# Influence of Open Differential Design on the Mass Reduction Function
## 3 Design of the ODT
### Loads on the Input and Output Side of the Differential Transmission  
ODT (Figure 2) is intended for road vehicles with rear drive. In the calculated load on the output side of the transmission, according to the specified standard ISO 23509:2006 [35], this standard does not cover and analyze the detailed influence of tire characteristics on \begin{table}
\begin{tabular}{c c} \hline \hline
**Design Requirements** & **Amount** \\ \hline Maximum vehicle speed at the highest transmission ratio (\(v_{\rm max}\)), km/h & 220 \\ Time required to reach a speed of 100 km/h (\(t_{\rm 0-100}\)), s & 8.9 \\ Vehicle mass (\(m_{\rm v}\)), kg & 1550 \\ Maximum vehicle mass (\(m_{\rm v}\), max), kg & 2100 \\ Vehicle acceleration (\(a_{\rm v}\)), m/s\({}^{2}\) & 2.5 \\ Dynamic wheel radius (\(r_{\rm d}\)), mm & 394.2 \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
**Design Requirements** & **Amount** \\ \hline Maximum vehicle speed at the highest transmission ratio (\(v_{\rm max}\)), km/h & 220 \\ Time required to reach a speed of 100 km/h (\(t_{\rm 0-100}\)), s & 8.9 \\ Vehicle mass (\(m_{\rm v}\)), kg & 1550 \\ Maximum vehicle mass (\(m_{\rm v}\), max), kg & 2100 \\ Vehicle acceleration (\(a_{\rm v}\)), m/s\({}^{2}\) & 2.5 \\ Dynamic wheel radius (\(r_{\rm d}\)), mm & 394.2 \\ \hline \hline \end{tabular}
\begin{tabular}{c c} \hline \hline
**Technical characteristics of the driving machine** \\ \hline Max. engine torque (\(T_{\rm max}\)), Nm & 340 \\ Number of revolutions at which \(T_{\rm max}\) is reached (\(n_{\rm Tmax}\)), min\({}^{-1}\) & 1600 \\ Power delivered to the drive bevel gear (\(P_{1}\)), kW & 53.05 \\ Input torque to the differential transmission (\(T_{1}\)), Nm & 1108.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vehicle design requirements and technical characteristics of the driving machine. Figure 2: Kinematic chain of an ODT. transmission properties. This influence manifests in the effect of longitudinal, lateral and combined slippage on the form of traction/braking force [37]. Loads on the input side required for designing a differential transmission are determined by the technical characteristics of the drive machine, and their values are listed in Table 1.  
The engine torque is transmitted to the hypod gears of the differential transmission from the engine shaft to the gearbox, cardan shaft and drive shaft (Figure 2). For the number of revolutions \(n_{\text{Tmax}}\) (Table 1) at which \(T_{\text{max}}\) (Table 1) is achieved, the power on the motor output shaft is determined by the expression:  
\[P_{\text{O max}}=T_{\text{max}}\cdot\omega_{\text{max}}=T_{\text{max}}\cdot \frac{\pi\cdot n_{  
The friction force is determined for the case of wheel contact with asphalt according to the expression:  
\[F_{\rm f}=F_{\rm w}\cdot\mu, \tag{5}\]  
where \(\mu\) represents friction factor for asphalt surface (\(\mu\) = 0.9). The calculated amount of the friction force is presented in Table 2.  
Traction force is determined by the expression:  
\[F_{\rm TR}=2\cdot F_{\rm f}. \tag{6}\]  
The calculated amount of the traction force is presented in Table 2.  
During straight line movement of the vehicle on a dry surface, with an ODT, the torque on the drive wheels is equally divided between the left and right wheel (\(T^{\prime}{}_{\rm w}\) = \(T^{\prime}{}_{\rm L}\) = \(T^{\rm T}{}_{\rm R}\)). The torque of the drive wheels is determined by the expression:  
\[T^{\prime}_{\rm w}=T^{\prime}_{\rm L}=T^{\prime}_{\rm R}=\frac{F_{\rm TR}}{2} \cdot r_{\rm d}=1827.206\ \ {\rm Nm}. \tag{7}\]  
where \(T^{\prime}{}_{\rm L}\) and \(T^{\prime}{}_{\rm R}\) are the torques on the left and right drive wheels, \(r_{\rm d}\) is the dynamic wheel radius. Since the dimension of the tire is determined by the request (205/55 R16), the dynamic wheel radius is 97% of the length of the actual wheel radius.