unloading cycles of 12.0% for the lubricated Stack vs 23.9% for the unlubricated Stack. However, Series C also saw the smallest comparative performance gain when using lubrication as opposed to a Stack with no lubrication.

• The largest immediate benefit from using lubrication in a Disc Stack was observed with Series A Disc Springs.
• The smallest immediate benefit from using lubrication was observed with Series C Disc Springs, which also showed the least energy dissipation as additional Discs were stacked in parallel.
  • While this may appear promising as a way to reduce energy dissipation due to frictional hysteresis, in practice if an application would require the use of more than two Series C Discs in parallel, it would likely be better to use a single Series A or B Disc Spring instead, which would by merit of lacking parallel contact surfaces between Discs create less of a friction-induced hysteresis “loop” effect.
• Ultimately, unless the natural damping qualities of a parallel Disc Stack are explicitly desired, the ideal Disc Stack should have as few Discs in a parallel set as possible to reduce energy dissipation.
• If the highest force single Disc Spring that is compatible with a design still does not provide sufficient spring force to meet an application’s load requirements, parallel stacking should be used in conjunction with a suitable lubricant to mitigate friction between Disc contact surfaces.

Proper Disc Spring selection, Stack configuration, and lubrication are important considerations in achieving the desired performance and service life of an assembly. SPIROL’s Application Engineers are available to provide complimentary Application Engineering support for your specific application requirements.