Electric Vehicle Mechanics and capacity estimation for battery packs

Power point presentation on EV Design Calculations

1. Vehicle Mechanics Module 5

2. Contents Vehicle forces – tractive effort and vehicle speed, estimation of power, range, and energy consumption, rolling resistance power, downgrade force and regeneration. Sizing of power train components in a hybrid drive. Maximum speed of the vehicle. Gradeability. Vehicle acceleration. Vehicle fuel economy estimation in a hybrid drive.

3. Introduction According to Newton's second law the acceleration of an object is proportional to the net force exerted on it. Hence, an object accelerates when the net force acting on it is not zero. In a vehicle several forces act on it and the net or resultant force governs the motion according to the Newton's second law . The propulsion unit of the vehicle delivers the force necessary to move the vehicle forward. This force of the propulsion unit helps the vehicle to overcome the resisting forces due to gravity, air and tire resistance. To maximise the fuel efficiency of any vehicle the mass, aerodynamic drag and rolling resistance have to be minimised, while at the same time maximising motor and transmission efficiencies. It is particularly important to design battery electric vehicles with high efficiencies in order to reduce the mass of expensive batteries required.

4. Parameters of Electric Vehicles The design of electric vehicle includes: • Dynamics of the vehicle • Capacity and weight of the vehicle • Torque and type of motor used • Speed required • Range of the vehicle • Type of battery and • DC/DC or DC/AC power converter used

5. General description of vehicle movement The vehicle motion can be completely determined by analysing the forces acting on it in the direction of motion. The tractive force (Ft) in the contact area between the tires of the driven wheels and the road surface propels the vehicle forward. The tractive force (Ft) is produced by the power plant and transferred to the driving wheels via the transmission and the final drive. When the vehicle moves, it encounters a resistive force that tries to retard its motion. The resistive forces are • Rolling resistance • Aerodynamic drag • Uphill resistance

6. Aerodynamic Drag A vehicle traveling at a particular speed in air encounters a force resisting its motion. This force is referred to as aerodynamic drag. It mainly results from two components: • shape drag • skin friction Bearing in mind the high cost of onboard electrical energy, the aerodynamics of electric vehicles is particularly important, especially at high speeds.

7. The drag force F ad on a vehicle is The power P adw (W) at the vehicle’s wheels required to overcome this air resistance is The battery power P adb needed to overcome aerodynamic drag is obtained by dividing the overall power delivered at the wheels Padw by the overall efficiency η0 (power at wheels/battery power): where ρ is the density of air (kg m −3 ), A is the frontal area (m 2 ), v is the velocity (m s −1 ) and Cd is the drag coefficient, which is dimensionless.

8. The battery mass m b (kg) of a battery with specific energy SE (W h kg −1 ) required to overcome the aerodynamic drag at a velocity v (m s −1 ) over a distance d(m) is given by

9. Indicative drag coefficients for different body shapes

10. Rolling Resistance Rolling resistance refers to the resistance experienced by your car tyre as it rolls over a surface . The main causes of this resistance are tyre deformation, wing drag, and friction with the ground. The higher the rolling resistance is, the more energy to overcome it is needed. The higher the rolling resistance is, the more energy to overcome it is needed. Hence a considerable impact of tyre rolling resistance on fuel consumption  (and on how long your tyres will last). A 30% increase in rolling resistance generates between 3 and 5% of fuel overconsumption.

11. Rolling Resistance Several elements have an effect on  rolling resistance : tyre pressure, tread, diameter, width, or the materials used in tyres or their construction. Regarding tyre pressure for instance, studies carried out on French roads have shown that more than 50% of cars run at least 0.3 bar below the required tyre pressure. This results in a considerable increase in rolling resistance: +6% for an underinflation of 0.3 bar and +30% for underinflation of 1 bar.  The rolling drag on a vehicle F rr is given by where μ rr is the coefficient of rolling resistance. The rolling drag is independent of speed. The power needed to overcome rolling P rr is given by The value of μ rr varies from 0.015 for a radial ply tyre down to 0.005 for tyres specially developed for electric vehicles.

12. Rolling Resistance A reduction of rolling resistance to one-third is a substantial benefit, particularly for low-speed vehicles such as buggies for the disabled. For low-speed vehicles of this type the air resistance is negligible and a reduction of rolling resistance drag to one-third will either triple the vehicle range or cut the battery mass and cost by one-third – a substantial saving in terms of both cost and weight.

13. Gradient Resistance The gradient resistance, F hc in newtons along the slope for a car of mass m(kg) climbing a hill of angle ψ is given by F hc = mg sin ψ It follows that the power P hc in watts for a vehicle climbing a slope at a velocity v(m s −1 ) is given by P hc = Fhc × v = mgv sin ψ

14. Gradeability Gradeability by definition is the ability of a commercial vehicle to negotiate a grade(slope/acclivity) in Gross Vehicle Weight (GVW) condition and it can vary from 0% to 45% (maximum). A 45° gradient is equivalent to 100%. In other words, gradeability is the highest grade a vehicle can ascend maintaining a particular speed. Example: A truck with a gradeability of 7% at 60 mph can maintain 60 mph on a grade with a rise of 7%.

15. AIS – 003 – Starting Gradeability Starting Gradeability: The starting gradeability of a vehicle is the maximum gradient, on which the vehicle can start climbing from stand-still condition, with all the wheels of the vehicle on the gradient at the time of start.

16. Power required to propel the vehicle P tot = P aero + P roll + P grad (watts) Torque on each wheel, T = P tot x effective radius of the wheel (r), ( N.m ) The energy requirement per km is given by the ratio of power and velocity. (P tot /v), where v is the average velocity of the vehicle in km/hr. The capacity required per km is given by the ratio of per km power to the voltage. ( ( P tot /v ) / V ) , where V is the Voltage of the battery pack. Total capacity of the battery pack is given by, ( ( P tot /v ) / V ) × Range, Ah It is advisable to keep a factor of safety ( fos ) to account for various losses and degradation in the cells over time. This won’t let the cell’s state of charge (SoC) to be 0 and will also increase the cell’s life cycle. Required Capacity of the battery pack is given by ( ( P tot /v ) / V ) × Range x fos

17. Cells are the building blocks of a battery pack. Every cell has a specified voltage and capacity. Combining them in series and parallel connections gives the desired output. For example, using a cell having a nominal voltage of 3.6V and 3Ah capacity, the total number and configuration of battery pack can be found. The number of cells in series is given by, n s = ( V /V cell ) The number of cells in parallel is given by, n p = Capacity required /Capacity cell