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Real Time Simulation of Hydraulic Systems Using Multibody Dynamics Analogy

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Real Time Simulation of Hydraulic Systems Using Multibody Dynamics Analogy Real Time Simulation of Hydraulic Systems Using Multibody Dynamics Analogy Jeryes Daniel dit Rabih Master of Engineering Department of Mechanical Engineering McGill University Montreal, Quebec 2016-08-15 Thesis submitted to McGill University in partial fulllment of the requirements of the degree of Master of Engineering (M.Eng.); Mechanical Engineering (Thesis) c Jeryes Daniel dit Rabih, 2016 DEDICATION To my family. ii ACKNOWLEDGMENTS I would like to thank my supervisor, Professor Jozsef Kovecses for his guidance and support during the research. I would also like to thank my colleagues at CM Labs: Marek Teichmann, Martin Hirschkorn, Danial Alizadeh and Ali Azimi for their help in the project. Finally, I would like to thank my family for their unconditional love, patience and encouragement. iii ABSTRACT The research objective of this thesis is to develop a real-time simulation model for hydraulic systems used to transmit power in machines such as excavators and cranes. Hydraulic simulation usually requires slow, expensive computation due to sti dierential equations and steep characteristics which make it hard to achieve real-time simulation. The solution model described in this thesis uses a mechani- cal system equivalent to the hydraulic circuit using a multibody dynamics analogy. Hydraulic circuits consisting of a pump, cylinders, motors, pressure relief valves, a servovalve and check valves are simulated. The model is tested using a real-time rigid body dynamics engine (Vortex) and results were compared and validated with a hydraulic simulation engine (simHydraulics). The model is validated by applying it to the simulation of a hydraulic excavator. iv ABRÉGÉ L'objectif de recherche de cette thèse est de développer un modèle de simulation en temps réel pour les systèmes hydrauliques utilisés pour transmettre la puissance dans des machines telles que les excavatrices et les grues. La simulation hydraulique est généralement lente, coûteuse en raison des équations diérentielles raides et des caractéristiques abruptes qui rendent la simulation en temps réel dicile. La so- lution décrite dans cette thèse utilise un système mécanique équivalent au circuit hydraulique à l'aide de la dynamique multicorps. Les circuits hydrauliques consis- tent d'au moins une pompe, de cylindres, de moteurs, de soupapes de décompression, d'une servovalve et de clapets qui sont simulés. Le modèle est validé à l'aide d'un engin de simulation en temps-réel basé sur la dynamique des corps rigides (Vortex) et les résultats sont comparés et validés avec un moteur de simulation hydraulique (simHydraulics). Le modéle est validé en utilisant un exemple concret de simulation de pelle hydraulique. v TABLE OF CONTENTS DEDICATION . ii ACKNOWLEDGMENTS . iii ABSTRACT . iv ABRÉGÉ . .v LIST OF TABLES . viii LIST OF FIGURES . ix 1 Introduction . .1 1.1 Motivation . .1 1.2 Objective . .3 1.3 Literature Review . .4 1.4 Thesis Overview . 10 2 Multibody Dynamics Formulations . 11 2.1 Introduction . 11 2.1.1 Equations of Motion . 11 2.1.2 Solution . 12 2.2 Constraints Derivation . 13 2.2.1 Gear Ratio . 13 2.2.2 Dierential . 16 2.3 Real-Time Simulation Engines . 19 3 Hydraulic Components Modelling . 21 3.1 Pump . 21 3.2 Hydraulic Motor . 26 3.3 Hydraulic Cylinder . 28 3.4 Power Transmission Junctions . 32 vi 3.4.1 1-1 Junction . 33 3.4.2 1-2 Junction . 35 3.4.3 1-n Junction . 37 3.4.4 Rotation to translation Junction . 38 3.5 Pipes . 39 3.5.1 Fluid Inertance . 39 3.5.2 Fluid Resistance . 41 3.5.3 Fluid Compliance . 43 3.6 Valves . 45 3.6.1 Orice . 46 3.6.2 Directional Control Valve . 48 3.6.3 Pressure Relief Valve . 49 3.6.4 Check Valve . 51 4 Hydraulic Circuits Modeling and Simulation . 53 4.1 Hydrostatic Transmission - One Motor . 53 4.2 Hydrostatic Transmission - One Motor with Pipe Losses . 60 4.3 Hydrostatic Transmission - Two Motors . 64 4.4 Hydraulic Cylinder Circuit . 71 5 Application: Front Loader Actuation System . 75 5.1 Hydraulic System . 75 5.2 Simulation Inputs . 78 5.3 Simulation Results . 81 6 Conclusions . 84 A Simhydraulics Circuits . 86 References . 93 vii LIST OF TABLES Table page 1.1 Analogy between mechanical, electrical and hydraulic systems [9]. .9 4.1 Pump Parameters . 54 4.2 Motor Parameters . 54 4.3 Pressure Relief Valve Parameters . 54 4.4 Fluid Parameters . 54 4.5 Pipe Parameters . 60 4.6 Cylinder Parameters . 72 4.7 4-Way Directional Valve Parameters . 73 5.1 Excavator Pump Parameters . 75 5.2 Fluid Parameters . 76 5.3 Tilt Cylinder Parameters . 76 5.4 Lift Cylinder Parameters . 76 5.5 Tilt Pipes Parameters . 76 5.6 Lift Pipes Parameters . 77 5.7 Tank Return Pipes Parameters . 77 5.8 Excavator Pressure Relief Valve Parameters . 77 5.9 5/3 Way Directional Valve Parameters . 77 viii LIST OF FIGURES Figure page 1.1 Tower Crane Simulator Developed by CM Labs Simulations . .1 1.2 Hydraulic Shovel [1] . .2 1.3 Example for Compressibility Eects [5] . .4 1.4 Hydraulic junctions with constant and variable volumes [2] . .6 1.5 Pressure drop in an orice [2]. .8 1.6 Combination of smooth and non-smooth components [2]. .8 2.1 Gear Ratio Constraint . 14 2.2 Dierential Constraint . 17 3.1 Pump Main Parts . 22 3.2 Revolute Joint . 22 3.3 Pump . 24 3.4 motor . 27 3.5 Cylinder Main Parts . 29 3.6 Prismatic Joint . 29 3.7 Cylinder . 31 3.8 Junction 1-1 example . 33 3.9 Junction 1-2 . 35 3.10 Junction 1-n . 37 3.11 Rack and Pinion . 38 ix 3.12 Rotation to Translation Junction . 39 3.13 Fluid Inertance Analogy . 40 3.14 Pipe Flow Inertance and Damping Analogy . 43 3.15 Mixture of Gas and Liquid . 44 3.16 Pipe Simulation Model . 45 3.17 Orice . 46 3.18 Valve Flow Versus Spool Position [16] . 47 3.19 Four Way, Three Position Valve . 48 3.20 Pressure Relief Valve . 49 3.21 Check Valve . 51 4.1 Hydrostatic Transmission Circuit - One Motor . 53 4.2 Equivalent Mechanical System of One Motor Circuit . 55 4.3 No Load Test Results for One Motor Circuit . 57 4.4 Damping Load Test Results for One Motor Circuit . 58 4.5 Stiness Load Test Results for One Motor Circuit . 59 4.6 Hydrostatic Transmission Circuit - One Motor with Pipe Losses . 60 4.7 Equivalent Mechanical System of One Motor Circuit with Pipe Losses 61 4.8 Motor Velocity with 5m Pipe Length . 62 4.9 Motor Velocity with 10m Pipe Length . 63 4.10 Motor Velocity with 15m Pipe Length . 63 4.11 Hydrostatic Transmission Circuit - Two Motors . 64 4.12 Equivalent Mechanical System of Two Motor Circuit . 65 4.13 No Load Test Results for Two Motor Circuit . 67 x 4.14 Dierent Motor Displacement Test Results for Two Motor Circuit . 68 4.15 Damping Load Test Results for Two Motor Circuit . 69 4.16 Stiness Load Test Results for Two Motor Circuit . 70 4.17 Hydraulic Cylinder Circuit . ..
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