# Modeling of Dry Clutch Wear for a Wide Range of Operating Parameters
## 8 Validation and Analysis of Overall Wear Model
### Model Analysis  
For the sake of overall wear model response analysis, the response of absolute and relative width of 95% CI is calculated for the following predefined clutch plate wear levels: 10%, 20%, 50% and 100%. The friction plate is considered to be worn-out (the level of 100%) when the worn depth of friction material is equal to 1 mm. The run-in phase is omitted from the analysis and the modeling operating points are involved.  
A preparatory procedure for calculating the worn volume 95% CI width is executed in two steps: (i) select the wear level \(x\) in percentage (e.g., 20%) and an operating point (among 101 modeling points from Figure 3), (ii) calculate the related wear rate expectation \(w_{\mu}\) and standard deviation \(w_{\
u}\) using the models (15) and (21), respectively, and determine the mean recorded dissipated energy per one cycle \(E_{1}\). The worn volume expectation and standard deviation per one cycle are then determined as: \(\Delta V_{w,\mu,1}=w_{\mu}E_{1}\) and \(\Delta V_{w,\
u,1}=w_{\sigma}E_{1}\), respectively, while after \(n_{x}\) cycles they read: \(V_{w,\mu}=n_{x}\Delta V_{w,\mu,1}\) and \(V_{w,\
u}=\sqrt{n_{x}}\Delta V_{w,\sigma,1}\) (see Appendix A for mathematical background). Thus, the expected number of cycles needed to wear out the plate up to the selected level \(x\) [%] can be determined as:  
\[n_{x}=\frac{x}{100}\frac{V_{w,total}}{\Delta V_{w,\mu,1}}, \tag{24}\]  
where \(V_{w,total}\) is the fully worn plate volume.  
Figure 18: Cycle-wise validation results for floating (**a**) and constant (**b**) temperature conditions.  
The 95% CI of worn volume after \(n_{x}\) cycles is defined as two standard deviations around the expected value \(V_{w,\mu}\):  
\[95\% CI_{Vw}(n_{x})=2V_{w,\sigma}=2\sqrt{n_{x}}\Delta V_{w,\sigma,1}. \tag{25}\]  
The relative 95% CI width is calculated by dividing the above absolute width with the expected worn volume after \(n_{x}\) repetitive cycles:  
\[95\% CI_{rvlvw}(n_{x})=\frac{2V_{w,\sigma}}{V_{w,\mu}}=\frac{2\sqrt{n_{x}}w_{ \sigma}E_{1}}{n_{x}w_{\mu}E_{1}}=\frac{2w_{\sigma}}{w_{\mu}\sqrt{n_{x}}}. \tag{26}\]  
Hence, the absolute width of 95% CI is proportional to \(\sqrt{n_{x}}\), while the relative width of 95% CI is inversely proportional to \(\sqrt{n_{x}}\).  
Figure 19 shows the absolute and relative widths of 95% CI for 101 modeling points from Figure 3 and the four wear levels. The same results are presented in Figure 20 in a different, wear response form. These results confirm that the absolute CI width grows with the wear level, while the relative CI reduces as the clutch is more worn. Hence, as the clutch wears out the confidence to the model prediction according to the expectation value reduces in the absolute sense, but it grows in the generally more relevant relative sense (see also validation results in Figure 18). The relative width ranges from around 7% to 33% for 10% wear level, but it falls down to low values in the range of around 3% to 10% for the fully worn-out plate. Figures 19 and 20 also reveals that higher the expected wear rate, the larger is the wear rate (and worn volume) variability, both in absolute and relative 95% CI width sense (see monotonic