STUDY OF ELECTRIC SCOOTER MOTOR
AIM:
1. To calculate the maximum speed of the motor used in electric scooter.
2. To calculate the vehicle propulsion power using Excel.
3. To calculate total traction power by varying rolling resistance.
4. To study the gradeability, average speed and forces acting on the range rover sport car.
KEYWORDS: Electric Scooter, Motor, Traction, Excel, Gradeability, Range rover.
SOFTWARE: Matlab, Excel
OBJECTIVE:
1. Calculating speed of the motor by given tire specification, gear ratio and velocity of the vehicle.
2. Calculating vehicel propulsion power by using given input data and proper formula.
3. Calculating total traction power for different rolling resistance and obtain the difference of total traction power.
4. By gonethrough the video, study the gradeability, average speed and forces acting on the car.
Introduction:
Study 1:-
( i ) . Tyre Specification: 90/100 R10 53J
where,
90 indicates width of tyre in mm
100 indicates aspect ratio (H/W) i.e., the ratio of tyre height to the width of the tyre
i.e., (H = W) for 100.
R indicates the radial construction.
Radial Constructed tyres utilizes a series of steel cords, extending from the beads and across the tread, so that the cords are laid at approximately right angles to the centre line of the tread, and parallel to each other, as well as belts directly beneath the tread.
Advantage of Radial construction,
- Due to the all steel radial construction the sidewall of a radial tyre is more flexible compared to a bias tyre.
- Less rolling resistance
- Lower fuel consumption
- More grip and greater ride comfort at greater speeds.
10 indicates the rim diameter of the wheel in inches.
1 inch is equal to 0.0254 meter
53 indicates the load index which the maximum load withstand the tyre (206 kg)
J indicates the speed range of the tyre in full load (approx. 100 kmph)
Given:
W = 90mm = 0.09 m
H = 90mm = 0.09 m
dr = (10*0.0254) = 0.254 m
dw = (dr + 2H)
dw = (0.254 + 2*0.09) = 0.434 m
rw = dw/2 = 0.217 m
Gear ratio (G) = 7
Velocity (V) = 90kmph
Angular velocity,
w = (G*V)/rw
w = (7 * 90 * 5) / (18 * 0.217)
1 kmph is equals to (5/18) meter per second
w = 806.45 rad/s
1 radians per second = 60/2pi rpm
therefore,
N = (806.45 * 60) / (2 * 3.142)
N1 = 7700 rpm
( ii ). Tyre Specification: 90/90 R18 51P
where,
90 indicates width of tyre in mm
90 indicates aspect ratio (H/W) i.e., the ratio of tyre height to the width of the tyre
i.e., (H = 0.9*W).
R indicates the radial construction.
18 indicates the rim diameter of the wheel in inches.
1 inch is equal to 0.0254 meter
51 indicates the load index which the maximum load withstand the tyre (195 kg)
P indicates the speed range of the tyre in full load (approx. 150 kmph)
Given:
W = 90mm = 0.09 m
H = 81mm = 0.081 m
dr = (18*0.0254) = 0.457 m
dw = (dr + 2H)
dw = (0.457 + 2*0.081) = 0.619 m
rw = dw/2 = 0.309 m
Gear ratio (G) = 7
Velocity (V) = 90kmph
Angular velocity,
w = (G*V)/rw
w = (7 * 90 * 5) / (18 * 0.309)
1 kmph is equals to (5/18) meter per second
w = 566.34 rad/s
1 radians per second = 60/2pi rpm
therefore,
N = (566.34 * 60) / (2 * 3.142)
N2 = 5407 rpm
Study 2 & 3:-
Calculating Total tractive force,
Total tractive force is the sum of Rolling resistance force and Air drag force
1. Fa = 0.5 * Cd * p * A * V^2
It is the force of wind or air resistance pushing opposite direction to the motion of the object.
where,
Fa = Aerodynamic drag force (N)
Cd = Coefficient of drag
p = density of air (kg/m3)
A = Frontal area (m2)
V = velocity (m/s)
2. Fr = Mu * m * g
The driving force applied to the wheel produces a moment to balance the rolling resistance moment.
where,
Fr = Rolling resistance force (N)
Mu = Coefficient of Rolling resistance
m = Mass of the vehicle (kg)
g = Acceleration due to gravity (m/s2)
3. Pa = Fa*V
where,
Pa = Aerodynamic drag power (kW)
4. Pr = Fr*V
where,
Pr =Rolling resistance power (kW)
MATLAB CODE:
#1
% Calculation of difference of Total power with 15% reduction and without reduction
clear all
close all;clc
% Variation of Speed in meter per second
V = linspace(1,42,42);
% Data taken from SUV car
A = 3.44; % Frontal Area
p = 1.25; % Density of Air
Cd = 0.6; % Coefficient of drag
Rr = 0.018; % Coefficient of Rolling resistance
Rr1 = 0.036; % Coefficient of Rolling resistance for reduction in tire pressure
m = 3100; % Mass of total Vehicle (Kerb weight + Payload)
g = 9.81; % acceleration due to gravity (m/s2)
% Total traction Force in Newton
Fte = ((Rr*m*g) + (0.5*p*A*V.^2*Cd));
% Total traction Force for 15% reduction in tire pressure
Fte1 = ((Rr1*m*g) + (0.5*p*A*V.^2*Cd));
% Total Power calculation in kW
Pte = (Fte.*V)/1000;
% Total Power calculation for 15% reduction in tire pressure
Pte1 = (Fte1.*V)/1000;
% Converting Speed to kmph
Vel = V.*3.6;
% Plotting Velocity vs Total Power
plot(Vel,Pte)
hold on
plot(Vel,Pte1)
xlabel('Velocity (kmph)' )
ylabel('Power (kW)')
grid onBy increase in rolling resistance, the force also increases which means the force acting on the tyre is more.
Refer Excel sheet1 for Total power calculation without any reduction in tyre pressure and sheet2 for with 15% reduction in Tyre pressure.
https://drive.google.com/open?id=1zHD_6ZMUCfAreCMX29uJoHUJWXIOnyVI
Calculation of total tractive power without reduction in tyre pressure
Calculation of difference in total power with 15% reduction in tyre pressure
LIMITATION:
1. As the mass of the vehicle increases, the motion of the vehicle decreases which inturn the power required to achieve the particular velocity is more.
2. The rolling resistance force increases by increasing the coefficient of rolling resistance which depends on the tyre prerssure which defines that the force acting on the tyre is more which causes the reduce in velocity.
3. Aerodynamic drag force depends on the coefficient of drag, surface and frontal area which is directly proportional. The drag is less when the surface is smooth than roughened surface which is also called as skin friction.
Study 4:-
By gonethrough the video of Range rover sport dragon challenge, the gradability can be calculated by,
Gradability = tan(Theta) = (opposite / adjecent)*100
where,
Theta is 45 degree which is mentioned in the video (3:30 sec), from this reference calculating the grade of the vehicle.
Gradability = tan(45)*100
Gradability = 100%
The steepness of grade that a motor vehicle is capable of climbing at efficient speed.
The car is about to travel 99 turns and climb 999 steps at the slope. The average speed of the car while turning is maintained around 80-100 kmph at 5000 rpm. The average speed of the car while climbing they maintained around 33 - 40 kmph at 7000 rpm. The torque requirement is more at the climbing than the turning. The car consist of Torque convertor, differential, independent suspension more over it is a 4 wheel drive which is more efficient than other 2 wheel drive.
In the above figure shows the free body diagram of the car is moving upward slope, where Theta is 45 degree. The forces acting on the car is friction force, normal force and gravity force is nothing but hill climbing force.
Fx = mg sin(Theta)
where,
m = mass of vehicle and load (2115+65) kg
g = acceleration due to gravity (m/s2)
theta in radians
Fx = 2180 * 9.81 * sin(Theta)
Fx = 18.197 kN (approx.)
Friction force defines the contact between the wheel and brake, which slow down the vehicle and actuate more torque from the motor at an approx. speed of 6000 - 7000 rpm in second gear.
Aerodynamic drag force acts on the vehicle, in which the air flow on the vehicle is more than the normal due to high altitude,
Fa = 0.5 * Cd * A * p * V^2
where,
Cd = coefficient of drag
A = Frontal area (m2)
p = Density of air (kg/m3)
V = Velocity (m/s)
Fa = 0.5 * 0.32 * (2.22*1.803) * 1.25 * 8.889^2
Fa = 63.25 N (approx.)
NOTE:
The assumed values are taken from the standard data of Range rover sport car.
The advanced feature of this car as Adaptive cruise control with steering assist, tow assist, parking assist etc.,
OUTPUT:
Study 2 & 3:-