# Modeling of Dry Clutch Wear for a Wide Range of Operating Parameters
## 3 Design of Wear Characterization Experiments
### Run-In Experiments  
The wear rate is naturally increased in the initial, so-called run-in phase (see Figure 7 and Section 4). To characterize the run-in behavior, each tested friction plate was initially exposed to run-in experiments for the fixed (run-in) operating point: \(\omega_{0R}=2800\) rpm, \(M_{zR}=50\) Nm, \(t_{2R}=3.4\) s, \(T_{dR}=170\)\({}^{\circ}\)C until a stabilized wear rate is reached (Figure 4 [25]). The same experiments were also conducted in the final phase, i.e., just before the friction  
Figure 3: Illustration of design of experiments [24].  
lining was worn-out (so-called run-out (RO) phase; blue points in Figure 4), in order to serve as a basis for analysis and compensation of wear rate variability among different friction plates (so-called piece-to-piece variation) [26]. The interval between run-in and run-out phases was used for regular wear rate characterization experiments (filled red rectangles in Figure 4). Depending on a combination of operating parameters, between 3 and 14 operating points were recorded per one friction plate, and 13 friction plates were worn out in total to complete all 121 experiments from Figure 3 (see Figure 5). Note that the wear rate and the corresponding dissipated energy values are shown in Figure 4 and throughout the paper in a normalized (per unit; p.u.) form.  
Each wear rate point in Figure 4 was recorded after a certain, relatively large number of closing cycles was executed on the tribometer test rig. Plate mass measurements were conducted before and after each wear rate point tests to derive the corresponding worn mass \(\Delta m\), which yielded worn volume as \(V_{w}=\Delta m/\rho\), with \(\rho\) denoting the measured friction material density. The cumulative energy dissipated during the same interval, \(E_{dis,i}\), was calculated from the slip speed and torque responses, and it was finally used to calculate the wear rate as: \(w=\Delta m/(\rho\sum_{i=1}^{n}E_{dis,i})\)[25] (see Equation (1)). The number of closing cycles \(n\) was determined based on the requirement that the worn mass would be at least 0.3 g to minimize the scale measurement imprecision influence. To suppress the wear rate variance (see Appendix A), the number of closing cycles was additionally limited to the minimum value set to a relatively high value of \(n_{\text{min}}\) = 750 cycles.  
Figure 4: Wear rate response in dependence of cumulative dissipated energy throughout full characterization period of single friction plate [24].  
Figure 5: Number of recorded operating points for each friction plate.  
Since the friction material was hydroscopic, several measures were taken to minimize the moisture influence on the mass and, thus, wear rate measurement [27]: (i) the operating parameters imposed on a single friction plate had all the same temperature target level, (ii) each friction plate was stored overnight in a sealed container with a silica gel and dried in an electric oven for one hour at 100 \({}^{\circ}\)C at the start of each workday, (iii) prior to recording the first characterization experiment (i.e., after the oven drying), a one-hour preparatory experiment was carried out at the target temperature level (other inputs are set to their run-in values) to heat up the machine and thermally precondition the friction plate (see non-standard run-in empty magenta circle points in Figure 4), and (iv) the first regular characterization experiment weight difference in the workday was determined from the weight measurements recorded after the preparatory experiment and the subsequent wear characterization experiment (the first red square after the empty magenta circles in 4).