Modeling, Optimization, and Detailed Design of a Hydraulic Flywheel-Accumulator A THESIS

343 Pages·2014·5.84 MB·English

Modeling, Optimization, and Detailed Design of a Hydraulic
Flywheel-Accumulator

A THESIS
SUBMITTED TO THE FACULTY OF THE
UNIVERISTY OF MINNESOTA
BY

Kyle Glenn Strohmaier

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
MASTER OF SCIENCE

Adviser: James Van de Ven, Ph.D.

July 2014
© 2014 Kyle Glenn Strohmaier
I would like to thank my adviser, Dr. James Van de Ven, for providing me the
opportunity to partake in this fascinating research and for his guidance and patience
throughout the process.
This work was sponsored by the National Science Foundation through the Center for
Compact and Efficient Fluid Power, grant EEC-0540834.

i
Abstract
Improving mobile energy storage technology is an important means of addressing
concerns over fossil fuel scarcity and energy independence. Traditional hydraulic
accumulator energy storage, though favorable in power density, durability, cost, and
environmental impact, suffers from relatively low energy density and a pressure-
dependent state of charge. The hydraulic flywheel-accumulator concept utilizes both the
hydro-pneumatic and rotating kinetic energy domains by employing a rotating pressure
vessel. This thesis provides an in-depth analysis of the hydraulic flywheel-accumulator
concept and an assessment of the advantages it offers over traditional static accumulator
energy storage.
After specifying a practical architecture for the hydraulic flywheel-accumulator, this
thesis addresses the complex fluid phenomena and control implications associated with
multi-domain energy storage. To facilitate rapid selection of the hydraulic flywheel-
accumulator dimensions, computationally inexpensive material stress models are
developed for each component. A drive cycle simulation strategy is also developed to
assess the dynamic performance of the device. The stress models and performance
simulation are combined to form a toolset that facilitates computationally-efficient
model-based design.
The aforementioned toolset has been embedded into a multi-objective optimization
algorithm that aims to minimize the mass of the hydraulic flywheel-accumulator system
and to minimize the losses it incurs over the course of a drive cycle. Two optimizations
have been performed – one with constraints that reflect a vehicle-scale application, and
one with constraints that reflect a laboratory application. At both scales, the optimization
results suggest that the hydraulic flywheel-accumulator offers at least an order of
magnitude improvement over traditional static accumulator energy storage, while
operating at efficiencies between 75% and 93%. A particular hydraulic flywheel-
accumulator design has been selected from the set of laboratory-scale optimization results
and subjected to a detailed design process. It is recommended that this selection be

constructed and tested as a laboratory prototype.
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Table of Contents

List of Tables .......................................................................................................................... vi
List of Figures ....................................................................................................................... viii
1 Introduction .............................................................................................................................. 1
1.1 Greenhouse Gas Emissions and Traditional Vehicles ..................................................... 1
1.2 Alternative Powertrains ................................................................................................... 2
1.3 Hydraulic Powertrain Components .................................................................................. 5
1.4 The Hydraulic Flywheel-Accumulator Concept .............................................................. 8
1.5 Research Goals and Approach ....................................................................................... 10
2 General Architecture and Operation ...................................................................................... 12
2.1 Architecture and Design Variables of the Hydraulic Flywheel-Accumulator ............... 12
2.2 Basic Kinetic and Pneumatic Energy Storage ................................................................ 17
2.3 Fluid Centrifugation ....................................................................................................... 19
2.4 Interaction of the Energy Storage Domains ................................................................... 22
2.5 Controlling the Hydraulic Flywheel-Accumulator ........................................................ 24
2.6 Optimization Objectives and Constraints ...................................................................... 27
3 Model-Based Structural Design ............................................................................................. 29
3.1 System-Level Considerations ........................................................................................ 29
3.2 Axle ................................................................................................................................ 34
3.3 End Caps ........................................................................................................................ 41
3.4 Piston ............................................................................................................................. 45
3.5 Housing .......................................................................................................................... 50
3.6 Bearing Selection ........................................................................................................... 58
3.7 Material Selection and Static Calculations .................................................................... 64
4 Energy Loss Mechanisms ...................................................................................................... 67
4.1 Bearing and Aerodynamic Drag .................................................................................... 68
4.2 Storage Pump-Motor Losses .......................................................................................... 72
4.3 Losses Related to the High-Speed Rotary Union ........................................................... 75
4.4 Vacuum Pumping Energy Consumption ........................................................................ 81
5 Internal Fluid Modeling ......................................................................................................... 86
5.1 Motivation for Fluid Modeling ...................................................................................... 86
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5.2 Theory and Assumptions ............................................................................................... 88
5.3 Modeling Approach ....................................................................................................... 94
5.4 Experimental Approach ................................................................................................. 96
5.5 Model Development ..................................................................................................... 102
5.6 Model Validation ......................................................................................................... 109
5.7 Closing Remarks about the Internal Fluid Modeling ................................................... 116
6 Drive Cycle Simulation ........................................................................................................ 118
6.1 Road Loads and Vehicle Parameters ........................................................................... 118
6.2 Control Strategy and Pump-Motor Selection ............................................................... 121
6.3 Studies on the Band Control Strategy Parameters ....................................................... 125
6.4 Calculation Sequence ................................................................................................... 132
6.5 Calculation of Performance Metrics ............................................................................ 139
7 Design Optimization ............................................................................................................ 141
7.1 Optimization Strategy .................................................................................................. 141
7.2 Posing the Optimization Problem ................................................................................ 144
7.3 Vehicle-Scale Optimization Results ............................................................................ 147
7.4 Laboratory-Scale Optimization Results ....................................................................... 159
7.5 Contextualizing the Optimization Results ................................................................... 168
7.6 Selection of a Design Solution for the Laboratory Prototype ...................................... 174
8 Detailed Design .................................................................................................................... 179
8.1 Torque Transmission Mechanisms .............................................................................. 179
8.2 End Caps ...................................................................................................................... 184
8.3 Piston ........................................................................................................................... 197
8.4 Housing ........................................................................................................................ 201
8.5 Axle .............................................................................................................................. 205
8.6 High-Speed Rotary Union Case ................................................................................... 208
8.7 Relative Radial Strain Analysis ................................................................................... 213
9 Conclusions and Recommendations .................................................................................... 221
9.1 Summary of the Research ............................................................................................ 221
9.2 Conclusions .................................................................................................................. 222
9.3 Future Work ................................................................................................................. 224
Bibliography ........................................................................................................................ 227
Appendix A: Nomenclature ................................................................................................. 233
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Appendix B: MATLAB© Code for the Model-based Design and Simulation Toolset ........ 240
Appendix C: Complete Experimental Results from the Fluid Behavior Model Development
............................................................................................................................................. 286
Appendix D: Simulated Prototype Performance .................................................................. 320
Appendix E: Additional FEA Results .................................................................................. 324

v
List of Tables

Table 1: The Nine Design Variables which Constitute a Design Solution for the HFA ................ 16
Table 2: Load Cases for a Study on Stresses in a Hybrid Housing ................................................ 54
Table 3: Selected Materials and their Mechanical Properties [45] ................................................ 65
Table 4: Properties of the Composite Material for the Housing Wrap [35] ................................... 66
Table 5: List of Energy Loss Mechanisms and their Symbols (Given as Rates of Energy
Dissipation), Categorized as Kinetic or Pneumatic ....................................................................... 67
Table 6: Volumetric and Mechanical Efficiency Definitions for Pumping and Motoring ............ 73
Table 7: Selected Loss Coefficients for the Storage Pump-Motor [54] ......................................... 74
Table 8: Selected Values for the Minor Loss Coefficients in the Axial Ports ............................... 77
Table 9: Minor Loss Coefficients in Pneumatic Charging and Discharging ................................. 77
Table 10: Assumptions for the Reduction of the Navier-Stokes Equations for Flow in the
Circumferential Seal ...................................................................................................................... 79
Table 11: General Specifications for the Experimental Setup ....................................................... 97
Table 12: Specifications of the Equipment Used for the Experimental Setup ............................... 98
Table 13: Ranked Performance of the Viscous Dissipation Rate Correlations, Based on
Coefficient of Determination ....................................................................................................... 105
Table 14: Ranked Performance of the Dynamic Time Constant Correlations, Based on Coefficient
of Determination .......................................................................................................................... 107
Table 15: Characteristics of the Urban Dynamometer Driving Schedule (UDDS) ..................... 119
Table 16: Vehicle Characteristics for Drive Cycle Simulation, Selected to Represent a Typical
Mid-Size Passenger Sedan ........................................................................................................... 121
Table 17: HFA Design Solution for the Control Strategy Study ................................................. 128
Table 18: Selected Control Strategy Parameter Values for the Control Strategy Study .............. 128
Table 19: Summary of the Genetic Algorithm Parameters .......................................................... 143
Table 20: Redefined Design Solution, Used for the Purposes of a Design Optimization ............ 145
Table 21: Design Variable Bounds for the Design Optimization ................................................ 146
Table 22: Summary of the Extreme Pareto-optimal Solutions from the Vehicle-Scale
Optimization ................................................................................................................................ 149
Table 23: Summary of the Extreme Pareto-optimal Solutions from the Laboratory-Scale
Optimization ................................................................................................................................ 163
Table 24: Results of the Energy Density Comparison Study ....................................................... 170
Table 25: Design Variable Values for the Selected Laboratory Prototype Design ...................... 176
Table 26: Non-design Variables of Interest for the Selected Laboratory Prototype Design ........ 177
Table 27: Static Performance Metrics for the Selected Laboratory Prototype Design ................ 178
Table 28: Drive Cycle (UDDS) Performance Metrics for the Selected Laboratory Prototype
Design .......................................................................................................................................... 178
Table 29: Selected Shoulder Screws for the Pin System ............................................................. 182
Table 30: The Three Potential Worst-case Loading Scenarios for the Housing .......................... 202
Table 31: Loads and Radial Displacements for the Worst-case Leakage Scenario at the Axle-
Piston Interface ............................................................................................................................ 215
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Table 32: Loads and Radial Displacements for the Worst-case Binding Scenario at the Axle-
Piston Interface ............................................................................................................................ 216
Table 33: Loads and Radial Displacements for the Worst-case Leakage Scenarios at the Piston-
Housing Interface ......................................................................................................................... 217
Table 34: Loads and Radial Displacements for the Worst-case Binding Scenarios at the Piston-
Housing Interface ......................................................................................................................... 218
Table 35: Loads and Radial Displacements for the Worst-case Leakage Scenario at the Axle-End
Cap Interface ................................................................................................................................ 219
Table 36: Loads and Radial Displacements for the Worst-case Leakage Scenarios at the End Cap-
Housing Interface ......................................................................................................................... 220

vii
List of Figures

Figure 1: Global Greenhouse Gas Emissions by Sector [1] ............................................................. 2
Figure 2: The Two Most Basic Hybrid Vehicle Powertrain Architectures, Series and Parallel. The
ICE and secondary energy storage-conversion pairs are labelled “A” and “B,” respectively. ........ 3
Figure 3: Illustration of a Traditional Piston-type Hydraulic Accumulator [17] ............................. 6
Figure 4: Dimensionless Pressure as a Function of Dimensionless Energy for a Traditional
Accumulator ..................................................................................................................................... 7
Figure 5: Pure Hydraulic Powertrain with a Hydraulic Flywheel Accumulator as the Sole Energy
Storage Medium. Shown with a Fixed-Displacement Storage Pump-Motor .................................. 9
Figure 6: Illustration of the Parabolic Oil Pressure Distribution with System Pressure at the
Vertex (Gas Pressure Distribution Not Shown) ............................................................................. 10
Figure 7: Hybrid Housing, Made of Metallic Liner and Composite Wrap .................................... 13
Figure 8: End Cap and Axle System .............................................................................................. 14
Figure 9: Illustration of the Spatial Relations between the Piston, Axle and End Caps ................ 14
Figure 10: Schematic of the High-Speed Rotary Union (HSRU) Concept .................................... 15
Figure 11: Force Balance on an Infinitesimal Fluid Element in a Rotating Fluid Volume [23] .... 19
Figure 12: Qualitative Illustration of the Gas (Left) and Oil (Right) Pressure Distributions for
Different Angular Velocities, with the Arrows Indicating Increasing Angular Velocity .............. 22
Figure 13: Sign Convention for Tractive (Total) Power, Power in the Kinetic Domain, and Power
in the Pneumatic Domain ............................................................................................................... 24
Figure 14: Three Possible Mounting Orientations for the HFA, Showing Forces that Contribute to
Bearing Loads ................................................................................................................................ 30
Figure 15: Illustration of the HFA Mounting Architecture ............................................................ 31
Figure 16: Exploded View of the Retaining Ring System for Torque Transmission between the
Axle and End Caps......................................................................................................................... 32
Figure 17: Illustration of the Pins (As Shown, 𝑵𝒔𝒔= 𝟐) which Produce an Axial and Tangential
Constraint between the Housing and the Gas Side End Cap ......................................................... 33
Figure 18: Axle Dimensions .......................................................................................................... 34
Figure 19: Free Body Diagram of the Major Loads on the Axle-End Cap System ....................... 35
Figure 20: Free Body Diagram (Excluding Radial Forces) of the Lower Portion of the Axle ...... 37
Figure 21: Loading on the Portion of Axle that Forms the Circumferential Seal .......................... 39
Figure 22: Pressure Loading on the Oil Side End Cap (Retainer Pressure 𝑷𝒓 Acts on the
Counterbore Surface) ..................................................................................................................... 43
Figure 23: Piston Design ................................................................................................................ 46
Figure 24: Packaging Region of the Piston Seals .......................................................................... 46
Figure 25: Maximum von Mises Stress (Non-dimensionalized) for the Same System Pressure at
Different Angular Velocities; Two Piston Geometries Shown ...................................................... 48
Figure 26: Oil, Gas, and Net Pressure Distributions for Three Different Angular Velocities which
Produce the Same Maximum von Mises Stress for a Given HFA Geometry and System Pressure
....................................................................................................................................................... 49
Figure 27: Non-dimensional Radial and Circumferential Stress Distributions due to
Centrifugation of an Isotropic Hollow Cylinder ............................................................................ 51
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