25 x 0 i we know that the input speed or the speed of

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Unformatted text preview: TB TC – x× +y TB TD y – x× TB TE × TD TF +y TB TC y – x× TB TE × TD TF Chapter 13 : Gear Trains l 461 1. Speed of the output shaft when gear C is fixed Since the gear C is fixed, therefore from the fourth row of the table, y –x× TB =0 TC or y – x× 20 =0 80 ∴ y – 0.25 x = 0 ...(i) We know that the input speed (or the speed of gear B ) is 1000 r.p.m. counter clockwise, therefore from the fourth row of the table, x + y = + 1000 ...(ii) From equations (i) and (ii), x = + 800, and y = + 200 ∴ Speed of output shaft = Speed of gear F = y – x × TB TE × TD TF 20 30 × = 200 – 187.5 = 12.5 r.p.m. 80 32 = 12.5 r.p.m. (counter clockwise) Ans. = 200 – 800 × 2. Speed of the output shaft when gear C is rotated at 10 r.p.m. counter clockwise Since the gear C is rotated at 10 r.p.m. counter clockwise, therefore from the fourth row of the table, y – x× TB = + 10 TC ∴ y – 0.25 x = 10 From equations (ii) and (iii), x = 792, ∴ Speed of output shaft or y – x× 20 = 10 80 ...(iii) and y = 208 = Speed of gear F = y – x × 20 30 TB TE × = 208 – 792 × × 80 32 TD TF = 208 – 185.6 = 22.4 r.p.m. = 22.4 r.p.m. (counter clockwise) Ans. Example 13.18. Fig. 13.24 shows a differential gear used in a motor car. The pinion A on the propeller shaft has 12 teeth and gears with the crown gear B which has 60 teeth. The shafts P and Q form the rear axles to which the road wheels are attached. If the propeller shaft rotates at 1000 r.p.m. and the road wheel attached to axle Q has a speed of 210 r.p.m. while taking a turn, find the speed of road wheel attached to axle P. Solution. Given : T A = 12 ; T B = 60 ; N A = 1000 r.p.m. ; N Q = N D = 210 r.p.m. Since the propeller shaft or the pinion A rotates at 1000 r.p.m., therefore speed of crown gear B , 12 TA = 1000 × 60 TB = 200 r.p.m. The table of motions is given below : NB = NA × Fig. 13.24 462 l Theory of Machines Table 13.20. Table of motions. Revolutions of elements Step No. Conditions of motion Gear B Gear C Gear E + TC TE Gear B fixed-Gear C rotated thro...
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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.

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