Dynamic calculations of electric vehicle with BLDC motor

We require a  BLDC motor which can sustain a load torque of 25.4291 N-m (according to equation 3). A BLDC motor with ratings 48V, 29A, 32.92 N-ms considered. The mathematical calculations for the BLDC motor are as follows:

P_electrical = P_mechanical + P_{copper losses}                                         (1)

Where,

P_electrical is input electrical power in watts

P_mechanical is output mechanical power in watts

P_{copper losses} is copper losses i.e. I²R losses in watts

P_electrical = V*I                                                         (2)

Where,

V is supply voltage in volts (48V)

I is current in amps (29A)

Therefore, P_electrical = 48*29 = 1392 W

Load torque need to be calculated to know the amount of torque required to move the vehicle. It is also essential in selecting a perfect motor for the desired qualities.

T_load = F*r*µ                                                                              (3)

Where,

T_load is load torque in N-m

F is the force required to spin the wheel in Newton =251.40N (from force equation)                         

R is the radius of the wheel in meters = 0.2023m

µ is the coefficient of friction = 0.5

Therefore, T_load = 251.40*0.2023*0.5 = 25.4291 N-m

Considering the BLDC motor with torque greater than or equal to the load torque (T_load) with an output speed of 300 rpm and output torque of about 32.62 N-m.

P_mechanical = T_m*ω                                                                   (4)

Where,

T_m is motor torque in N-m i.e. 32.62 N-m

ω is angular velocity in rad/sec i.e. ω_rpm*(2π/60)

Therefore, P_mechanical = (2πNT_m)/60 = (2*3.14*300*32.62)/60 = 1024.268 W

P_{copper losses} = I²R                                                                        (5)

Therefore, P_{copper losses} = 29²*0.139 = 116.899 W

                                                                                                      (6)

Therefore, Efficiency =  = 81.98%

Horse Power (1hp=750W)	1hp
Operating voltage	48 v
Operating current	15.62A
Starting /max current	29A
Maximum torque	32.62 N-m
Maximum output speed	300 rpm