# Influence of Drivetrain Hybridization on Transmission Lifetime
## 4 Summary, Conclusions and Outlook
For this purpose, condensed durability tests mentioned in the introduction can be carried out on a test bench, or the manufacturer's return data can be evaluated. Furthermore, the control influences of the modeled TCU and HCU (e.g., calibration) should be validated. Specific use cases should be investigated through more detailed and usage-specific, experimental cycles, taking special events into account. In the future, both the method and the model can be used for more detailed investigations. For example, the influences of a variation in operating strategy, transmission layout or components can be systematically quantified. Conceptualization, C.H., S.N. and K.W. ; methodology, C.H., G.J., S.N. and K.W. ; formal analysis, C.H. ; writing--original draft preparation, C.H. and K.W. ; writing--review and editing, G.J. and S.N. ; supervision, G.J. and S.N. All authors have read and agreed to the published version of the manuscript. This research was funded by the European Regional Development Fund (ERDF) as part of the research project DUETT (Diesel hybrid vehicles for environmentally conscious mobility: networked system development in a physical and virtual environment). Reference number ERDF-0800852. The authors declare no conflict of interest. \(\dot{\phi}_{\rm wheel,r}\) Right wheel angular velocity (s\({}^{-1}\))  
a\({}_{\rm ISO}\) Life modification factor (1)  
b Shape parameter (1)  
B\({}_{\rm 10}\) Bearing lifetime with a failure probability of 10%  
c Stiffness (Nm\(\cdot\)rad\({}^{-1}\))  
C Dynamic load rating (N)  
d Damping (N\(\cdot\)m\(\cdot\)s\(\cdot\)rad\({}^{-1}\))  
d\({}_{\rm G}\) Gear diameter (mm)  
d\({}_{\rm m}\) Mean bearing diameter (mm)  
D Damage (1)  
f\({}_{\rm d0}\) Driving resistance parameter (N)  
f\({}_{\rm d1}\) Driving resistance parameter (N\(\cdot\)s\(\cdot\)m\({}^{-1}\))  
f\({}_{\rm d2}\) Driving resistance parameter (N\(\cdot\)s\({}^{2}\)\(\cdot\)m\({}^{-2}\))  
F\({}_{\rm a}\) Axial gear force (N)  
F\({}_{\rm b}\) Bearing force (N)  
F\({}_{\rm A}\)(t) Axial force (N)  
F\({}_{\rm B}\)(t) Failure probability of all bearings over time (1)  
F\({}_{\rm drag}\) Driving resistance force (N)  
F\({}_{\rm i}\) Force i  
F\({}_{\rm j}\)(t) Failure probability of a single bearing j over time (1)  
F\({}_{\rm r}\) Radial gear force (N)  
F\({}_{\rm t}\) Tangential gear force (N)  
F\({}_{\rm R}\)(t) Radial force (N)  
i Index (1)  
i\({}_{\rm G}\) Gear ratio (1)  
j Index (1)  
J Inertia (kg\(\cdot\)m\({}^{2}\))  
k Number of load classes (1)  
l Length of a shaft section (mm)  
L\({}_{\rm i}\) Bearable number of rotations of a load class i  
m Vehicle mass (kg)  
M\({}_{\rm i}\) Moment i (N\(\cdot\)m)  
n\({}_{\rm i}\) Number of bearing revolutions in a load class i  
p Lifetime exponent (1)  
P(t) Dynamically equivalent bearing load (N)  
P\({}_{\rm i}\) Dynamically equivalent bearing load of a load class i  
r\({}_{\rm tire}\) Tire radius (m)  
t time (s)  
t\({}_{\rm 0}\) Failure free time (h)  
t\({}_{\rm EM}\) EM time constant (s)  
t\({}_{\rm ICE}\) ICE time constant (s)  
Tcycle Cycle duration (s)  
Tact,EM Acting EM torque (N\(\cdot\)m)  
Tact,ICE Acting ICE torque (N\(\cdot\)m)  
Tact,MB Acting MB torque (N\(\cdot\)m)  
Tdem,brk Demand deceleration torque (N\(\cdot\)m)  
Tdes,EM Desired EM torque (N\(\cdot\)m)  
Tdes,ICE Desired ICE torque (N\(\cdot\)m)  
Tdes,MB Desired MB torque (N\(\cdot\)m)  
Tdrag Equivalent driving resistance torque (N\(\cdot\)m)  
TGear torque (N\(\cdot\)m) \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value and Unit** \\ \hline \(\mathrm{f_{d0}}\) & 160 N \\ \(\mathrm{f_{d1}}\) & 4 N\(\cdot\)s\(\cdot\)m\({}^{-1}\) \\ \(\mathrm{f_{d2}}\) & 0.37 N\(\cdot\)s\({}^{2}\)\(\cdot\)m\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bearing parameters. Position according to Figure 2. Dynamic load rating C and mean diameter \(\mathrm{d_{m}}\).