11hw11-13apr-Soln - EML4321HW#11Due13April,Spring2011 1...

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EML 4321 – HW #11 – Due 13 April, Spring 2011 1. Assuming r = 0, find the Taylor tool life equation if you have the following experimental data. (Hint: fit p, q, and C to the data.) (Note that we are assuming no error, noise, or scatter in the data.) v (m/min) f r (mm) T (min) 300 0.2 30 400 0.2 15 400 0.3 9 2 1 1 2 ; 1 2 400 30 4 ; ; log 300 15 3 st nd p p Find p use and rows v T p v T = = log 2 = p = 2.41 3 2 3 2 ; 2 3 0.2 9 2 9 ; ; log 0.3 15 3 15 nd rd q q Find q use and rows T f q f T = = = log q = 1.26 2.41 1.26 2.41 1.26 ( ); 1 300 0.2 30 st p q Find C Taylor tool life equation use row C v f T v f T = = = = 6 3.684 10 So the equation is: v 2.41 f 1.26 T = 3.684 x 10 6 The problem with doing this sort of thing is that this is a collocation, not a regression. Any slight error will cause the exponents and the constant to vary widely. For accuracy, it would be better to have much more data and do a (probably nonlinear) regression fit.
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