Simulation Tools for Predicting Energy Consumption and Range of Electric Two-wheelers A Thesis Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Nathan Lord, B.S. Electrical Engineering Graduate Program in Mechanical Engineering The Ohio State University 2016 Master s Examination Committee: Marcello Canova, Advisor Giorgio Rizzoni
Copyright by Nathan Lord 2016
Abstract This research investigates the design and implementation of simulation tools used to predict the energy consumption and range of electric two-wheelers. The simulation tools developed can be used as design tools or as a real-time prediction of available range. These simulation tools can be used to design electric motorcycles which could decrease traffic congestion and pollution in urban areas. The first simulator was developed in collaboration with GenZe to develop a simulation tool to help design their next electric scooter. The equations for each component were developed to accurately estimate the energy consumption of the first GenZe scooter and developed to be modular in order to be used as a design tool in the future. Each component of the simulator was calibrated to the current GenZe scooter by conducting multiple experiments on the individual components and full vehicle testing. The motor and inverter models were calibrated using data collected at the Center for Automotive Research (CAR) using a dynamometer and a power analyzer. The data collected was used to find the motor constants and efficiency of the motor and inverter. The battery model was calibrated using a battery tester and a environmental chamber at CAR. The data collected was used to find the internal resistance and firstorder equivalent circuit RC parameters of a single cell at multiple states of charge and temperatures. ii
The electric powertrain model and the full GenZe model were validated using a chassis dynamometer and riding the scooter at the Transportation Research Center. The electric powertrain model was validated with low error between the predicted results and data collected on a chassis dynamometer which met the requirements of the GenZe project. Errors were found between the full GenZe model and collected data from riding the scooter on the road which suggested the chassis model does not accurately predict energy consumption during turning. In light of the limitations seen in the GenZe model an investigation into twodimensional vehicle dynamics modeling was conducted. Two additional chassis models were developed to model a turning two-wheeler. The first model predicts the two-dimensional location of the vehicle by estimating the lateral tire forces on the motorcycle. The second model extends the first model by estimating the lean of the motorcycle given the speed and corner radius. The predicted energy consumption of the two models and the GenZe chassis model were compared to BikeSim through multiple turning profiles. It was found the models underestimate the energy consumption compared to BikeSim, which suggested the models do not predict all the forces that slow a twowheeler during turning. Further comparison between the models and BikeSim shows a difference between the predicted normal forces on the tires and the rear tire radius suggesting future work should investigate the pitching and tire dynamics of a twowheeler during turning. This work uncovers the complexity of estimating the road forces on a two-wheeler. Ultimately future work should focus on the road forces of two-wheelers in order to increase the accuracy of energy consumption prediction of electric motorcycle simulation tools. iii
This work is dedicated to my friends and family. iv
Acknowledgments Thank you to the Ohio State University Center for Automotive Research faculty and research staff including Dr. Canova, Dr Rizzoni, Jeff Christos, Walt Dudek, Jim Shively, and Bill Sparks for sharing your time, advice, and expertise. I also thank my fellow OSU students including Lauren Alman, Yupeng Cheng, and Sarah Norris for helping me conduct all the required tests to complete the project. Thank you GenZe including Mobashar Ahmad and Chad Allison for supporting my masters and giving me their time and knowledge to build the best simulator possible. Thank you again for all your help! v
Vita 2010........................................Upper Arlington High School 2014........................................B.S. Electrical Engineering 2014 to present............................. Graduate Research Associate, Center for Automotive Research, The Ohio State University Fields of Study Major Field: Mechanical Engineering vi
Table of Contents Page Abstract....................................... Dedication...................................... Acknowledgments.................................. Vita......................................... List of Tables.................................... ii iv v vi ix List of Figures................................... xii 1. Introduction and Motivations........................ 1 1.1 Importance of Energy Consumption for Electric Motorcycles.... 1 1.2 The GenZe Project........................... 2 1.3 Objectives of This Work........................ 2 1.4 Structure of the Thesis......................... 3 2. Model of Electric Powertrain......................... 4 2.1 Structure of Model........................... 4 2.2 Models of the Powertrain Components................ 6 2.2.1 Inverter............................. 7 2.2.2 Motor.............................. 8 2.2.3 Gearing............................. 9 2.2.4 Brakes.............................. 11 2.2.5 BMS............................... 12 2.2.6 Auxiliary Load......................... 13 2.2.7 Battery............................. 14 2.2.8 Inverter Cooling........................ 16 vii
2.2.9 Motor Cooling......................... 18 2.2.10 Battery Cooling........................ 20 2.2.11 BMS Cooling.......................... 21 2.3 Calibration............................... 22 2.3.1 Motor and Inverter Model Calibration............ 22 2.3.2 Battery Pack Model Calibration............... 30 2.3.3 Calibration of all Thermal Models.............. 40 2.4 Conclusion............................... 48 3. GenZe Scooter Model and Validation.................... 49 3.1 Chassis, Tire, and Rider Models.................... 50 3.1.1 Chassis............................. 50 3.1.2 Tire............................... 53 3.1.3 Rider.............................. 55 3.2 Chassis and Tire Calibration..................... 56 3.3 Verification of the Scooter Model................... 60 3.3.1 HBM Datalogger........................ 60 3.3.2 Chassis Dynamometer Validation............... 64 3.3.3 Road Validation........................ 67 3.4 Limitations of the GenZe Scooter Model............... 73 3.5 Conclusions............................... 77 4. Motorcycle Dynamics............................. 79 4.1 Classification of Models........................ 79 4.2 Equations................................ 81 4.2.1 Two Dimensional Vehicle Dynamics............. 81 4.2.2 Extended 2D model...................... 90 4.3 Calibration and Verification...................... 94 4.3.1 Calibration of 2D and Extended 2D Models......... 95 4.3.2 Verification of 2D and Extended 2D Models......... 98 4.4 Comparative Study........................... 102 4.5 Conclusion............................... 111 5. Conclusions and Future Work........................ 112 Bibliography.................................... 114 viii
List of Tables Table Page 2.1 List of symbols.............................. 6 2.2 Summary of inverter model I/O..................... 8 2.3 Summary of inverter model parameters................. 8 2.4 Summary of motor I/O.......................... 9 2.5 Summary of motor parameters...................... 9 2.6 Summary of gearing I/O......................... 11 2.7 Summary of gearing parameters..................... 11 2.8 Summary of brake I/O.......................... 12 2.9 Summary of brake parameters...................... 12 2.10 Summary of BMS I/O.......................... 13 2.11 Summary of BMS parameters...................... 13 2.12 Summary of auxiliary load I/O..................... 14 2.13 Summary of auxiliary load parameters................. 14 2.14 Summary of battery I/O......................... 16 2.15 Summary of battery parameters..................... 16 ix
2.16 Summary inverter cooling I/O...................... 17 2.17 Summery of inverter cooling parameters................ 18 2.18 Summary of motor cooling I/O..................... 19 2.19 Summary of motor cooling parameters................. 19 2.20 Summary of battery cooling I/O..................... 20 2.21 Summary of battery cooling parameters................ 20 2.22 Summary of BMS cooling I/O...................... 21 2.23 Summary of BMS cooling parameters.................. 21 3.1 List of chassis symbols.......................... 50 3.2 Summary of chassis model I/O...................... 52 3.3 Summary of chassis model parameters................. 53 3.4 Summary of tire model I/O....................... 54 3.5 Summary of tire model parameters................... 55 3.6 Summary of rider model I/O....................... 56 3.7 Summary of rider model parameters................... 56 3.8 List of sensor connected to the HBM datalogger............ 61 4.1 Summary of 2D model I/O........................ 89 4.2 Summary of 2D model parameters.................... 90 4.3 Summary of extended 2D model I/O.................. 94 4.4 Summary of extended 2D model parameters.............. 94 4.5 Zero roll model comparison....................... 105 x
4.6 5 degree roll model comparison..................... 106 4.7 10 degree roll model comparison..................... 106 4.8 20 degree roll model comparison..................... 106 4.9 30 degree roll model comparison..................... 107 xi
List of Figures Figure Page 1.1 Diagram of the GenZe scooter model.................. 3 2.1 Powertrain model diagram........................ 5 2.2 Rigid gearing............................... 10 2.3 Battery equivalent circuit........................ 15 2.4 Inverter cooling diagram......................... 17 2.5 Motor cooling diagram.......................... 19 2.6 Side view picture of the motor and inverter test setup......... 23 2.7 Top view picture of the motor and inverter test setup......... 23 2.8 Motor and inverter dyno testing diagram................ 24 2.9 Power analyzer AC wiring (3-phase 3-wire)............... 25 2.10 Power analyzer DC wiring (1-phase 1-wire)............... 25 2.11 Motor speed and torque profile..................... 26 2.12 Motor speed constant results....................... 27 2.13 Motor torque constant results...................... 28 2.14 Inverter efficiency results......................... 29 xii
2.15 Motor efficiency results.......................... 30 2.16 Battery current profile.......................... 32 2.17 Battery open circuit voltage....................... 33 2.18 Example of battery experimental data at a single temperature.... 34 2.19 Calibrated battery parameters vs. SOC at 25............ 36 2.20 two dimensional tables of battery parameters.............. 38 2.21 Battery validation profile......................... 39 2.22 Battery validation............................. 40 2.23 Motor thermal model calibration.................... 42 2.24 Inverter thermal model calibration................... 43 2.25 Motor thermal model validation..................... 44 2.26 Inverter thermal model validation.................... 45 2.27 Battery thermal model calibration.................... 47 2.28 BMS thermal model calibration..................... 47 3.1 GenZe scooter model diagram...................... 49 3.2 Chassis model force and parameter diagram.............. 51 3.3 Graphical description of the magic formula [6]............. 53 3.4 Coast-down test data........................... 57 3.5 Coast-down calibration results...................... 59 3.6 Mounting and measurement diagram for the steering angle and suspension travel sensors........................... 62 xiii
3.7 Inertial measurement unit diagram................... 64 3.8 Speed validation.............................. 65 3.9 SOC validation.............................. 66 3.10 Battery voltage validation........................ 67 3.11 Road testing open-loop model vehicle speed comparison........ 68 3.12 Road testing open-loop model state of charge comparison....... 69 3.13 Road testing open-loop model battery voltage comparison...... 70 3.14 Road testing driver model vehicle speed comparison.......... 71 3.15 Road testing driver model throttle command comparison....... 71 3.16 Road testing driver model state of charge comparison......... 72 3.17 Road testing driver model battery voltage comparison......... 73 3.18 TRC profile................................ 74 3.19 Open-loop comparison.......................... 75 3.20 Driver results............................... 76 4.1 Two dimensional reference frames.................... 82 4.2 Two-dimensional acceleration diagram................. 83 4.3 2D vehicle frame............................. 85 4.4 2D lateral forces.............................. 87 4.5 Tire angles diagram............................ 88 4.6 Steering geometry diagram........................ 93 4.7 Road load coast-down calibration.................... 96 xiv
4.8 Tire calibration.............................. 97 4.9 BikeSim roll angle profile......................... 98 4.10 2D model validation........................... 99 4.11 Extended 2D model validation...................... 101 4.12 Roll profiles................................ 103 4.13 Comparative study results plot..................... 105 4.14 20 degree roll comparison......................... 108 4.15 Tire normal force comparison during coast-down............ 110 xv
Chapter 1: Introduction and Motivations Electric vehicles are becoming more popular because they are cheaper to maintain compared to gas vehicles [1], especially as gas prices rise. Motorcycle use is also increasing because two-wheeled vehicles are cheaper to maintain than four-wheeled vehicles and help with traffic congestion in urban cities. starting to purchase electric motorcycles in urban areas. In turn, consumers are For example, China has seen a dramatic growth in electric two-wheelers over the past five years [2]. 1.1 Importance of Energy Consumption for Electric Motorcycles The down side of electric motorcycles is their lack of range. Consumers want to be able to ride as long as possible before having to recharge the battery pack. Companies selling electric motorcycles must be able to precisely estimate the range of their products. In order to estimate the range, it is critical to know both the energy consumption of the vehicle and the amount of energy carried in the battery pack. Predicting energy consumption for an electric motorcycle is particularly complicated because the uncertainties in estimating the road load, efficiency of the powertrain and battery can drastically affect the energy consumption of a light weight vehicle. 1
One solution to this problem is to use a simulation tool that predicts the dynamic behavior of the electric motorcycle including the energy flows on board. A design engineer can use the simulation tool to iterate over multiple motorcycle designs to determine the optimal battery pack size. Alternatively, the simulator could be use to provide a real-time estimate of the energy consumption and of the available range. 1.2 The GenZe Project GenZe is a company based in Ann Arbor, Michigan that builds electric scooters [3]. GenZe has recognized the importance of using a simulation to predict energy consumption and range of their electric scooters and collaborated with the Center of Automotive Research at the Ohio State University to develop this simulation. The goal of the project is to develop an electric scooter model for the generation scooter, so that they can use it as a development tool for their next products. 1.3 Objectives of This Work This work describes the development, calibration and verification process of the GenZe scooter model. As per the project specifications, the model must predict, within 20% error, the following simulated signals, compared to the signals collected from the actual scooter: Battery pack current, Battery pack voltage, Motor torque, Motor speed. This error requirement was chosen because, based on previous experience, achieving less than 20% error of the given signals lead to a reasonably accurate prediction of the energy consumption and range of electric vehicles. Additionally, the simulation must be built in modular fashion, so that it can be updated easily. GenZe wants to be able to update the simulation for two reasons. First GenZe wants to be 2
able to update the simulation to new motorcycle designs. Second they want to be able to increase the fidelity of simulation to diagnose problems in specific components of the scooter. 1.4 Structure of the Thesis This thesis presents the development, calibration, validation and analysis of the GenZe scooter model. The model is presented in two parts, the powertrain model and the chassis model as shown in Figure 1.1. The powertrain model predicts how the electrical and mechanical components provide torque to the tires. The chassis model predicts the speed and dynamics of the motorcycle. Figure 1.1: Diagram of the GenZe scooter model Chapter 2 presents the equations and calibration process for the powertrain model. Chapter 3 presents the chassis model, shows the validation results of the powertrain model, and shows the GenZe scooter model as a whole. Chapter 3 also discusses the limitations of the GenZe scooter model. Chapter 4 presents an investigation into potential chassis models that could increase the accuracy of the GenZe scooter model in predicting energy consumption and range. 3
Chapter 2: Model of Electric Powertrain A model of an electric powertrain will be presented in this chapter. The equations and calibration process used for each component are discussed. The inputs to the powertrain model are the rider throttle, brake command, and the tire torque. The output is the torque applied to the rear tire. The powertrain components are designed to be modular and to achieve less than 20% error in order to meet the requirements of the GenZe project. The equations used in this chapter are based on the theory presented in Vehicle Propulsion Systems [4]. The purpose of developing a powertrain model is to isolate the function of the powertrain from the vehicle dynamics. 2.1 Structure of Model The powertrain model can be seen in Figure 2.1 and is a forward-looking model where the force signals move forward (to the right) to calculate vehicle speed and the vehicle speed signals move backwards (to the left) through the powertrain. The force signals are DC voltage from the battery, AC current from the inverter, torque from the motor, and force from the gearing. The speed signals are angular velocity from the gearing, AC voltage from the motor, and DC current from the battery. The controller block provides current and brake commands to the inverter and to the gearing. The dyno block provides a speed-dependent resistive load to the gearing. 4
This type of model structure was chosen because forward-looking models are used for energy consumption modeling. Figure 2.1: Powertrain model diagram To meet the requirements of the GenZe project the powertrain model must predict the battery pack current, battery pack voltage, motor torque, and motor speed. These must be within 20% error when compared to experimental data. The model must also be modular which means it facilitates the integration of new components and modification of existing components. In order to meet the error requirement the equations and calibration procedures described in this chapter were developed to produce results that give no more than 10% error for each component. The components were also developed to be modular by choosing inputs and outputs for each component so the model equations can be updated without changing the inputs and outputs. The properties of this model were chosen so that it can be used for further 5
powertrain simulation development and as a design tool for engineers building an electrical vehicle. 2.2 Models of the Powertrain Components This section presents a model of each component within the powertrain. For each component a rationale with equations and a list of input and outputs and parameters are given. Table 2.1 lists the general symbols used in the model equations. Symbol T τ t w V v I i η P Q J m R C M C F Description Temperature Torque Time Angular velocity DC voltage RMS voltage DC current RMS current Efficiency Power Heat flux Rotational inertia Mass Resistance Capacitance Thermal mass Force Table 2.1: List of symbols 6
2.2.1 Inverter The inverter block models the conversion of power from the AC motor to the DC battery using the battery voltage (V b ), AC motor current command (i m ), and motor back-emf (v emf ). The DC power is calculated using the AC power and the provided inverter efficiency. The battery current is calculated using the predicted DC power and the input battery voltage. The heat loss ( Q loss ) is calculated as the difference between the AC and DC power. It is assumed power is conserved between the AC power, DC power, and heat loss. It is also assumed the efficiency is a function of motor back-emf and motor current which is provided by the manufacturer or from other testing. Tables 2.2 and 2.3 summarize the input and output variables, and the model parameters. i m = i mcmd (2.1) P c = abs(v bms i m ) (2.2) P eff = P c η c (v emf, i m ) (2.3) Q mc = P eff P c (2.4) I eff = P eff V bms (2.5) I c = I eff sign(i m ) (2.6) 7
Input/Output Signal Name Unit Description Input i mcmd A (RMS) Motor current command Input V bms V (DC) Battery voltage Input v emf V (RMS) Motor back-emf Output Q mc W Power Loss Output I c A (DC) Battery current Output i m A (RMS) Motor current Table 2.2: Summary of inverter model I/O Parameter Unit Description η c - Efficiency table Table 2.3: Summary of inverter model parameters 2.2.2 Motor The motor block models the conversion from AC current (i m ) to motor torque (τ m ) and the motor speed (w m ) to back-emf (v emf ). The relationship between speed and back-emf is linear and is calculated using constant C v. The relationship between current and torque is linear and is calculated using the constant C i. The heat loss ( Q loss ) is predicted using the provided efficiency. The efficiency is assumed to be a function of motor back-emf and motor torque and must be provided by the manufacturer or from other testing. Tables 2.4 and 2.5 summarize the input and output variables, and the model parameters. 8
v emf = C v w m (2.7) τ motor = C i i m (2.8) P motor = abs(v emf τ motor ) (2.9) Q loss = P motor (1 η m (v emf, τ m )) (2.10) Input/Output Signal Name Unit Description Input i m A (RMS) Motor current Input w m rad/s Motor angular velocity Output Q loss W Power loss Output τ m Nm Motor torque Output v emf V (RMS) Motor back-emf Table 2.4: Summary of motor I/O Parameter Unit Description C v V/(rad/s) Voltage constant of the motor C i Nm/A (RMS) Torque constant of the motor η m - Motor efficiency Table 2.5: Summary of motor parameters 2.2.3 Gearing The gearing block models the motor speed (w m ) and the back tire speed (w t ) using motor torque (τ m ), tire torque (τ t ), and brake torque (τ b ). The model assumes the 9
motor and tire have constant inertias (J m and J t, respectively) connected through a rigid gear with a constant ratio (r) and efficiency (η). It was decided to use a rigid connection instead of a flexible connection because a rigid connection is a less complex model and is sufficient to meet the 10% error requirement. The motor speed is calculated using the torque inputs and lumped inertias. The tire speed is calculated using the gear ratio and motor speed. Tables 2.6 and 2.7 summarize the input and output variables, and the model parameters. Figure 2.2: Rigid gearing dw m dt = η gτ m r g (τ t τ b ) J m + r 2 gj t (2.11) w t = r g w m (2.12) 10
Input/Output Signal Name Unit Description Input τ m Nm Motor torque Input τ b Nm Brake torque Input τ t Nm Tire/dyno torque Output w m rad/s Motor velocity Output w t rad/s Tire velocity Table 2.6: Summary of gearing I/O Parameter Unit Description η g - Gearing efficiency J m kg m 2 Inertia of the motor J t kg m 2 Inertia of the tire r g Gear ratio Table 2.7: Summary of gearing parameters 2.2.4 Brakes The brake block models the brake force and torque using the brake command (β) assuming a linear resistance constant and a constant brake disc radius. Tables 2.8 and 2.9 summarize the input and output variables, and the model parameters. F b = abs(w t ) β C b (2.13) τ b = F b r brake (2.14) (2.15) 11
Input/Output Signal Name Unit Description Input w t rad/s Tire angular velocity Output F b N Brake force Output τ b Nm Brake torque Table 2.8: Summary of brake I/O Parameter Unit Description C b - Brake resistance coefficient r brake m Brake disc radius Table 2.9: Summary of brake parameters 2.2.5 BMS The BMS block models the Battery Management System of the vehicle. The model predicts the heat loss ( Q loss ) of the BMS assuming a constant resistance (R bms ) in series with the battery pack. This model adds the current draw of the auxiliary load (I aux ) to the inverter command (I c ) to provide an input to the battery (I bms ). The BMS model also provides the battery voltage to the inverter. Tables 2.10 and 2.11 summarize the input and output variables, and the model parameters. 12
I bms = I c + I aux (2.16) Q bms = R bms I 2 bms (2.17) V bms = V b (2.18) Input/Output Signal Name Unit Description Input I c A Inverter current command Input V b V Battery voltage Input I aux A Auxiliary load current draw Output I bms A Current draw Output V bms V BMS measurement of battery voltage Output Q bms W Power loss Table 2.10: Summary of BMS I/O Parameter Unit Description R bms Ω Heating resistance Table 2.11: Summary of BMS parameters 2.2.6 Auxiliary Load The auxiliary load block models the auxiliary current (I aux ) of the vehicle as a constant power draw (P aux ) using battery voltage (V bms ). Tables 2.12 and 2.13 summarize the input and output variables, and the model parameters. 13
I aux = P aux V bms (2.19) Input/Output Signal Name Unit Description Input V bms V Battery voltage Output I aux A Auxiliary current Table 2.12: Summary of auxiliary load I/O Parameter Unit Description P aux W Auxiliary power draw Table 2.13: Summary of auxiliary load parameters 2.2.7 Battery The battery block models the battery pack using the first-order equivalent circuit model [5] shown in Figure (2.3). Our model is an improvement of the basic firstorder equivalent circuit model because it updates the internal resistance (R 0 ) and RC parameters (C 1,R 1 ) based on the state of charge (SOC) and the cell temperature (T b ). The parameters of the model are for a single cell. The parameters are functions of SOC and temperature. The number of cells in the pack is determined by cells in parallel (P ) and the cells in series (S). The SOC is calculated using the Coulomb counting method. The open circuit voltage is assumed to be a function of SOC and which is provided by the manufacturer or determined from data. Due to the empirical 14
nature of the model it is necessary to perform testing to generate the tables predicting the internal resistance and RC parameters. Tables 2.14 and 2.15 summarize the input and output variables, and the model parameters. Figure 2.3: Battery equivalent circuit I cell = I bms P SOC = SOC 0 1 Ah dv 1 dt = 1 R 1 (SOC, T b )C 1 (SOC, T b ) V 1 + (2.20) I cell dt (2.21) 1 C 1 (SOC, t b ) I cell (2.22) V b = V oc (SOC) R 0 (SOC, t b )I cell V 1 )S (2.23) Q b = abs[((v oc (SOC) V b )I cell )(S P )] (2.24) 15
Input/Output Signal Name Unit Description Input I bms A BMS current Input T b Battery temperature Output V b V Battery voltage Output Q b W Power loss Table 2.14: Summary of battery I/O Parameter Unit Description Ah Ah Capacity V oc V Open circuit voltage R 0 Ω Internal resistance R 1 Ω RC resistance C 1 F RC capacitance P - Cells in Parallel S - Cells in Series SOC 0 Ah Initial state of charge Table 2.15: Summary of battery parameters 2.2.8 Inverter Cooling The inverter cooling block models the temperature of the inverter electronics (T c ) using the ambient air temperature (T amb ) and inverter heat loss ( Q loss ). The model was developed using multiple iterations until the model was calibrated to the required error limit. Seen in Figure 2.4 the model contains three thermal masses (board, air in box, and box) with a thermal sink and four thermal resistances. The model assumes the thermal mass of air in the box is very small compared to the board and box thermal 16
masses. The air in the box temperature is assumed to be the average of the board and box temperatures. Tables 2.16 and 2.17 summarize the input and output variables, and the model parameters. Figure 2.4: Inverter cooling diagram T a = T bha b + T c ha c ha b + ha c (2.25) dt b dt = Q loss ha b (T b T a ) R c (T b T c ) MC b (2.26) dt c dt = ha c(t a T c ) + R c (T b T c ) ha out (T c T amb ) MC c (2.27) Input/Output Signal Name Unit Description Output T c Inverter board temperature Input Q loss W Power loss Input T amb Ambient temperature Table 2.16: Summary inverter cooling I/O 17
Parameter Unit Description R c W/ Thermal resistance between board and ambient MC b /W Thermal mass of board MC c /W Thermal mass of box ha b W/ Thermal resistance between board and box air ha c W/ Thermal resistance between and box air ha out W/ Thermal resistance between board and ambient Table 2.17: Summery of inverter cooling parameters 2.2.9 Motor Cooling The motor cooling block models the temperature of the motor stator (T s ) using the ambient air temperature (T a ) and motor heat loss ( Q loss ). The model was developed using multiple iterations until the model was calibrated to the required error limit. Figure 2.5 shows the model containing two thermal masses (stator and rotor) with a thermal sink and two thermal resistances. It is assumed the air only cools the rotor, and the cooling of the stator is only dependent on the temperature of the rotor. It is assumed the heat loss goes to the stator and the rotor. The percent of heat loss to the rotor is defined by α. Tables 2.18 and 2.19 summarize the input and output variables, and the model parameters. 18
Figure 2.5: Motor cooling diagram dt s dt = α Q loss R gap (T s T r ) MC s (2.28) dt r dt = (1 α) Q loss R gap (T s T r ) ha r (T r T a ) MC r (2.29) Input/Output Signal Name Unit Description Output T s Stator temperature Input Q loss W Power loss Input T a Ambient temperature Table 2.18: Summary of motor cooling I/O Parameter Unit Description R gap W/ Thermal resistance between rotor and stator MC r /W Thermal mass of the rotor MC s /W Thermal mass of the stator ha r W/ Thermal resistance between rotor and ambient α - Percent of heat going to stator Table 2.19: Summary of motor cooling parameters 19
2.2.10 Battery Cooling The battery cooling block models the temperature of the center cell in the battery pack (T b ) using the ambient air temperature (T a ) and battery heat loss ( Q loss ). The battery cooling is a single thermal mass (MC b ) system that cools to the ambient air. Tables 2.20 and 2.21 summarize the input and output variables, and the model parameters. dt b dt = Q loss R b (T b T a ) MC b (2.30) Input/Output Signal Name Unit Description Output T b Battery pack temperature Input Q loss W Power loss Input T a Ambient temperature Table 2.20: Summary of battery cooling I/O Parameter Unit Description R b W/ Resistance between the battery and ambient MC b /W Thermal mass of the battery pack Table 2.21: Summary of battery cooling parameters 20
2.2.11 BMS Cooling The BMS cooling block models the temperature of the battery management system (T bms ) using the ambient air temperature (T a ) and BMS heat loss ( Q loss ). The battery cooling is a single thermal mass (MC bms ) that is cooled to the ambient air. It is assumed the temperature of the ambient air and the battery are the same because of the placement of the BMS in the motorcycle. Tables 2.22 and 2.23 summarize the input and output variables, and the model parameters. dt bms dt = Q loss R bms (T bms T a ) MC bms (2.31) Input/Output Signal Name Unit Description Output T bms BMS temperature Input Q loss W Power loss Input T a Ambient/battery temperature Table 2.22: Summary of BMS cooling I/O Parameter Unit Description R bms W/ Thermal resistance between the BMS and ambient MC bms /W Thermal mass of the BMS Table 2.23: Summary of BMS cooling parameters 21
2.3 Calibration This section presents the calibration procedure for the motor, inverter, battery pack, and related thermal models. In general the calibration process uses a nonlinear least squares method to find the model parameters that reduce the cumulative square error of the model output when compared to experimental data. 2.3.1 Motor and Inverter Model Calibration The motor and inverter calibration procedure estimates the efficiency of both the inverter and the motor while measuring the motor speed and torque constants. The experimental data was collected at the Center for Automotive Research using a dynamometer and a ZES high frequency power analyzer. The efficiency data is mapped to a two dimensional mesh and the speed and torque measurements are fit to their respective constants. Experimental Data The GenZe inverter, GenZe motor, dyno, and a power source were connected to each other to calibrate the inverter and motor models. Picture 2.6 shows the side view of the motor connected to the dyno and Picture 2.7 shows a top view of the inverter. A high frequency power analyzer was used to measure all the required powers (DC, AC, Mechanical) seen in Figure 2.8. The dyno is used to spin the motor at specified speeds. 22
Figure 2.6: Side view picture of the motor and inverter test setup. Figure 2.7: Top view picture of the motor and inverter test setup. 23
Figure 2.8: Motor and inverter dyno testing diagram A LMG670 ZES Zimmer power analyzer was used to measure and log all required signals. The AC measurements were obtained using the 3-phase 3-wire configuration with three current sensors and three pole-to-pole voltage measurements shown in Figure 2.9. The power analyzer measures the Wye voltage and current of the motor and inverter. The power analyzer internally converts between Wye and Delta measurements assuming a balanced load which is correct when measuring a motor and inverter. For our testing the Wye current and voltage measurements are used because the modeled motor back-emf and motor current signals are Star measurements. The DC measurements were obtained using the 1-phase 1-wire configuration with one current sensor and one voltage measurement shown in Figure 2.10. The current is measured on the neutral pole and the voltage is measured between the single pole and neutral. No conversion is necessary for the DC measurements. 24
Figure 2.9: Power analyzer AC wiring (3-phase 3-wire) Figure 2.10: Power analyzer DC wiring (1-phase 1-wire) 25
Two different torque/speed profiles were developed to find motor constants and the motor and inverter efficiencies. The first profile runs the motor at zero torque through the full operating range of speed while measuring the AC voltage and motor speed. The test provides all the necessary data to calibrate the motor speed constant by finding a linear fit to the collected speed and back-emf voltage. The second profile runs the motor and inverter at the full operating range of torque and speed. This profile is performed by setting the dyno to a specified speed (allowing the dyno to provide any required torque to stay at that speed) while ramping the motor torque. The specified speed is then increased and the test is repeated seen in Figure 2.11. 120 100 80 Motor Torque [Nm] 60 40 20 0-20 -40-60 0 100 200 300 400 500 600 Motor Speed [r/min] Figure 2.11: Motor speed and torque profile 26
During second profile all measurements are logged (AC power, DC power, mechanical power). The inverter efficiency is calculated by dividing the AC power by the DC Power. Motor efficiency is calculated by dividing the mechanical power by the AC power. The efficiencies are then fit to a two dimensional mesh. Also by collecting the torque and AC current the motor torque constant can be estimated by finding a linear fit between collected AC current and motor torque data. Results Figure 2.12 shows the data and linear fit of the motor speed constant. The data follows a linear relationship between motor back-emf and motor speed with a 0.9993 R 2 fit. The graph shows bumps in the motor back-emf measurement caused by the dyno increasing to the next motor speed. It is assumed these bumps are caused by quick dynamics in the inverter. These points are not included in the fit. Motor Back-EMF [V (RMS] 18 16 14 12 10 8 6 4 data fit C v = 0.057 R 2 = 0.9993 2 0 0 50 100 150 200 250 300 350 Motor Speed [r/min] Figure 2.12: Motor speed constant results 27
Figure 2.13 shows the data and linear fit of the motor torque constant. The data follows a linear relationship between motor AC current and motor torque with a 0.9804 R 2 fit. The graph shows outliers around zero torque caused by the low accuracy of torque measurements in this region. These measurements were included in the fit, resulting in a low fit correlation. There are other data points collected between 50 and 150 A on the graph. These data points are not included in the fit because they are outside of the motor operating range. 120 100 data fit Motor Torque [Nm] 80 60 40 20 0-20 C i = 0.47 R 2 = 0.9804-40 -60-80 -100-50 0 50 100 150 200 250 Motor Current [A (RMS)] Figure 2.13: Motor torque constant results Figures 2.14 and 2.15 show the results of efficiency testing for both the inverter and motor. The inverter mesh and motor mesh fit the data with 0.9949 and 0.8774 R 2, respectively. Importantly the shape of the efficiency curves match data in [4]. 28
The inverter efficiency fit was expected to be accurate because the measurements (DC power and AC power) were performed with highly accurate and calibrated sensors giving a high fit correlation. However, the motor efficiency was difficult to measure around zero torque because torque accuracy was low in that range. Artifacts of this poor measurement can be seen in Figure 2.15 and cause low a R 2. data table 95 Inverter Efficiency [%] 90 85 80 75 200 R 2 = 0.9949 150 100 50 Motor Current [A (RMS)] 0-50 500 400 300 200 100 Motor Speed [r/min] Figure 2.14: Inverter efficiency results 29
data table Motor Efficiency [%] 80 60 40 20 0-20 100 R 2 = 0.8774 50 0-50 400 500 300 200 Motor Speed 100 [r/min] Motor Torque [Nm] Figure 2.15: Motor efficiency results 2.3.2 Battery Pack Model Calibration This section presents calibration and validation procedures of the empirical battery model. The model is based on a first order equivalent circuit model with an internal resistance, an RC loop, and open circuit voltage as a function state of charge. For added accuracy all the internal resistance and RC parameters are functions of state of charge and battery temperature described in Section 2.2.7. The cell used in the GenZe scooter is a LiF ep O 4 - graphite, in a 18650 format, with nominal voltage of 3.7 V and capacity of 2.8 Ah. The battery pack is configured with 14 cells in series and 12 in parallel giving a nominal bus voltage of 51.8 V and capacity of 1.74 kwh. 30
To find the open circuit voltage the cell is discharged/charged at a low current while logging the voltage and current. A map can be generated from collected state of charge and open circuit voltage data [5]. To determine the relationship of the internal resistance and the RC loop parameters to state of charge and temperature a set of experiments were developed to test the full operating range of a cell. A current profile was developed to pulse the cell at multiple currents at multiple states of charge. This profile was also ran at multiple cell temperatures. Figure 2.16 shows the battery current profile that pulses between -8 and 8 A. The battery current profile also properly charges/discharges the cell to multiple states of charge. Importantly, the cell is assumed to start at 20% state of charge. In turn the cell is tested between 20% and 95% states of charge. 31
10 8 6 Battery Current [A] 4 2 0-2 -4-6 -8-10 0 5 10 15 20 25 30 35 40 Time [h] 80 70 60 50 SOC [%] 40 30 20 10 0-10 0 5 10 15 20 25 30 35 40 Time [h] Figure 2.16: Battery current profile Experimental Data/Calibration Procedure The two battery current profiles are performed on a single GenZe cell. The low current profile is performed to estimate the open circuit voltage. Then multiple pulse 32
profiles are performed at different temperatures to estimate the internal resistance and RC parameters. The low current profile is performed with a Maccor battery tester which logs the voltage and current during the test. The data is used to create a state of charge to open circuit voltage map seen in Figure 2.17. 4.2 4 3.8 Open Circuit Voltage [V] 3.6 3.4 3.2 3 2.8 2.6 2.4 0 10 20 30 40 50 60 70 80 90 100 SOC [%] Figure 2.17: Battery open circuit voltage The pulse profile is performed multiple times at different temperatures using a Maccor battery tester and CSZ environmental chamber. The CSZ environmental chamber controlled the temperature of the cell. The Maccor battery tester charged/discharged the cell according the test profile and logged the voltage and current of the cell. Figure 2.18 shows an example of the collected data for a single temperature. 33
4.4 4.2 4 10 8 6 Cell Voltage [V] 3.8 3.6 3.4 3.2 3 4 2 0-2 -4 Current [A] 2.8 2.6-6 -8 2.4-10 0 5 10 15 20 25 30 35 40 Time [h] Figure 2.18: Example of battery experimental data at a single temperature Each single temperature dataset is post-processed to estimate the internal resistance (R 0 ) and RC parameters (C 1,R 1 ) at each SOC step. The internal resistance is estimated by dividing voltage drop by current difference at large current step pulses. R 0 = V I (2.32) A non-linear least square method was used to find the remaining RC parameters using the average internal resistance calculated for each SOC and the open circuit voltage as parameters. The method uses a non-linear method to find the combination of RC parameters that minimizes cumulative square error between the model and experimental data. The minimization procedure is run at each SOC step and finds the RC parameters for each SOC step at a single temperature. 34
This calibration process produces tables showing internal resistance and the RC parameters at each tested state of charge. Figure 2.19 shows an example of the values found at 25. 35
0.047 0.046 0.045 R 0 Parameters [ Ω ] 0.044 0.043 0.042 0.041 0.04 0.039 0.038 0.037 0 10 20 30 40 50 60 70 80 90 SOC [%] 0.14 0.12 R 1 Parameters [ Ω ] 0.1 0.08 0.06 0.04 0.02 0 0 10 20 30 40 50 60 70 80 90 SOC [%] 4000 3500 3000 C 1 Parameters [F] 2500 2000 1500 1000 500 0 10 20 30 40 50 60 70 80 90 SOC [%] Figure 2.19: Calibrated battery parameters vs. SOC at 25 36
All the single temperature calibrated values are combined and fit to a two dimensional mesh. Results and Validation Figure 2.20 shows the result of performing the pulse profiles at multiple temperatures on a GenZe cell. The two dimensional meshes of the three parameters (R 0,R 1,C 0 ) fit the experimental data with 0.9976, 0.9210, and 0.9600 R 2, respectively. The results match our general intuition of lithium polymer cells and the data seen in [5]. 37
R 0 Parameters [ Ω ] 0.1 0.09 0.08 0.07 0.06 data table R 2 = 0.9976 0.05 0.04 0 10 20 30 Cell Temperature [C] 40 0 20 40 60 SOC [%] 80 100 R 1 Parameters [ Ω ] 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 R 2 = 0.9210 data table 0 10 20 30 Cell Temperature [C] 40 0 20 40 60 80 100 SOC [%] data table 3500 R 2 = 0.9600 C 1 Parameters [F] 3000 2500 2000 1500 1000 500 100 0 10 20 30 Cell Temperature [C] 40 38 0 20 40 60 SOC [%] 80 Figure 2.20: two dimensional tables of battery parameters
To validate the model an extra current profile was generated to simulate a road profile. The current profile was performed using the Maccor battery tester. The cell voltage and current were measured and the simulation results were compared to the data. Figure 2.21 shows the current profile and Figure 2.22 shows the simulation results and the instantaneous error. The simulation results match the data with less than +/- 0.02 volt error which is expected for this type of model and is within the 10% error goal for the component. The largest error occurs between 1500 and 2000 seconds. The equivalent circuit model does not predict the slow relaxation dynamics, unlike, for instance, physics-based electrochemical models. 4 3.5 3 Cell Current [A] 2.5 2 1.5 1 0.5 0-0.5 0 500 1000 1500 2000 2500 Time [s] Figure 2.21: Battery validation profile 39
3.75 3.7 Data Model 3.65 Cell Voltage [V] 3.6 3.55 3.5 3.45 3.4 3.35 0 500 1000 1500 2000 2500 Time [s] 0.02 0.015 0.01 0.005 Error [V] 0-0.005-0.01-0.015-0.02 0 500 1000 1500 2000 2500 Time [s] Figure 2.22: Battery validation 2.3.3 Calibration of all Thermal Models This section presents the calibration process for all of the thermal models (motor, inverter, battery, and BMS). It is important to note the thermal models were 40
developed with an iterative calibration process. If a model did not meet the error requirements after calibration the model was updated with a higher fidelity and the process was repeated until the model achieved an error of +/- 10. Motor and Inverter Cooling Calibration The experimental data collected for the motor and inverter cooling model calibration were logged from the dyno setup discussed in Section 2.3.1. For calibration the dyno was set to a speed, then a high motor current was commanded until the temperature rise started to slow in both components. The motor and inverter were allowed to cool. During the test the temperature of the motor and inverter were measured in real-time. The test was conducted at constant power loss and constant ambient temperature. These values were noted. The motor and inverter models are calibrated using a non-linear least squares method. The method finds the combination of thermal masses and thermal resistances that minimize the cumulative error between the model and the experimental data. Figures 2.23 and 2.24 show the results of the calibration of the motor and inverter with +/- 4 C and +/- 1 C error, respectively. 41
Motor Temperature [C] 100 90 80 70 60 data model 50 4 Error [C] 2 0-2 -4 0 500 1000 1500 2000 2500 Time [s] Figure 2.23: Motor thermal model calibration 42
Inverter Temperature [C] 65 60 55 50 45 40 data model 35 1.5 1 Error [C] 0.5 0-0.5-1 0 200 400 600 800 1000 1200 1400 Time [s] Figure 2.24: Inverter thermal model calibration For validation, a similar test was conducted except multiple current steps are commanded before cool-down. Figures 2.25 and 2.26 show the results of the motor and inverter validation with +/- 10 C and +/- 6 C error, respectively, suggesting the calibrated parameters work for profiles other than the calibration dataset shown in Figures 2.23 and 2.24. 43
Motor Temperature [C] 100 80 60 40 data model 20 10 Error [C] 5 0-5 0 200 400 600 800 1000 1200 1400 1600 Time [s] Figure 2.25: Motor thermal model validation 44
Inverter Temperature [C] 70 60 50 40 30 data model 20 6 4 Error [C] 2 0-2 0 100 200 300 400 500 600 700 800 900 Time [s] Figure 2.26: Inverter thermal model validation It is important to note that the data is collected in a closed room. As a result, the parameters calibrated during this test will probably differ from real driving parameters. From previous experience we find that the discrepancies between simulation results and road data can be manually tuned by adjusting the thermal resistance between the components and the air. Battery/BMS This section presents the calibration process of both the battery and BMS thermal models. The calibration data was collected by using a chassis dyno (discussed more in Section 3.3.2). The test requires the rider to run full throttle on the chassis dyno 45
until the state of charge drops by 10% then allows the scooter to cool-down. The temperatures and the estimated power loss are recorded. First, the battery thermal model is calibrated using a non-linear least squares method that finds the combination of the thermal resistance and the thermal mass to minimize the cumulative square error between the model and experimental data. Next, the same minimizing process is performed for the BMS model using combinations of the thermal mass, thermal resistance, and the BMS resistance. The battery thermal model must be calibrated first because the battery temperature is an input to the BMS thermal model. Figures 2.27 and 2.28 show the battery and BMS thermal validation with error between the model and experimental within +/- 1 C and +/- 4 C of error, respectively. Notably, the battery pack never cools during the test, which makes sense because the battery pack is enclosed in a plastic case. The calibration procedure could be improved by creating conditions that allow the battery pack to cool. 46
26 Cell Temperature [C] 25.5 25 24.5 24 data model 23.5 0.8 Error [C] 0.6 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Time [s] Figure 2.27: Battery thermal model calibration BMS Temperature [C] 40 38 36 34 32 data model 30 4 Error [C] 2 0-2 -4 0 200 400 600 800 1000 1200 Time [s] Figure 2.28: BMS thermal model calibration 47
2.4 Conclusion This chapter presented the electric powertrain model developed for the GenZe scooter. This chapter described the model equations and the calibration procedure for each model component. Each component in the model was calibrated to meet the 10% error requirement, suggesting that the GenZe scooter model as a whole will achieve less than 20% error. The following chapter will present a powertrain validation procedure and test results, in addition to test results for the GenZe scooter model to determine if the 20% requirement is met. 48
Chapter 3: GenZe Scooter Model and Validation The GenZe scooter model predicts the scooter speed given the throttle and brake inputs and is shown in Figure 3.1. The GenZe model contains the powertrain model discussed in Chapter 2 and includes chassis and tire models that will be presented in this chapter. The GenZe scooter model also contains a controller model that models the proprietary algorithms used to limit the motor current given the vehicle speed and component temperature which will not be discussed in this thesis. Figure 3.1: GenZe scooter model diagram 49
The GenZe scooter model can be used in two ways, as a validation tool where the simulation is run in open-loop provided with throttle and brake commands, and as a predictive tool where a driver model predicts the throttle and brake commands in order to follow a provided speed profile. The results of using the model in both ways are presented in this chapter ultimately describing the potential shortcomings of the model. 3.1 Chassis, Tire, and Rider Models This section presents the chassis, tire, and rider models used in the GenZe scooter in conjunction with the powertrain model presented in Figure 2. The models presented in this chapter are based on the models in [6]. Table 3.1 shows a list of symbols used in this chapter. Symbol τ t w m F V r Description Torque Time Angular velocity Mass Force Velocity Radius Table 3.1: List of chassis symbols 3.1.1 Chassis The chassis block models the external forces, the pitch dynamics, and the acceleration of the motorcycle given the tire force (F t ), brake force (F b ), road gradient (g r ), 50
and wind speed (V w ). The external forces are modeled using the well known road load equation. The road is assumed to have a time varying slope with no banking thus the force can be estimated with the road grade and the scooter mass (m). The aerodynamic drag force of the scooter is assumed to be a speed dependent quadratic function with a constant air density (ρ), frontal area (A), and friction coefficient (C d ). The pitch dynamics of the scooter are modeled using an algebraic expression described in [6] which assumes the pitching motion of the scooter is in equilibrium using the chassis geometry parameters (b,p, and h). Figure 3.2 shows a diagram of the chassis forces and parameters. Note that the rolling resistance is modeled in the tire model. Figure 3.2: Chassis model force and parameter diagram Tables 3.2 and 3.3 summarize the input and output variables, and the model parameters. 51
F d = 1 2 ρc da(v c + V w ) 2 (3.1) F r = mg sin g r (3.2) dv c dt = F t F r F d F b m (3.3) dd dt = V c (3.4) F n = mg cos g r (3.5) p b h F nr = F n + F t p p b F nf = F n p F h t p (3.6) (3.7) Input/Output Signal Name Unit Description Input F t N Force exerted on the chassis from the tire Input F b N Force exerted on the chassis from the brakes Input g r rad Road gradient Input ρ kg/m 3 Air density Output V c m/s Speed of vehicle Output F nr N Normal force of vehicle on rear tire Output F nf N Normal force of vehicle on front tire Output F n N Total normal force Output D m Distance traveled Table 3.2: Summary of chassis model I/O 52
Parameter Unit Description m Kg Mass of vehicle and rider g m/s 2 Gravity C d - Air resistance coefficient A m 2 Cross sectional area V w m/s Wind speed b m Horizontal Distance between rear wheel center of gravity p m Horizontal Distance between both tires h m Vertical distance between road and center of gravity Table 3.3: Summary of chassis model parameters 3.1.2 Tire The tire block models the longitudinal force acting on the back tire using the magic formula slip model described in [6] and a linear rolling resistance model. The magic formula is a non-linear function that relates tire force to tire slip shown in Figure 3.3. The rolling resistance is assumed to be a linear function of speed and normal force. Figure 3.3: Graphical description of the magic formula [6] 53
Tables 3.4 and 3.5 summarize the input and output variables, and the model parameters. T t = (F rr + F t )r t (3.8) F rr = F n V c C r (3.9) F t = k u F nr (3.10) k = V c V t max (V c, V t, ɛ) (3.11) u = D sin (C arctan [Bk E(Bk arctan (Bk))]) (3.12) Input/Output Signal Name Unit Description Input V t rad/s Velocity of tire Input V c m/s Vehicle velocity Input F n N Total normal Force Input F nr N Rear tire normal force Output T t Nm Tire torque Output F t N Force exerted on the chassis Table 3.4: Summary of tire model I/O 54
Parameter Unit Description r t m Radius of tire C r - Rolling resistance coefficient B - Magic formula coefficient C - Magic formula coefficient D - Magic formula coefficient E - Magic formula coefficient ɛ - Tunable value Table 3.5: Summary of tire model parameters 3.1.3 Rider The rider model simulates the throttle and brake command required to follow the input speed profile. The rider model uses a PI controller and a piecewise function that commands throttle when the vehicle speed is below the target speed and brake when above the target speed. Tables 3.6 and 3.7 summarize the input and output variables, and the model parameters. e = v cmd v c (3.13) c = P I(e) (3.14) 0 c > 0 β = 1 c < 1 (3.15) c otherwise 0 c < 0 α = 1 c > 1 (3.16) c otherwise 55
Input/Output Signal Name Unit Description Input v c m/s Motorcycle velocity Input v cmd m/s Target motorcycle velocity Output β - Brake command Output α - Throttle command Table 3.6: Summary of rider model I/O Parameter Unit Description P - Proportional term of PI controller I - Integral term of PI controller Table 3.7: Summary of rider model parameters 3.2 Chassis and Tire Calibration There are two types of parameters used in the chassis and tire models. There are parameters that must be measured from the scooter and parameters that must be calibrated with experimental data. The measured parameters for the chassis model are the scooter geometry parameters (b,p, and h), the scooter mass (m), and the cross-sectional area (A). The measured parameters are physically measured or estimated before calibration testing. The only calibrated parameter for the chassis is the air resistance constant (C d ) The measured parameters for the tire model are the magic formula parameters (A, B, C, D and E). Although magic formula values could be calibrated it was chosen to use the general scooter tires parameterized in BikeSim. The calibrated parameter for the tire model is the rolling resistance (C r ). BikeSim is discussed in Chapter 4. 56
All calibrated parameters of the tire and chassis model are calibrated using a coast-down test. A coast-down test is when a driver accelerates the vehicle to top speed then completely zeros all throttle and brake commands to allow the vehicle to coast to zero speed. It is assumed the only forces acting on the scooter during the test are from the aerodynamic drag and rolling resistance. Many coast-down tests were performed on the GenZe scooter at the Transportation Research Center (East Liberty, Ohio) on a road with a slight slope. The coastdown test was carried out going both directions (up and down slope) multiple times. A mobile data-logging system logged the required calibration and validation data during the test. Figure 3.4 shows the speed data collected during the coast-down testing. 600 500 down slope up slope Motor Speed [r/min] 400 300 200 100 0-100 0 10 20 30 40 50 60 70 Time [s] Figure 3.4: Coast-down test data 57
A non-linear least squares method was used to find the C d and C r parameters that minimized the cumulative square error between the test data vehicle speed and the model vehicle speed. Figure 3.5 shows the results of the calibration within +/- 2 m/s of error going up and down slope. 58
Velocity [m/s] 15 10 5 0 Up Slope Model Data -5 2 Error [m/s] 1 0-1 -2 0 5 10 15 20 25 30 35 40 45 Time [s] Velocity [m/s] 15 10 5 Down Slope Model Data 0 2 Error [m/s] 1 0-1 -2 0 10 20 30 40 50 60 70 Time [s] Figure 3.5: Coast-down calibration results 59
Calibrating to the coast-down dataset was difficult for multiple reasons. First, there are many phenomena not measured or modeled in the road load model used, including the rider position, road material, and small changes in wind. Second, the data is not consistent, as seen in Figure 3.4, which makes it difficult to decide which coast-down test should be used for calibration. After using the non-linear least squares algorithm the final parameters were hand tuned to reduce the overall error in the up and down slope tests. 3.3 Verification of the Scooter Model This section presents the verification of the scooter model by comparing the model to two datasets. The first dataset is from chassis dyno testing where the scooter was connected to a chassis dyno and a rider modulated the throttle to follow a specified speed profile. The second dataset is from road testing where the scooter was ridden at the Transportation Research Center. This section also describes the mobile datalogger and instrumentation of the scooter used to collect the validation results. 3.3.1 HBM Datalogger The HBM edaqlite datalogger is used as a mobile data acquisition system for the scooter during all validation tests. The HBM unit was chosen because it is a standalone unit that can be powered from the 12 volt bus of the scooter. The HBM datalogger is also easy to use and highly configurable. The datalogger is connected to the sensors shown in Table 3.8. 60
Measurement Sensor Type Quantity Front and rear suspension travel Linear string potentiometer 2 Steering angle Linear string potentiometer 1 Front and back wheel speed VR sensor 2 DC auxiliary current Current shunt 1 Ambient temperature Thermocouple 1 Chassis temperature Thermocouple 1 Inverter temperatures Thermocouple 3 Battery pack temperatures Thermocouple 6 Front and rear brake pressure Pressure transducer 2 GPS Serial GPS unit 1 Vehicle CAN bus CAN 1 Inertial measurement unit CAN 1 Table 3.8: List of sensor connected to the HBM datalogger The suspension travel and steering angle sensors were mounted in the locations shown in Figure 3.6. This Figure also show the distance measured by the sensors. The suspension travel sensors and the steering angle sensor were calibrated using the HBM software which uses a 2-point linear calibration method. 61
Figure 3.6: Mounting and measurement diagram for the steering angle and suspension travel sensors The wheel speed sensors were mounted to the tire assembly such that a hole in the brake disc would trigger a pulse. The datalogger measures the pulses per second, and calculates and logs the rotations per second of the wheel. The DC current shunt was mounted between the inverter and the DC-DC converter and spliced into the high voltage wire. This measures the current draw of the DC-DC converter and, in turn, the auxiliary current of the scooter. The HBM logger measures the voltage drop across the shunt and logs auxiliary current using the resistance of the shunt. The thermocouples are measured using a 16-channel CAN-enabled thermocouple measurement device and are logged by the HBM logger. The ambient temperature thermocouple was mounted on the scooter rear bin and the chassis thermocouple was mounted under the foot mat. The inverter temperature thermocouples were mounted 62