L10-Statistics+and+Probability2

L10-Statistics+and+Probability2 -...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Uncertainty in design and manufacturing: Statistics, reliability, and probability VM250, Design and Manufacturing I Mechanical Engineering SJTU UM Joint Institute 1 Primary source: A. John Hart. Includes material from D. Dutta and K. Saitou
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Outline Introduction Random variables Normal distributions Absolute and statistical tolerances Non normal distributions; statistics of failure Reliability of manufacturing sequences Accuracy, repeatability and resolution Summary Covered last lecture Cover today
Background image of page 2
Tolerance “stackup”: combining normal distributions Sum and difference of two independent normally distributed random variables For n independent normally distributed random variables… 12 yx x  x 22 x   x  x x  , 1 x N x   , y N y , 2 x N x
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Why do we need to combine distributions? 2 2 2 1 0 2 2 2 1 2 0 1 2 0 During operation, parts are typically subjected to wear/fatigue loads N( , ). However, they are designed to withstand loads N( 2 , 2 ) under normal operating conditions Suppose is stress and is strength The distribution of safety margin (strength minus applied stress)
Background image of page 4
Absolute vs. statistical tolerances Absolute tolerances (worst case): We assume that the part dimension cannot exceed the tolerance limits Statistical tolerances: We assume that the tolerance limits represent a certain number of standard deviations (e.g., 3) of a normal distribution Always: the nominal value is the mean of the distribution (symmetric distribution)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Absolute vs. statistical tolerances Pin in hole D Dt d dt nominal dimension tolerance (absolute or statistical)
Background image of page 6
Absolute vs. statistical tolerances Actual pin and hole diameters: x D and x d Clearance x w = x D x d Need x w > 0 to fit D Dt d dt
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Absolute tolerances Peg in hole example: absolute tolerance No “out of range” dimensions are possible Range of clearance x w = x D x d DD D dd d Dt x dt x   x x  () ( ) ( ) ( ) ( ) L LH D d D d H HL D d D d wD d D t d t D d tt d D t d t D t       ww w Wt x d Dd t W where Nominal clearance Maximum clearance added by tolerances
Background image of page 8
Generalization: absolute tolerances a b c d w wa b c d tt t t W abc t d  
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Statistical tolerances Pin in hole example again, with statistical tolerance window of 3 standard deviations from mean “out of range” dimensions are possible! (realistic) Distribution of clearance x w = x D x d DD dd x Dt x dt  22 wD d tt W t Dd where   3 / , D D t D N x   3 / , d d t D N x   3 / , w w t W N x
Background image of page 10
Window size 3 x x t Prob( ) 99.7% xx xt x   3 / , x t x N x
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Generalization: statistical tolerances a b c d w 2222 wa b c d tt t W d abc  
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/31/2011 for the course ME 250 taught by Professor Limian during the Spring '11 term at Shanghai Jiao Tong University.

Page1 / 48

L10-Statistics+and+Probability2 -...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online