MAE486_Fall11_L18_S

MAE486_Fall11_L18_S - MAE 486 Design of Mechanical Systems...

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Unformatted text preview: MAE 486 Design of Mechanical Systems Lecture 17 Fall 2011 Today s topics: Modeling (Chapter 10); Review Models in Engineering Design •  What is model? Why model is needed in product/system design? •  What are the different models? •  What are the steps? –  What is the model for in the design? –  What is the model for? (For what decision?) –  Boundary condi7on: •  Modeled domain vs. The rest of physical situa7on. –  What do we know? –  What physical law to apply? –  What are the assump7ons can we make? –  Construct the model and verify the model Review MathemaAcal Model ­Building Process •  Problem statement: decide what it is your need to learn. •  What are the steps? –  What is the model for in the design? –  What is the model for? (For what decision?) –  Boundary condi7on: •  Modeled domain vs. The rest of physical situa7on. –  What do we know? –  What physical law to apply? –  What are the assump7ons can we make? –  Construct the model and verify the model. •  Analysis: Determine how the equaAons of the model will be solved to produce meaningful output. •  Validate the model: The results should be validated by experimental data. Review One Modeling Example •  Problem Statement: What size motor should be selected to drive a conveyor belt to deliver sand at a flow rate of 100 tons/hr using the following design. •  •  •  •  •  •  •  Design decision space: Boundaries of the model: Data to support the model Physical principles: Assump=ons: Construct the model: Analysis: Dimensional Analysis •  What is it? •  Why use it? What are the advantages? •  What does it based on? –  The Buckingham π theorem. Dimensional Analysis (cont’d) •  What is the main idea? •  What is the procedure to determine the pi terms using the method of repeaAng variable? Example of Dimensional Analysis •  Goal: Analysis how the fricAon in the bearing varies with operaAon condiAons of a lubricated journal bearing. Example of Dimensional Analysis •  List all the variables in the problem (k=?): •  Express each of the variables in terms of their basic dimensions: •  Determine the required number of pi terms •  Select the repeaAng variables. –  In this problem, we select three repeaAng variables, D, N, and p. •  Select the variable to be the dependent variable. –  The dependent variable is pf. The nonrepeaAng variables are pf, C and μ. •  Form a pi term by mulAplying one of the nonrepeaAng variables by the product of the repeaAng variables Example of Dimensional Analysis •  Form a pi term by mulAplying one of the nonrepeaAng variables by the product of the repeaAng variables. For example Similarly, we obtain Example of Dimensional Analysis •  When these three dimensionless groups are ploYed, a clear picture of bearing performance is given. Similitude and Scale Models •  What does similitude mean? •  What is scale model? •  Geometric similarity: •  Use of dimensional analysis—The pi number of the model must equal to that of the prototype (Example?) Geometric Similarity •  Consider the example of a cylindrical bar of length L with deformaAon δ under force P. What is the scale factor? •  What are the variables? •  Choose repeaAng variables: •  Find pi groups: Geometric Similarity (cont’d) •  Find similarity relaAonship •  How to use the above relaAon in model study? –  Suppose we wish to use a plasAc model, Em=0.4 x 10^6 lb/in2 to model a steel bar, Ep=30 x 10^6 lb/in2, loaded to 50000 lbs, if the model is built to a 1 to 10 scale (S=0.1), what is the load we should apply to the model? Finite ­Difference Method •  When numerical methods become necessary and powerful? •  Finite ­difference method: q – rate of energy generaAon per unit volume, k– thermal conducAvity. •  Consider two ­dimensional case Finite ­Difference Method (cont’d) Finite ­Difference Method (cont’d) •  First, approximate the first ­order derivaAve: •  Secondly, approximate the second ­order derivaAve: •  Do the same for y: Finite ­Difference Method (cont’d) •  Finite difference equaAon: •  Understanding the equaAon: •  One example: Steady ­state boundary temperatures on the four sides of the furnace wall are shown. Calculate temperatures at all nodes. Finite ­Difference Method (cont’d) •  QuesAon: How to improve the accuracy? ...
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This note was uploaded on 02/26/2012 for the course 650 486 taught by Professor Zou during the Fall '11 term at Rutgers.

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