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Modeling of Axial Piston Pump Input Torque and Output Flow Rate using MATLAB (R) Simulink: a thesis submitted to the faculty of the Milwaukee School of Engineering in partial fulfillment of the requirements for the degree of Master of Science in Engineering / by Pawan Panwar.

by Panwar, Pawan author., Williams, Dr. Daniel thesis advisor , Michael, Paul , Shimek, Gary , committee member , Milwaukee School of Engineering

[Milwaukee School of Engineering], [ 2018]

Hydraulic machinery

leaves : illustrations, some of which are in color ; 29 cm

List of Figures -- List of Tables -- Nomenclature -- Chapter 1: Introduction -- Chapter 2: Background and Literature Review; 2.1 Positive Displacement Machine; 2.2 Axial Piston Swash-Plate Pump; 2.3 Empirical Modeling -- Chapter 3: Physical and Thermal Properties of the Hydraulic Fluids; 3.1 Introduction; 3.2 Bulk Modulus; 3.3 Viscosity; 3.3.1 Kinematic Viscosity; 3.4 Density; 3.5 Thermal Properties -- Chapter 4: Mathematical Modeling of Axial Piston Pump; 4.1 Pump Kinematics; 4.2 Volumetric Flow Rate; 4.2.1 Theoretical Flow Rate and Ripple; 4.2.2 Instantaneous Displacement Chamber Pressure; 4.2.3 Overall Flow Rate of Pump; 4.3 Torque Input on the Shaft and Swash Plate; 4.3.1 Piston Dynamic Loading; 4.3.2 Instantaneous Torque on the Shaft; 4.3.3 Overall Torque on the Shaft of the Pump; 4.4 MATLAB Simulink Models -- Chapter 5: Experimental Methodology -- Chapter 6: Results and Discussion; 6.1 Empirical Modeling; 6.1.1 Pump Discharge Flow Model; 6.1.2 Pump Torque Model; 6.2 Mathematical Modeling in MATLAB Simulink -- Chapter 7: Summary -- References -- APPENDIX; Appendix A: MATLAB Function to Determine Fluid Properties Model; Appendix B: MATLAB Function to Acquire Parameter of the Fluids; Appendix C: MATLAB Function to Determine Theoretical Flow Ripple; Appendix D: MATLAB Function for TOET Method; Appendix E: MATLAB Script for Empirical Model of Flow and Torque; Appendix F: MATLAB Function for Best Subset Regression.

The purpose of this project was to examine and to develop a steady-state MATLAB Simulink model of the variable displacement axial piston pump. Axial piston pumps are widely used both in industry and off-highway machinery because of their design's compactness, flexibility in power transfer, a broad range of operating pressure and speed, variable flow rate, and high efficiencies as compared to their manufacturing costs.

Work was carried out with the goal of developing detailed steady-state Simulink models of the axial piston pump using physical parameters based on first principles (i.e., actual measurements) to assist in determining the pump outlet flow, leakage flow, and torque input. The pressure and temperature dependent fluid properties that influence the efficiency of hydraulic machinery were also incorporated to validate the model for multiple fluids and to determine the most evergy efficient hydraulic oil. In the first phsase of the project, fluid properties that affects the performance of the hydraulic system were developed as a function of pressure and temperature of the fluid. In the second phase, the empirical models for the discharge flow and torque input were developed using best subset regression analysis. Finally, the MATLAB Simulink of discharge flow and torque on the shaft was developed using the dimensions of a pump.

Four fluids that differ in their physical properties were evaluated in a dynamometer at 80 C using a modified ISO 4409 procedure. The dynamometer consists of an open-loop axial piston swash plate type pump, to test hydraulic fluid effciency for off-highway machinery. For developing a robust and high-fidelity empirical model, a Latin Hypercube sampling (LHS) based design of experiment (DOE) was planned and to validate the developed MATLAB model, a full factorial based DOE was implemented.

The fluid properties model developed for this project very well correlated fluid properties for a broad range of operating conditions. Empirical models based on LHS DOE were shown very effective in predicting both discharge flow and torque input and in distinguishing the fluids that differ in their physical properties. Hence, they could be used in predicting energy efficient fluid for off-highway machinery. In addition, the MATLAB Simulink models that were developed for this project, which incorporate the developed fluid properties model, were successful in forecasting discharge flow and torque input. However, the developed torque input model has a considerable difference as compared to the flow rate model. A higher fidelity model for gap height and viscus friction would enhance the accuracy of torque model.

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