3.share gear-trains
TRANSCRIPT
Gear Train
Main types:
• Simple gear train: one gear per
shaft
• Compound gear train: two or
more gears per shaft, but for the
first, last
• Reverted gear train: input and
output gears are coaxial.
• Planetary/epicyclic gear train:
one with a relative motion of
the axes.
A combination of gears used to transmit motion from one shaft to another.
Why combination?: to obtain large speed reduction within a small space.
Simple Gear Train
Gear Ratio
+ : Internal gearing
- : External gearing
Simple Gear Train
- -
Intermediate gears
Odd Even
Input :Output motion Alike Opposite
Intermediate gears are called idlers in SGT as they do not affect the speed ratio of the
gear train. They are primarily used to;
(a) Connect gears with large center distance
(b) To obtain the desired direction for the driven
Compound Gear Train
The compound gears are rigidly fixed to the shaft,
hence have the same speed.
- - -
-
(-1)pairs
Reverted Gear Train
Epicyclic Gear TrainThe axes of the shafts over which the gears are mounted may
move relative to the fixed axis.
Gear A and the arm C have a common axis at O1 about which
they can rotate.
The gear B meshes with gear A, and has its axis on the arm
at O2 about which it can rotate.
If the arm is fixed: Simple gear train
If the gear A is fixed and the arm is rotated about O1 then the gear B is forced to
rotate upon and around gear A. Such a motion is called epicyclic (epi: upon; cyclic:around)
EGTs are useful for transmitting high speed ratios with gears of moderate size………
….backgear of lathe; Differential gears of automobiles, wrist watches…
Epicyclic Gear Train
Planetory Gear Train
Sun (Center)
Planet (Around Sun
Annulus (Internal T)
Epicyclic Gear TrainSpeed ratio: Algebraic method; Tabular method
The motion of each element of the EGT relative to the arm is written in the form of equations
These equations are solved using two conditions:
(i) Some element is fixed, implying zero velocity
(ii) Motion of some other element is specified.
One caution: You’ll need to associate
+/- signs to clockwise and anticlockwise directions
Anticlockwise: +
Clockwise: -
Epicyclic Gear Train: Problem-1
- No. of teeth are as shown in the diagram
-A is fixed
-B and C are carried on an arm which revolves at 100 rpm about the axis of A or D.
# Find the number of teeth of C and the speed & sense of rotation of C?
Epicyclic Gear Train: Problem-1tA= 150; tB=25; tD=40; NA=0; Narm =100 CL =-100
NC=?
Geometry:
dA/2 = dB + dC + dD/2
tA/2 = tB + tC + tD/2
75=25+tC+20 tC=30
Engagement of AB: Internal implies +
(NB-Narm) / (NA-Narm) = tA/tB
NB- (-100) = (150/25) * (0-(-100)) NB=500
Engagement of BC: External implies -
(NB-Narm) / (NC-Narm) = -tC/tB
NC- (-100) = (-25/30) * (500-(-100)) NC=-600 = 600 rpm clockwise
Epicyclic Gear Train: Problem-2
# Find the speed and direction of wheel D when wheel A is fixed and arm F makes 200rpm
clockwise.
Epicyclic Gear Train: Problem-2tA= 80; tC=72; tD=48
NA=0; Narm =200 CL =-200
Note: NB=NC due to compound shaft; ND?
Geometry:
rA + rB = rC + rD
tA + tB = tC + tD
tB = 40
Engagement of AB: External implies -
(NB-Narm) / (NA-Narm) = -tA/tB
NB- (-200) = (-80/40) * (0-(-200)) NB=-600 600 rpm CL
Engagement of CD: External implies -
(ND-Narm) / (NC-Narm) = -tC/tD
Note NC= NB
ND = 400 = 400 rpm CCL
Torques in Epicyclic Gear Train
When a geared system transmits power, torques are transmitted from one element
to another.
Torques in Epicyclic Gear Train
When the rotating parts of an epicyclic
gear train have uniform speeds, i.e., zero
angular acceleration, then the gear train
is kept in equilibrium by three externally
applied torques. The net (external)
torque applied must be zero.
There are no losses in power transmission,
i.e., there are no internal friction losses at
the bearings and at the contact surfaces. In
other words, the net energy dissipated by the
gear train is zero.
Torques in Epicyclic Gear Train: Problem 2Shown is a compound epicyclic
gear train in which two gears S1
and S2 are integral with the
Input shaft B. The arm A2 is
integral with the output shaft, C.
The planet gear P2 revolves on a
pin attached to the arm A2, and
meshes with the Sun gear S2 and
internal gear I2 that is co-axial
with the input shaft.
The planet gear P1 meshes with
the fixed internal gear I1 and sun
gear S1.
The planet gear P1 revolves on a pin fixed to internal gear I2.
Arm
A1
The number of teeth are as stated in the figure.
The input power on the shaft B is 10.47 kW
at 1000 rpm (CCL). Find:
•The speed and torque at the output shaft
•The torque required to hold the internal gear I1.
I1 P1 A1
I2 P2S1
S2
Torques in Epicyclic Gear Train: Problem 2
Arm
A1
The input power on the shaft B
is 10.47 kW at 1000 rpm (CCL).
Find:
•The speed and torque at the
output shaft
•The torque required to hold the
internal gear I1.
Inp:B S1 P1 I1 A1 I2 P2 S2 A2/C
Teeth
(T)
26 88 83 31
Speed
(N)
1000
CCL
1000
CCL
0 1000
CCL
Inp:B S1 P1 I1 A1 I2 P2 S2 A2/C
Teeth
(T)
26 31 88 83 26 31
Speed
(N)
1000
CCL
1000
CCL
0 1000
CCL
Rad(S1) + Dia (P1) = Rad(I1) Rad(S2) + Dia (P2) = Rad(I2)
(TS1)/2 + TP1 = (TI1)/2 (TS2)/2 + TP2 = (TI2)/2
Torques in Epicyclic Gear Train: Problem 2
The input power on the shaft B is 10.47
kW at 1000 rpm (CCL).
Find:
•The speed and torque at the output
shaft
•The torque required to hold the
internal gear I1.
I1 P1 A1
S1
Torques in Epicyclic Gear Train: Problem 2
The input power on the shaft B is 10.47
kW at 1000 rpm (CCL).
Find:
•The speed and torque at the output
shaft
•The torque required to hold the
internal gear I1.
I2 P2 S2
Torques in Epicyclic Gear Train: Problem 2
The input power on the shaft B is 10.47
kW at 1000 rpm (CCL).
Find:
•The speed and torque at the output
shaft
•The torque required to hold the
internal gear I1.
Epicyclic Gear Train with Bevel Gear
Bevel gears are used for high speed reduction with fewer gears.
The method applicable for EGT with spur gears is also applicable for EGT with bevel gears
with some change:
For those gears whose axes are inclined to the main axis, the terms clockwise and
anticlockwise are not applicable, because direction of rotation for different gears ought to
be with respect to the same axis.
Epicyclic Gear Train with Bevel Gear: Problem 1
The figure shows an epicyclic bevel GT (Humpage’s reduction gear) in which the gear B is
connected to the input shaft, and gear F is connected to the output shaft.
The Arm (A), carrying the compound wheels D & E, turns freely on the output shaft.
If the input speed is 1000 rpm CCL (seen from the right), determine the speed of the
output shaft, when:
I: gear C is fixed
II: gear C is rotated at 10 rpm CCL.
Epicyclic Gear Train with Bevel Gear: Problem 1
NB = 1000 rpm CCL, determine NF, when:
I: gear C is fixed
II: gear C is rotated at 10 rpm CCL.
C D B
F E
3
2 1
To find NF, find NE
to find which, find ND
Epicyclic Gear Train with Bevel Gear: Problem 1
NB = 1000 rpm CCL, determine NF, when:
I: gear C is fixed
II: gear C is rotated at 10 rpm CCL.
C D B
F E
3
2 1