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Modeling, Analysis, and Experimental Investigation of a Variable Displacement Linkage Pump

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Modeling, Analysis, and Experimental Investigation of a Variable Displacement Linkage Pump Modeling, Analysis, and Experimental Investigation of a Variable Displacement Linkage Pump A Dissertation SUBMITTED TO THE FACULTY OF UNIVERSITY OF MINNESOTA BY Shawn Wilhelm IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Advisor James D. Van de Ven, PhD July 2015 © Shawn Wilhelm 2015 Acknowledgements No one accomplishes anything on their own and I would like to acknowledge a few of the people who carried me as completed my degree. I would like to thank my lab mate Alex who helped me pull my thesis defense together and wouldn’t let me give up. He saved me when I needed it most. To my friends who supported me and helped me through stressful times despite my neglect, I thank you. To my parents who made me who I am today, I am indebted. My mother always engaged my creativity and indulged my curiosity. She never directly answered my incessant childhood questions, but instead replied with her own to help me find the answers myself. My father always encouraged me to push myself to succeed. He never let me compare myself to anyone else and supported me as I attempted more and more challenging undertakings. Any success I achieve, I owe to them. I am forever grateful to my advisor, Jim Van de Ven. He has acted as a teacher, advisor, mentor, and friend. His guidance has brought me where I am today and I am in awe of his humility despite many accomplishments. I am honored to have worked with him and lucky to have had him as an advisor. i Dedication This work is dedicated to my wife Jennifer, who moved across the country to be with me while I “finished up my thesis” two years ago. Without her love, support, and remarkable patience, I never would have been able to complete this work. ii Abstract Hydraulic power systems offer a robust, compact, and flexible method of power transmission and are used widely in both industrial and mobile applications. While 2% of the energy consumed in the US passes through hydraulic systems, less than half of it does any useful work largely due to the use of inefficient flow control valves. Variable displacement pumps offer a method of delivering the required flow to an actuator without suffering the losses associated with a flow control valve. However, current variable displacement pumps exhibit poor efficiency at low displacement because their primary sources of energy loss are largely independent of displacement. Here, a novel adjustable linkage is proposed as the driving mechanism of a variable displacement pump. The linkage is constructed such that the pumping piston returns to the same top-dead-center position at all displacement, and can also achieve zero displacement. As a result of these features, the pump displacement is infinitely variable, and the unswept volume is remains constant at all displacements. By using pinned joints rather than sliding joints, the majority of the energy losses scale with output power resulting in a pump that is efficient over a wide range of operating conditions. In this thesis, a complete model of a variable displacement linkage pump is developed. A method of constructing the adjustable sixbar mechanism and the possible embodiments is presented. A new solution rectification technique is developed providing a robust method of generating valid linkages that is generally applicable to other mechanisms. The kinematics of the mechanism are then presented to describe the motion of the links and output piston. A kinetostatic model of the mechanism provides a means of determining the internal mechanical energy losses. A non-linear model of the bearing friction augments the model, but requires numerical methods to solve, and increases computational complexity. A dynamic model of the pumping cylinders and pump manifold provide a means of determining the fluid behavior of the pump including output flowrates and pressures. These models are coupled to create a complete understanding of the variable displacement linkage pump. The model is designed to be predictive and computationally inexpensive for use in multi-objective optimizations. As such, no experimentally determined performance coefficients are required. No model of this level of completeness exist for linkage driven pumps, variable displacement or otherwise. Two prototype pumps are presented and used to validate the models. A single cylinder pump is used to validate the mechanical energy loss model but was limited to low pressure operation due to large torque variations. Close agreement is demonstrated between the model and experiment. The model predicts a pump efficiency greater than 90% at displacements as low as 15% if roller bearings are used in the pin joints. To validate this prediction, a multi-cylinder prototype which uses roller bearings in the joints is designed. The kinematic and mechanical energy loss models are coupled to a basic pumping model for use in a multi-objective genetic algorithm to optimize the mechanism. The resulting pump demonstrates close agreement between the model and experimentally measured shaft torque and mechanical energy loss at various pressures, displacements, and input shaft speeds. However, out-of-plane deflection of the mechanism reduced the piston displacement and altered the trajectory reducing pump output. The true temporal iii piston position is measured and used as an input to the dynamic fluid model. The predicted and experimentally measured cylinder pressures demonstrate the effectiveness of the model at predicting the dynamic behavior of the fluid end of the pump. It is shown that the models can accurately capture the physics of the pump without using tuning parameters or experimentally determined coefficients over a wide range of operating conditions. It is recommended that single shear linkage arrangements are avoided in future designs to increase the mechanism stiffness and improve performance. The variable displacement linkage pump offers the opportunity for high efficiency flow control at a wide range of operating conditions due to the nature of the energy loss mechanisms scaling with the output power. The flexibility of the driving sixbar mechanism allows for the optimization of the architecture for particular applications and the presented model provides a means of predicting performance. iv Table of Contents Chapter 1 Background and Literature Review ................................................ 1 1.1 Introduction ..................................................................................... 1 1.1.1 Current Variable Displacement Piston Machines ........................... 2 1.1.2 Linkage Solution ............................................................................. 5 1.2 Literature Review............................................................................ 7 1.2.1 Kinematic synthesis ........................................................................ 8 1.2.2 Variable Displacement Internal Combustion Engines .................... 8 1.2.3 Pump Models .................................................................................. 9 1.3 Contribution of Thesis .................................................................. 11 1.3.1 Overview of Thesis ....................................................................... 12 Chapter 2 Adjustable Linkage Mechanism: Construction, Kinematics and Single Cylinder Validation ........................................................... 14 2.1 Introduction ................................................................................... 14 2.2 Mechanism Synthesis and Construction ....................................... 14 2.2.1 Task Specification and Type Synthesis ........................................ 14 2.2.2 Dimensional Synthesis .................................................................. 18 2.3 Equations of Motion ..................................................................... 24 2.3.1 Vector Representation and Mechanism Definition ....................... 25 v 2.3.2 Position ......................................................................................... 27 2.3.3 Velocity Analysis .......................................................................... 30 2.3.4 Acceleration .................................................................................. 30 2.4 Prototype Design for Kinematic Validation ................................. 32 2.4.1 Design Criteria .............................................................................. 32 2.4.2 Kinematic Optimization ................................................................ 34 2.4.3 Prototype Sizing ............................................................................ 37 2.5 Experimental Validation ............................................................... 38 2.5.1 Results ........................................................................................... 40 2.6 Discussion ..................................................................................... 42 2.7 Conclusions ................................................................................... 46 Chapter 3 Solution Rectification of Fourbar Mechanisms Including a Prismatic Joint with Transmission Angle Control ........................ 48 3.1 Introduction ................................................................................... 48 3.2 Methods......................................................................................... 50 3.2.1 Linkage Geometry Definition ....................................................... 50 3.2.2 Slider Driven Mechanism ............................................................
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