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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/ •
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process Noise factors: What are they? –
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– 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 –
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– 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.
 Fall '11
 Zou

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