Chap.5 Gear Trains
Chap.5.1 Introduction
Chap.5.2 The fundamental law of gearing
Chap.5.3 Gear tooth nomenclature
Chap.5.4 Condition for Correct Meshing
Chap.5.5 Contact Ratio
Chap.5.6 Interference and undercutting
Chap.5.7 Gear types and Application
Chap.5.8 Ordinary gear trains
Chap.5.9 Epicyclic or planetary gear trains
Chap.5.10 Applications of gear train
Chap.5.1 Introduction
Can you give some example the gearsets?
Gears are machine elements that transmit
motion by means of successively engaging teeth,
Gears may be classified according to the relative
position of the axes of revolution,The axes may
be
1,parallel
2,intersecting
3,neither parallel nor intersecting
Gears for connecting parallel shafts
1,Spur gears
external contact internal contact
Chap.5.1 Introduction(1)
2,Parallel helical gears
3,Herringbone gears (or double-helical gears)
Gears for connecting parallel shafts
Chap.5.1 Introduction(2)
4,Rack and pinion (The rack is like a gear whose axis is at infinity.)
Gears for connecting parallel shafts
Chap.5.1 Introduction(3)
Gears for connecting intersecting shafts
1,Straight bevel gears
2,Spiral bevel gears
Chap.5.1 Introduction(4)
Neither parallel nor intersecting shafts
1,Crossed-helical gears
2,Hypoid gears
3,Worm and worm gear
Chap.5.1 Introduction(5)
Chap.5.2 The fundamental law of gearing
1,The Fundamental Law of Gearing
2,The Involute Tooth Form
3,Pressure Angle
4,Changing Center Distance
5,Backlash
Chap.5.2 The fundamental law of gearing(1)
? Tooth profile 1 drives tooth
profile 2 by acting at the
instantaneous contact point K,
? N1N2 is the common normal of
the two profiles,
? velocities V1 and V2 at point K,
along N1N2 are equal in both
magnitude and direction,
Otherwise the two tooth profiles
would separate from each other,
1,The Fundamental Law of Gearing
222111 ?? ??? NONO
The fundamental law of gearing,
The angular velocity ratio between the
gears of a gearset remains constant
throughout the mesh,
PO
PO
NO
NOm
in
o u t
V
1
2
11
22
1
2 ????
?
?
?
?
PO
PO
NO
NO
T
Tm
o u t
in
in
o u t
T
2
1
22
11
2
1 ?????
?
?
?
?
Chap.5.2 The fundamental law of gearing(2)
r1
r2
.
1
2
11
22
1
2 c o n s t
PO
PO
NO
NOm
in
o u t
V ????? ?
?
?
?
222111 ?? ??? NONO
? Point P is very important to the velocity ratio,
and it is called the pitch point,
? For a constant velocity ratio,the position of
P should remain unchanged,
? The motion transmission between two gears
is equivalent to the motion transmission
between two imagined slipless cylinders with
radius r1 and r2 or diameter d1 and d2,
?Two circles whose centers are at O1 and O2,
and through pitch point P are termed pitch
circles,
Chap.5.2 The fundamental law of gearing(3)
Pitch circles
r1
r2
Pitch point Pitch circle Constant Angular Velocity Ratio
P
2,The Involute Tooth Form
The involute curve is the path
traced by a point on a line as
the line rolls without slipping
on the circumference of a
circle,It may also be defined
as a path traced by the end of a
string which is originally
wrapped on a circle when the
string is unwrapped from the
circle,The circle from which
the involute is derived is called
the base circle,
Chap.5.2 The fundamental law of gearing(4)
What is the involute?
How does the involute form?
involute
Base circle
2,The Involute Tooth Form
involute
base circle
1,The line(string) is always
tangent to the basic circle,
4,There is no involute curve
within the base circle,
Chap.5.2 The fundamental law of gearing(5)
2,The center of curvature of the
involute is always at the point
of tangency of the string with
the cylinder,
3,A tangency to the involute is
then always normal to the
string,the length of which is
the instantaneous radius of
curvature of the involute curve,
2,The Involute Tooth Form
involute
base circle
Involute function
Chap.5.2 The fundamental law of gearing(6)
kkkk
k
b
k
i n v
r
r
????
?
???
?
t a n
c o s
.
.
2
1
2
1
1
2
2
1
2
1
2
1
2
1
22
11
1
2
C o n s t
r
r
r
r
m
C o n s t
r
r
r
r
r
r
PO
PO
NO
NO
m
b
b
in
o u t
V
b
b
in
o u t
V
?????
??
?????
?
?
?
?
?
?
?
?
The fundamental law of gearing
The ratio of the driving gear radius
to the driven gear radius remains
constant as the teeth move into
and out of mesh,
Chap.5.2 The fundamental law of gearing(7)
r1
r2
Important lines
Conclusion,these three lines
are the same line,
Axis of transmission(啮合线或传动线 )
Line of action（力作用线）
Tangency of the both base circles
（基圆公切线） is the common
normal,
rbp
rbg
rp
rg
Chap.5.2 The fundamental law of gearing(8)
3,Pressure angle（节圆压力角）
The pressure angle in a gearset is
defined as the angle between the axis
of transmission or line of
action(common normal) and the
direction of velocity at the pitch point,
Standard value of the pressure angle are
14.50,200 and 250,200 is the most
commonly used,
Meshing angle(啮合角 )
4,Changing Center Distance
Chap.5.2 The fundamental law of gearing(9)
21'c o s' bb rra ???
21''c o s'' bb rra ???
.''c o s'''c o s' c o n s taa ?? ??
.
1
2
1
2
1
2 C o n s t
r
r
r
rm
b
b
in
out
V ????? ?
?
?
?
4,Changing Center Distance
Conclusion,
1,To the gear with an involute form,center
distance errors do not affect the velocity
ratio,for the base circle diameters are
unchanging once the gear is cut,
2,But the pressure angle is affected by the
change in center distance,
3,The pitch point and pitch circles are
changed
Chap.5.2 The fundamental law of gearing(10)
5,Backlash(侧隙 )
Is there any other factor affected by changing
center distance? What is it?
Chap.5.2 The fundamental law of gearing(11)
Increasing the center distance will increase the backlash,
Backlash is defined as the clearance between mating teeth
measured along the circumference of the pitch circle,
Is there any problem if there is backlash between the
mating gears?
Chap.5.3 Gear tooth nomenclature（ 1）
Dedendum circle
顶隙
齿槽宽
齿厚
齿宽
齿顶高
齿根高
Explanation
Face of a tooth,That part of the tooth surface lying outside the pitch
surface,
Flank of a tooth,The part of the tooth surface lying inside the pitch
surface,
Circular thickness (also called the tooth thickness), The thickness
of the tooth measured on the pitch circle,It is the length of an arc and
not the length of a straight line,
Tooth space,The distance between adjacent teeth measured on the
pitch circle,
Backlash,The difference between the circle thickness of one gear and
the tooth space of the mating gear,
Circular pitch p,The width of a tooth and a space,measured on the
pitch circle,
Fillet, The small radius that connects the profile of a tooth to
the root circle,
Circular pitch pc(周节 ),the arc length along the pitch circle
circumference measured from a point on one tooth to the same
point on the next,(The width of a tooth and a space,measured
on the pitch circle.)
Ndp c ??
d= pitch diameter N= number of the teeth
Base pitch pb (基节 ), the tooth pitch measured along the
base circle,
?c o scb pp ?
Chap.5.3 Gear tooth nomenclature（ 2）
Diametral pitch Pd (径节 ), The number of teeth of a gear per
inch of its pitch diameter,
dNp d ?
cd p
p ??
Chap.5.3 Gear tooth nomenclature（ 3）
Module m,Pitch diameter divided by number of teeth,The
pitch diameter is usually specified in inches or millimeters; in
the former case the module is the inverse of diametral pitch,
dp
mNdm 4.25??
Standard gear and its teeth(China)
1,Number of teeth,N
2,Module m,
3,Pressure angle at pitch circle,200 is commonly used,and
14.50,200,150,14.50,22.50,250 is also used,
4,Coefficient of addendum,ha*
5,Coefficient of dedendum,c *
In GB,to full depth,if m >=1mm,ha* =1,c *=0.25
m <1mm,ha* =1,c *=0.35
to stub,ha* =0.8,c *=0.3
Chap.5.3 Gear tooth nomenclature（ 4）
?cpm ?
Chap.5.3 Gear tooth nomenclature（ 5）
分度圆 （ pitch circle）,
Tooth thickness,
Space width,
Addendum,
Dedendum,
mNd ?
22 mpes c ????
mhh aa ??
mcmhh af ?? ??
standard module
The table of the gears
Pitch circle (节圆）
（分度圆 ),An imaginary circle which has the standard
module and pressure angle,
Standard Module
Chap.5.4 Condition for Correct Meshing
rb1
rb2
1,2
Can any two gears mesh
together correctly?
Involute-two-point 21
21
2
2
1
1
2
2
222
1
1
111
21
c o s
1
c o s
1
c o sc o s
c o sc o s
??
??
?
?
?
?
?
?
?
?
?
??
??
?
pp
pp
p
pp
p
pp
pp
b
b
bb
Length of action is B1B2
Chap.5.5 Contact Ratio( 重合度 )
Contact ratio mp=Z/pb = pd Z/? cos ?
The minimum acceptable contact ratio for
smooth operation is 1.2
Let B1B2=Z
If the pressure is 200,ha*=1,then
the maximum of the contact
ratio is 1.981(理论极限值 )
* Manufacturing methods of involute gears
Cutting is the most widely used method,
There are generally two types of cutting
methods,forming cutting（仿形法） and
generating cutting （范成法）,(video)
Casting 铸造,forging热轧,powder process 粉末成形,
pressing冲压,cutting切削 milling磨削,shaving剃齿
? forming cutting 盘状铣刀、指状铣刀 拉齿
? generating cutting 插齿, 滚齿 Generating theory 原理
Cutting tool
Disk milling cutter
End milling cutter
成型铣刀刀号和加工齿数范围
shaping
Rack-shaped shaper cutter
hobbing
Interference & Undercutting
Pitch circle
Base circle
undercutting
根圆 （ dedendum circle）
Chap.5.6 Interference and undercutting(1)
1,Interference,In some cases,the dedendum will be
large enough to extend below the base circle,If so,
then the portion of tooth below the base circle will
not be an involute and will interfere with the tip of
the tooth on the mating gear,which is an involute,
2,Undercutting,If the gear is cut with a standard
gear shaper or a,hob”,the cutting tool will also
interfere with the portion of tooth below the base
circle and will cut away the interfering material,or
sometimes it is found that the top of the cutter
enters the profile of the gear and some part of the
involute profile near the root portion is removed,This
result in an undercutting tooth,
3,Disadvantage:The undercutting weakens the
tooth by removing material at its root,Severe
undercutting will promote early tooth failure,
How to avoid undercutting?
Chap.5.6 Interference and undercutting(2)
Addendum Modified
Tooth Form(变位齿形 )
Increase the number
of the teeth,
To avoid interference between a full-depth pinion
and a full-depth rack,the minimum number of
pinion teeth are,
Chap.5.6 Interference and undercutting(3)
Pressure angle(deg) Minimum number of teeth
14.5 32
20 18
25 12
video of cutting the gears
Advantage,1,Avoid the undercutting;
2,Improve the strength of
the pinion;
3,To fit the center distance,
Addendum Modified tooth form (fig.)
Chap.5.7 Gear types and Application(1)
Parallel
1,Spur gears.(Simple and least expensive form of gear to
make,only the gears who have the same module and pressure
angle can mesh together,More noise,Efficiency,98-99%,Easy
to be shifted)
2,Helical gears.(right-hand,left-hand,opposite-hand
helical gears in mesh,Quieter and gradual contact,Efficiency,
96-98%,Need the synchromesh mechanism to allow shifting.)
3,Herringbone gears.(more expensive,be used in
large,high-power application,)
Chap.5.7 Gear types and Application(2)
Worms and Worm gears
mv
The center distance must be maintainted accurately,
Efficiency is 40-85%(slip)
It can be designed to be impossible
to backdrive,
direction,
driving
Chap.5.7 Gear types and Application(3)
Rack and Pinion,
Motion conversion
Cutting tool
Chap.5.7 Gear types and Application(3)
Bevel,
Any angle between the shafts,900 is common,
Noncircular gears,
Belt and chain drives,
Chap.5.8 Ordinary gear trains(1)
Classification,
1,ordinary gear train or gear train with fixed axes,(定轴轮系 )
2,Epicyclic gear train,(周转轮系 )
Gear train
Gear train with fixed axes
Epicyclic gear trains
Gear trains with fixed parallel axes
Gear trains with fixed non-parallel axes
Elementary epicyclic gear trains
Combined gear trains
Planetary gear trains
Differential gear trains
Chap.5.8 Ordinary gear trains(2)
Example,
Chap.5.8 Ordinary gear trains(3)
Chap.5.8 Ordinary gear trains(4)
Conclusion,
The gear train with fixed axes
1,In a gear train with fixed parallel shaft,the
sign of train ratio can be determined by (-
1)m,where m is the number of external
gear pairs in the gear train,
2,In a gear train with fixed non-parallel axes
can not be determined by (-1)m,They can
only be determined by drawing arrows,
Chap.5.8 Ordinary gear trains(5)
Chap.5.9 epicyclic or planetary gear trains(1)
Sun gear
Planet gear
Arm
Converted gear train
Converted gear train(转化机构 )
The sign of the transmission(negative or
positive) cannot be neglected,
Example
Determine i1H
Known,
Chap.5.9 epicyclic or planetary gear trains(2)
70,24,18,28 3'221 ???? zzzz
Differential gear train
Converted gear train
Determine:nH
Known,
24,18,48,48 3'221 ???? zzzz
m i n/100m i n,/250 31 rnrn ??
n1
n3
Brief Summery
Converted gear train(转化机构 )
The sign of the transmission(negative
or positive) cannot be neglected,
Be careful the value and sign of n,
Algebraic value of the n which
directions are not parallel each other is
meaningless,
Combined gear train
Chap.5.9 epicyclic or planetary gear trains(3)
Known,
Determine,Transmission ratio of
shaft Ⅰ, Ⅱ,
15,30,40,30
,20,90,30,30
5'4'34
'1321
????
????
zzzz
zzzz
Summery
1,Dividing the gear train
2,Deriving the train ratios of sub-trains
independently
3,Find the train of the combined gear
train
Chap.5.10 Applications of gear train
1,To get large train ratio
2,To change the speed of rotation
3,Branching transmission
4,To combine or resolve the motion
5,To use in power transmission
Chap.5.1 Introduction
Chap.5.2 The fundamental law of gearing
Chap.5.3 Gear tooth nomenclature
Chap.5.4 Condition for Correct Meshing
Chap.5.5 Contact Ratio
Chap.5.6 Interference and undercutting
Chap.5.7 Gear types and Application
Chap.5.8 Ordinary gear trains
Chap.5.9 Epicyclic or planetary gear trains
Chap.5.10 Applications of gear train
Chap.5.1 Introduction
Can you give some example the gearsets?
Gears are machine elements that transmit
motion by means of successively engaging teeth,
Gears may be classified according to the relative
position of the axes of revolution,The axes may
be
1,parallel
2,intersecting
3,neither parallel nor intersecting
Gears for connecting parallel shafts
1,Spur gears
external contact internal contact
Chap.5.1 Introduction(1)
2,Parallel helical gears
3,Herringbone gears (or double-helical gears)
Gears for connecting parallel shafts
Chap.5.1 Introduction(2)
4,Rack and pinion (The rack is like a gear whose axis is at infinity.)
Gears for connecting parallel shafts
Chap.5.1 Introduction(3)
Gears for connecting intersecting shafts
1,Straight bevel gears
2,Spiral bevel gears
Chap.5.1 Introduction(4)
Neither parallel nor intersecting shafts
1,Crossed-helical gears
2,Hypoid gears
3,Worm and worm gear
Chap.5.1 Introduction(5)
Chap.5.2 The fundamental law of gearing
1,The Fundamental Law of Gearing
2,The Involute Tooth Form
3,Pressure Angle
4,Changing Center Distance
5,Backlash
Chap.5.2 The fundamental law of gearing(1)
? Tooth profile 1 drives tooth
profile 2 by acting at the
instantaneous contact point K,
? N1N2 is the common normal of
the two profiles,
? velocities V1 and V2 at point K,
along N1N2 are equal in both
magnitude and direction,
Otherwise the two tooth profiles
would separate from each other,
1,The Fundamental Law of Gearing
222111 ?? ??? NONO
The fundamental law of gearing,
The angular velocity ratio between the
gears of a gearset remains constant
throughout the mesh,
PO
PO
NO
NOm
in
o u t
V
1
2
11
22
1
2 ????
?
?
?
?
PO
PO
NO
NO
T
Tm
o u t
in
in
o u t
T
2
1
22
11
2
1 ?????
?
?
?
?
Chap.5.2 The fundamental law of gearing(2)
r1
r2
.
1
2
11
22
1
2 c o n s t
PO
PO
NO
NOm
in
o u t
V ????? ?
?
?
?
222111 ?? ??? NONO
? Point P is very important to the velocity ratio,
and it is called the pitch point,
? For a constant velocity ratio,the position of
P should remain unchanged,
? The motion transmission between two gears
is equivalent to the motion transmission
between two imagined slipless cylinders with
radius r1 and r2 or diameter d1 and d2,
?Two circles whose centers are at O1 and O2,
and through pitch point P are termed pitch
circles,
Chap.5.2 The fundamental law of gearing(3)
Pitch circles
r1
r2
Pitch point Pitch circle Constant Angular Velocity Ratio
P
2,The Involute Tooth Form
The involute curve is the path
traced by a point on a line as
the line rolls without slipping
on the circumference of a
circle,It may also be defined
as a path traced by the end of a
string which is originally
wrapped on a circle when the
string is unwrapped from the
circle,The circle from which
the involute is derived is called
the base circle,
Chap.5.2 The fundamental law of gearing(4)
What is the involute?
How does the involute form?
involute
Base circle
2,The Involute Tooth Form
involute
base circle
1,The line(string) is always
tangent to the basic circle,
4,There is no involute curve
within the base circle,
Chap.5.2 The fundamental law of gearing(5)
2,The center of curvature of the
involute is always at the point
of tangency of the string with
the cylinder,
3,A tangency to the involute is
then always normal to the
string,the length of which is
the instantaneous radius of
curvature of the involute curve,
2,The Involute Tooth Form
involute
base circle
Involute function
Chap.5.2 The fundamental law of gearing(6)
kkkk
k
b
k
i n v
r
r
????
?
???
?
t a n
c o s
.
.
2
1
2
1
1
2
2
1
2
1
2
1
2
1
22
11
1
2
C o n s t
r
r
r
r
m
C o n s t
r
r
r
r
r
r
PO
PO
NO
NO
m
b
b
in
o u t
V
b
b
in
o u t
V
?????
??
?????
?
?
?
?
?
?
?
?
The fundamental law of gearing
The ratio of the driving gear radius
to the driven gear radius remains
constant as the teeth move into
and out of mesh,
Chap.5.2 The fundamental law of gearing(7)
r1
r2
Important lines
Conclusion,these three lines
are the same line,
Axis of transmission(啮合线或传动线 )
Line of action（力作用线）
Tangency of the both base circles
（基圆公切线） is the common
normal,
rbp
rbg
rp
rg
Chap.5.2 The fundamental law of gearing(8)
3,Pressure angle（节圆压力角）
The pressure angle in a gearset is
defined as the angle between the axis
of transmission or line of
action(common normal) and the
direction of velocity at the pitch point,
Standard value of the pressure angle are
14.50,200 and 250,200 is the most
commonly used,
Meshing angle(啮合角 )
4,Changing Center Distance
Chap.5.2 The fundamental law of gearing(9)
21'c o s' bb rra ???
21''c o s'' bb rra ???
.''c o s'''c o s' c o n s taa ?? ??
.
1
2
1
2
1
2 C o n s t
r
r
r
rm
b
b
in
out
V ????? ?
?
?
?
4,Changing Center Distance
Conclusion,
1,To the gear with an involute form,center
distance errors do not affect the velocity
ratio,for the base circle diameters are
unchanging once the gear is cut,
2,But the pressure angle is affected by the
change in center distance,
3,The pitch point and pitch circles are
changed
Chap.5.2 The fundamental law of gearing(10)
5,Backlash(侧隙 )
Is there any other factor affected by changing
center distance? What is it?
Chap.5.2 The fundamental law of gearing(11)
Increasing the center distance will increase the backlash,
Backlash is defined as the clearance between mating teeth
measured along the circumference of the pitch circle,
Is there any problem if there is backlash between the
mating gears?
Chap.5.3 Gear tooth nomenclature（ 1）
Dedendum circle
顶隙
齿槽宽
齿厚
齿宽
齿顶高
齿根高
Explanation
Face of a tooth,That part of the tooth surface lying outside the pitch
surface,
Flank of a tooth,The part of the tooth surface lying inside the pitch
surface,
Circular thickness (also called the tooth thickness), The thickness
of the tooth measured on the pitch circle,It is the length of an arc and
not the length of a straight line,
Tooth space,The distance between adjacent teeth measured on the
pitch circle,
Backlash,The difference between the circle thickness of one gear and
the tooth space of the mating gear,
Circular pitch p,The width of a tooth and a space,measured on the
pitch circle,
Fillet, The small radius that connects the profile of a tooth to
the root circle,
Circular pitch pc(周节 ),the arc length along the pitch circle
circumference measured from a point on one tooth to the same
point on the next,(The width of a tooth and a space,measured
on the pitch circle.)
Ndp c ??
d= pitch diameter N= number of the teeth
Base pitch pb (基节 ), the tooth pitch measured along the
base circle,
?c o scb pp ?
Chap.5.3 Gear tooth nomenclature（ 2）
Diametral pitch Pd (径节 ), The number of teeth of a gear per
inch of its pitch diameter,
dNp d ?
cd p
p ??
Chap.5.3 Gear tooth nomenclature（ 3）
Module m,Pitch diameter divided by number of teeth,The
pitch diameter is usually specified in inches or millimeters; in
the former case the module is the inverse of diametral pitch,
dp
mNdm 4.25??
Standard gear and its teeth(China)
1,Number of teeth,N
2,Module m,
3,Pressure angle at pitch circle,200 is commonly used,and
14.50,200,150,14.50,22.50,250 is also used,
4,Coefficient of addendum,ha*
5,Coefficient of dedendum,c *
In GB,to full depth,if m >=1mm,ha* =1,c *=0.25
m <1mm,ha* =1,c *=0.35
to stub,ha* =0.8,c *=0.3
Chap.5.3 Gear tooth nomenclature（ 4）
?cpm ?
Chap.5.3 Gear tooth nomenclature（ 5）
分度圆 （ pitch circle）,
Tooth thickness,
Space width,
Addendum,
Dedendum,
mNd ?
22 mpes c ????
mhh aa ??
mcmhh af ?? ??
standard module
The table of the gears
Pitch circle (节圆）
（分度圆 ),An imaginary circle which has the standard
module and pressure angle,
Standard Module
Chap.5.4 Condition for Correct Meshing
rb1
rb2
1,2
Can any two gears mesh
together correctly?
Involute-two-point 21
21
2
2
1
1
2
2
222
1
1
111
21
c o s
1
c o s
1
c o sc o s
c o sc o s
??
??
?
?
?
?
?
?
?
?
?
??
??
?
pp
pp
p
pp
p
pp
pp
b
b
bb
Length of action is B1B2
Chap.5.5 Contact Ratio( 重合度 )
Contact ratio mp=Z/pb = pd Z/? cos ?
The minimum acceptable contact ratio for
smooth operation is 1.2
Let B1B2=Z
If the pressure is 200,ha*=1,then
the maximum of the contact
ratio is 1.981(理论极限值 )
* Manufacturing methods of involute gears
Cutting is the most widely used method,
There are generally two types of cutting
methods,forming cutting（仿形法） and
generating cutting （范成法）,(video)
Casting 铸造,forging热轧,powder process 粉末成形,
pressing冲压,cutting切削 milling磨削,shaving剃齿
? forming cutting 盘状铣刀、指状铣刀 拉齿
? generating cutting 插齿, 滚齿 Generating theory 原理
Cutting tool
Disk milling cutter
End milling cutter
成型铣刀刀号和加工齿数范围
shaping
Rack-shaped shaper cutter
hobbing
Interference & Undercutting
Pitch circle
Base circle
undercutting
根圆 （ dedendum circle）
Chap.5.6 Interference and undercutting(1)
1,Interference,In some cases,the dedendum will be
large enough to extend below the base circle,If so,
then the portion of tooth below the base circle will
not be an involute and will interfere with the tip of
the tooth on the mating gear,which is an involute,
2,Undercutting,If the gear is cut with a standard
gear shaper or a,hob”,the cutting tool will also
interfere with the portion of tooth below the base
circle and will cut away the interfering material,or
sometimes it is found that the top of the cutter
enters the profile of the gear and some part of the
involute profile near the root portion is removed,This
result in an undercutting tooth,
3,Disadvantage:The undercutting weakens the
tooth by removing material at its root,Severe
undercutting will promote early tooth failure,
How to avoid undercutting?
Chap.5.6 Interference and undercutting(2)
Addendum Modified
Tooth Form(变位齿形 )
Increase the number
of the teeth,
To avoid interference between a full-depth pinion
and a full-depth rack,the minimum number of
pinion teeth are,
Chap.5.6 Interference and undercutting(3)
Pressure angle(deg) Minimum number of teeth
14.5 32
20 18
25 12
video of cutting the gears
Advantage,1,Avoid the undercutting;
2,Improve the strength of
the pinion;
3,To fit the center distance,
Addendum Modified tooth form (fig.)
Chap.5.7 Gear types and Application(1)
Parallel
1,Spur gears.(Simple and least expensive form of gear to
make,only the gears who have the same module and pressure
angle can mesh together,More noise,Efficiency,98-99%,Easy
to be shifted)
2,Helical gears.(right-hand,left-hand,opposite-hand
helical gears in mesh,Quieter and gradual contact,Efficiency,
96-98%,Need the synchromesh mechanism to allow shifting.)
3,Herringbone gears.(more expensive,be used in
large,high-power application,)
Chap.5.7 Gear types and Application(2)
Worms and Worm gears
mv
The center distance must be maintainted accurately,
Efficiency is 40-85%(slip)
It can be designed to be impossible
to backdrive,
direction,
driving
Chap.5.7 Gear types and Application(3)
Rack and Pinion,
Motion conversion
Cutting tool
Chap.5.7 Gear types and Application(3)
Bevel,
Any angle between the shafts,900 is common,
Noncircular gears,
Belt and chain drives,
Chap.5.8 Ordinary gear trains(1)
Classification,
1,ordinary gear train or gear train with fixed axes,(定轴轮系 )
2,Epicyclic gear train,(周转轮系 )
Gear train
Gear train with fixed axes
Epicyclic gear trains
Gear trains with fixed parallel axes
Gear trains with fixed non-parallel axes
Elementary epicyclic gear trains
Combined gear trains
Planetary gear trains
Differential gear trains
Chap.5.8 Ordinary gear trains(2)
Example,
Chap.5.8 Ordinary gear trains(3)
Chap.5.8 Ordinary gear trains(4)
Conclusion,
The gear train with fixed axes
1,In a gear train with fixed parallel shaft,the
sign of train ratio can be determined by (-
1)m,where m is the number of external
gear pairs in the gear train,
2,In a gear train with fixed non-parallel axes
can not be determined by (-1)m,They can
only be determined by drawing arrows,
Chap.5.8 Ordinary gear trains(5)
Chap.5.9 epicyclic or planetary gear trains(1)
Sun gear
Planet gear
Arm
Converted gear train
Converted gear train(转化机构 )
The sign of the transmission(negative or
positive) cannot be neglected,
Example
Determine i1H
Known,
Chap.5.9 epicyclic or planetary gear trains(2)
70,24,18,28 3'221 ???? zzzz
Differential gear train
Converted gear train
Determine:nH
Known,
24,18,48,48 3'221 ???? zzzz
m i n/100m i n,/250 31 rnrn ??
n1
n3
Brief Summery
Converted gear train(转化机构 )
The sign of the transmission(negative
or positive) cannot be neglected,
Be careful the value and sign of n,
Algebraic value of the n which
directions are not parallel each other is
meaningless,
Combined gear train
Chap.5.9 epicyclic or planetary gear trains(3)
Known,
Determine,Transmission ratio of
shaft Ⅰ, Ⅱ,
15,30,40,30
,20,90,30,30
5'4'34
'1321
????
????
zzzz
zzzz
Summery
1,Dividing the gear train
2,Deriving the train ratios of sub-trains
independently
3,Find the train of the combined gear
train
Chap.5.10 Applications of gear train
1,To get large train ratio
2,To change the speed of rotation
3,Branching transmission
4,To combine or resolve the motion
5,To use in power transmission
