**4. Contact parameters variability and contact model adequacy**

The purpose of this section is to detail the level of uncertainty of each of the contact parameters estimated in Section 3.2 and to investigate their variability. Results are summarized in **Table 3** and will be further commented on in the following subsections.


**Table 3.** Uncertainty bands and normal load dependence of contact parameters obtained at CF = 4.65 kg.

**4.1. Nonconforming (non-rolling) contacts**

stiffness and damping.

least square fitting of the hysteresis slope.

repeatable and with a minor sample-to-sample variability.

**4.2. Remark on rolling nonconforming contacts**

impairs the effectiveness of this technique.

contact area (flat-on-flat contact).

load5

5

to-sample variability can be investigated by looking at **Figure 7a**.

The uncertainty on μR is the combination of the uncertainty on TR/NR (3–5% from **Table 1**) and the reading error (typical values ≈ ±0.05 as shown in **Figure 5a**). The repeatability and sample-

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**Figure 7a** shows the TR/NR force ratio during slip under increasing values of normal load NR, achieved by increasing the centrifugal load (4.6–8.6 kg). Different dampers are represented with different colors and positive and negative slipping stages (see **Figure 7a** for sign convention) are represented using different symbols. "Clusters" of points of the same color and symbol belong to the same stage of the same experiment of the damper samples, represented with different colors. Despite some inevitable variabilities (e.g. T/N ratios display minor variations during a single slip stage), μR can be set at a "unique value" for all investigated dampers. Furthermore, these variabilities are in the same range as the uncertainty introduced by the measuring and postprocessing techniques. Choosing μ<sup>R</sup> = 0.65, a value mediated over all those encountered in **Figure 7a** is a perfectly adequate choice, which guarantees a controlled error on the equivalent

Similarly, ktR (which is plotted as function of NR in **Figure 7b**) is not influenced by the normal

It can therefore be concluded that contact parameters of the nonconforming contact are both

The case of rolling contact is of scarce interest for curved-flat dampers, as it was demonstrated that large rotations (damper in lift-off) lead to a sharp decrease in dissipation capabilities [40]. However, purely cylindrical dampers are widely used and thus require a separate investigation.

The procedure to evaluate ktR described in Section 3.2 cannot be operated if the damper is rotation is large (~10 times higher than that observed in **Figure 5c**). In fact, in that case, the reading "tRD-tRP" would give a false indication. As shown in **Figure 8a**, the laser, which is initially tracking point A ends up tracking point A\*. However, the physical point initially corresponding to A is now A′, not A\*. This apparently minor difference, at micrometer level,

Fortunately, an alternative procedure based on the equivalent slopes of the platform-to-platform hysteresis cycle can be successfully carried out, both for cylindrical dampers and for curved-flat dampers [37, 39]. It is interesting to notice that the resulting ktR values are 3.5–4 times lower than those obtained for non-rolling cylinder-on-flat contacts, all other parameters

This is to be expected, as the cylinder-on-flat surface has a line contact, and an increase in normal load will lead to a number of asperities coming into contact which is proportionately much smaller than that obtained for a rectangular

 at the contact in the investigated range, is remarkably repeatable and no sample-tosample variability is detected. In **Figure 7b**, the error bars are obtained by performing the

**Figure 6.** (a) Measured (dotted) vs. simulated (solid) contact forces diagram. (b) Representative scheme of the distribution of normal contact springs. (c) Derived position of NL and resulting q(x) at stage 2.

**Figure 7.** (a) TR/NR during slip as a function of NR. (b) ktR values as a function of the mean value of NR during the corresponding stick stage. Three different damper samples are represented.

The level of uncertainty is estimated taking into account two contributions: measurement uncertainty and the uncertainty introduced by data processing techniques (e.g. reading error). Variability will be investigated at different levels in order to answer the following questions:

1. If the same damper is tested more than once under the same nominal conditions, do the estimated contact parameters change? 2. Are contact parameters dependent on the damper working conditions (e.g. normal contact pressure)?<sup>4</sup> 3. How different are contact parameters of different damper samples working under very similar working conditions?

The answer to point 3 is investigated using three pre-optimized damper configurations [40], that is, curved-flat dampers not affected by lift-off/rolling, jamming or partial detachment.

<sup>4</sup> The user-controlled working conditions investigated during this chapter are limited to a variation of centrifugal load on the damper (i.e. normal load at the contact). Other factors such as temperature, length/area of contact may affect the contacts. These dependences can and should be mapped in order to build a "database" and avoid testing each new component. This chapter should be intended as a first attempt in this direction.
