Design and analysis of the powertrain performance for a series configuration hybrid electric vehicle operating in Bogotá, Colombia

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Degree Project

Design and analysis of the powertrain performance for a series configuration

Hybrid Electric Vehicle operating in Bogotá, Colombia

Nicolás Esteban Taylor Cañón

Project advisor:

Luis Ernesto Muñoz Camargo

Universidad de Los Andes

Faculty of Engineering

Mechanical Engineering Department

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Acknowledgements

First of all, I would like to express my gratitude to both my parents, who have been my support during my whole life, encouraging me to do my best every time. They were always there when I needed strength, and thanks to their motivation I kept going. Secondly, I would like to thank my project assessor Luis Muñoz, for his patience and guidance. He was a mentor during this last part of my career. Finally, I would like to thank all the people that were there for me during this project, for their help and support.

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List of Figures

Figures

Figure 1. HEV energy flow diagram. (Husain, 2003)... 9

Figure 2. Parallel HEV diagram. (Husain, 2003) ... 10

Figure 3. Series HEV diagram. (Husain, 2003) ... 11

Figure 4. Series HEV energy diagram and main components. (Ehsani, Gao, Gay, & Emadi, 2005) .. 13

Figure 5. Table with types of batteries and their features. (Ehsani, Gao, Gay, & Emadi, 2005) ... 14

Figure 6. Example of a HEV battery of a Toyota Prius 2014. (Batteries for Hybrid, 2016) ... 15

Figure 7. HiTor Motor. (UQM, 2016) ... 19

Figure 8. HiTor Motor power vs. rotational speed graph ... 19

Figure 9. . HiTor Motor torque vs. rotational speed graph ... 20

Figure 10. Free body diagram of a vehicle with acting forces and relevant distances. (Gillespie, 1992) ... 22

Figure 11. ... 37

Figure 12. Scaled graph of the path traveled in La Calera municipality, with horizontal and vertical distances marked. ... 38

Figure 13. Scaled graph of the path traveled in La Calera municipality, with horizontal and vertical distances marked. ... 39

Tables

Table 1. Table with types of batteries and their features. (Ehsani, Gao, Gay, & Emadi, 2005) ... 14

Table 2. Vehicle parameters, defined previously by Sergio Roa. (Roa Melo, 2011) ... 17

Table 3. Posible choices of electric motors with their respective specs. ... 18

Table 4. HiTor Motor specifications. (UQM, 2016) ... 18

Table 5. Rolling resistance coefficient on hard dry concrete for different types of wheel. (Nice, 2000) ... 24

Table 6. Power, weight and Inertia values for EVD 35kW IP67 (EV Drive, 2016) and WEG 90 kW Motors (WEG, 2016). ... 26

Table 7. Color of the lines used to find the horizontal and vertical distances in the graphs. ... 38

Table 8. Comparative table with the values of the performance requirements of Ntf =9 and Ntf = 10. ... 43

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Graphs

Graph 1. Correlation graph between motor weight and inertia. ... 26

Graph 2. Power vs. angular velocity of the electric motor simulated in Matlab ... 28

Graph 3. Torque vs. angular velocity of the electric motor simulated in Matlab. ... 28

Graph 4. Distance vs. time graph for a simulation of the vehicle with a Ntf = 9 ... 29

Graph 5. Velocity vs. time graph for a simulation of the vehicle with a Ntf = 9 ... 30

Graph 6. ¼ mile times simulation for different Ntf values ... 30

Graph 7. Theoretical and real maximum velocity simulation vs. Ntf comparative graph ... 31

Graph 8. Maximum velocity at 5% grade vs. Ntf graph. ... 32

Graph 9. Acceleration vs. time simulation graph in Matlab, for Ntf = 9. ... 33

Graph 10. Constant cceleration time and maximum acceleration vs. Ntf comparative graph. ... 33

Graph 11. Time it takes the vehicle to accelerate to V = 48.3 km/h vs. Ntf. ... 34

Graph 12. Maximum torque transmited to the wheel vs. Ntf graph. ... 35

Graph 13. Acceleration for different Ntf vs. grade percentage comparative graph. ... 36

Graph 14. Both distance and velocity vs. time graphs for vehicle simulation at 13.7% grade and Ntf = 9. ... 40

Graph 15. 1/4 mile times vs. Ntf simulation graph for a 13.7% grade. ... 41

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1 Introduction

Mankind has always had the need for transportation; human beings have been looking for ways to transport themselves, as well as goods, the most efficient and economical way possible. The internal combustion engine was one of the most outbreaking inventions of humanity, making transportation easier. Greater distances could be travelled and more goods could be transported faster than ever before, by consuming only fossil fuel to make these machines work.

Nevertheless, transportation is facing some mayor issues nowadays. Because of the amount of Internal Combustion Engine – ICE – vehicles, as well as factories, the excess of carbon emissions to the atmosphere is causing environmental damage. Besides this, most of the vehicles that use this type of fuel, have a low efficiency, meaning that a lot of fuel has to be used for them to function. Due to the fact that fossil fuels reserves are limited, this is a major concern not only for car manufacturers but for industry in general, and this is why so much money is being invested in research of alternative energies and electric motors, as well as more efficient ICEs.

In contrast with the ICEs, the electric motors have a high energy conversion efficiency, don’t produce contamination because they don’t emit particles or residues to the atmosphere, they are smaller, cheaper and the working mechanism is simpler that one of an ICE. They do not produce that much vibration, do not need that much oil or refrigeration, and compared to its internal combustion counterpart, they barely make any noise. The main challenge in this kind of powertrains are the batteries; the amount of energy that can be stored in a battery is extremely low, compared with the amount of energy that a fossil fuel can provide by combustion. According to Phil Barker, Lotus Engineering HEV Chief Engineer, 6kg of diesel are equivalent to 200kg of batteries in terms of energy storage, meaning that it will be a point where additional batteries will be needed to transport the mass of the batteries themselves (Artés, 2011).

It is because of this, that an intermediate solution will be a Hybrid Electric Vehicle – HEV –. These vehicles work with both electric motors and internal combustion engines, providing a better energy conversion efficiency because of the electric motors, but being able to store a significantly greater amount of energy due to the ICE. The series configuration HEV

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consists of electric motors that move the wheels, and that get their energy from the batteries or the ICE of the car. This ICE works as an electric fuel generator, using the fuel combustion to produce electricity to charge the batteries of the vehicle or to provide direct energy to the electric motors. By this means, the atmospheric emissions are lowered and the fuel economy of the car is improved. This happens because the ICE functions in the best efficiency point, meaning that it is producing the most amount of energy by using the less fuel possible. Another advantage of a HEV is the regenerative braking system, which improves energy efficiency by recycling part of the energy used for braking; this way part of the kinetic energy is transformed in electricity when braking and stored again in the batteries.

It is important to highlight that the electricity that charge the batteries comes from the electric grid of the city where the vehicle is being charged. For this reason, these vehicles are only as “green” as the electricity provider; if the electricity of a place comes from fuel combustion – as it is the case of San Andres and Providence islands, which have a diesel combustion power plant that produces the electricity for the main cities (National Renewable Energy Laboratory, 2015) – an electric vehicle would not be sustainable, because the energy used to charge the batteries would not be clean energy. For the city of Bogotá, where most of the electricity is produced by hydroelectric power plants, the batteries of EV and HEV would charge with clean energy.

Taking this into account, this project is going to focus on an indispensable component of a HEV: the powertrain. A preliminary design is going to be made, defining the restrictions of the vehicle as well as performance parameters in order to find the best reduction ratio for the vehicle to have a desirable operation. This will be made by doing a comparative analysis by numerical methods of the performance of the vehicle operating in the atmospheric and geographic conditions of the city of Bogotá. Following, the objectives of the project and the state of the art of the HEV will be presented, followed by the methodology of the project used.

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2 Objectives

2.1 General objective

Design a powertrain for a HEV in series configuration by simulating the vehicle’s performance in the city of Bogotá to find the most desirable gearbox reduction ratio.

2.2 Specific objectives

 Select and define the parameters and performance requirements needed for a desirable performance of an HEV functioning at the geographical and atmospheric conditions of the city of Bogotá.

 Raise the equations for the longitudinal model and restrictions of the HEV to be able to simulate the vehicle’s performance by numerical methods.

 Find the critical grade in the city of Bogotá and its surroundings, to simulate the vehicle’s performance under this condition.

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3 Hybrid vehicles

This part of the document is going to explain the Hybrid Electric Vehicle’s operation, as well as the 2 main types of HEV and their advantages and disadvantages due to their configuration and performance in different scenarios.

3.1 Introduction to HEV Operation

A hybrid vehicle is, essentially, a vehicle that uses more than one energy source to function. Most of the times, in order not to complicate the well-functioning of the system, the drive train consists of no more than two power trains. The current project is going to focus in HEVs (Hybrid Electric Vehicles) that work with an internal combustion energy source as well as an electric energy source. In order to recapture part of the braking energy dissipated as heat – regenerative braking system –, a hybrid drivetrain usually has a bidirectional energy source and converter. (Ehsani, Gao, Gay, & Emadi, 2005)

Figure 1. HEV energy flow diagram. (Husain, 2003)

This offers a more flexible and versatile way of energy acquisition; the vehicle can use both of the energy sources at the same time to operate, use one at a time, or even one energy

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source can charge a battery for when the other source has run out of power, like an internal combustion engine charging batteries to have electric energy available for the electric motors to use later. This fact, although making the vehicle much more efficient in terms of energy usage, also adds up the need for a complex control system, due to the amount of combinations of different energy sources, sometimes being bidirectional, like the regenerative braking system.

3.2 Types of Hybrid Vehicles

3.2.1 Parallel HEVs

A parallel hybrid is one in which the heat engine and the electric motor are configured in parallel, connected to the driveshaft through separate clutches. The propulsion power may be supplied by the heat engine, by the battery – motor set or by the two systems in combination. (Husain, 2003) The component arrangements can be seen in the following figure:

Figure 2. Parallel HEV diagram. (Husain, 2003)

Advantages of parallel HEVs

 It only needs two propulsion components: ICE and motor/generator. The motor can be used as a generator.

 A smaller engine and smaller motor may be used in order to obtain the same performance.

 Their composition makes them more efficient for highway driving at higher, more constant speeds.

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 The power flow has to be regulated and blended from two parallel sources, making the control system complexity higher than the one needed in a series configuration.  The power blending of the two sources, the ICE and the motor, needs a complex

mechanical device.

3.2.2 Series HEVs

A series hybrid is one in which only one energy converter can provide propulsion power. Two power sources feed a single power plant (electric motor) that propels the vehicle. A heat engine drives a generator that supplements the batteries and charges them when they fall below a certain state of charge. Beyond the engine and the generator, the propulsion system is the same as in an Electric Vehicle (EV).

Figure 3. Series HEV diagram. (Husain, 2003)

Advantages of series HEVs

 The engine is fully mechanical when decoupled from the driven wheels. Therefore, it can be operated at any point on its speed–torque characteristic map, and can potentially be operated solely within its maximum efficiency region.

 Simplicity of drivetrain; because electric motors have near-ideal torque–speed characteristics, they do not need multiple gear transmissions.

 Simple control strategies may be used as a result of the mechanical decoupling provided by the electrical transmission.

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 Suitability for short trips; they are more efficient for driving in the city because their drivetrain structure reduces the strain on the engine in stop-and-go driving situations.

Disadvantages of series HEVs

 The energy from the engine is converted twice (mechanical to electrical in the generator and electrical to mechanical in the traction motor). The inefficiencies of the generator and traction motor add up and the losses may be significant.

 The generator adds additional weight and cost.

 The traction motor must be sized to meet maximum requirements since it is the only power plant propelling the vehicle. However, the vehicle operates below the maximum power most of the time.

3.3 HEV Configuration Selection

This type of hybrid vehicle is more efficient for in-city driving, due to the fact that driving in a city experience more stop-and-go situations. Jeremy Michalek, a professor of mechanical engineering and engineering and public policy at CMU, made a research on the effect hybrid cars have on greenhouse effect: “For drivers who experience a lot of idling and stop-and-go traffic, a hybrid could lower lifetime costs by 20 percent and cut greenhouse gas emissions in half,” Michalek said. The main reason for this to happen is that part of the energy is recovered by the regenerative braking system, recycling some of the energy lost by braking, and therefore resulting in a lower energy consumption. (Carnegie Mellon University College of Engineering, 2013)

Taking this into account the series HEV is the best choice for driving in-city, not only because of the energy efficiency – that will reflect in money saving as well – but in the lowering of greenhouse emissions; this is due to the fact that the ICE functions as an electric generator, working always in the point of maximum efficiency, thus, making fuel consumption more efficient than the internal combustion vehicles or even the parallel configuration HEVs. Operation modes of the series HEV

Due to the fact that the series HEV has two different energy sources and a regenerative braking system, the vehicle has different operation modes:

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1. Pure electric mode: The engine is turned off and the vehicle is propelled only by the batteries.

2. Pure engine mode: The vehicle traction power only comes from the engine-generator. The electric machines serve as an electric transmission from the engine to the driven wheels.

3. Hybrid mode: The traction power is drawn from both the batteries and the engine-generator.

4. Engine traction and battery charging mode: The engine-generator supplies power to charge the batteries and to propel the vehicle.

5. Regenerative braking mode: The engine-generator is turned off and the traction motor is operated as a generator. The power generated is used to charge the batteries.

6. Battery charging mode: The traction motor receives no power and the engine-generator charges the batteries.

7. Hybrid battery charging mode: Both the engine-generator and the traction motor operate as generators to charge the batteries.

3.4 Batteries

“An electric battery is a device consisting of one or more electrochemical cells with external connections provided to power electrical devices.” (Crompton, 2000) A battery is then an energy storage device that turns the chemical energy inside it into electricity that can be used to feed different electric devices. The batteries used in an EV or a HEV are rechargeable batteries, that allow themselves to charge electrically when they ran out of power. In an EV they can only be charged electrically by a power source or by the regenerative braking system, and in an HEV it can be charged by these 2 ways as well, but also using the ICE as an electric generator to produce the electric energy necessary to charge them. The current problem of the EV is that the batteries have a much lower specific energy than fossil fuels, which can have a specific energy of up to 12700 Wh/kg, compared with the 200-300 Wh/kg that a battery can have; this make their autonomy low compared to the one of an internal combustion engine counterpart. In the following chart the different battery types and their features:

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3.3 Batteries

“An electric battery is a device consisting of one or more electrochemical cells with external connections provided to power electrical devices.” (Crompton, 2000) A battery is then an energy storage device that turns the chemical energy inside it into electricity that can be used to feed different electric devices. The batteries used in an EV or a HEV are rechargeable batteries, that allow themselves to charge electrically when they ran out of power. In an EV they can only be charged electrically by a power source or by the regenerative braking system, and in an HEV it can be charged by these 2 ways as well, but also using the ICE as an electric generator to produce the electric energy necessary to charge them. The current problem of the EV is that the batteries have a much lower specific energy than fossil fuels, which can have a specific energy of up to 12700 Wh/kg, compared with the 200-300 Wh/kg that a battery can have; this make their autonomy low compared to the one of an internal combustion engine counterpart. In the following chart the different battery types and their features:

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The battery that is most used in EV and HEV is the Lithium-ion battery, due to its high specific energy – up to 130 Wh/kg –, high peak power – up to 300 W/kg – and its energy efficiency, that is usually higher than 95%.

Figure 5. Example of a HEV battery of a Toyota Prius 2014. (Batteries for Hybrid, 2016)

The autonomy of a series HEV is higher than a normal combustion engine vehicle, due to the fact that it uses an ICE as an electric generator to charge the batteries of the vehicle. This electric generator is operating in its point of maximum efficiency, making the fuel consumption and the greenhouse effect emissions lower.

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4 Methodology

The current project is part of an off-road HEV design, more specifically the powertrain of the vehicle. This way a methodology has to be developed in order to accomplish the objective of the project. The methodology for the current project is:

 Define the restrictions of the vehicle in terms of weight and general dimensions, as well as the selection of the electric motor.

 Define objective requirements for the vehicle to evaluate its performance.

 Define a model to evaluate the performance of the vehicle and simulate it with numerical methods.

 With the simulation results make graphs in order to compare the performance of the vehicle for the different values of reduction ratios.

 Find the critical value of grade for the city of Bogotá to be able to simulate the vehicle’s performance under this particular scenario.

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5 Restrictions of the HEV

To be able to simulate the vehicle’s performance, the parameters and restrictions of the HEV have to be known. Following the description of the vehicle and electric motor selection will be shown.

5.1 General description of the vehicle

This project is developed as a top-down approach, where depending on the vehicle characteristics it is going to be possible to start the design process. Based on the state of the art in the current subject and on the restrictions and needs for the correct performance of the vehicle, the parameters that were taken into account for the posterior analysis and design of the powertrain were the gross vehicular weight rating, the frontal area of the vehicle and the size of the wheel. (Roa Melo, 2011)

Table 2. Vehicle parameters, defined previously by Sergio Roa. (Roa Melo, 2011)

Parameters Value Units

Gross Vehicular Weight Rating 5800 kg

Frontal Area 4.2 m^2

Wheel external diameter 0.94 m

These parameters were the ones selected in the previous project, and they are going to be used in the current one as well for the different simulations and selection of the gear reduction ratio.

5.2 Motor Selection

In order to select an electric motor that can fulfill the vehicle restrictions, a selection process was made, where aspects as motor power, torque, and gross vehicular weight. In Roa’s project, various motors were evaluated using some performance markers to compare them. After the comparative results of the motors, the following 3 were the possible choices (Roa Melo, 2011):

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Table 3. Possible choices of electric motors with their respective specifications.

Reference Manufacturer Continuous torque (Nm) @RPM

Continuous power (kW) @ RPM

weight (kg)

Max. rotational speed (RPM)

HiTor UQM 180 @ 0 - 1000 30 @ 1200-6500 41 6500

AFM 140 EVO Electric 220 @ 0 - 4000 75 @ NA 40 5000

HSM1 6.17.12 Brusa 130 @ 0 - 5000 57 @ 4200-11000 53 11000

Due mostly to prices, arrival times and the ability to contact manufacturers, the motor selected is the Hitor UQM. This motor meets the restrictions and specifications of torque and power, has brake regenerative capacity and a good structural stability. In the following table the motor specifications are shown:

Table 4. HiTor Motor specifications. (UQM, 2016)

Specifications Magnitude Unit

Maximum Torque 440 Nm

Maximum Power 50 kW

Weight 57 kg

Continuous torque 180 Nm

Continuous power 30 kW

Maximum rotational speed 6500 RPM

Efficiency 93 %

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The following pictures show the motor, as well as the manufacturer’s power and torque graphs given for it.

Figure 6. HiTor Motor. (UQM, 2016)

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6 Vehicle’s Objective performance

Continuing the design process for the powertrain of the vehicle, it is important to define some performance indicators in order to have the minimum and objective requirements in terms of vehicle response in certain situations. The USA Army has a vehicle development project called Joint Light Tactical Vehicle (JLTV) that has as an objective to improve the current tactical vehicles of this country (Procnet-US Army, 2011). Taking this documents into account, it is possible to define the performance requirements for the vehicle (Roa Melo, 2011):

Performance on grade

 (Minimum) The vehicle must be capable of moving over a hard and dry surface with a grade of 40%.

 (Objective) The vehicle must be capable of moving over a hard and dry surface with a grade of 60%

Acceleration performance

 (Minimum) The vehicle must be capable of accelerating in a hard, dry and flat surface from 0 to 48.3 km/h in less than 9.4 seconds.

 (Objective) The vehicle must be capable of accelerating in a hard, dry and flat surface from 0 to 48.3 km/h in less than 7 seconds.

Velocity performance

 (Minimum) The vehicle must be capable of ascending a 5% grade with a speed of 72.4 km/h.

 (Objective) The vehicle must be capable of ascending a 5% grade with a speed of 96.6 km/h.

 The vehicle must have a final velocity of at least 112.7 km/h in a hard, dry and flat surface.

The objective requirements are the desirable parameters for the vehicle’s performance. In case that there is no reduction ratio that meets the objective requirements there are the minimum requirements, which are the ones that have to be complied as a minimum for the vehicle to have an acceptable operation.

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7 Model for evaluating vehicle’s performance

For the proper simulation of the vehicle’s performance, it is necessary to define a longitudinal model of the vehicle. This way the model can be simulated using numerical methods to solve the equations and find the performance parameters for the different reduction ratios to be able to compare them.

7.1 Longitudinal model of the vehicle

Considering the parameters and restrictions made for the current project, the model that is going to be used for the analysis and simulations is going to be a quarter car longitudinal model. By this simplified model is going to be possible to get to an accurate prediction of the performance parameters for the vehicle, such as:

 Acceleration  Velocity  Race times

 Performance on grade  Torque and traction forces

 Effect of rolling and aerodynamic resistance

For the simulation of the performance of the vehicle, due to the model that is going to be used, the motor torque and forces will be multiplied by 4, to have an estimative of the whole car. No load transfer is considered in the current model.

In the current model of quarter of a vehicle, the front half is equal to the rear half. The free body diagram for the vehicle will be shown in the following figure:

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Therefore, the forces actuating on the vehicle will be:

∑ 𝐹_𝑥 = 𝑚 ∗ 𝑎

𝑚 ∗ 𝑎 = 𝐹_𝑥− 𝑅_𝑥− 𝐷_𝐴 − 𝑊𝑠𝑖𝑛𝜃

where 𝑚 is the effective mass of the vehicle, 𝑎 is the acceleration, 𝐹𝑥 is the tractive force applied to the floor by the wheel, 𝑅_𝑥 is the rolling resistance, 𝐷_𝐴 is the aerodynamic drag and 𝑊𝑠𝑖𝑛𝜃 is the force caused by the slope.

By these means we have that:

𝐹𝑥 =

𝑇_𝑒∗ 𝑁_𝑡𝑓∗ 𝜂 𝑟

𝑅_𝑥 = 𝑚_𝑣∗ 𝑔 ∗ 𝜇

𝐷_𝐴 =𝐶𝑑∗ 𝐴 ∗ 𝜌 ∗ 𝑉 2

2

𝑚 = 𝑚_𝑣+ 𝑚_𝑟

𝑉 =𝜔 ∗ 𝑟 𝑁_𝑡𝑓

Where 𝑇𝑒 is the torque of the engine, 𝑁𝑡𝑓 is the reduction ratio, η is the motor efficiency, 𝑟 is the radius of the wheel, 𝑚_𝑣 is the mass of the vehicle, 𝑚_𝑟 is the rotational mass of the vehicle, 𝑐_𝑑 is the drag coefficient, 𝐴 is the frontal area of the car, 𝜌 is the air density, 𝑉 is the vehicle’s velocity and 𝜔 is the rotational speed of the motor.

Due to the fact that the city of Bogota is at an altitude of 2640 m above sea level, the air density value is low compared to air density at sea level. Taking an average temperature of 20 degrees Celsius, the air density of Bogotá is:

𝜌𝐵𝑜𝑔𝑜𝑡á= 0.8878 𝑘𝑔 𝑚3

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The drag coefficient had to be estimated, taking into account the size of the vehicle. A typical SUV truck has a drag coefficient between 0.33 and 0.4, for which we assume this last value as a close approximation of the real value:

𝐶_𝐷 = 0.4

The rolling resistance coefficient rises approximately linearly with the speed, in which case we have:

𝜇 = 0.01 ∗ (1 +𝑉𝑚𝑝ℎ 100)

(Gillespie, 1992) Where Vmph is the vehicle’s velocity in miles per hour.

Due to the fact that the velocity achieved by the HEV will not be high enough, the tire is assumed as a perfect wheel and the vehicle analysis will not be made for sudden velocity change scenarios, this parameter can be approximated to a constant value (Gillespie, 1992). The following table shows typical values of the rolling resistance coefficient on hard dry concrete depending on the type of wheel:

Table 5. Rolling resistance coefficient on hard dry concrete for different types of wheel. (Nice, 2000) Tire Type Coefficient of Rolling Friction

Low rolling resistance car tire 0.006 - 0.01

Ordinary car tire 0.015

Truck tire 0.006 - 0.01

Train wheel 0.001

The value of the rolling resistance coefficient for this particular case will be the one of the ordinary car tire:

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Rotational mass and moment of inertia

In order to find the effective mass of the vehicle is necessary to find the rotational mass of it. This is an equivalent in mass of the inertia of the rotational components of the motor. According to Gillespie, an estimate of the rotational mass for an internal combustion engine vehicle is (Gillespie, 1992):

𝑚𝑟 = (0.04 + 0.0025 ∗ 𝑁𝑡𝑓2) ∗ 𝑚

This approximation cannot be used for the electric motor, due to the difference in the mechanism of action. This is why the rotational mass has to be found using a different approach. To find it, both the formula of kinetic energy and linear speed must be used:

𝐾 =𝑚𝑟∗ 𝑉 2

2 =

𝐼_𝑒∗ 𝜔2 2

𝑉 =𝜔 ∗ 𝑟 𝑁_𝑡𝑓

If the term of velocity is changed in the first equation, we have:

𝑚_𝑟∗ (𝜔 ∗ 𝑟_𝑁 𝑡𝑓 )

2

2 =

𝐼𝑒∗ 𝜔2 2

𝑚𝑟∗ 𝜔2∗ 𝑟2 2 ∗ 𝑁_𝑡𝑓2 =

𝐼𝑒∗ 𝜔2 2

𝑚𝑟 =

𝐼_𝑒∗ 𝑁_𝑡𝑓2 𝑟2

This way, by finding an approximate value for the motor inertia (𝐼_𝑒), the rotational mass can be found. The problem is to find a value for this inertia, because the motor manufacturers rarely give out this number. This is why an approximation had to be done, in order to find a coherent value for this variable. The fact that the inertia of the motor is correlated to its weight is accurate; the bigger the motor, the more power and the more inertia it is going to have – in most cases at least –. This way, by finding the values of inertia and weight of different motors, a correlation can be found. By doing so it is only necessary to have the value of the motor weight in order to find the value of the rotational inertia.

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Two motors were found in which the manufacturer gave both the weight and the inertial value. They are presented in the following table:

Table 6. Power, weight and Inertia values for EVD 35kW IP67 (EV Drive, 2016) and WEG 90 kW Motors (WEG, 2016).

EVD 35kW IP67 WEG 90kW Motor

Power 16kW cont. - 35kW peak @ 5500 RPM 50kW cont. - 90 kW peak @ 1500 RPM

Weight 16 kg 90 kg

Inertia 0.0045 kg*m2 _{0.063 kg*m}2

With this data a graph can be made to see the correlation between the inertia and the weight, and this way it would be possible to find an approximate value of inertia for the current motor just by knowing its weight:

Graph 1. Correlation graph between motor weight and inertia.

In the graph the trendline was set with an intercept in (0, 0) – a motor with no weight have zero inertia –. Knowing that the weight of the motor is 41 kg, by looking at the graph, it can be seen that an approximate value for the inertia would be:

𝐼𝑒 = 0.03 𝐾𝑔 ∗ 𝑚2

y = 0.0007x R² = 0.9775

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

0 10 20 30 40 50 60 70 80 90 100

In

e

rtia ()

Weight (kg)

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By having this value, it is now possible to find the rotational mass of the vehicle and to solve the differential equation of force for the longitudinal model:

𝑚 ∗ 𝑎 = 𝐹𝑥− 𝑅𝑥− 𝐷𝐴 − 𝑊𝑠𝑖𝑛𝜃

(𝑚𝑣+ 𝑚𝑟) ∗ 𝑑𝑉

𝑑𝑡 =

𝑇𝑒 ∗ 𝑁𝑡𝑓∗ 𝜂

𝑟 − (𝑚𝑣∗ 𝑔 ∗ 𝜇) −

𝐶_𝑑∗ 𝐴 ∗ 𝜌 ∗ 𝑉2

2 − 𝑊𝑠𝑖𝑛𝜃

Due to the vehicle restrictions of weight and size, the effect of the wheel’s deformation is not going to be taken into account. For the purposes of this project, the wheels of the vehicle are assumed as perfect wheels, which means the effect of slip is not going to be taken into account.

Having the equation in this form makes it possible to solve with a numerical method. The program used for this task will be Matlab.

7.2 Simulation of the vehicle performance

To be able to make an analysis and simulation of the vehicles performance, it was necessary to have both the power and torque curves of the motor in the Matlab program; this way the program will be able to simulate correctly in terms of the power and torque delivered to the vehicle. These functions will be used later to solve the differential equation in the program and to find the efficiency of the motors. The motor manufacturer had the power graph in the motor catalog, from which the torque graph can be found, by using the following formula:

𝑃 = 𝑇 ∗ 𝜔

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This way both power and torque functions can be introduced in the program, for later use in the analysis:

Graph 2. Power vs. angular velocity of the electric motor simulated in Matlab

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To be able to transmit the necessary power from the motor to the wheels of the vehicle as torque, a reduction gearbox is needed. This way, part of the speed of the motor will be transformed in torque that will be transmitted to the wheels for the vehicle to move. Due to the weight of the vehicle, a high torque will be needed for it to be able to accelerate and get to a desirable speed. Without the reduction gearbox, the motor would not be able to deliver the necessary torque for the vehicle to move. This is the reason why the reduction ratio of the gearbox is such an important part in the drivetrain design; if the reduction ratio is low, the vehicle may not develop the necessary torque, and if it is too high, it would not get to a desirable speed.

7.2.1 ¼ Mile times

In order to have a comparative analysis of the vehicle’s performance with different gear reduction ratios, a Matlab code is developed to give a solution to de differential equation for the acceleration of the vehicle. Using the ODE45 Matlab function, the program is capable of not only solving the change of velocity over time, but also the time the vehicle took to travel a certain distance, in this case, 402 m (1/4 mile).

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Graph 5. Velocity vs. time graph for a simulation of the vehicle with a Ntf = 9

The graphs previously showed were simulated for 𝑁_𝑡𝑓 = 9. To be able to compare the different velocities and times, the simulation is run for 𝑁_𝑡𝑓 from 6 to 12:

Graph 6. ¼ mile times simulation for different Ntf values

As seen in the previous graph, the best times traveling 404 m were with the 𝑁_𝑡𝑓 from 9 to 11, being the lowest one, although not by much, 𝑁_𝑡𝑓 = 10. This gives a first glance at the racing performance of the vehicle, with slope angle = 0 degrees.

The simulation also found the final velocities and accelerations for different reduction ratios. It is then proceeded to graph the different final velocities of the vehicle for each 𝑁_𝑡𝑓.

18.0 18.2 18.4 18.6 18.8 19.0 19.2 19.4 19.6 19.8 20.0

6 7 8 9 10 11 12

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(s

)

Ntf

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7.2.2 Maximum velocity

The same simulation not only finds the race times, but also the final velocity of the vehicle for a given 𝑁𝑡𝑓. With this information a comparative graph was done, comparing the theoretical kinematic velocity – the velocity that depends only on the reduction ratio – and the final velocity of the simulation – the one that takes drag and rolling resistance forces into account –.

Graph 7. Theoretical and real maximum velocity simulation vs. Ntf comparative graph

The graph shows how the lower 𝑁_𝑡𝑓 will not reach the maximum kinematic velocity, due to the rolling coefficient as well as the aerodynamic drag. On the other hand, the values of 𝑁_𝑡𝑓 of 11 and 12 have maximum velocities of 105 km/h and 96 km/h respectively, not meeting the performance requirements defined previously of 112.7 km/h (JLTV).

7.2.3 Velocity performance at 5% grade

Another velocity requirement is that the vehicle’s maximum speed in a grade of 5% is at least 96.6 km/h. To find the maximum velocities of the vehicle with the different 𝑁_𝑡𝑓 the same simulation is run, changing the angle from 0 to 5% – approximately 0.05 radians –. The results of the simulation will be shown in the following graph:

80.0 100.0 120.0 140.0 160.0 180.0 200.0

6 7 8 9 10 11 12

V (m

/s

)

Ntf

Vmax - theoretical and real vs. Ntf

Vmax(real)-km/h

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Graph 8. Maximum velocity at 5% grade vs. Ntf graph.

As it can be seen, the maximum velocity accomplished by the vehicle is higher than 96.6 km/h for every 𝑁_𝑡𝑓 except for 𝑁_𝑡𝑓 = 12. The reduction ratio from 6 to 10 get to a similar speed, between 112 km/h and 114 km/h.

This first analysis shows that in terms of race times and maximum velocity, the range of 𝑁𝑡𝑓 that is more desirable due to its performance is 9 to 10; the reduction ratios from 6 to 8 do not reach the final kinematic top speed due to friction and drag and do not have the best race times. This is due to the fact that a smaller reduction ratio is going to convert less rotational speed in torque, and due to the vehicle specifications and mostly because of its weight, a big torque is needed to be able to accelerate it. The reduction ratios of 11 and 12, have a higher torque, but then they sacrifice too much the final speed that the vehicle can accomplish, failing to meet with the initial velocity restrictions given.

7.2.4 Acceleration

The acceleration graph has the same shape as the torque graph. This is because as torque is continuous, it is also the force applied to the wheel, meaning that the acceleration is continuous. When the torque starts decreasing, the acceleration does as well. The maximum acceleration, as well as the time that this acceleration lasts, it is going to depend on the reduction ratio used.

90.0 95.0 100.0 105.0 110.0 115.0 120.0

6 7 8 9 10 11 12

V (m

/s

)

Nt

Vmax with 5% grade

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Graph 9. Acceleration vs. time simulation graph in Matlab, for Ntf = 9.

Graph 10. Constant acceleration time and maximum acceleration vs. Ntf comparative graph.

This graph shows the value of the maximum acceleration achieved with each 𝑁_𝑡𝑓, as well as the time the vehicle maintains this acceleration. It can be seen that the acceleration increases and the time it lasts decreases with a greater value of the reduction ratio. This means that a higher value of 𝑁_𝑡𝑓 results in a greater value of constant acceleration that lasts 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

6 7 8 9 10 11 12

A cc e le ration t im e s (s) Acc ele ra tio n (m /s ^2) Ntf

Acceleration time and Maximum acceleration vs Ntf

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less time. A higher reduction ratio means more torque applied to the wheels, hence, more acceleration, but as it can be seen in the graph, it also means a shorter time of constant acceleration for the vehicle.

For the evaluation of the acceleration performance requirement, the simulation is run again to find out if a reduction ratio can accelerate from 0 to 48.3 km/h in 7 seconds or less:

Graph 11. Time it takes the vehicle to accelerate to V = 48.3 km/h vs. Ntf.

As shown by the graph, all of the values simulated for 𝑁𝑡𝑓 meet the requirement of getting to V = 48.3 km/h in less than 7 seconds. It can be seen that as 𝑁𝑡𝑓 increases, the time the vehicle needs to obtain this speed is less; the higher the reduction ratio, the higher the torque applied to the wheels, making the vehicle accelerate faster.

3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.80 5.00

6 7 8 9 10 11 12

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Ntf

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7.3 Torque

Due to the gear reduction, the torque applied to the wheels is going to vary depending on the 𝑁_𝑡𝑓 that is being used. Therefore, the maximum torque applied to the wheel can be found for every 𝑁_𝑡𝑓:

Graph 12. Maximum torque transmitted to the wheel vs. Ntf graph.

These values have to be taken in account when looking for a gear reduction; the maximum torque that is transmitted to the wheel represents a restriction for the gearbox, and a gearbox that has a lower permitted torque will not be useful. The higher the torque means the gearbox has to overcome higher values of stress, needing to have a high structural toughness for it not to fail.

8 Performance on grade

8.1 Simulation for acceleration at different percentage of grade

In order to find the response of the vehicle at different percentages of grade, a simulation was made to find at which percentage the vehicle will no longer accelerate, hence will not be able to move. This was made for every 𝑁_𝑡𝑓, in order to see which ones do not meet the requirements presented before.

y = 407.43x + 11.321 R² = 1

0 1000 2000 3000 4000 5000 6000

6 7 8 9 10 11 12

To

rq

u

e (N

m

)

Ntf

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For this part of the simulation there was no differential equation to solve, due to the fact that what needs to be found is the acceleration, which can be found directly from the equation of force. The same equation of longitudinal model was used, but without the aerodynamic loses, because the initial speed is not high enough for making these force negligible:

𝑚 ∗ 𝑎 = 𝐹_𝑥− 𝑅_𝑥− 𝑊𝑠𝑖𝑛𝜃

𝑎 =

(𝑇𝑒∗ 𝑁_𝑟𝑡𝑓∗ 𝜂− (𝑚_𝑣∗ 𝑔 ∗ 𝜇) − 𝑊𝑠𝑖𝑛𝜃)

𝑚_𝑣 + 𝑚_𝑟

The initial acceleration of the vehicle was found for a range of different slopes, to see at which percentage of grade the vehicle presented acceleration = 0; at this point, it would not be able to start moving. This was made for each of the 𝑁_𝑡𝑓 that have been evaluated in the project to put the data found in a graph in order to compare them.

The results are shown in the following graph:

-3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

0% 10% 20% 30% 40% 50% 60% 70% 80%

Acc ele ra tio n (m /s ^2) Grade Percentage

Acceleration on grade

Nt = 6 Nt = 7 Nt = 8 Nt = 9 Nt = 10 Nt = 11 Nt = 12

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As shown in the graph, the values of 𝑁_𝑡𝑓 of 6, 7 and 8 do not meet the performance on grade objective requirement, which was to be able to move on a grade of 60%. The ones that meet with this requirement are the 𝑁𝑡𝑓 of over 9.

A 60% of grade is an extremely steep road, which is never going to be found in a city. This parameter is made for off road extreme situations, and it only measures the ability of the vehicle of producing the necessary torque to start moving in such a steep slope. A critical angle has to be measured in the proximities of the city, to have a real value of the steepest grade possible the vehicle has to overcome.

8.2 Critical angle measurement

In order to determine the critical angle of the slope for which the vehicle has to be designed to operate, it was necessary to somehow measure the angles of the most critical roads in the city of Bogota and its surroundings. This was done using a Polar V800 sports watch, which allows measuring the horizontal as well as the vertical distance traveled by someone.

The data collected was gathered traveling throughout the steepest roads of Bogotá and of the surrounding municipalities in a bicycle. The data was then uploaded to a computer, exporting a graph of height vs. horizontal distance traveled. By doing this in the steepest areas found in the city and its surroundings, it is possible, by a simple trigonometrical operation, to find the critical angle for which the vehicle has to be designed.

Figure 10. Picture of the Polar watch V800 used and a picture of a road in La Calera municipality from a bicycle (Duncan & Bilbao, 2011)

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The two places with the steepest roads that were found were in La Calera and in Tabio municipality. With the data found thanks to the Polar V800 watch, a scaled graph was made in order to find the distances traveled. In the following graphs, the horizontal and vertical distances are highlighted for the steepest slope found:

Table 7. Color of the lines used to find the horizontal and vertical distances in the graphs.

Color Description

Marks the initial and final height of the road

Marks the horizontal distance traveled in the steepest slope

Marks the segment used to determine the grade and angle of the road

La Calera municipality roads

Figure 11. Scaled graph of the path traveled in La Calera municipality, with horizontal and vertical distances marked.

With the distances correctly marked in the graph, a simple trigonometrical relation is used to find the percentage of grade and the critical angle value:

Horizontal distance traveled:

𝑥 = 1930 𝑚

Height:

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𝑠𝑙𝑜𝑝𝑒_% = 180.1𝑚

1930𝑚 ∗ 100% = 9.33%

tan 𝜃 =180.1𝑚 1930𝑚

𝜃 = 5.33°

Tabio municipality roads

Figure 12. Scaled graph of the path traveled in La Calera municipality, with horizontal and vertical distances marked.

Horizontal distance traveled:

𝑥 = 547𝑚 Height:

𝑦 = 74.8 𝑚

Grade percentage and critical angle value:

𝑠𝑙𝑜𝑝𝑒_% = 74.8𝑚

547𝑚 ∗ 100% = 13.7%

tan 𝜃 =74.8𝑚 547𝑚

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As can be seen above, the critical angle for which the gear reduction has to be designed is 13.7 % (7.79 degrees), which was found in Tabio municipality.

It is important to highlight that the two points that were found for each of the steepest grades were taken directly from the scaled graphs that were made from the data collected for each of the journeys. Therefore, the graphs can be seen as an average result of all the data that was gathered. This way if there is a single point that presented an error of measurement generated from different events such as road imperfections, this error will not be relevant due to the amount of data collected. This being said, the distance between the two points used to find the critical angle can be seen an average of the distance traveled. With the value of the critical angles, the Matlab code is run again, to be able to find the performance of the different gear reduction ratios with this grade:

It can be seen that due to the percentage of grade, the final speed of the vehicle is lower than the one found for no grade; this is because a higher torque is necessary to go up hill.

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The simulation is then run for different values of 𝑁_𝑡𝑓, and the ¼ mile times and final velocities are found for each one. A comparative graph is made for each case, to see the performance of the vehicle with different reduction ratios.

Graph 15. 1/4 mile times vs. Ntf simulation graph for a 13.7% grade.

Graph 16. Maximum velocity vs. Ntf simulation graph for a 13.7% grade.

The graphs show a decrease in race time for the highest 𝑁𝑡𝑓, basically because these reduction ratios produce a higher torque, which at the percentage of grade results in a lower time for traveling the 402 meters.

As for the final velocity of the vehicle it can be seen a constant speed for the 𝑁𝑡𝑓 from 8 to 12, reaching a final velocity of 70 km/h approximately.

25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0

6 7 8 9 10 11 12

Tim

e

(s

)

Ntf

1/4 mile times vs Ntf

66.0 67.0 68.0 69.0 70.0 71.0 72.0

6 7 8 9 10 11 12

V (m

/s

)

Ntf

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9 Selection

The following analysis can be presented with respect to the simulations that were made and their results, with the objective of getting to an appropriate selection of the reduction ratio or 𝑁𝑡𝑓:

 The results of a race of ¼ mile with grade = 0% demonstrated a good performance for 𝑁_𝑡𝑓 of 9, 10 and 11; these showed the lower times, being 𝑁_𝑡𝑓 = 10 the lowest race time.

 In terms of maximum final velocity, the values of 𝑁_𝑡𝑓 of 11 and 12 do not meet with the performance requirement demanded, being their final speeds below 112.7 km/h. The 𝑁𝑡𝑓 that show a better performance are 8, 9 and 10, being able to reach or get close to reaching a final velocity close to the theoretic one. The reduction ratios of 6 and 7 cannot reach those speeds because of the drag and rolling resistance forces.

 For the performance at 5% grade all but 𝑁_𝑡𝑓 = 12 meet the requirement of having a speed higher than 96.6 km/h, having the reduction ratios from 6 to 10 approximately the same velocity.

 For the acceleration performance requirement, the results show all of the 𝑁_𝑡𝑓 meet with this requirement. The higher 𝑁_𝑡𝑓 presented lower times of acceleration, being this desirable when it comes to selection.

 As seen in the grade performance results, the 𝑁_𝑡𝑓 of 8 and lower could not meet with the requirement of start moving at a grade of 60%. For this specific demand, the reduction ratios that accomplished it were 9, 10, 11 and 12.

 For the critical angle results, the simulations showed a better performance for higher 𝑁𝑡𝑓 in the race times, and a similar performance of 𝑁𝑡𝑓 of 8 and higher in terms of maximum velocity.

Taking all of the requirements into consideration, the range of 𝑁_𝑡𝑓 which meets with every one of them is 𝑁_𝑡𝑓 between 9 and 10. The same way, in the requirements that most of the

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reduction ratios meet, 𝑁_𝑡𝑓 of 9 and 10 showed a more than desirable performance. The reduction ratio range that results most desirable for the vehicle simulated is:

9 ≤ 𝑁𝑡𝑓 ≤ 10

A range of values is presented due to the fact that most gearbox companies have predetermined values for the reduction ratios of their gearboxes. This way, a gearbox with a reduction ratio between these 2 values will be acceptable, as it will fulfill the performance requirements presented earlier in the document. Following, a comparative table with the values and the difference in percentage of the requirements will be shown, to show that this range of values operate both with an acceptable performance:

Table 8. Comparative table with the values of the performance requirements of Ntf =9 and Ntf = 10.

Performance requirement Ntf Difference

9 10

1/4 mile time (s) 19.2 19.1 0.5%

Maximum Velocity - 0% grade (Km/h) 127.9 115.2 9.9%

Maximum Velocity - 5% grade (Km/h) 113.0 113.6 0.5%

Time to accelerate to 48.3 km/h (s) 3.8 3.6 5.3%

Acceleration in 60% grade (m/s^2) Yes Yes 0.0%

Maximum Torque (Nm) 3677 4085 10.0%

Maximum Velocity - Critical angle (m/s) 70.1 70.1 0.0%

When manufacturing a gearbox for the vehicle the following has to be taken into account: the closer the 𝑁_𝑡𝑓 is to 9 the performance will slightly improve in terms of maximum speed. The closer it is to 10, the performance on grade will improve. It is worth noticing that it will be a slight improvement compared to one another, being no more than 10%.

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10 Conclusions

A preliminary design of the drivetrain for a series HEV could be made by doing a simulation analysis for the vehicle performance in the city of Bogotá. Based on the result of these simulations, a selection for a reduction ratio was done, showing a desirable performance for the requirements given:

 With the analyses made in previous projects a desirable selection of the motor could be made; this way it was possible to make the performance simulations based in its power and torque.

 With the values of air density, rolling coefficient and inertia found, the simulation for the longitudinal model could be done using the program Matlab as a tool for numerical analysis.

 The simulation results were evaluated in terms of the performance requirements earlier defined, in order to find a desirable reduction ratio for the gearbox. Race times, velocity and acceleration were evaluated, as well as the performance on grade.

 In order to simulate under a critical grade condition, the value had to be found by measuring the horizontal distance and altitude of different roads of the city of Bogotá and its surroundings. This was done with the help of a biking sport watch that measures both horizontal and vertical distance traveled when using it. By knowing this angle, simulations could be made to find the performance of the vehicle under this condition.

 Under the requirements and parameters exposed, a reduction ratio range was found for the vehicle to have a desirable operation. A range was given instead of a single value due to 2 reasons: the small percentage of difference in performance between the two values, and the fact that most of the gearbox manufacturing companies have determined values of 𝑁𝑡𝑓, being easier to find a gearbox with a reduction ratio value inside a range than one with an exact value.

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11 Future Work

For further analysis, it would be desirable to manufacture the gearbox with the reduction ratio found in this project. Having it, a comparative analysis could be made by doing practical tests; this way it would be possible to see the differences it presents in comparison to the simulations.

In the current project the electric energy acquisition from the batteries to the motor was not analyzed, for which a later step in the design process could be to find what type and size of batteries and of ICE have to be used in the current vehicle.

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Design and analysis of the powertrain performance for a series configuration hybrid electric vehicle operating in Bogotá, Colombia

Degree Project