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...
View
Full
Document
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.
 Fall '08
 CELGHORN

Click to edit the document details