fundamentals of engineering supplied-reference handbook - Ventech!

Only the tangential component Wt transmits torque from
one gear to another. Neglecting friction, the transmitted
force may be found if either the transmitted torque or
power is known:
2T
2T
Wt = = ,
d mN
2H
2H
Wt = = , where
dω
mNω
Wt = transmitted force (newton),
T = torque on the gear (newton-mm),
d = pitch diameter of the gear (mm),
N = number of teeth on the gear,
m = gear module (mm) (same for both gears in mesh),
H = power (kW), and
ω = speed of gear (rad/sec).
Stresses in Spur Gears: Spur gears can fail in either
bending (as a cantilever beam, near the root) or by surface
fatigue due to contact stresses near the pitch circle. AGMA
Standard 2001 gives equations for bending stress and
surface stress. They are:
Wt KaKm σ b =
KK s BKI, bending and
FmJ K
v
σ c = Cp Wt CaCm CsCf , surface stress , where
FId Cv
σb = bending stress,
σc = surface stress,
Wt = transmitted load,
F = face width,
m = module,
J = bending strength geometry factor,
Ka = application factor,
KB = rim thickness factor,
K1 = idler factor,
Km = load distribution factor,
Ks = size factor,
Kv = dynamic factor,
Cp = elastic coefficient,
I = surface geometry factor,
d = pitch diameter of gear being analyzed, and
Cf = surface finish factor.
Ca, Cm, Cs, and Cv are the same as Ka, Km, Ks, and Kv,
respectively.
Rigid Body Dynamics
See DYNAMICS section.
208
MECHANICAL ENGINEERING (continued)
Natural Frequency and Resonance
See DYNAMICS section.
Balancing of Rotating and Reciprocating
Equipment
Static (Single-plane) Balance
n
mbRbx = −∑
miRix
,
n
mbRby
= −∑
i=
1
i=
1
⎛ mbR
θ = ⎜
b arctan
⎜
⎝ mbR
b
b
by
bx
⎞
⎟
⎠
( ) ( ) 2
2
m R m R
m R = +
b
bx
b
by
m R
where mb = balance mass
Rb = radial distance to CG of balance mass
mi = ith point mass
Ri = radial distance to CG of the ith point mass
θb = angle of rotation of balance mass CG with
respect to a reference axis
x,y = subscripts that designate orthogonal
components
Dynamic (Two-plane) Balance
A
B
Two balance masses are added (or subtracted), one each
on planes A and B.
n
n
1
1
mBRBx = − miRixli
mBRBy
l ∑ , = −
B
l ∑
i=
1
B i=
1
A
n
Ax = −∑
i=1
m R m R − m
n
Ay = −∑
i=1
m R m R − m
A
i
i
ix
iy
B
B
R
R
Bx
By
i
iy
m R
i
l
iy i
where
mA = balance mass in the A plane
mB = balance mass in the B plane
RA = radial distance to CG of balance mass
RB = radial distance to CG of balance mass
and θA, θB, RA, and RB are found using the relationships
given in Static Balance above.