GEAR GEOMETRY AND APPLIED THEORY docx
GEAR GEOMETRY AND APPLIED THEORY Second Edition docx
... 10:8
GEAR GEOMETRY AND APPLIED THEORY
Second Edition
Revised and expanded, Gear Geometry and Applied Theory, 2nd edition, cov-
ers the theory, design, geometry, and manufacture of all types of gears ... gears and gear
drives. Gear Geometry and Applied Theory is an invaluable reference for de-
signers, theoreticians, students, and manufacturers. Th...
GEAR GEOMETRY AND APPLIED THEORY docx
... 1.5.5
Gears 1 and 2 rotate about axes z
f
and z
p
that form the twist angle γ and the shortest
distance E (Fig. 1.5.5). Coordinate systems S
1
, S
2
, and S
f
are rigidly connected to
gear 1, gear ... geometry of modified spur gears, helical gears with parallel and crossed
axes, a new version of Novikov–Wildhaber helical gears, a new geometry of face-
gear drives, geometry...
Gear Geometry and Applied Theory Episode 1 Part 9 pot
... a
22
:
v
(1)
s
a
11
+ v
(1)
q
a
12
= a
13
v
(1)
s
a
12
+ v
(1)
q
a
22
= a
23
a
11
+ a
22
= κ
.
(9. 3 .11 )
Step 4: The solution of equation system (9. 3 .11 ) for the unknowns a
11
, a
12
, and a
22
allows ... equations:
κ
(1)
= κ
(2)
− κ
(9. 3 .14 )
tan 2σ
(12 )
=
2a
22
g
2
− (a
11
− a
22
)
=
2n
2
− κ
sin 2η
1
g
2
− 2n
1
+ κ
cos 2η
1
(9. 3 .15...
Gear Geometry and Applied Theory Episode 1 Part 10 pps
...
1
that is represented in S
1
by the following equations (Fig. 9.4.3):
x
1
= r
b1
(sin θ
1
− θ
1
cos θ
1
), y
1
= r
b1
(cos θ
1
+ θ
1
sin θ
1
), z
1
= 0. (9.4.23)
Figure 9.4.3: Profile
1
of gear ... follows:
m
12
=
dφ
1
dφ
2
=−
dθ
1
dθ
2
=
r
b2
r
b1
. (9.4. 41)
Step 7: The line of action is represented by the equation
r
(1)
f
= r
b1
[
sin(θ
1
− φ
1
) −...
Gear Geometry and Applied Theory Episode 2 Part 1 pot
... E
c
(φ
2
)is
E
(2)
c
= E
c
(2 a) = r
p2
−r
pc
=
N
2
− N
c
2P
. (11 .2. 14 )
(ii) It is obvious that
E
c
(φ
2
) − E
(1)
c
E
(2)
c
− E
(1)
c
=
φ
2
2πa
. (11 .2. 15 )
(iii) Equations from (11 .2. 13 ) to (11 .2. 15 ) ... system.
P1: FHA/JTH
CB6 72- 10 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 0 :19
10 .8 Contact Ratio 29 3
Thus,
l = KB
2
+ B
1
L − KL...
Gear Geometry and Applied Theory Episode 2 Part 2 doc
... ( 12. 2.4)
Equations ( 12. 2.1), ( 12. 2.3), and ( 12. 2.4) yield
tan µ
1
=−
m
12
(φ
1
) ± 1
m
12
(φ
1
)
( 12. 2.5)
tan µ
2
=±
m
12
(φ
1
) ± 1
m
12
(φ
1
)
. ( 12. 2.6)
Here, m
12
= (∂/∂φ
1
)[m
12
(φ
1
)].
Function ... ratio function is
m
12
=
dφ
1
dφ
2
=
k
1
k
2
y
x
( 12. 2.8)
P1: GDZ/SPH P2: GDZ
CB6 72- 12 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 0...
Gear Geometry and Applied Theory Episode 2 Part 3 pot
... equation
r
t
(θ
2
,φ
2
) = M
t2
(φ
2
)r
2
(θ
2
), ( 13. 6.5)
which yields
θ
2
≥ 90
◦
,φ
2
= 2( θ
2
− 90
◦
)
x
t
=−r
2
(φ
2
− sin φ
2
) +ρ
2
sin(θ
2
− φ
2
)
y
t
=−r
2
(1 −cos φ
2
) −ρ
2
cos(θ
2
− φ
2
).
( 13. 6.6)
Axis ... r
2
.
P1: GDZ/SPH P2: GDZ
CB6 72- 12 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 0: 32
12. 11 Evolute of Tooth Pro...
Gear Geometry and Applied Theory Episode 2 Part 4 pdf
... (Fig. 14. 3.3):
x
2
= r
b2
cos(θ
2
− η
2
) + u
2
cos λ
b2
sin(θ
2
− η
2
)
y
2
=−r
b2
sin(θ
2
− η
2
) + u
2
cos λ
b2
cos(θ
2
− η
2
)
z
2
= u
2
sin λ
b2
− p
2
θ
2
( 14. 3.15)
n
2
= [sin λ
b2
sin(θ
2
− ... λ
b2
sin(θ
2
− η
2
)
y
2
=−r
b2
sin(θ
2
− η
2
) + u
2
cos λ
b2
cos(θ
2
− η
2
)
z
2
=−u
2
sin λ
b2
+ p
2
θ
2
( 14. 3.17)
n
2
= [sin...
Gear Geometry and Applied Theory Episode 2 Part 5 pptx
... M
ba
[a
c
u
2
c
u
c
01]
T
( 15 .2. 7)
P1: GDZ/SPH P2: GDZ
CB6 72- 15 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 0:44
422 Modified Involute Gears
Figure 15. 5 .2: Determination of disk surface
D
: (a) and ... cases
P1: GDZ/SPH P2: GDZ
CB6 72- 15 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 0:44
15 .2 Axodes of Helical Gears and Rack-Cutters 409
Figur...
Gear Geometry and Applied Theory Episode 2 Part 6 ppsx
... 3D-space.
Worm
Helical gear
Figure 16. 1 .2: Gear drive formed by a worm and a helical
gear.
P1: GDZ/SPH P2: GDZ
CB6 72- 15 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 0:44
1
2
3
Figure 15.9.1: Whole gear drive ... arctan
tan α
pn
cos β
p1
= 34 .61 43
◦
α
pt 2
= arctan
tan α
pn
cos β
p2
= 32. 3 122
◦
.
P1: JTH
CB6 72- 16 CB6 72/ Litvin CB6 72/ Litvin-v2....
Gear Geometry and Applied Theory Episode 2 Part 7 pps
... Pressure
-8.935e+01
+2. 500e+01
+9.553e+01
+1.661e+ 02
+2. 366e+ 02
+3. 071 e+ 02
+3 .77 6e+ 02
+4.482e+ 02
+5.187e+ 02
+5.892e+ 02
+6.598e+ 02
+7. 303e+ 02
+8.008e+ 02
+8 .71 4e+ 02
1
2
3
(MPa)
Figure 16.6.5: Distribution of ... λ
o2
+ cos
2
λ
b2
−
2 cos
2
λ
b1
cos
2
λ
b2
cos
2
α
on
.
(16.B.9)
P1: JXR
CB6 72 - 17 CB6 72 / Litvin CB6 72 / Litvin-v2.cls February 27 ,...
Gear Geometry and Applied Theory Episode 2 Part 8 pps
... γ
1
=
m
12
+ cos γ
sin γ
, cot γ
2
=
m
21
+ cos γ
sin γ
=
1 + m
12
cos γ
m
12
sin γ
( 18 .2. 2)
P1: JXR
CB6 72- 18 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 1:5
18. 1 Introduction 509
Figure 18. 1.1: ... ”“s” and “1, ” and “1” and
2 are considered. Angle γ
s
that is formed between the shaper axis and IA
s2
is
P1: JXR
CB6 72- 18 CB6 72/ Litvin CB6 72/ Lit...
Gear Geometry and Applied Theory Episode 2 Part 9 pps
... JsY
CB6 72- 19 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 1 :28
19 .2 Pitch Surfaces and Gear Ratio 551
Figure 19 .2. 2: Velocity polygon for right-
hand worm -gear drive.
Figure 19 .2. 3: Operating ... pitch cylinders
for left-hand worm -gear drive.
P1: JsY
CB6 72- 19 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 1 :28
19 .2 Pitch Surfaces and...
Gear Geometry and Applied Theory Episode 2 Part 10 doc
... left-hand worm and worm -gear, we have
R
o
=
p
ax
N
2
cos λ
(o)
1
2 sin
γ + λ
(o)
1
. (19.3 .10)
P1: JsY
CB6 72- 19 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February 27 , 20 04 1 :28
19.5 Generation and Geometry ... d
sin α sin λ
p
(cos
2
α + sin
2
α sin
2
λ
p
)
0.5
(19.5 .20 )
where
d = r
p
−
s
p
2
cot α.
P1: JsY
CB6 72- 19 CB6 72/ Litvin CB6 72/ Litvin-v2.cls February...
Gear Geometry and Applied Theory Episode 3 Part 8 docx
... 30 2
Centrodes
circular gears, of, 38 , 45, 49, 50, 115, 137 , 211,
274, 280 , 288 , 289 , 296, 2 98, 35 2
noncircular gears, of, 31 8, 32 2 33 4, 33 7, 33 8,
34 1, 34 3 34 6, 34 8, 34 9, 35 5, 35 6, 35 9,
36 0
Circular pitch, 39 0
Clearance, ... types
cone, of, 82 , 83 , 88 , 1 83 , 185 , 186
helicoid, 90–95
involute screw, 82 , 83 , 93, 95, 185 , 547, 570,
5 73, 575,...
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