Final Exam Very good performance overall Essays were particularly good Mean 88 5 Standard deviation 5 7 16 881 MIT Homework HW 8 Mean 96 1 Standard Deviation 7 4 HW 9 Mean 94 9 Standard Deviation 5 5 16 881 MIT The Remainder of the Course Primary mission Complete your term projects Secondary mission Cover topics of interest 70 of your grades are set term project 30 Class sessions half new topics half consultation 16 881 Tolerance Design Projects Mahalanobis Taguchi System Projects Conceptual Robust Design Projects Final Project Presentations MIT Expectations on Final Project Should represent 30 hours of effort Options 16 881 Full robust design effort Planning phase only Post mortem analysis of a previous effort Study of an advanced topic in robust design Other possibilities with permission MIT Grading of the Final Project 75 Written report 25 Oral presentation Grading criteria include Impact and significance of the results Quality of the planning and analysis Clarity of technical exposition 16 881 MIT Tolerance Design The Interface Between Design and Manufacture 16 881 MIT Outline History of tolerances Tolerancing standards Tolerance analysis Tolerance design Taguchi s approach Case study 16 881 MIT History of Tolerances pre 1800 Craft production systems 1800 Invention of machine tools the English System of manufacture 1850 Interchangeability of components the American system of manufacture Jaikumar Ramachandran From Filing and Fitting to Flexible Manufacture 1988 16 881 MIT Craft Production Drawings communicated rough proportion and function Drawings carried no specifications or dimensions Production involved the master the model and calipers 16 881 MIT The English System Greater precision in machine tools General purpose machines Maudslay invents the slide rest Accurate measuring instruments Micrometers accurate to 0 001 inch Engineering drawings Monge La Geometrie Descriptive Orthographic views and dimensioning Parts made to fit to one another Focus on perfection of fit 16 881 MIT The American System Interchangeability required for field service of weapons Focus on management of clearances Go no go gauges employed to ensure fit Allowed parts to be made in large lots Go no go gauges 16 881 MIT Tolerances on Drawings Binary acceptance criteria Multiple quality characteristics All criteria must be met dominance 16 881 12 MIT Basic Tolerancing Principles ref ANSI Y14 5M Each dimension must have a tolerance Dimensions of size form and location must be complete No more dimensions than necessary shall be given Dimensions should not be subject to more than one interpretation Do not specify manufacturing method 16 881 MIT Tolerance Analysis Probabilistic Approaches Worst case stack up Root sum of squares Numerical integration Monte Carlo simulation 16 881 MIT Tolerance Analysis Problem 1 0 0 05 Extruded aluminum bar stock Cut two pieces Stacked end to end 1 0 0 1 What is the probability that the stack will fit in this bracket 2 2 0 1 16 881 MIT Specifying Tolerances to Minimize Required Precision How should this part be dimensioned How is optimal dimensioning determined by function 16 881 MIT Tolerance Analysis Geometric Kinematic Issues Will these parts mate Solution approaches Kinematic modeling Assembly simulation 16 881 MIT Variation Systems Analysis You supply geometry You define distributions Software provides Variance Defect rate Pareto diagram MIT Computer Aided Tolerancing Strengths Requires few probabilistic assumptions Can account for real assembly considerations Tooling Gravity Integrated with many CAD environments Major Pitfalls Compliance of parts Source of input data 16 881 MIT Process Capability Indices p q U L 2 L U L 2 U q Process Capability Index Bias factor U L 2 k U L 2 3 Performance Index 16 881 Cp U L 2 C pk C p 1 k 20 MIT Tolerance Cost Models p q U L 2 Cost L U L 2 U q Scrap cost Machining cost Tolerance 16 881 MIT Tolerance Cost Models Multiple Processes Cost Lapping Grinding Machining Tolerance 16 881 MIT Traditional Tolerance Design Select tolerances on components that optimize profitability Tighter tolerances higher costs of manufacture Looser tolerances higher scrap rates Approaches Linear programming Discrete optimization 16 881 MIT Taguchi Tolerance Design Use OAs in a noise experiment to determine the magnitude of tolerance factor effect How many levels would you choose Use the quality loss function as a basis for the trade off between higher manufacturing costs and lower customer satisfaction 16 881 MIT Tolerance Design Case Study Who would you involve in the tolerance design study 16 881 Singh K R Newton and C Zaas Tolerance Design on a Moveable Window System of an Automobile Door ASI 3rd International Symposium 1997 MIT Customer Requirements Smooth and quiet operation under all weather conditions Consistent closing and opening speeds No wind noise or water leakage Long life and high reliability 16 881 MIT System P Diagram 16 881 Noise Factors Levels Why use three level noise factors Why is there a difference in spread of the levels between a three level and two level factor 16 881 MIT Noise Factor Effects on Average Glass Velocity What is the significance of the range What is the significance of non linearity 16 881 MIT Noise Factor Effects on Stall Force How would you use this to make a Pareto diagram 16 881 MIT Window System Case Study Conclusions Cross functional team included design manufacture reliability and suppliers Motor power and regulator efficiency identified as major contributors to variation Computer simulation allowed redesign prior to prototyping Product development cycle time and cost reduced 16 881 MIT Next Steps Next off campus session SDM Conference room 16 881 MIT References Evans D H 1974 Statistical Tolerancing The State of the Art Part 2 Methods of Estimating Moments Journal of Quality Technology vol 7 no 1 pp 1 12 Bjorke O 1978 Computer Aided Tolerancing Tapir Publishers Trondheim Norway Harry Mikel J and J Ronald Lawson 1992 Six Sigma Producibility Analysis and Process Characterization Addison Wesley Reading MA 16 881 MIT References Cont ASME 1983 ANSI Y14 5M Dimensioning and Tolerancing Americain Society of Mechanical Engineering New York Craig M 1988 Variation by Design Mechanical Engineering vol 110 no 11 pp 5254 Greenwood W H and K W Chase 1987 A New Tolerance Analysis Method for Designers and Manufacturers ASME Journal of Engineering for Industry vol 109 pp 112 116 16 881 MIT References Cont Jaikumar Ramachandran 1988