fundamentals of engineering supplied-reference handbook - Ventech!

MECHANICAL DESIGN AND ANALYSIS
Stress Analysis
See MECHANICS OF MATERIALS section.
Failure Theories
See MECHANICS OF MATERIALS section and the
MATERIALS SCIENCE section.
Deformation and Stiffness
See MECHANICS OF MATERIALS section.
Components
Square Thread Power Screws: The torque required to
raise, TR, or to lower, TL, a load is given by
T
T
R
L
Fd
=
2
m
⎛ l + πµ d m ⎞ Fµ
cd
⎜ ⎟
⎜
+
d m l ⎟
⎝ π − µ ⎠ 2
Fd m ⎛ πµ d m − l ⎞ Fµ
cd
c
= ⎜ ⎟ +
2 ⎜ d m l ⎟
, where
⎝ π + µ ⎠ 2
dc = mean collar diameter,
dm = mean thread diameter,
l = lead,
F = load,
µ = coefficient of friction for thread, and
µc = coefficient of friction for collar.
The efficiency of a power screw may be expressed as
η = Fl/(2πT)
Mechanical Springs
Helical Linear Springs: The shear stress in a helical linear
spring is
8FD
τ = Ks , where
3
πd
d = wire diameter,
F = applied force,
D = mean spring diameter
Ks = (2C + 1)/(2C), and
C = D/d.
The deflection and force are related by F = kx where the
spring rate (spring constant) k is given by
4
d G
k =
3
8D
N
where G is the shear modulus of elasticity and N is the
number of active coils. See Table of Material Properties at
the end of the MECHANICS OF MATERIALS section
for values of G.
c
MECHANICAL ENGINEERING
,
203
Spring Material: The minimum tensile strength of common
spring steels may be determined from
Sut = A/d m
where Sut is the tensile strength in MPa, d is the wire
diameter in millimeters, and A and m are listed in the
following table.
Material ASTM m A
Music wire
Oil-tempered wire
Hard-drawn wire
Chrome vanadium
Chrome silicon
A228
A229
A227
A232
A401
0.163
0.193
0.201
0.155
0.091
2060
1610
1510
1790
1960
Maximum allowable torsional stress for static applications
may be approximated as
Ssy = τ = 0.45Sut cold-drawn carbon steel (A227,
A228, A229)
Ssy = τ = 0.50Sut hardened and tempered carbon and
low-alloy steels (A232, A401)
Compression Spring Dimensions
Type of Spring Ends
Term Plain
End coils, Ne
Total coils, Nt
Free length, L0
Solid length, Ls
Pitch, p
Term
End coils, Ne
Total coils, Nt
Free length, L0
Solid length, Ls
Pitch, p
0
N
pN + d
d (Nt + 1)
(L0 – d)/N
Squared or
Closed
2
N + 2
pN + 3d
d (Nt + 1)
(L0 – 3d)/N
Plain and
Ground
1
N + 1
p (N + 1)
dNt
L0/(N + 1)
Squared and
Ground
2
N + 2
pN + 2d
dNt
(L0 – 2d)/N
Helical Torsion Springs: The bending stress is given as
σ = Ki [32Fr/(πd 3 )]
where F is the applied load and r is the radius from the
center of the coil to the load.
Ki = correction factor
= (4C 2 – C – 1) / [4C (C – 1)]
C = D/d