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8/17/2019 Equation Sheet Final
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Vibration Analysis
( ) cos( ) x t X t
( ) sin( ) cos( / 2) x t X t X t
2 2
( ) cos( ) cos( ) x t X t X t
00( ) cos sinn n
n
x x t x t t
( ) cos sinn n x t A t B t
( ) cos sinnt d d t e a t b t
( ) st x t Xe
2
1 2, 2 2
c c k s s m m m
1
2 f
/ /n st k m g
21d n
2cc mk
/ cc c
1
22
2ln
1
x
x
( ) cos( ) p
x t X t
1 1
2 2
2tan tan
1
c
k m
0 / st X F k
/ n
0
2 2 2 2 2 2( ) ( ) (1 ) (2 )
st F X X k m c
2 2 2
2 2 2 2 2 2
( ) 1 (2 )
( ) ( ) (1 ) (2 )
k c X Y Y
k m c
0
2 21
st F X X k m
2 21
kY Y X k m
2 2 2
2 2 2 2 2 2
0
( ) 1 (2 )
( ) ( ) (1 ) (2 )
T
f
F k cT
F k m c
2 2 2
2 2 2 2 2 2
( ) 1 (2 )
( ) ( ) (1 ) (2 )d
X k cT
Y k m c
V f
Fall 2014 Mechanical Systems Design Equation Sheet (Final Exam)
A m p l i t u d e r a t i o
T r a n s m i s s i b
i l i t y
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Mechanical Springs
C =
τ max = K B
K B =
y =
k
L0 <
.
L0 < 2.63 S ut =
0.35 S ut ≤ S sy ≤ 0.52 S ut
ωn = π = π
Fasteners
2d + ¼ in L ≤ 6 in
LT =
2d + ½ in L > 6 in
2d + 6 L ≤ 125 d ≤ 48
LT = 2d + 12 125 200
k t =
, k d =
k b =
P = P b + P m
F b = P b + F i = C P + F i
F m = P m − F i = (1 – C ) P − F i
C =
T = K F i d
σ b =
=
n p = =
n L =
n0 = =
0.75 F p nonpermanent connections
0.9 F p permanent connections
F p = At S p
Gears
P =
m = p =
p P = π
r b = r cos ϕ
e = ωL / ωF
F i =
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e =
e =
W t = W cos ϕ
W t = 33
000
12
d nV
σ = W t K o K v K s
σ c = C P
S F =
S H =
K v =
K s =
If K s < 1, use K s = 1
K m = 1 + C mc (C pf C pm + C ma C e)
C ma = A + BF + CF 2
m B =
J =
m N =1 for spur gear
mG = =
If
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Table 8-2 Diameters and areas for unified screw threads
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Table 8-9 SAE specifications for steel bolts
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Table 8-10 ASTM specification for steel bolts
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Table 8-11 Metric mechanical-property classes for steel bolts
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Fig. 14.6 Spur-gear geometry factors, J .
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Figure 14-9 Dynamic factor, K v
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Table 14-9 Empirical constants A, B, and C for C ma
Figure 14-11, C ma
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Figure 14-12 Hardness ratio factor, C H
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Figure 14-14, Y N
Figure 14-15, Z N
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Figure 14-16 Rim-thickness factor