Modelling and performance analysis of free body dynamics of electric vehicles

ABSTRACT


INTRODUCTION
The rapid growth in the popularity of electric vehicles (EVs) has revolutionized the automotive industry, offering a sustainable and eco-friendly alternative to conventional internal combustion engine vehicles.The modelling and performance analysis of free body dynamics in electric vehicles (EVs) has gained significant attention in recent years.Free body dynamics refers to the study of forces and motions acting on the vehicle body, excluding the powertrain components.Understanding and accurately modelling these dynamics are crucial for optimizing the vehicle's behavior, handling, stability, and overall performance.
As the automotive industry shifts towards electric mobility, there is a growing need to develop advanced modelling techniques that capture the unique characteristics of electric vehicles.Compared to conventional internal combustion engine vehicles, EVs have different weight distributions, power delivery mechanisms, and handling characteristics.Therefore, specific modelling approaches are required to accurately represent the forces and motions acting on the EV body.The modelling process involves developing mathematical representations that consider various factors influencing the vehicle's dynamics.These factors include weight distribution, suspension characteristics, tire properties, and aerodynamic forces.By incorporating these elements into the model, researchers can simulate and analyze the vehicle's behavior under different operating conditions, such as acceleration, braking, and cornering.Performance analysis is a crucial aspect of studying free-body dynamics in EVs.Through simulations and experimental tests, researchers can evaluate key performance metrics such as vehicle response, stability limits, and ride comfort.These analyses provide insights into the vehicle's handling characteristics, allowing for the identification of areas for improvement and optimization.Optimizing the free-body dynamics of electric vehicles offers several benefits.Firstly, improved handling and stability contribute to enhanced driving experience and safety for EV users.By accurately modelling the forces and motions acting on the vehicle body, potential issues such as excessive body roll, understeer, or oversteer can be identified and addressed during the design phase.Secondly, optimizing the vehicle's dynamics can lead to improved energy efficiency and range.By reducing unnecessary energy losses due to excessive body movements or inefficient weight distribution, EVs can achieve better overall efficiency and extended driving range.Moreover, the findings from modelling and performance analysis studies in free body dynamics can inform the development of advanced driverassistance systems (ADAS) and autonomous driving technologies.Understanding how the vehicle body responds to external inputs and disturbances is crucial for designing robust control algorithms that enhance safety and stability in various driving conditions.
The modelling and performance analysis of free body dynamics in electric vehicles is essential for understanding and optimizing the behavior, handling, and stability of EVs.The unique characteristics of electric vehicles necessitate specific modelling approaches to accurately represent the forces and motions acting on the vehicle body.By analyzing the performance of EVs under different operating conditions, researchers can improve handling, enhance safety, optimize energy efficiency, and contribute to the development of advanced driver-assistance systems.Continued research and advancements in this field are crucial for realizing the full potential of electric vehicles and promoting sustainable and efficient transportation systems.
The modelling and performance analysis of the power drivetrain in electric vehicles (EVs) has been the subject of extensive research and development efforts.This literature review provides an overview of key studies and advancements in this field, highlighting the contributions and findings of previous research.The modelling of individual components within the power drivetrain is a crucial aspect of understanding their behavior and optimizing system performance.Several studies have focused on the accurate modelling of electric motors, considering factors such as electromagnetic behavior, power losses, and efficiency.A comprehensive model for a permanent magnet synchronous motor (PMSM) that captured the motor's torque characteristics and performance under various load conditions was developed [1].Similarly, a model for an induction motor, incorporating parameters such as stator and rotor resistance, inductances, and iron losses was proposed [2].
Battery modelling is another critical area of research in power drivetrain analysis.Researchers have aimed to capture the battery's behavior, including state of charge, voltage drop, and internal resistance.A battery model was developed that accounted for capacity fading and ageing effects, providing accurate predictions of the battery's performance over time [3].A comprehensive model was proposed for lithium-ion batteries that considered temperature variations and voltage hysteresis effects, enabling accurate characterization of battery behavior under different operating conditions [4].Power electronics components, such as DC-DC converters and inverters, also play a significant role in power drivetrain analysis.Researchers have developed models to analyze their impact on power transfer efficiency and system dynamics.A model for a bidirectional DC-DC converter was proposed that considered switching losses and control strategies, enabling accurate performance analysis of the converter within the power drivetrain system [5]- [7].Performance analysis is crucial for evaluating the efficiency and effectiveness of power drivetrain systems in electric vehicles.Researchers have conducted simulations and experimental tests to assess various performance metrics.The impact of different electric motor control strategies on powertrain efficiency and dynamic response was investigated [8]- [10].Field-oriented control, direct torque control, and sensor less control techniques, highlighting the trade-offs between efficiency and control complexity were compared during the instigation.Performance analysis of different battery management strategies was conducted, considering factors such as energy efficiency, charging time, and battery lifespan [11]- [14].
Furthermore, optimization techniques have been employed to improve the performance of power drivetrains in electric vehicles.A multi-objective optimization framework was proposed that simultaneously considered powertrain efficiency, energy consumption, and cost [15]- [18].The study demonstrated the potential for optimizing motor sizing, battery capacity, and gear ratios to achieve superior performance in terms of energy efficiency and cost-effectiveness.A hybrid optimization algorithm combining a genetic algorithm with a particle swarm optimization to optimize the powertrain control strategy, resulting in improved energy efficiency and reduced energy consumption [19]- [22].The integration of advanced control algorithms and energy management systems has been a focal point in power drivetrain analysis.Researchers have explored the use of model predictive control (MPC) and artificial intelligence techniques to optimize power distribution and improve overall system performance.MPC-based energy management strategy for hybrid electric vehicles, considering factors such as driver demand, traffic conditions, and energy availability was developed.The study demonstrated improved fuel economy and emissions reduction compared to traditional control strategies [23]- [26].
Modelling and performance analysis of free body dynamics of electric vehicles (Rajalingam Sakthivelsamy) The literature review highlights significant advancements in the modelling and performance analysis of power drivetrains in electric vehicles.Researchers have developed comprehensive models of individual components, conducted performance analyses, and explored optimization techniques and control strategies.These studies provide valuable insights for designing and optimizing power drivetrains, ultimately leading to more efficient and reliable electric vehicles and contributing to the transition to a sustainable transportation future.

PROPOSED METHOD
A battery, motor, power electronic controller, power converter, and vehicle body make up the proposed method as shown in Figure 1.The shaft of the vehicle is joined to the motor.The motor is connected to batteries and a controller through a power converter.The power converter modifies the voltage delivered to the motor, which modifies the vehicle's speed.The performance analysis of the proposed system is carried out using MATLAB.Modelling of an electric two-wheeler was performed and based on the mathematical modelling, the vehicle was constructed in the software and simulated for analysis.

Components of the proposed system
The real-world components such as a battery, motor, controller, converter and vehicle body are available in the MATLAB Simulink/Simscape library.These Simulink/Simscape components help us to construct and analyze the performance of the proposed electric vehicle.To analyze the free body dynamics, components such as vehicle body, and tire is enough.To measure the speed and distance covered, an ideal translational motion sensor will be used.The details of such components are discussed in this section.For the design of the dimension and chassis of a vehicle, the component "vehicle body" from the Simscape library is used and it represents a two-axle vehicle body that includes specifications such as body mass or kerb weight, aerodynamic drag force, road inclination and weight distribution due to acceleration and road profile.The number of wheels on each axle shall be adjustable.Horizontal motion (H) acts as the mechanical translational port for the vehicle body.Headwind speed (W) and road inclination angle act as input to this component.The output of these components is the velocity (V), normal front wheel force (NF) and normal rear wheel force (NR).
The component "tire magic formula" from the Simscape library is used to represent the vehicle tire.The effect of tire inertia and rolling resistance shall be included as specifications.Port A act as the mechanical rotational port and port H act as the mechanical translational port for the wheel hub.N is the input port that represents the normal force acting on the tire.S is the output port that represents the tire slip.The component "ideal translation motion sensor" from the Simscape library is used to measure the acceleration, velocity, and displacement or distance covered by the vehicle.The output ports A, V and P report the acceleration, velocity, and position of port R relative to port C.

Modelling
Modelling of the proposed model is carried out in MATLAB Simulink and Simscape environment.The shaft of the vehicle is joined to the motor.MATLAB Simulink and Simscape are powerful software tools developed by MathWorks that offer simulation and modelling capabilities for engineers and scientists across various disciplines.
MATLAB Simulink is a block diagram environment that enables users to model, simulate, and analyze dynamic systems.It provides a graphical user interface where users can build models by connecting functional blocks representing system components and specifying their interconnections.Simulink offers a wide range of pre-built blocks and libraries for modelling electrical, mechanical, control, and signal processing systems.Users can simulate their models and analyze system behavior, making it an invaluable tool for system design, optimization, and validation [27].
On the other hand, Simscape is a physical modelling toolbox within Simulink that focuses on the simulation of physical systems [28].It utilizes a component-based modelling approach, where system components are represented by fundamental physical elements such as resistors, capacitors, springs, and dampers [29].Simscape allows engineers to build complex multi-domain physical models that capture the interactions between mechanical, electrical, hydraulic, and thermal components.This enables the simulation and analysis of dynamic systems in a comprehensive and realistic manner [30].
Both Simulink and Simscape offer powerful simulation capabilities with a wide range of built-in solvers, allowing users to study system behavior under various conditions and evaluate performance metrics.These tools are widely used in industries such as automotive, aerospace, energy, and robotics for tasks such as control system design, powertrain analysis, mechatronic system development, and virtual prototyping.Moreover, Simulink and Simscape provide integration with MATLAB, allowing users to incorporate custom algorithms, perform data analysis, and automate complex workflows.The tools also support code generation, enabling the implementation of real-time systems and the deployment of models onto hardware platforms.The various specifications used to model the proposed vehicle is shown in Table 1.Tire modelling is done with a rolling radius of 9 inches.The tire inertia is 1×10-3 and with an initial velocity of 0 rad/s.The rolling resistance constant is 0.005.The horizontal distance from the centre of gravity to the front axle 615 mm 5 The horizontal distance from the centre of gravity to the rear axle 666 mm 6 CG height above ground 200 mm 7 Frontal area 1.12 m 2 8 Drag coefficient 1.2 9 Air density 1.3 kg/m 3

RESULTS AND DISCUSSION
The performance analysis of the proposed vehicle is discussed in this section.The specification of the proposed system is compared with the available market vehicle as shown in Table 2. Key parameters such as Ker weight, maximum load capacity, length of the vehicle body, width of the vehicle body and ground clearance are considered for effective comparison and analysis.The term weight is the total mass of the vehicle body with all parts and fuel excluding the load or passenger.The MATLAB Simscape/Simulink diagram of the proposed free-body vehicle is shown in Figure 2. All 'H' port of the tire and the vehicle body is connected.The normal front (NR) wheel and normal rear (NR) wheel force of the vehicle body is connected normal force (N) of the tire.The Simscape component "rotational free end" is connected to port 'A' of the tire since the motor is not connected, as it is free body modelling.
The headwind speed is negligibly small for horizontal free body analysis; hence it is ignored the performance analysis at the inclination angle or gradient of 0 rad, 10 rad and -10 radian has been simulated.When the gradient is zero, there is no motion.At the negative gradient of -10 rad, the vehicle starts to move in the forward direction and it reaches the maximum speed of 82.23 km/hr.It also reaches 13.48 km or 13480 m in 10 minutes.The simulation results at the negative gradient of -10 rad are shown in Figure 3. From the simulation results, it is also found that it takes 78 seconds to reach the maximum speed of 82.23 km/hr.
At the positive gradient of +10 rad, the vehicle starts to move in the reverse direction and it reaches the maximum speed of 82.23 km/hr.It also reaches 13.48 km or 13480 m in 10 minutes in the reverse ISSN: 2088-8694  Modelling and performance analysis of free body dynamics of electric vehicles (Rajalingam Sakthivelsamy) 5 direction.The simulation results at the positive gradient of +10 rad are shown in Figure 4. From the simulation results, it is also found that it takes 78 seconds to reach the maximum speed of 82.23 km/hr.The performance of the proposed vehicle is compared with the existing market vehicles.Table 3 shows the simulated results of various existing electric vehicles with the proposed vehicle.The comparison results show that the proposed model achieves a speed that is higher than other vehicles.The proposed model takes 78 seconds to reach its maximum which is higher than the existing models.The distance covered at 10 minutes is also higher comparatively.The higher free body performance analysis reveals that the steady state capability is greater than the existing vehicle models.The initial torque requirement will be a little higher whereas the steady-state torque requirement will be lower than other models.Thus, the proposed model will have better steady-state stability and higher distance coverage.This can be further developed by connecting suitable batteries, motors and controllers to analyze the performance of power drive train characteristics.By conducting simulations of power drive train modelling, researchers can assess key performance metrics, such as power output, torque characteristics, energy consumption, and thermal management.

CONCLUSION
The modelling and performance analysis of free body dynamics in electric vehicles is essential for optimizing their performance, enhancing safety, and promoting sustainable and efficient transportation systems.To analyze the performance of vehicle dynamics, the modelling of the proposed vehicle is developed in MATLAB Simulink and Simscape environment.Various dynamic forces such as rolling resistance force, aerodynamic force, and hill-climbing force were considered for modelling.From the simulated results, it is shown that the maximum speed of 82.23 km/hr.and the distance covered in 10 minutes is 13.46 km which is the highest in the category.The Proposed model has better performance with greater speed dynamics and long-distance coverage validating the better stability.The comparative analysis shows the current market trend in the dynamics and the gap to improve.This article shall be further developed by connecting different power drive train systems and their performance such as power output, torque characteristics, energy consumption, and thermal management shall be analyzed accordingly.In conclusion, the modelling and performance analysis of free body dynamics of electric vehicles holds immense promise in researching for budding young researchers to start in the area of electric vehicle technologies to analyze its various performance characteristics.

Figure 1 .
Figure 1.Block diagram of the proposed model

Table 1 .
Free-body specification of the proposed vehicle

Table 2 .
Comparison of the proposed system with the existing model