You're right, in the figure shown the addendum circles of the gears are interfering with each other, which is not desirable. Here are a few ways to avoid this interference:
1. Increase the center distance between the gears. This will move the gears further apart and create clearance between the addendum circles.
2. Use gears with a smaller addendum. Reducing the size of the addendum will reduce how far it extends out from the base circle.
3. Apply an offset to one or both gears. By offsetting the gears axially, you can shift one gear up/down relative to the other to create clearance.
4. Use bevel gears or hypoid gears instead of straight spur gears
This is the important topic from Kinematics of Manufacturing Machines, in which you can learn all about gear trains and can solve problems on the topic.
In epicyclic gear train ,the axis of at least one of the gears moves relative to the frame. A gear train having a relative motion of axes is called a planetary or an epicyclic gear train.
VTU Notes for Testing and commissioning of Electrical Equipment Department of Electrical and Electronics Faculty Name: Mrs Veena Bhat Designation: Assistant Professor SDM Institute of Technology Subject: Testing and Commissioning of Electrical equipment Semester: VII
Module 02: Energy exchange in Turbo machines
Modal 02: Question Number 3 a & 3 b
i. Basic Introduction
ii. Euler’s turbine equation
iii. Alternate form of Euler’s turbine equation
iv. Components of energy transfer
v. Degree of Reaction
vi. Velocity triangles for different values of degree of reaction
vii. Utilization factor
viii. Relation between degree of reaction and Utilization factor
ix. List of Formulas
x. Previous Year Question papers
Very essentially for any organization time management . Production is essential for Any project management . It increases profit with maximum project management . Each and every organization have impact to make business
This is the important topic from Kinematics of Manufacturing Machines, in which you can learn all about gear trains and can solve problems on the topic.
In epicyclic gear train ,the axis of at least one of the gears moves relative to the frame. A gear train having a relative motion of axes is called a planetary or an epicyclic gear train.
VTU Notes for Testing and commissioning of Electrical Equipment Department of Electrical and Electronics Faculty Name: Mrs Veena Bhat Designation: Assistant Professor SDM Institute of Technology Subject: Testing and Commissioning of Electrical equipment Semester: VII
Module 02: Energy exchange in Turbo machines
Modal 02: Question Number 3 a & 3 b
i. Basic Introduction
ii. Euler’s turbine equation
iii. Alternate form of Euler’s turbine equation
iv. Components of energy transfer
v. Degree of Reaction
vi. Velocity triangles for different values of degree of reaction
vii. Utilization factor
viii. Relation between degree of reaction and Utilization factor
ix. List of Formulas
x. Previous Year Question papers
Very essentially for any organization time management . Production is essential for Any project management . It increases profit with maximum project management . Each and every organization have impact to make business
Management is essential in Amy organization. Important point pf view to celebrate different activities also it os essential for time management in each and every field
Economics and management very useful information on how to study a bout basic concepts of economics and management also supply and demand curves co related with price and quality and quantity
Things to remember while upgrading the brakes of your carjennifermiller8137
Upgrading the brakes of your car? Keep these things in mind before doing so. Additionally, start using an OBD 2 GPS tracker so that you never miss a vehicle maintenance appointment. On top of this, a car GPS tracker will also let you master good driving habits that will let you increase the operational life of your car’s brakes.
𝘼𝙣𝙩𝙞𝙦𝙪𝙚 𝙋𝙡𝙖𝙨𝙩𝙞𝙘 𝙏𝙧𝙖𝙙𝙚𝙧𝙨 𝙞𝙨 𝙫𝙚𝙧𝙮 𝙛𝙖𝙢𝙤𝙪𝙨 𝙛𝙤𝙧 𝙢𝙖𝙣𝙪𝙛𝙖𝙘𝙩𝙪𝙧𝙞𝙣𝙜 𝙩𝙝𝙚𝙞𝙧 𝙥𝙧𝙤𝙙𝙪𝙘𝙩𝙨. 𝙒𝙚 𝙝𝙖𝙫𝙚 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙥𝙡𝙖𝙨𝙩𝙞𝙘 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙪𝙨𝙚𝙙 𝙞𝙣 𝙖𝙪𝙩𝙤𝙢𝙤𝙩𝙞𝙫𝙚 𝙖𝙣𝙙 𝙖𝙪𝙩𝙤 𝙥𝙖𝙧𝙩𝙨 𝙖𝙣𝙙 𝙖𝙡𝙡 𝙩𝙝𝙚 𝙛𝙖𝙢𝙤𝙪𝙨 𝙘𝙤𝙢𝙥𝙖𝙣𝙞𝙚𝙨 𝙗𝙪𝙮 𝙩𝙝𝙚 𝙜𝙧𝙖𝙣𝙪𝙡𝙚𝙨 𝙛𝙧𝙤𝙢 𝙪𝙨.
Over the 10 years, we have gained a strong foothold in the market due to our range's high quality, competitive prices, and time-lined delivery schedules.
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5 Warning Signs Your BMW's Intelligent Battery Sensor Needs AttentionBertini's German Motors
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"Trans Failsafe Prog" on your BMW X5 indicates potential transmission issues requiring immediate action. This safety feature activates in response to abnormalities like low fluid levels, leaks, faulty sensors, electrical or mechanical failures, and overheating.
Comprehensive program for Agricultural Finance, the Automotive Sector, and Empowerment . We will define the full scope and provide a detailed two-week plan for identifying strategic partners in each area within Limpopo, including target areas.:
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Tyre Industrymarket overview with examples of CEAT
Gear .pdf
1. Gear Trains
•A mechanism used to transmit power or
motion from one shaft to another with the
help of gear wheels.
• Like belt, rope and chain drives
• Widely used in modern world. Clocks,
watches, lathes, ships, automobiles etc.
Prof. N Mohan Rao, JNTUK 1
2. Train value
• The value of a gear train is defined as
Train value=
Prof. N Mohan Rao, JNTUK 2
5. Simple gear train
Follower C
Intermediate
Prof. N Mohan Rao, JNTUK 5
Driver A
Follower C
Intermediate
wheel B
6. Train Value (Simple gear train)
V= Pitch line velocity of the gears A and B at the
contact point P
V
P
A B
But
Therefore
Prof. N Mohan Rao, JNTUK 6
Therefore
From (1) and (2), Train value is
Similarly, for gears B and C
Thus the train value of the simple gear train does not depend
on the intermediate wheel. But, direction of rotation of the
follower will be influenced by the intermediate wheel in the
simple gear train.
7. Compound gear train
Each intermediate gear shaft carries two gears
which are fastened together rigidly.
A
B
C
D
E
F
Prof. N Mohan Rao, JNTUK 7
A B
C
D
E
F
8. Train value of Compound gear train
---------------- (1)
---------------- (2)
---------------- (3)
From (1), (2) and (3)
Prof. N Mohan Rao, JNTUK 8
From (1), (2) and (3)
Intermediate gears affect the train value and
direction. Smaller size of the gears.
Compound gear trains are compact i.e. provide larger
velocity ratio in limited space.
9. Reverted gear train
Special type of compound
gear train where the first
and the last gear have the
same axis.
Eg. Clock wherein minute
and hour hands are
A
B
C
D
RA RB
Prof. N Mohan Rao, JNTUK 9
and hour hands are
attached to gears on the
same axis, back gear of a
lathe.
RA + RB=RC +RD
TA + TB = TC + TD
A B
C
D
RA RB
RC
RD
(m=D/T)
(D=mT)
10. Epicyclic Gear Train
• Axes are fixed in simple and compound gear trains
• In Epicyclic gear trains, the axes of some of the
gears revolve about one fixed axis.
A
B
Prof. N Mohan Rao, JNTUK 10
Arm C
P Q
An Epicyclic gear train can provide larger velocity ratio for
a given number of gears.
Applications: differential gear of automobile, wrist
watches, hoists, pulley blocks
11. Train value of epicyclic gear train
https://youtu.be/sNBooUaVf7w
A
B
Prof. N Mohan Rao, JNTUK 11
P Q
Arm C
12. Train value of epicyclic gear train
• Various methods are employed to determine
the velocity ratio of an epicyclic gear train.
• Relative velocity method
• Tabular or Algebraic method
• Tabular or Algebraic method
Prof. N Mohan Rao, JNTUK 12
13. Tabular or Algebraic method
Operation Revolution of the
Arm C
Revolution of the
gear A
Revolution of the
gear B
Arm C fixed 0 +1 - (TA/TB)
Multiply by x 0 +x - x . (T /T )
Prof. N Mohan Rao, JNTUK 13
Multiply by x 0 +x - x . (TA/TB)
Add y + y x + y y - x . (TA/TB)
14. Torques in epicyclic gear train
• Assuming that different gears constituting the
epicyclic gear are moving with uniform speed,
Algebraic sum of the torques applied
externally must be equal to zero.
• In three torques are applied externally,
In three torques are applied externally,
• Td - driving torque
• Tr - resisting torque
• Th - holding down or braking torque
therefore, Td + Tr + Th = 0
Prof. N Mohan Rao, JNTUK 14
15. Torques in epicyclic gear train…
• Neglecting friction losses of teeth during mesh
and at bearings, the total energy must be
equal to zero.
Therefore, T . ω + T . ω + T . ω = 0
Therefore, Td . ωd + Tr . ωr + Th . ωh = 0
Since ωh = 0,
Td . ωd + Tr . ωr = 0
Prof. N Mohan Rao, JNTUK 15
17. Speeds in Sun and Planet gear
Tabular or Algebraic method
Operation Revoluti
on of
the Arm
C
Revoluti
on of the
Sun gear
S
Revolution of the
Planer gear P
Revolution of the Annular
wheel A
Arm C
fixed
0 +1 - (TS/TP) - (TS/TP) . (TP/TA)=
- (T /T )
Prof. N Mohan Rao, JNTUK 17
fixed
- (TS/TA)
Multiply
by x
0 +x - x . (TS/TP) - x . (TS/TA)
Add y + y x + y y - x . (TS/TP) y - x . (TS/TA)
18. Numerical example 1
P1
P2
Prof. N Mohan Rao, JNTUK 18
The number of teeth on S1=24, A1=96, S2=30 ,A2=90.
If the shaft P rotates at 1980 rpm and annular wheel A2 is fixed, find the speed
of the shaft Q. Also, find the speed of the shaft Q if the annular wheel A2
rotates at 198 rpm in the same direction as that of S1.
19. Numerical Example
Operatio
n
Arm S1 P1 A1 S2 P2 A2
Arm
fixed
0 +1 - (24/P1) -(24/96)
= - (1/4)
-(24/96)
= -(1/4)
+(24/96)
× (30/P2)
+(24/96)
× (30/P2)
×
(P2/90)=
+ (1/12)
Prof. N Mohan Rao, JNTUK 19
Arm
fixed
+ x
revolutio
n to S1
0 + x - (1/4) x - (1/4) x +(1/12).
x
Add + y
to arm
+ y x+y - (1/4)x
+y
- (1/4)x
+y
(1/12)x
+y
20. Numerical example
Case 1:
• Annular wheel A2 is fixed.
• Therefore (1/12)x +y=0
• or x = - 12 y
• Speed S1 = x+y =1980 rpm
• -12 y +y=1980
• -12 y +y=1980
• Speed of arm i.e shaft Q= y= - 1980/11
• = - 180 rpm
• Shaft Q rotates at 180 rpm in the direction opposite to that
of the shaft P.
• x=1980-y=1980+180=2160 rpm
• Speed of S2 = - (1/4)x +y= -2180/4 – 180
• = -545 – 180= - 725 rpm
Prof. N Mohan Rao, JNTUK 20
21. Case 2
• Speed of Annular wheel A2 =198 rpm
• Therefore (1/12) x +y=198
• or x = 12 (198 – y)
• Speed S1 = x+y =1980 rpm
• 12(198-y)+y=1980
• 12(198-y)+y=1980
• 12×198 -11 y=1980
• y=(12 × 198-1980)/11
• =2×198/11=36 rpm
• Speed of arm i.e shaft Q= y= 36 rpm
• Shaft Q rotates at 36 rpm in the same direction as that
of the shaft P.
Prof. N Mohan Rao, JNTUK 21
22. Numerical example 2
• Refer to the previous numerical example.
• If the torque on the shaft P is 300 N-m, find
the torque on the shaft Q and the holding
down torque on A when is A fixed.
down torque on A2 when is A2 fixed.
• Td . ωd + Tr . ωr + Th . ωh = 0
• Td . Nd + Tr . Nr + Th . Nh = 0
• 300 x 1980 + Tr x -180 + Th x 0 = 0
• Tr = 300 x 1980/180= 3300 N-m
Prof. N Mohan Rao, JNTUK 22
23. Numerical example 2
• Also, Td + Tr + Th = 0
• Therefore, 300 +3300 + Th = 0
• or Th = -3600 N-m
Prof. N Mohan Rao, JNTUK 23
24. Questions on Gear trains
1. An epicyclic gear train is shown in the figure below. The number of teeth on
the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth
on the inner surface and 100 teeth on the outer surface. If the carrier arm
AB is fixed and the sun gear A rotates at 300 rpm in the clockwise
direction, then the rpm of D in the clockwise direction is
(A) 240
(B) -240
(C) 375
(C) 375
(D) -375
Answer : (C) 375
Solution: when arm is fixed, it becomes simple train.
24
26. 2. A frictionless gear train is shown in the figure.
The leftmost 12-teeth gear is given a torque of
100 N-m. The output torque from the 60-teeth
gear on the right in N-m is
(A) 5
(B) 20
(C) 500
(D) 2000
(D) 2000
Answer : (D) 2000
Solution:
26
27. 3. In an epicyclic gear train, shown in the figure, the outer ring
gear is fixed, while the sun gear rotates counterclockwise at
100 rpm. Let the number of teeth on the sun, planet and
outer gears to be 50, 25, and 100, respectively. The ratio of
magnitudes of angular velocity of the planet gear to the
angular velocity of the carrier arm is ____________.
• Answer : 3
• Sol:
• Sol:
27
28. 4. A gear train shown in the figure consist of gears P, Q, R and S.
Gear Q and gear R are mounted on the same shaft. All the
gears are mounted on parallel shaft and the number of teeth
of P, Q, R and S are 24, 45, 30 and 80, respectively. Gear P is
rotating at 400 rpm. The speed (in rpm) of the gear S
is_________
• Answer : 120
28
29. 5. In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with
gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and
100, respectively. If gear 2 is fixed and gear 4 rotates with an angular
velocity of 100 rpm in the counterclockwise direction, the angular speed
of arm 5 (in rpm) is
(A) 166.7 counterclockwise
(B) 166.7 clockwise
(C) 62.5 counterclockwise
(D) 62.5 clockwise
(D) 62.5 clockwise
Answer : (C) 62.5 counterclockwise
30. 6. A gear train is made up of five spur gears as shown in the figure.
Gear 2 is driver and gear 6 is driven
member. N2, N3, N4, N5 and N6 represent number of teeth on gears
2,3,4,5, and 6 respectively, The gear(s) which act(s) as idler(s) is/ are
(A) Only 3
(B) Only 4
(C) Only 5
(D) both 3 and 5
Answer : (C) Only 5
Solution:
30
31. Clarifications
• Sir,
In the concept of addendum circle cutting at
the tangent to avoid interference. i the figure
the addendum is passing into the base
the addendum is passing into the base
circle(tooth tip of one gear into other) which is
not desired. what will we do to avoid it?.Is it
possible for such type of gears to function?
Prof. N Mohan Rao, JNTUK 31