mws_mec_inp_txt_spline_examples

# mws_mec_inp_txt_spline_examples - Chapter 05.05 Spline...

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05.05.1 Chapter 05.05 Spline Method of Interpolation – More Examples Mechanical Engineering Example 1 For the purpose of shrinking a trunnion into a hub, the reduction of diameter D of a trunnion shaft by cooling it through a temperature change of T is given by T D D where D original diameter  in. coefficient of thermal expansion at average temperature   F in/in/ The trunnion is cooled from F 80 to F 108 , giving the average temperature as F 14 . The table of the coefficient of thermal expansion vs. temperature data is given in Table 1. Table 1 Thermal expansion coefficient as a function of temperature. Temperature,  F T Thermal Expansion Coefficient,  F in/in/ 80 6.47 6 10 0 6.00 6 10 –60 5.58 6 10 –160 4.72 6 10 –260 3.58 6 10 –340 2.45 6 10

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05.05.2 Chapter 05.05 Figure 1 Thermal expansion coefficient vs. temperature. If the coefficient of thermal expansion needs to be calculated at the average temperature of F 14 , determine the value of the coefficient of thermal expansion at F 14 T using linear splines. Solution Since we want to find the coefficient of thermal expansion at F 14 T and we are using linear splines, we need to choose the two data points that are closest to F 14 T that also bracket F 14 T to evaluate it. The two points are 0 0 T and F 60 1 T . Then 6 0 0 10 00 . 6 ) ( , 0 T T 6 1 1 10 58 . 5 ) ( , 60 T T gives ) ( ) ( ) ( ) ( ) ( 0 0 1 0 1 0 T T T T T T T T ) 0 ( 0 60 10 00 . 6 10 58 . 5 10 00 . 6 6 6 6 T Hence 0 60 ), 0 ( 10 007 . 0 10 00 . 6 ) ( 6 6 T T T At , 14 T ) 0 14 ( 10 007 . 0 10 00 . 6 ) 14 ( 6 6
Spline Method of Interpolation-More Examples: Mechanical Engineering 05.05.3 F in/in/ 10 902 . 5 6 Linear spline interpolation is no different from linear polynomial interpolation. Linear splines still use data only from the two consecutive data points. Also at the interior points of the data, the slope changes abruptly. This means that the first derivative is not continuous at these

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## This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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mws_mec_inp_txt_spline_examples - Chapter 05.05 Spline...

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