Airball Demo Modeling Dimensional Analysis Method Based on
Airball Demo Modeling ——Dimensional Analysis Method Based on Genetic Algorithm for Key Parameters Identification Name:Zhisheng Team Advisor: Zhang Chenghui, Li Ke
CONTENTS 1 2 3 4 Introduction Mechanism Modeling Key Parameters Identification Experiment and Analysis
1. Introduction Dimensi on π theorem Dimensional Analysis and Modeling are widely used techniques in fluid mechanics. A qualitative description of physical quantities can be given in terms of basic dimensions such as mass , length and time. The basis for Dimensional Analysis’ application to a wide variety of problems is found in the Buckingham π theorem:if an equation involving n variables is dimensionally homogeneous, it can be reduced to a relationship among n-m independent dimensionless products,where m is the minimum number of basic dimensions.
1. Introduction Supposing an physical expression as , which involves n variables and m basic dimensions. It can be reduced to a relationship among n-m independent dimensionless products: where we use to represent dimensional products.
2. Mechanism Modeling 1. Hardware Analysis 2. Modeling Figure 1 Airball Demo
2. Mechanism Modeling 1. Hardware Analysis The fan rotates to push against air with the effect of input voltage and air flow directionally through the pipe. A B The flow of air in the pipe generates a driving force on airball. The airball move through the pipe and finally keep in a certain height. C D Airball Demo The airball height is converted into output voltage using ultrasonic sensor.
2. Mechanism Modeling 2. Modeling Based on Newton motion law, force analysis of airball is illustrated in Figure 2. The equation of airball is established as follows, F G=mg Figure 2 Force analysis of airball
2. Mechanism Modeling A 614 JH-EBM-Papst model fan is applied by Airball Demo. Based on the Theory of Electric Machine, we can get Table 1 Nominal data of fan .
2. Mechanism Modeling Pressure over air flow is illustrated in Figure 3. If pressure is definite, the speed characteristics of electric machine is directly proportional to air flow and air flow varies directly as the speed of air in the pipe. Thus, we can get if pressure is zero, Concerning about the influence of Airball Demo on pressure,so the speed of air is modified to: Figure 3 Characteristic:Pressure where k 1, k 2 need to be identified. over air flow
2. Mechanism Modeling The first step to study this problem would be to decide on the factors that will have effects on Airball Demo. We expect the list to include the pipe diameter , the fluid density , the airball diameter and the velocity , at which the fluid is flowing through the pipe. Thus we can express this relationship as Ø Applying Dimensional Analysis and pi theorem,
2. Mechanism Modeling Ø Next we express all the variables in terms of basic dimensions. Using , , as basic dimensions it follows that where dim represents the dimension of certain physical quantity. Ø Choosing , , , thus we get dimensionless products as follows:
2. Mechanism Modeling Ø thus Ø So we can write Ø Finally, give the relationship among dimensionless products, that is,
2. Mechanism Modeling Ø Airball height measurement A Baumer UNAM 186903/S 14 model ultrasonic sensor is applied by Airball Demo. It is almost linear on [100 mm , 1000 mm] interval. Height(mm) Sample result Slope 130 4637 0. 02801 130 6700 0. 02766 180 6464 0. 02784 230 8251 0. 02787 Average slope 0. 02784 Table 2 Ultrasonic sensor experiment data
2. Mechanism Modeling Ø Conclusion Based on the work mentioned above, the model of Airball Demo is got, that is
3. Key Parameters Identification Introduction to model parameters identification using Genetic Algorithms(GA) Data acquisition k 1, k 2, k 3 The method of programming
3. Key Parameters Identification Ø Introduction Genetic Algorithms is used to identify model parameters: k 1, k 2 and k 3. Objective function is: Fitness function is: Figure 4 parameters identification schematic diagram
3. Key Parameters Identification Ø Data acquisition Step voltage input are imposed on Airball Demo. The height output is sampled in Automation Studio software based on the fixed interval time. Figure 5 Airball Demo step response curve
3. Key Parameters Identification Ø The method of programming Start Initializing the GA paprmeters Select, cross, mutation Initializing the population Calculating the fitness N Exit End Y
4. Experiment and Analysis Ø Set GA parameters: Ø Run the GA program, then we can get the fitness curve and k 1, k 2, k 3. fitness: 0. 2163 k 1: 0. 0547 k 2: 0. 2437 k 3: 0. 5872 Figure 6 Fitness curve
4. Experiment and Analysis The simulated curve in AS environment is shown in Figure 7 Simulated curve The Airball Demo curve is shown in Figure 8 Airball Demo curve
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