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# Mathematical Modeling and Analysis of a Variable Displacement Hydraulic Bent Axis Pump Linked to High Pressure and Low Pressure Accumulators

Abstract (Summary)
Working prototypes of a Hydraulic Hybrid Vehicle (HHV) are already under testing and investigation. One of the problems reported from testing is that the noise levels emitted by the hydraulic system are not acceptable. Therefore, there is a need to perform extensive research to improve the HHV systems in terms of noise and performance. The pump is the main source of noise in HHV systems. However, the lack of space, the high pressure and the dynamics of components within the pump have prevented either direct observation or measurement of potential noise causing mechanisms within the pump structure. As a result, there are several theories as to the source of the noise from the pump units but little concrete information to further isolate and reduce the noise generation. Currently, the industry use “cut and try” methods in order to study the noise issue. This necessities the development of a theoretical tool that will enable us to avoid the costly (time and money) cut and try procedure already employed in the current efforts. This work creates a dynamic and geometric model of a bent axis pump for this purpose. Elements of the model include finding the variation of pressure, flow rate, and dynamic forces acting on the pump components and case as a function of angular rotations of both the main shaft and the yoke. The model was constructed using MathematicaTM” software and verified against test data. In turn, this study identifies and analyzes the dominant forces in both the time and frequency domains. The solution of the theoretical model using MathematicaTM is verified by a dynamic model created using ADAMS/View software. The kinematic model was able to predict the variations of the angular velocities and accelerations and the velocities and the accelerations of the center of gravity of the entire pump’s parts starting from the main shaft up to the yoke. This work presents all equations necessary to solve for the piston pressure and pump flow rate as a function of main shaft and yoke rotations. These equations were tested, and verified at a constant angular speed of the main shaft and yoke angles ranging from 5° to 40° . Results indicate that the model can predict the variations of pressure profile and flow rate as well as the forces acting on the pump’s case both in the time and frequency domains. Conclusions and recommendations are at the end of this research effort. The harmonics of the reaction forces acting on the pump case occur at frequencies of 25, 50, 100, 200, 220, 250, 350, and 450 Hz respectively.
Bibliographical Information:

School:University of Toledo

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:bent axis pump piston swash plate noise mathematical modeling dynamic flow rate pressure high accumulator low valve constant velocity joint equation of motion

ISBN:

Date of Publication:06/16/2009