Motor and battery sizing for an electric scooter

Aim: The aim of this project to estimate the sizing of the motor and battery capacity needed to propel a scooter. 

 

Objectives: To determine the tractive effort for an electric scooter by calculating the following forces acting on it:

• Rolling Resistance 
• Drag Resistance
• Hill climb force 
• Acceleration force

 

Theory:

Forces acting on a vehicle:

 

 

Rolling resistance: It is the force needed to overcome the resistance acting on the wheels of the vehicle.

The tire is subjected to hysteresis, a characteristic property of rubber that causes uneven distribution of load along the patch area. Rolling resistance cannot be completely avoided but can be reduced by using the right compound and pressure.

`underset(" "rr)(F) = underset(" "rr)(mu).m.g`, where

 m = mass of the vehicle, `Kg`

 g = acceleration due to gravity, `m/s^2`

`mu` = coefficient of rolling resistance

 

Drag resistance: It is the force acting on the vehicle due to the opposing motion of air. Drag is generated by the difference in velocity between the solid object and the fluid. Wind speed also plays a key role, if the wind is flowing along the direction of the vehicle then the drag force decreases, and vice-versa. 

`underset(" "ad)(F) = 0.5.rho.A.V^2.underset(d)(C)`, where

 `rho` = Air density, `kg/m^3`

`underset(" "d)(C)` = Drag coefficient

 A = Frontal area, `m^2`

 V = Speed, `m/s`

 

Hill climb force: It is the force acting on the vehicle when overcoming a slope. 

`underset(" "hc)(F) =m.g.sin(psi)`, where

 m = mass of vehicle, kg

 g = acceleration due to gravity, `m/s^2`

`psi` = grade angle in radians

 

Acceleration force: This is the force needed to accelerate a body. Acceleration is defined as the rate of change of velocity wrt time.

`underset(" "a)(F) =m.a`, where

 m = mass of the vehicle, kg

 

a = acceleration of the vehicle, `m/s^2` 

Tractive effort: It is the force needed at the wheels to overcome the resistive forces and propel the vehicle.

`underset(" "t)(F) = underset(" "rr)(F) +underset(" "ad)(F) +underset(" "hc)(F) +underset(" "a)(F)`

 

Scooter Parameters:

Tire: 90/90 12 54 J

Section width = 90mm

Wall thickness = 90% of 90mm = 81mm = 0.081m

Rim diamter = 12inches = 0.3048m

Rolling radius = `0.3048/2`+ 0.081 = 0.2334 m

Load index = 54 = 212Kg

Speed rating = J = 100kmph

 

Li-ion battery chemistry: 

1)ANR26650M1-B is a Lithium Iron Phosphate(LiFePO₄) — LFP cell, having (LiFePO₄) as cathode material and graphite as the anode. 

 

Strengths:

LFP cells offer good electrochemical performance with low resistance.

It is more resistant to full charge conditions and less stressed in comparison to other Li-ion systems if kept at a high voltage for a prolonged time. 

LFP cells offer superior chemical and thermal stability.

High current rating.

Long cycle life.

 

Drawbacks: 

Lower nominal voltage

Higher self-discharge in comparison to NMC 

 

2)Lithium Nickel Manganese Cobalt Oxide(NMC), where the cathode is a combination of Ni, Mn, and CoO2 in the ratio of 1:1:1. 

Samsung INR18650 is an NMC battery which is widely used in power tool and EV applications.

 

Strengths: 

Low self-heating rate

Offers high energy density

 

Drawbacks:

The mining of cobalt has been a controversial situation because of the use of inhumane mining practices 

 

Procedure:

1. The calculations were carried out using a Google sheet.

2. The coefficient of rolling resistance was considered to be equal to 0.008.

3. The rolling resistance, drag force, hill climbing force, and acceleration forces were calculated.

For rolling resistance, the total weight of the vehicle(kerb weight+passenger weight) was multiplied with the coefficient of resistance and acceleration due to gravity.

For drag force, a constant velocity of 40Kmph was assumed. 

For the hill-climbing force, a grade of 10degrees was assumed. 

For acceleration force, 0 to 40Kmph in 4 seconds was assumed. 

4. Once the resistive forces were calculated, the tractive force was determined.

Tractive force, `underset(t)(F) = underset(" "rr)(F) +underset(" "ad)(F) +underset(" "hc)(F) +underset(" "a)(F)`.

5. With the tractive force, the torque acting on the wheel was determined. 

Considering a gear ratio of 8, the torque at the motor was calculated.

Motor torque, `underset(" "m)(T) = underset(" "w)(T)/g`, where `underset("  "w)(T)` is the wheel torque and g is the gear ratio.

The wheel angular velocity was determined using `v=romega` and the wheel RPM was calculated using `underset(" "w)(N) = (60omega)/(2pi)`. 

Motor rpm, `underset(" "m)(N) =underset(" "W)(N).g`

Motor mechanical power `underset(m)(P)= (2piunderset(" "m)(N)underset(" "m)(T))/60`, kW

The motor and controller efficiency was considered to be 0.95 and 0.95.

6. Using the motor power, the battery power was determined. The number of cells needed in series and parallel was calculated for a 48V motor.

 

Google sheet link:Electric scooter motor sizing google sheet

Google sheet snip:

 

7.Battery pack calculation:

Case 1: A123 ANR26650M1-B (LiFePO4)

Diameter: Ø26
Length: 65.0

underset(nom)(V) = 3.3V

Capacity = 2.5Ah

Max discharge current = 50A

Weight = 76g

Number of cells in series = Motor voltage/cell voltage = 48/3.3 = 14.54 = 15 cells

Battery power needed = 14kW 

Battery current = 14kW/48V = 291.6A

Assuming battery pack capacity of 20 Ah

Number of cells in parallel = battery pack capacity/cell capacity = 20Ah/2.5Ah = 8cells

Total number of cells = underset(s)(N)*(p)(N) = 8*15 = 120 cells.

Battery pack  peak current = 50*8 = 400A

Battery pack  peak power = 400*48 = 19,200W 

Battery pack  weight = 0.076*120 = 9.12Kg

Battery pack volume =  120* cell volume = `120*(pi*0.013^2*0.065) = 0.00414m^3`

 

Case 2: Samsung  INR18650 (NMC) 

Diameter: Ø18
Length: 65.0

underset(nom)(V) = 3.7V

Capacity = 2.5Ah

Max discharge current = 50A

Weight = 45.0g

Number of cells in series = Motor voltage/cell voltage = 48/3.7 = 12.9= 13 cells

Battery current = 14kW/48V = 291.6A

Assuming battery capacity of 20 Ah

Number of cells in parallel = battery capacity/cell capacity = 20Ah/3.0Ah = 6.6 = 7 cells

Total number of cells = underset(s)(N)*(p)(N) = 7*13 = 91 cells.

Battery pack peak current = 50*7 = 350A

Battery pack peak power = 350*48 = 16,800W 

Battery pack weight = 0.045*91 = 4.095Kg

Battery pack volume =  91* cell volume = `91*(pi*0.009^2*0.065) = 0.00150m^3`

 

The LFP pack consists of 120 cells, weighing 9.12Kg and offers a peak power of 19,200W whereas NMC pack consists of 91 cells and weighs 4.095Kg offering a peak power of 16,800W.  

 

Conclusion:

The motor size and battery capacity needed to propel the vehicle with the given parameters is calculated using an excel sheet. 

 

Limitations:

The following factors are not taken into consideration:

Change in speed

Change in rolling resistance coefficient at higher speeds

Air density based on different weather conditions

Drag coefficient based on different riding positions and rider height

Ignoring these changes may lead to a drop in actual power and efficiency, which may be undesirable for the user.

These calculations provide us a basic idea to begin with, which is useful. Further improvements on these calculations help build a better-performing vehicle.

 

Learning outcomes of this project:

• The flow of the design of an electric vehicle
• The resistive forces acting on a vehicle
• Battery parameters and different Li-ion chemistries
• Battery pack calculations

 

 

References:

https://www.researchgate.net/figure/Free-body-diagram-of-the-different-longitudinal-forces-acting-on-the-vehicle_fig2_323138473

https://www.grc.nasa.gov/www/k-12/airplane/drag1.html