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Modeling a Hydraulic Hybrid Drivetrain: Efficiency

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Modeling a Hydraulic Hybrid Drivetrain: Efficiency MODELING A HYDRAULIC HYBRID DRIVETRAIN: EFFICIENCY CONSIDERATIONS _______________________________________ A Thesis presented to the Faculty of the Graduate School at the University of Missouri-Columbia _______________________________________________________ In Partial Fulfillment of the Requirements for the Degree Master of Science _______________________________________________________ by SEAN DOUGLAS VERMILLION Dr. Noah Manring, Thesis Supervisor DECEMBER 2011 The undersigned, appointed by the dean of the Graduate School, have examined the thesis entitled MODELING A HYDRAULIC HYBRID DRIVETRAIN: EFFICIENCY CONSIDERATIONS presented by Sean Douglas Vermillion, a candidate for the degree of Master of Science, and hereby certify that, in their opinion, it is worthy of acceptance. Dr. Noah Manring Dr. Douglas Smith Dr. Steven Borgelt ACKNOWLEDGEMENTS I would like to express my appreciation to my thesis advisor, Dr. Noah Manring, for his constant guidance, advice, and motivation to overcome any and all obstacles faced while conducting this research. Furthermore, I extend my appreciation to Dr. Doug Smith and Dr. Steve Borgelt for serving on my thesis committee. I also would like to express my gratitude to the entire Mechanical & Aerospace Engineering department for creating an exceptional environment in which to work and study. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS………………………………………………………………. ii ABSTRACT………………………………………………………………………………vi LIST OF FIGURES……………………………………………………………………... vii LIST OF TABLES……………………………………………………………………….. ix LIST OF VARIABLES……………………………………………………………………x Chapter 1. INTRODUCTION………………………………………………………………... 1 1.1 Introduction…………………………………………………………………. 1 1.2 Background…………………………………………………………………. 1 1.3 Literary Review…………………………………………………………….. 7 1.4 Research Objective………………………………………………………... 11 1.5 Thesis Outline……………………………………………………………... 12 2. SYSTEM ANALYSIS…………………………………………………………... 14 2.1 Introduction………………………………………………………………... 14 2.2 Vehicle Dynamics…………………………………………………………. 14 2.3 Drivetrain Model…………………………………………………………... 17 2.3.1 Mechanical Transmission…………………………………………. 18 2.3.2 Planetary Gearbox…………………………………………………. 19 2.3.3 Hydraulic Transmission…………………………………………… 23 2.3.4 Spur Gearbox……………………………………………………… 26 2.3.5 Differential Gearbox………………………………………………. 27 2.4 Engine Model……………………………………………………………… 29 iii 2.5 Power Efficiency…………………………………………………………... 33 2.6 Summary…………………………………………………………………... 36 3. NUMERICAL SIMULATION………………………………………………….. 38 3.1 Introduction………………………………………………………………... 38 3.2 Simulation Parameters…………………………………………………….. 38 3.2.1 Vehicle Parameters and Driving Conditions……………………….39 3.2.2 Engine Parameters………………………………………………… 41 3.2.3 Drivetrain Parameters……………………………………………... 44 3.3 Simulation Algorithms…………………………………………………….. 47 3.3.1 Conventional Vehicle Simulation…………………………………. 47 3.3.2 Hybrid Vehicle Simulation………………………………………... 49 3.4 Summary…………………………………………………………………... 52 4. RESULTS AND DISCUSSION………………………………………………… 54 4.1 Introduction………………………………………………………………... 54 4.2 Results……………………………………………………………………... 54 4.2.1 New York City Cycle Results……………………………………... 55 4.2.2 Highway Fuel Economy Driving Schedule Results………………..58 4.3 Interpretations……………………………………………………………... 61 4.4 Summary…………………………………………………………………... 64 5. CONCLUSION………………………………………………………………….. 65 5.1 Introduction………………………………………………………………... 65 5.2 Conclusions………………………………………………………………... 65 5.3 Scope of Future Work……………………………………………………... 66 iv REFERENCES…………………………………………………………………………...68 APPENDIX A. MATLAB FUNCTION objFun…………………………………....... 70 APPENDIX B. MATLAB FUNCTION convTrans………………………………… 76 APPENDIX C. MATLAB FUNCTION mConv……………………………………….. 78 v MODELING A HYDRAULIC HYBRID DRIVETRAIN: EFFICIENCY CONSIDERATIONS Sean Douglas Vermillion Dr. Noah Manring, Thesis Supervisor ABSTRACT Increasing petroleum prices and environmental concerns have caused a demand for more fuel efficient vehicles. Hybrid vehicles provide a solution to this demand, and hydraulic hybrid vehicles are shown to have a cheaper cost of ownership compared to electric hybrid vehicles. A hybrid drivetrain with a hydraulic continuously variable transmission (CVT) is modeled to include efficiency information of the engine and hydraulic components. Since the expressions comprising the model can be set as functions of a control input, which is related to the swashplate angle of the hydraulic motor in the CVT, an optimization algorithm can determine a control input that maximizes the overall vehicle efficiency allowing the vehicle to increase its fuel economy. Simulations are conducted using two driving schedules: one to represent city driving and the other to represent highway driving. Based on the results of these simulations, the hybrid vehicle produces a 1.28% increase in fuel economy over a similar conventional vehicle in city driving and a 22.62% increase in fuel economy for highway driving. vi LIST OF FIGURES Figure 1-1 Break down of retail gasoline price factors………………………………………... 2 1-2 Geographic location of OPEC members…………………………………………... 3 1-3 History of weekly US retail gasoline prices……………………………………….. 4 1-4 Increase in CO2 concentration levels from 1959 to 2009 measured at Mauna Loa, HI…………………………………………………………………………………... 4 1-5 Energy requirements for combined city/highway driving…………………………. 5 1-6 Two hybrid vehicle configuration types: A) series and B) parallel………………...6 1-7 Generic CVT layout………………………………………………………………...7 2-1 Vehicle free body diagram with emphasized typical wheel……………………… 15 2-2 Hybrid transmission schematic……………………………………………………18 2-3 Planetary gearbox schematic……………………………………………………... 19 2-4 Partial free-body diagrams for components within a planetary gear set…………. 20 2-5 Hydraulic CVT schematic………………………………………………………... 23 2-6 Compound spur gearbox schematic……………………………………………….27 2-7 Engine WOT line featuring important engine parameters……………………….. 32 3-1 NYCC vehicle velocity profile…………………………………………………… 40 3-2 HWFET vehicle velocity profile…………………………………………………. 40 3-3 NYCC vehicle acceleration profile………………………………………………. 41 3-4 HWFET vehicle acceleration profile……………………………………………... 41 3-5 BSFC map using coefficient values listed in [16]………………………………... 43 vii 3-6 Scaled BSFC map with WOT line; BSFC isolines are labeled…………………... 44 3-7 Conventional vehicle simulation…………………………………………………. 48 3-8 Hydraulic hybrid vehicle simulation……………………………………………... 50 4-1 NYCC Simulation: A) Vehicle efficiency profile of the conventional vehicle. B) Vehicle efficiency profile of the hybrid vehicle………………………………….. 56 4-2 CVT control input over the course of the NYCC simulation…………………….. 56 4-3 Inequality constraint values over the course of the NYCC simulation…………... 57 4-4 Equality constraint value over the course of the NYCC simulation……………... 58 4-5 HWFET Simulation: A) Vehicle efficiency profile of the conventional vehicle. B) Vehicle efficiency profile of the hybrid vehicle………………………………….. 59 4-6 CVT control input over the course of the HWFET simulation…………………... 59 4-7 Inequality constraint values over the course of the HWFET simulation………….60 4-8 Equality constraint value over the course of the HWFET simulation……………. 61 −1 4-9 Vehicle efficiency profile illustrating the two distinct regions when vx =10 ms −2 and vx = 0 ms …………………………………………………………………... 62 −1 4-10 Comparison of threshold locations. A) Efficiency profile when vx = 2 ms and −2 −1 −2 vx = 0 ms . B) Efficiency profile when vx = 30 ms and vx = 0 ms …………63 −1 4-11 Vehicle efficiency profile illustrating the two distinct regions when vx =10 ms −2 and vx =1 ms …………………………………………………………………… 63 viii LIST OF TABLES Table 2-1 Efficiency coefficients and parameters…………………………………………... 36 3-1 Overall vehicle parameters for a 1997 Ford Ranger……………………………... 39 3-2 Engine performance specifications………………………………………………..42 3-3 BSFC map coefficients…………………………………………………………… 42 3-4 Fuel specifications………………………………………………………………... 44 3-5 Hydraulic pump and motor specifications………………………………………... 45 3-6 Hydraulic fluid specifications……………………………………………………..45 3-7 Test vehicle manual transmission gear ratios and shift schedule………………… 46 3-8 Transmission gear ratios………………………………………………………….. 46 4-1 Simulation results for NYCC driving schedule for both conventional and hybrid vehicles…………………………………………………………………………… 55 4-2 Simulation results for HWFET driving schedule for both conventional and hybrid vehicles…………………………………………………………………………… 58 ix LIST OF VARIABLES m Vehicle Mass vx Vehicle Velocity vx Vehicle Acceleration Fx Total Wheel Propulsive Force Fd Aerodynamic Drag Force Fr Rolling Resistance Force g Gravitational Constant β Driving Surface Incline l Number of Axles n Number of Wheels per Axle J Wheel Moment of Inertia r Wheel Radius ωw Wheel Angular Speed ωw Wheel Angular Acceleration Tw Wheel Torque T Maximum Wheel Torque wmax ρ Air Density Cd Drag Coefficient Ad Reference Area Cr Rolling Resistance Coefficient ωe Engine Angular Speed x Te Engine Torque ωs Sun Gear Angular Speed Ts Sun Gear Torque Ξt Mechanical Transmission Gear Ratio rh Hydraulic Path Gear Radius rR Ring Gear Outer Radius rr Ring Gear Inner Radius rA Arm Gear Radius ra Arm Length rs Sun Gear Radius rp Planet Gear Radius rm Mechanical Path Gear Radius Fs Sun Gear Reaction Force Fa Arm Reaction Force ωr Ring Gear Angular Speed Tr Ring Gear Torque ωa Arm Gear Angular Speed Ta Arm Gear Torque ξa Arm Gear Gear Ratio ωr Ring Gear Angular Speed Tr Ring Gear Torque ξr Ring Gear Gear Ratio ω1 Mechanical Path Angular Speed xi T1 Mechanical Path Torque ξm Mechanical Path Gear Gear
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