Eu com certeza

Chapter 13
13-1
dP = 17/8 = 2.125 in dG = N2
N3
dP = 1120
544
(2.125) = 4.375 in
NG = PdG = 8(4.375) = 35 teeth Ans.
C = (2.125 + 4.375)/2 = 3.25 in Ans.
13-2
nG = 1600(15/60) = 400 rev/min Ans. p = πm = 3π mm Ans.
C = [3(15 + 60)]/2 = 112.5 mm Ans.
13-3
NG = 20(2.80) = 56 teeth Ans. dG = NGm = 56(4) = 224 mm Ans. dP = NPm = 20(4) = 80 mm Ans.
C = (224 + 80)/2 = 152 mm Ans.
13-4 Mesh: a = 1/P = 1/3 = 0.3333 in Ans. b = 1.25/P = 1.25/3 = 0.4167 in Ans. c = b − a = 0.0834 in Ans. p = π/P = π/3 = 1.047 in Ans. t = p/2 = 1.047/2 = 0.523 in Ans.
Pinion Base-Circle: d1 = N1/P = 21/3 = 7 in d1b = 7 cos 20° = 6.578 in Ans.
Gear Base-Circle: d2 = N2/P = 28/3 = 9.333 in d2b = 9.333 cos 20° = 8.770 in Ans.
Base pitch: pb = pc cos φ = (π/3) cos 20° = 0.984 in Ans.
Contact Ratio: mc = Lab/pb = 1.53/0.984 = 1.55 Ans.
See the next page for a drawing of the gears and the arc lengths.
334 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design
13-5
(a) AO =
__
2.333
2
_2
+
_
5.333
2
_2
_1/2
= 2.910 in Ans.
(b) γ = tan−1(14/32) = 23.63° Ans.
_ = tan−1(32/14) = 66.37° Ans.
(c) dP = 14/6 = 2.333 in, dG = 32/6 = 5.333 in Ans.
(d) From Table 13-3, 0.3AO = 0.873 in and 10/P = 10/6 = 1.67
0.873 < 1.67 ∴ F = 0.873 in Ans.
13-6
(a) pn = π/5 = 0.6283 in pt = pn/cosψ = 0.6283/cos 30° = 0.7255 in px = pt/tanψ = 0.7255/tan 30° = 1.25 in
30_
P G
21
3
"
51
3
"
AO
_
_
10.5_
Arc of approach _ 0.87 in Ans.
Arc of recess _ 0.77 in Ans.
Arc of action _ 1.64 in Ans.
Lab _ 1.53 in
10_
O2
O1
14_ 12.6_
P
A B
Chapter 13 335
(b) pnb = pn cos φn = 0.6283 cos 20° = 0.590 in Ans.
(c) Pt = Pn cosψ = 5 cos 30° = 4.33 teeth/in φt = tan−1(tan φn/cosψ) = tan−1(tan 20°/cos 30◦) = 22.8° Ans.
(d) Table 13-4: a = 1/5 = 0.200 in Ans. b = 1.25/5 = 0.250 in Ans. dP = 17
5 cos 30°
= 3.926 in Ans. dG = 34
5 cos 30°
= 7.852 in Ans.
13-7
φn = 14.5°, Pn = 10 teeth/in
(a) pn = π/10 = 0.3142 in Ans.