# 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
Its calculation amount is shown in Table 1.  
Therefore, the torque of the hypoid ring bevel gear (\(T^{\prime}{}_{2}\)), which was obtained without including the losses of the kinematic chain, is equal to the sum of the torques of the left (\(T^{\prime}{}_{\rm L}\)) and of the right (\(T^{\prime}{}_{\rm R}\)) drive wheels. This torque is determined by the expression:  
\[T^{\prime}_{2}=T^{\prime}_{\rm L}+T^{\prime}_{\rm R}=3654.412\ \ {\rm Nm}. \tag{8}\]  
In order to obtain the real value of the torque of the hypoid ring bevel gear (\(T_{2}\)), it is necessary to include in the calculation the losses of the open differential transmission, i.e., efficiency of the open differential (\(\eta_{\rm d}\)). For the determination of \(T_{2}\), it is necessary to determine the output power of the differential transmission. This calculation includes the efficiency of the open differential (\(\eta_{\rm d}\)). The output power of the differential transmission is determined by the expression:  
Figure 2:0  
The calculated amount of \(P_{2}\) is presented in Figure 2:1 Hence, the torque of the hypoid ring bevel gear is determined by the expression:  
Figure 2:2  
where \(\omega_{2}\) is the angular velocity of the hypoid ring bevel gear. The angular velocity of the hypoid ring bevel gear is determined by the expression:  
Figure 2:3 \begin{table}
\begin{tabular}{c c} \hline
**Differential Transmission Forces and Torques** & **Amount** \\ \hline Total resistance force of driven machine (\(F_{\rm TRD}\)) & 8681.66 \\ Torque of the hypoid ring bevel gear (\(T_{2}\)), Nm & 3546.31 \\ Torque of drive wheel (\(T_{\rm W}\), \(T_{\rm R}\), \(T_{\rm L}\)), Nm & 1773.16 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._where \(i_{\rm d}\) is the transmission ratio of the differential transmission (Table 2). The transmission ratio of the differential transmission is determined by the expression:  
\[i_{\rm d}=\frac{T_{2}^{\prime}}{T_{1}}. \tag{12}\]  
The final amount of torque \(T_{2}\) is shown in Table 2. Also, the final amounts of the torque on the drive wheels are equally divided between the left and right wheels (\(T_{\rm w}=T_{\rm L}=T_{\rm R}=T_{2}/2\)). Their calculated amounts are presented in Table 2.  
Rolling resistance force, rising resistance force and vehicle's inertial force, together determine the total resistance force of the driven machine. These forces represent loads on the output side of the differential transmission. The sum of these forces represents the total resistance force of the driven machine (\(F_{\rm TRD}\)), whose calculation value is presented in Table 2. In the calculation of the total resistance force, the geometry of the vehicle body is not defined, and therefore air resistance is not included in this calculation [38]. In order to achieve the movement of the vehicle, the amount of the traction force (\(F_{\rm TRD}\)) should be greater than the amount of the total resistance force (\(F_{\rm TRD}\)). The values of these forces are presented in Table 2.  
The rolling resistance force is the result of tire deformation at the point of contact with the ground. This force is calculated by the expression:  
\[F_{\rm RO}=f_{\rm RO}\cdot G_{\rm v}, \tag{13}\]  
where \(f_{\rm RO}\) is the rolling resistance factor. The amount of this factor for rolling on the asphalt is \(f_{\rm RO}=0.02\). The calculated amount of this force is presented in Table 2.  
The rising resistance force is a component of the weight force vector that acts in the opposite direction to the motion of the vehicle, at the moment when the vehicle climbs the slope. This force is calculated by the expression:  
\[F_{\rm RI}=G_{\rm V}\cdot\sin\gamma, \tag{14}\]  
where \(\gamma\) is the rising angle (slope angle) for road vehicles (\(\gamma=6^{\circ}\)).