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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. •
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• 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.
 Fall '11
 Zou

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