# Example 133 the speed ratio of the reverted gear

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Unformatted text preview: ar train, as shown in Fig. 13.5, is to be 12. The module pitch of gears A and B is 3.125 mm and of gears C and D is 2.5 mm. Calculate the suitable numbers of teeth for the gears. No gear is to have less than 24 teeth. Solution. G iven : Speed ratio, N A/ N D = 1 2 ; m A = m B = 3.125 mm ; m C = m D = 2.5 mm Let Fig. 13.5 N A = Speed of gear A , T A = Number of teeth on gear A , rA = Pitch circle radius of gear A , N B, N C , N D = Speed of respective gears, T B, T C , T D = Number of teeth on respective gears, and rB, rC , rD = Pitch circle radii of respective gears. * We know that circular pitch, pc = ∴ 2πr = πm T r1 = m.T1 m.T2 m.T3 m.T4 ; r2 = ; r3 = ; r4 = 2 2 2 2 Now from equation (i), m.T1 m.T2 m.T3 m.T4 + = + 2 2 2 2 T 1 + T 2 = T 3 + T4 or r= m.T , where m is the module. 2 436 l Theory of Machines Since the speed ratio between the gears A and B and between the gears C and D are to be same, therefore N * NA = C = 12 = 3.464 NB ND Also the speed ratio of any pair of gears in mesh is the inverse of their number of teeth, therefore TB TD = = 3.464 TA TC ...(i) We know that the distance between the shafts x = rA + rB = rC + rD = 200 mm or ∴ and and and m .T ... 3 r = 2 m .T mA .TA m .T m .T + B B = C C + D D = 200 2 2 2 2 3.125 (T A + T B) = 2.5 (T C + T D) = 400 ...(∵ mA = m B, and m C = m D) T A + T B = 400 / 3.125 = 128 ...(ii) T C + T D = 400 / 2.5 = 160 ...(iii) From equation (i), T B = 3.464 T A. Substituting this value of T B in equation (ii), T A + 3.464 T A = 128 or T A = 128 / 4.464 = 28.67 say 28 Ans. T B = 128 – 28 = 100 Ans. Again from equation (i), T D = 3.464 T C. Substituting this value of T D in equation (iii), T C + 3.464 T C = 160 or T C = 160 / 4.464 = 35.84 say 36 Ans. T D = 160 – 36 = 124 Ans. Note : The speed ratio of the reverted gear train with the calculated values of number of teeth on each gear is NA TB × TD 100 × 124 = = = 12.3 N D TA × TC 28 × 36 13.7. Epicyclic Gear Train We have already discussed that in an epicyclic gear train, the axes of the shafts, over which the gears are mounted, may move relative to a fixed axis. A simple epicyclic gear train is shown in Fig. 13.6, where...
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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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