15 rpm 20 50 tb td 3715 rpm anticlockwise ans torque

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Unformatted text preview: that the speed of the motor or the speed of the pinion A i s 1000 r.p.m. Therefore x + y = 1000 ...(i) Also, the annular wheel E is fixed, therefore y –x× TA =0 TE y = x× or 15 TA =x× = 0.273 x 55 TE ...(ii) From equations (i) and (ii), x = 786 and y = 214 ∴ Speed of machine shaft = Speed of wheel D, ND = y – x × TA TC 15 15 × = 214 – 786 × × = + 37.15 r.p.m. 20 50 TB TD = 37.15 r.p.m. (anticlockwise) Ans. Torque exerted on the machine shaft We know that Torque developed by motor × Angular speed of motor = Torque exerted on machine shaft × Angular speed of machine shaft or 100 × ωA = Torque exerted on machine shaft × ωD ∴ Torque exerted on machine shaft = 100 × 1000 ωA N = 100 × A = 100 × = 2692 N-m Ans. 37.15 ωD ND l Chapter 13 : Gear Trains 465 Example 13.20. An epicyclic gear train consists of a sun wheel S, a stationary internal gear E and three identical planet wheels P carried on a star- shaped planet carrier C. The size of different toothed wheels are such that the planet carrier C rotates at 1/5th of the speed of the sunwheel S. The minimum number of teeth on any wheel is 16. The driving torque on the sun wheel is 100 N-m. Determine : 1. number of teeth on different wheels of the train, and 2. torque necessary to keep the internal gear stationary. Solution. Given : NC = NS 5 Fig. 13.27 1. Number of teeth on different wheels The arrangement of the epicyclic gear train is shown in Fig. 13.27. Let T S and T E be the number of teeth on the sun wheel S and the internal gear E respectively. The table of motions is given below : Table 13.22. Table of motions. Revolutions of elements Step No. Conditions of motion Planet carrier C Sun wheel S Planet wheel P TS TP 1. Planet carrier C fixed, sunwheel S rotates through + 1 revolution (i.e. 1 rev. anticlockwise) 0 +1 – 2. Planet carrier C fixed, sunwheel S rotates through + x revolutions 0 +x – x× 3. Add + y revolutions to all elements +y +y Total motion +y x +y y –x× – TS TP T × =– S TP TE TE +y 4. Internal gear E TS TP – x× TS TE +y TS TP y –x× TS TE We know that when the sunwheel S makes 5 revolutions, the planet carrier C makes...
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto- Toronto.

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