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

which motor suits the best for this vehicle?

Motor is the most important part of an electric vehicle as motor is the sole machine which is running the vehicle. Motor being a major device converting electrical energy into mechanical energy to bring the vehicle into motion, we need to consider important parameters in selecting the motor those are horsepower, efficiency, life, starting torque, speed, cost, size, weight and its characteristics under operating conditions. In this report, the selection of motor is done considering the reduction of overall wieght and cost of the vehicle. A brushless direct current motor is best suited for this type of vehicle. BLDC motor is a synchronous motorpower by a dc source through a switching power supply. The rotor of this motor is a permanent magnet synchronous motor. Although there are many technical details for the selection of BLDC motor to run the vehicle, a brief note of avantages are as follows while the others can be viewed through the reference. BLDC motor commutation is done based on rotor position information, high efficiency as voltage drop on electronic device is smaller than that on brushes, no maintenance as the brushes are absent, lower acoustic noises due to absence of arcs from the brushes to generate noise, greater dynamic response due to lower rotor inertia because of permanent magnets, smaller and lighter in weight , better speed vs torque characteristics as there is no brush friction to reduce useful torque, higher speed range as no mechanical limitation is offered by brushes or commutatotrs, better thermal performance as only the armature windings generate heat, which is the stator and is connected to the external part of BLDC motor and longer life. Due to the above mentioned advantages the BLDC motor is recommended in this report. The mechanical force required to move the vehicle and the force required to move the wheel can be revied from the reference. Force required to move the wheel is generated from reference. Input electrical power is equal to sum of the output mechanical power and power losses due to copper winding in armature. Field copper losses are neglected.

As for the complete details about BLDC motors, you can take time and google it. There are lots of websites giving you information about them.

For calculation of motor properties please wait till the next post.