## 5 Methodology
### Vehicle Electric Steering Simulation Model  
In the case of an electric vehicle, in addition to the components of the propulsion system, other relevant energy consumers should be considered, with particular attention to the impact of safety-critical system elements on consumption. Although the braking system is one of the most safety-critical components of the vehicle, its impact is not investigated in detail in this study, as recuperation is not considered and, therefore, the impact on energy consumption is negligible. In contrast to the brakes, the steering system is not negligible and its operation and impact on energy consumption are examined in detail. The implementation of power steering in vehicles has been a standard feature since the 1980s, conferring numerous benefits to drivers. In particular, when maneuvering in a parking situation, a reduced level of torque is required from the driver in order to rotate the wheels. Furthermore, the torque can be regulated in a consistent manner, thus enabling the driver to perceive a uniform torque sensation when operating the steering wheel. Regardless of the type of steering servo, these components are instrumental in maintaining the vehicle's lateral alignment. These should be calibrated to provide the driver with the optimum level of tire/road contact information using the processed sensor data collected from the inputs. From a safety perspective, it is of paramount importance to facilitate rapid response times through the provision of rapid feedback in order to circumvent the potential for accidents. The typical urban driving route comprises a high number of turning maneuvers, which has a considerable effect on the overall electric consumption of the vehicle in question. A simplified model is employed for the purpose of calculating the consumption of the system. The steering system of the test vehicle incorporates an electric motor that is integrated into the steering rack, as illustrated in Figure 8. In the simulation, the following equations were employed to calculate the electronic power steering data [64]:  
To calculate the power consumption of the power steering, we created a simplified model, as shown in Figure 8. The relationship between the steering wheel and the pinion can be expressed as follows:  
\[J_{S}\dot{\theta_{S}}=T_{d}-K_{S}(\theta_{S}-\theta_{r})-B_{S}\dot{\theta_{S}} \tag{29}\]  
where  
* \(J_{s}\) is the inertia of the steering column and the steering wheel,
* \(T_{d}\) is the torque generated by the driver,\(K_{s}\) is the stiffness of the steering column,
* \(B_{s}\) is the deboosting of the steering column,
* \(\theta_{S}\) is the steering wheel angle,
* \(\theta_{r}\) is the steering shaft angle. The system torque support equation is as follows:  
\[J_{m}\ddot{\theta_{m}}=T_{m}-K_{m}(\theta_{m}-i_{m}\theta_{r})-B_{m}\dot{ \theta_{m}} \tag{30}\]  
where  
* \(J_{m}\) is the generated inertia of the motor,
* \(T_{m}\) is the torque of the motor,
* \(K_{m}\) is the stiffness of the motor,
* \(i_{m}\) is the ratio at the end of the motor shaft,
* \(B_{m}\) is the deboost of the motor,
* \(\theta_{m}\) is the motor shaft angle. The total steering equation, which describes the relationship between the steering wheel and the steering column, is as follows:  
\[m\dot{x}=\frac{1}{r_{p}}[K_{m}(\theta_{m}-i_{m}\theta_{r})i_{m}+K_{s}(\theta_ {s}-\theta_{r})]-B_{r}\dot{x}-K_{r}x \tag{31}\]  
where  
* \(m\) is the mass of the rack and pinion,
* \(x\) is the displacement of the rack
* \(r_{p}\) is the pinion radius
* \(B_{r}\) is the rack and pinion deboost,
* \(K_{r}\) is the linear rigidity of the rack. To set up the PMSM model, we need a number of simplifying assumptions. Firstly, the saturation of the motor iron core and the influence of the leakage magnetic flux are ignored. Secondly, the eddy current and hysteresis losses in the motor are excluded. Thirdly, the motor current is considered as a symmetrical three-phase sinusoidal current. Fourthly, we assume that the air gap between the stator and rotor is evenly distributed.