Principles of Small-Scale Hydraulic Systems for Human Assistive Machines A Dissertation SUBMITTED TO THE FACULITY OF UNIVERSITY OF MINNESOTA BY Brett Cullen Neubauer IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Advisor: William K. Durfee, PhD March 2017 © Brett C. Neubauer 2017 Acknowledgements I would like to thank my parents Paul and Linda Neubauer in the continuous support of my academic pursuits. It is their guidance from a young age that led me to pursue my aspirations in education and of knowledge. I would also like to give thanks to my adviser Professor William Durfee at the University of Minnesota for sharing his expertise and guidance during my graduate education. There are several individuals that need to be acknowledged for their efforts in this research. Jonathan Nath is a mechanical engineering student completing his master degree at the University of Minnesota, and he provided assistance in designing and building the electrohydraulic power supply for the hydraulic ankle-foot orthosis. He has also provided assistance and expertise in the design and construction of the ankle actuator assemblies of the pediatric hydraulic ankle-foot orthosis. Sangyoon Lee, a PhD candidate in the mechanical engineering program at the University of Minnesota, assisted in developing the axial piston pump performance model. Dr. Andre Ries is a PhD graduate working at Gillette Children’s Hospital in St. Paul, MN, and he assisted with the collection of AFO stiffness data using the BRUCE measurement system. Dr. Ries also provided gait data collected with 3D motion capture for patients with cerebral palsy. This work was supported the National Institutes of Health, grant number R21 EB 019390-02, and by the Center for Compact and Efficient Fluid Power, a National Science Foundation Engineering Research Center, EEC-0540834. In addition, I had the opportunity and privilege to be receive the National Science Foundation’s Graduate Research Fellowship from 2012-2015 providing additional financial support for my graduate education. i | P a g e Abstract The high power and force density of hydraulic actuators, along with the ability to distribute system weight through the separation of the power supply and actuators makes hydraulic technology ideal for use in human assistive machines. However, hydraulic systems often operate inefficiently due to throttling losses in the control valves and have increased viscous losses in small-scale applications as bore size is decreased. The objective of this research is to address the limitations of small-scale hydraulics using validated modeling techniques to optimize performance and minimize system weight. This research compares and contrasts the use of different hydraulic technology as well as develops detailed models of small-scale hydraulic components. These models are used to construct a software tool that optimizes the design of a hydraulic system using specified input requirements of actuation, conduit lengths, operating pressure, and runtime. A system-level energetics analysis provides estimates of efficiencies and weights, while a heat transfer analysis estimates the working fluid and component surface temperatures. In addition, the dynamic performance of different small-scale pump and valve controlled hydraulic systems are simulated to compare the cycle efficiencies, rise times, and flow rate capabilities as a function of duty cycles. The use of an accumulator, unloading valves, variable displacement pumps, and proportional pressure control are explored to improve the efficiency of the system during intermittent operation. In addition a small-scale, digital, high frequency switching valve is designed and simulated to reduce the throttling losses of a traditional proportional control valve. This body of knowledge is used to design, prototype, and performance test two hydraulic powered ankle-foot orthoses. The first orthosis is an untethered system that provides active gait assistance. Hydraulics allows the system to be separated into two parts as the actuator is secured to the ankle, and the portable electrohydraulic power supply is positioned on the lower back. The second orthosis emulates the dynamics of a passive ankle-foot orthosis providing torque assistance to bring the ankle to a neutral position. This device is specifically designed to reduce the time and resources in the clinical prescription of passive ankle-foot orthoses while providing more quantitative metrics. ii | P a g e Table of Contents Table of Contents------------------------------------------------------------------------------------------------------iii List of Figures----------------------------------------------------------------------------------------------------------viii List of Tables-----------------------------------------------------------------------------------------------------------xiii Chapter 1 Applications, Research Objectives, and Prior Art ------------------------------------------------ 1 1.1 Introduction ----------------------------------------------------------------------------------------------------- 1 1.1.1 Applications ----------------------------------------------------------------------------------------------- 1 1.1.2 Comparison of actuation methods with human muscle --------------------------------------- 2 1.1.3 Limitations of small-scale hydraulic systems ------------------------------------------------------ 5 1.1.4 Research objectives ------------------------------------------------------------------------------------- 6 1.2 Prior art on small-scale hydraulics in human assistive machines ---------------------------------- 7 Chapter 2 Comparisons, Models, and Properties of Small-Scale Hydraulic Components----------- 13 2.1 Introduction ---------------------------------------------------------------------------------------------------- 13 2.2 Working fluids ------------------------------------------------------------------------------------------------- 13 2.3 Cylinders and Seals ------------------------------------------------------------------------------------------- 18 2.4 Hose, Tubing, and Viscous Losses ------------------------------------------------------------------------ 22 2.5 Accumulators -------------------------------------------------------------------------------------------------- 25 2.5.1 Comparison of compressed gas and spring loaded accumulators -------------------------- 26 2.6 Valves ------------------------------------------------------------------------------------------------------------ 32 2.6.1 Valve function ------------------------------------------------------------------------------------------- 34 2.6.2 Electromechanical Valves ----------------------------------------------------------------------------- 35 2.7 Motors and Pumps Technology --------------------------------------------------------------------------- 38 2.7.1 Comparison gear and axial piston pumps -------------------------------------------------------- 40 2.7.2 Model of hydraulic axial piston pump ------------------------------------------------------------- 43 Chapter 3 Steady State Modeling and Optimal Design of Small-Scale Hydraulic Systems ---------- 53 3.1 Objective -------------------------------------------------------------------------------------------------------- 53 3.1.1 Pump and Valve controlled actuation ------------------------------------------------------------- 54 3.1.2 Prior art in the design of small-scale hydraulic systems --------------------------------------- 54 3.2 Methods -------------------------------------------------------------------------------------------------------- 55 iii | P a g e 3.2.1 Cylinder Design ------------------------------------------------------------------------------------------ 56 3.2.2 Conduit Design ------------------------------------------------------------------------------------------ 59 3.2.3 Valve Design---------------------------------------------------------------------------------------------- 61 3.2.4 Axial piston pump design ----------------------------------------------------------------------------- 63 3.2.5 Motor and battery modeling ------------------------------------------------------------------------- 66 3.2.6 Heat Transfer -------------------------------------------------------------------------------------------- 68 3.3 Results ----------------------------------------------------------------------------------------------------------- 70 3.3.1 Ankle-Foot Orthosis Case Study --------------------------------------------------------------------- 70 3.3.2 Design Guidelines for Small-Scale Hydraulic Systems ----------------------------------------- 76 3.4 Discussion ------------------------------------------------------------------------------------------------------ 83 3.4.1 Summary of results & design guidelines ---------------------------------------------------------- 83 3.4.2 Limitations of the design guidelines --------------------------------------------------------------- 85 Chapter 4 Dynamic Modeling of Small-Scale Pump and Servo Valve Controlled Hydraulic Systems ---------------------------------------------------------------------------------------------------------------------------- 87 4.1 Introduction ---------------------------------------------------------------------------------------------------- 87 4.2 Methods -------------------------------------------------------------------------------------------------------- 87 4.2.1 Linearized algebraic models of hydraulic actuation -------------------------------------------