MAE486_Fall11_L23_S - MAE 486 Design of Mechanical Systems...

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Unformatted text preview: MAE 486 Design of Mechanical Systems Lecture 22 Fall 2011 Today s topics: Manufacturing consideration of design (Chapter 13); Robust design (Chapter 15); Review Process Capability •  Process capability index Cp A spindle has a spec. on its diameter of 1.5+/ ­0.009 inch. If Cp=1. what is ?. ould be std to achieve Cp=1.33? •  What w •  If Cp=1.33 and mean is centered within the range, how many oversize parts? •  Control charts Process Capability •  If the mean is not centered within the tolerance range, process capability index Cpk •  The distance of the process mean differs from the midpoint of the tolerance region is give by •  How does Cpk and Cp relate to each other? Taguchi Methods •  The input parameters affecOng the quality of the product/ •  •  process  Noise factors: What are they? –  –  –  –  Varia1onal noise: Inner noise: Design noise: External noise (outer noise):. Robust Design •  What is it? –  Approach  OpOmum values of design factors  economical design & low variability. •  Parameter design: –  IdenOfy the seWngs of the design parameters or process variables  Reduce the sensiOvity of the design to sources of variaOon. •  How to do parameter design? –  Step 1: IdenOfy Control factors •  Design parameters that primarily affect the S/N raOo but not the mean. –  Step 2: Adjust the mean response by using a suitable design parameter (the signal factor) once the variance has been reduced. Parameter Design (cont’d) •  What is the trade ­off? –  Min (# of tests) vs. Loss (Detailed informaOon of interacOons). •  Two commonly used orthogonal arrays. (a)  L4 deals with three control factors at two levels. A total of 4 runs of DOE is needed. (b) L9 array considers four control factors each at three levels. A total of 9 runs of DOE is needed. Taguchi Robust Design Method What are the steps? •  Step 1: Problem definiOon. –  Select the parameter to be opOmized and the objecOve funcOon. •  Step 2: SelecOon of design parameters; –  The control parameters (controlled under the designer) and the noise parameters (contribute to the variaOon caused by the environment. •  Step 3: Experiment design –  Select the appropriate fracOonal factorial array, the number of levels to be used, and the range of the parameters that correspond to these levels. •  Step 4: Do the experiments –  Follow DOE; •  Step 5: Results analysis; –  Calculate the S/N. •  Step 5: Repeat steps 1 to 4 if no clear opOmum value. OR: •  Step 5: Validate the results; –  Perform a confirming experiment when the method gives a set of opOmal parameter values. Robust Design Example •  Problem: –  A new prototype of new game box has indicator light failure •  Causes: –  Poor solder joints. •  Root cause: –  Use of improper solder paste (i.e., solder balls and flux). •  ObjecOve: –  Design the best condiOons for making strong solder joints by using the Taguchi method. Robust Design Example (cont’d) •  Step 2: Select control Parameters: –  Four control parameters (with L9 orthogonal array, i.e., three levels) •  Step 2: Select noise parameters •  Three noise parameters (with L4 orthogonal array, i.e., two levels) Robust Design Example (cont’d) •  Step 3: Experiment design –  Conduct four experiments for each run in L9 (e.g., run 2 in L9 is executed four Omes to include the noise matrix.) –  The first trial condiOon: a new can of paste, water rinse, and horizontal spray –  The last trial condiOon: a can of paste opened one year ago, a chlorocarbin cleaning agent, and horizontal spray for cleaning. •  Step 4: Experiment run –  For each of the four trials of each run, measure a response that represents the objecOve funcOon that we are ahempOng to opOmize: •  Shear strength of the solder joint measured at room temperature. Parameter Design (cont’d) •  Two commonly used orthogonal arrays. (a)  L4 deals with three control factors at two levels. A total of 4 runs of DOE is needed. (b) L9 array considers four control factors each at three levels. A total of 9 runs of DOE is needed. Robust Design Example (cont’d) •  Step 5: Results analysis –  For four trials, average the strength measurements and determine the standard deviaOon. For example, for run 2, we have •  Step 5: Results analysis •  In the robust design, the appropriate response parameter is the S/N raOo. Which type to use here? Robust Design Example (cont’d) •  Step 5: We obtain the following parameter matrix. Robust Design Example (cont’d) •  Step 5: Determine the average response for each of the four control parameters at each of its three levels. •  Step 5: The average S/N raOos are plohed against test level for each of the four control parameters. Robust Design Example (cont’d) •  Step 5: Observe the plots: Which factor is not important? S/N larger the beher, or the other way around? •  Step 6: Obtain the opOmum seWng of the control parameters Cost EvaluaOon •  Why is it useful? –  InformaOon  Selling price / QuotaOon; –   The most economical method, process, or material (4 manufacturing); –  Basis 4 cost ­reducOon; –   Standards of producOon performance 4 control costs –  Input  Profitability of a new product Categories of Costs What are the costs? •  Fixed costs (period costs): Over a period of Ome regardless of the amount (volume) made or sold •  General and administraOve expenses (Q&A expenses): Categories of Costs (cont’d) •  Variable costs (product costs): costs that vary with each unit of product made –  –  –  –  –  –  –  –  –  Materials Direct labor (including fringe benefits) Direct producOon supervision Maintenance costs Power and uOliOes Quality ­control staff Royalty payments Packaging and storage costs Scrap losses and spoilage Elements of Costs Example Given: The annual cost data of a manufacturer of small hydraulic turbines below, QuesOon: Calculate the manufacturing cost and the selling price for a turbine. Example (cont’d) Example (cont’d) The figure in the previous slide should be used for breaking down the costs listed as follows. Break ­Even Point •  Break ­even point: –  sales or producOon volume at which sales and costs balance •  P ­ unit sale price, v – variable cost, f – fixed cost Q – number of producOon unit, Example: Break ­Even Point •  A new product has the following cost structure Labor cost: $2.5/unit; Material cost: $6/unit G & A expenses: $1200 DepreciaOon on equipment: $5000 Factory expenses: $900 Sales & distribuOon overhead: $1000 Profit: $1.7/unit Determine the break ­even point. Example: Break ­Even Point (cont’d) •  Total variable costs: •  Total fixed cost: •  Sales price: •  Break ­even point: •  If producOon at 1000 units, then what the price should be for break ­even? Overhead Costs •  What does an overhead cost included? •  How to esOmated? •  What are the main categories? ...
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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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