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Unformatted text preview: P a g e | 1 The system in question is a hydro-mechanical system that uses a hydraulic pump to drive a motor that spins a mass such as cutting blade on a circular saw. Both the pump and motor leak, there is a fluid reservoir, and a resistance on the shaft coming out the hydraulic motor. The goal of this project is to model the system mathematically, find its steady state operation, and linearize the states in order to use them in a Matlab model. With this we are able to create a transfer function for the system based on the three inputs and three outputs. We wish to model this system mathematically for the same reason we would model any system – we want to understand certain properties of the system. By understanding things like the resonance of the system, the stability, the time constants around a system that is already in place just as easily as we can then modify certain parts of the design if the system does not meet our loading requirements. a) Develop the state equations of motion for the system. Clearly label all states. Include the temperature of the machine in the states. This is the system given on the project A free body diagram looks like the following P a g e | 2 This simplifies to: The first step in the problem was to model the system mathematically. The states are defined as any element that stores energy, and in this system there were 4 states; the flow through the inerter Q5 , the pressure drop across the fluid tank (Capacitance) Pr , the angular velocity of the mass the motor was...
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This note was uploaded on 04/22/2010 for the course ME 124514565 taught by Professor Sanchez during the Spring '10 term at Texas Tech.
- Spring '10