Answered: The motor shown in the figure supplies…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The motor shown in the figure supplies 16.5 kW at 1540 rpm at A. Shafts (1) and (2) are each solid 28 mm diameter shafts. Shaft (1) is made of an aluminum alloy [ G=26 GPa], and shaft (2) is made of bronze [ G=45 GPa]. The shaft lengths are L1=3.3m and L2=2.9m, respectively. Gear B has 56 teeth, and gear C has 97 teeth. The bearings shown permit free rotation of the shafts. Determine: the rotation angle of gear D with respect to flange A. [Answer φD/A = 0.314 rad]

Expert Solution

Step 1

Given that,

$P o w e r s u p p l i e d b y m o t o r, P = 16.5 k W, R o t a t i o n o f m o t o r, N = 1540 r p m, D i a m e t e r o f s o l i d s h a f t, D = 28 m m, M o d u l u s o f r i g i d t y o f a l u m i n u m s h a f t, G_{a} = 26 G P a, M o d u l u s o f r i g i d t y o f b r o n z e s h a f t, G_{b} = 45 G P a, L e n g t h o f s h a f t 1, L_{1} = 3.3 m, L e n g t h o f s h a f t 2, L_{2} = 2.9 m, N u m b e r o f t e e t h o f g e a r B, N_{B} = 56 N u m b e r o f t e e t h o f g e a r C, N_{C} = 97$

Calculate the torque provided by the motor using the relationship given below,

$P o w e r, P = \frac{2 π N T}{60} W h e r e N i s t h e r o t a t i o n o f m o t o r i n r p m, T i s t h e t o r q u e, T = \frac{60 P}{2 π N} T = \frac{60 \times 16.5 \times 1000}{2 \times π \times 1540} T = 102.314 N . m$

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