Solved: Apply the rules of Prob. 1626 to the three-shaft
Chapter 16, Problem 16-27(choose chapter or problem)
Apply the rules of Prob. 16-26 to the three-shaft system shown in the figure to create a motor shaft shish kebab.
(a) Show that the equivalent inertia \(I_e\) is given by
\(I_e=I_M+I_P+n^2 I_P+\frac{I_P}{n^2}+\frac{m^2 I_P}{n^2}+\frac{I_L}{m^2 n^2}\)
(b) If the overall gear reduction R is a constant nm, show that the equivalent inertia becomes
\(I_e=I_M+I_P+n^2 I_P+\frac{I_P}{n^2}+\frac{R^2 I_P}{n^4}+\frac{I_L}{R^2}\)
(c) If the problem is to minimize the gear-train inertia, find the ratios n and m for the values of \(I_P=1, I_M=10, I_L=100\), and R=10.
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