ISYE 3039 hw5

# ISYE 3039 hw5 - think the speciﬁcations for the component...

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ISyE 3039 A Homework 5 Due April 15, 2008 1. 7.24 from textbook (7.32 in new edition) 2. 7.27 from textbook (7.35 in new edition) 3. 7.28 from textbook (7.36 in new edition) 4. The contact angle ( y ) in an overrunning clutch assembly is related to the hub dimension ( x 1 ), ball diameters ( x 2 and x 3 ), and cage diameter ( x 4 ) by the relation y = cos - 1 ± x 1 + ( x 2 + x 3 ) / 2 x 4 - ( x 2 + x 3 ) / 2 ! Suppose the speciﬁcations of the components are given as hub dimension: 55 . 29 ± 0 . 156 mm, ball diameter : 22 . 86 ± 0 . 013 mm, cage diameter: 101 . 60 ± 0 . 156 mm. Assume that the C p ’s of these components are 1. Find the mean and standard deviation of the contact angle using Monte carlo simulations. (Give a histogram for the contact angle). Suppose the speciﬁcations for the contact angle is 0 . 122 ± 0 . 035 radians, then do you
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Unformatted text preview: think the speciﬁcations for the component dimensions are adequate? Explain. 5. Two components A and B are placed inside a box C as shown in the ﬁgure below. The speciﬁcations of some dimensions are also shown in the ﬁgure. (a) Find the speciﬁcations for the gap using worst-case method and root sum of squares method. (b) Suppose the dimensions of A and B are negatively correlated and we want to utilize this information to revise the tolerance for the gap. Do you think we should increase or decrease the tolerance? Explain. (Hint: V ar ( X 1 + X 2 ) = σ 2 1 + σ 2 2 + 2 ρσ 1 σ 2 , where ρ is the correlation between X 1 and X 2 .) 1...
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