Motor sizing for EV

MOTOR SIZING FOR AN ELECTRIC CAR.

         
                      Selecting the best suitable motor for electric vehicles involves maths and physics.
Our aim is to calculate the torque requirement of the vehicle under different driving condition and selecting the motor which can deliver the required amount of torque.

Factor to be considered:
1. Rolling resistance.
2. Grading resistance.
3.Aerodynamic drag.

Electric vehicle parameters required:
GVM-gross vehicle mass.
r - wheel radius,
v - velocity of the vehicle.
A = frontal area.
Cd- aerodynamic drag co-efficient.
Crr- rolling resistance co-efficient.

1.Rolling resistance.

             Rolling resistance is afforded by the floor on which the car is moving. It is also dependent on the tire material.
Frr = GVM x g x Crr.

Frr = Rolling resistive force.
Crr - depends on tyre material, road/surface type(sand, gravel, grass, asphalt), dry or wet surface.

2. Grading resistance.

During the uphill drive, due to a component of the gravitational force, the vehicle gets dragged back.

Fgr = GVM x g x sin(θ).

Fgr - Grading resistance force.

3.Aerodynamic drag.

       

   
          While driving, the car experiences the aerodynamic drag. Aerodynamic drag is more when the car is moving fast. It also depends on air density. Air density changes with temperature and height.

Fa = (0.5)x ρ x Cd x A  x v²

Cd - aerodynamic drag co-efficient. (It is calculated by tunneling method)

Total tractive force:

Ft = Frr + Fgr + Fa + (m x a)

This is the amount of force required to overcome all resistive force and put the vehicle on the motion.

Wheels Torque:

Twh = Ft x r 

r - wheel radius

Some important relations:

v = r x w

w - angular velocity

Nwh = (60 x w) / (2 x pi)

pi = 3.14

Nwh = Wheel RPM

(Not promoting Kona electric and some of the parameters are not from Hyundai official, All calculations are done considering ideal conditions with some approximations, practically the results are little different).

Let's calculate the motor torque for  KONA ELECTRIC CAR.

Kona electric car is from Hyundai automotive company. It's India's first electric SUV(sport utility vehicle). You will go mad when you hear it's range per charge, it's 452km. And you can charge it to 80% in 57 minutes using DC fast charging technique. And takes 6 hours to with a medium-fast charger at home.

Specifications:

range = 452km/charge

GVM = 1685 (when empty) + 400(5 people,80kg/person) = 2085kg. 

Crr = 0.015 -- 0.02. (in general car tire on asphalt surface).

Aerodynamic drag coefficient.

Cd = 0.29   (Nice body design 😃)

Height = 1570mm

Width =  1800mm

Frontal area = Height x width = 1.57 x 1.8 = 2.826 m²

Gear ratio(GR)  = 7.981. (Motor shaft isn't directly coupled with wheel, It is connected to gears and then to the wheel to get high torque).

Not from Kona electric car

Acceleration: 0 to 100Kmph in 9.7s wow!!!!!!  a = 2.86 m/s^2.

Get ready with pen and paper,let's do some math :

Let's take v = 50 kmph = 13.9 m/s.

v = r x w

13.9 = 0.334 x w

w = 41.61 rad/s

N(wheel) = (60 x w) /(2 x pi) 

N(wheel) = 398 Rpm.

Let's calculate the total tractive force:

Ft = Frr + Fgr + Fa + (m x a) 

Fgr = GVM x g x sin(θ)

Fgr = 2085 x 9.81 x sin(0)   -- flat road 

Fgr = 0.

Fa = (0.5)x ρ x Cd x A  x v²

Fa =(0.5)x 1.225 x 0.29 x 2.826  x (13.9)²

^{Fa = 46.98 N}

Frr = GVM x g x Crr

Frr = 2085 x 0.015

Frr = 306.495 N

Ft = Frr + Fgr + Fa + (m x a) 

Ft = 306.495 + 0 + 96.98 + (2085 x 2.86)

Ft = 462.675  + 5963.1

Ft = 6366.58 N 

Let's calculate the wheel torque.

Twh = Ft x r

Twh = 6366.58 x 0.334

Twh = 2126.43Nm  (This the wheel torque not the motor shafts)

Let's now calculate torque generated by the motor.

T(Motor):T(Wheel) = 1: GR

T-motor = 266.438 Nm

But motors won't be 100% efficient.

Let's consider 90% efficiency.

Tmotor = 266.438/0.9 = 296.04Nm.

Motor power:

Pm= Tmotor x w(motor)

so Nmotor = Nwh x GR

Nm = 398 x 7.981

Nm = 3176 rpm

w= (2 x pi x Nm)/60

w(motor) = 331.63 rad/s

Pm= Tmotor x w(motor)

Pm = 296.04 x 331.63

Pm = 98kw (approx)

This is not a peak or minimum or average power, it's for v = 13.9s

To get peak toque we need to consider the proper vehicle drive cycle and calculate peak and nominal power. In future articles, this will be covered.

By Madhukumar.s