Download Transmission Components

Transmission Machine Components
ME14
Introduction to Mechanical Engineering Design
Gears
• Gears simply change
the parameters of
mechanical power
Pitch-Line Velocity
Tinin  Toutout
V p  r11  r22
in
NG 
out
NG 
1 r2

2 r1
P
r1
pinion
gear
ME14
Introduction to Mechanical Engineering Design
r2
Tooth Forces
T1  F1r1
T2
T1
F2
T2  F2 r2
F2   F1
r2
T2  T1
r1
r1
r2
F1
ME14
Introduction to Mechanical Engineering Design
ME14
Introduction to Mechanical Engineering Design
Normal velocity must match. Using similar triangles
v2 cosθ2 = v1 cosθ1
where v1 = ω1 . O1C ;
v2 = ω2 . O2C
Want constant rotation rate ratio
ω2 /ω1 = v2 . O1C/v1 . O2C = O1C.cosθ1 /O2C.cosθ2
= O1 C1 /O2 C2
= O1 P / O 2 P
Point P must be fixed
ME14
Introduction to Mechanical Engineering Design
ME14
Introduction to Mechanical Engineering Design
Effect of Errors
ME14
Shafts at spec. Shafts farther
distance apart than spec.
Introduction to Mechanical Engineering Design
Involute Tooth Profile
• The two curved surfaces of mating teeth,
contact as a line
ME14
Introduction to Mechanical Engineering Design
Types of Gears
• Spur Gears
– Teeth are parallel to rotation axis
– Transmit power between shafts with
parallel axes
• Helical Gears
– Teeth inclined to the axis of rotation
– Used for the same applications as spur
gears, but have less noise due to
gradual tooth engagement
ME14
Introduction to Mechanical Engineering Design
Types of Gears, cont.
• Bevel Gears
– Teeth on a conical Surface
– Used with intersecting shafts
• Worm Gears
– Similar to a screw
– Used with non-parallel and nonintersecting shafts typically with
high speed ratios
ME14
Introduction to Mechanical Engineering Design
Rack and Pinion
• A rack is an unwound spur gear
• Turns rotary motion in to linear motion
ME14
Introduction to Mechanical Engineering Design
Anatomy of a Gear
• Pitch Circle
– Theoretical circle upon with all calculations are based
• Diametral Pitch
• Module
N
P=
d
d
m=
N
• Pressure Angle
• For gears to work together they must have the same
pitch (or module) and pressure angle
ME14
Introduction to Mechanical Engineering Design
Multiple Gear Stages
• Gear ratios from a multi-stage gear train
multiply together
T2
T3
T4
T1
2:1 reduction
2:1 reduction
2:1 reduction
Overall a 8:1 reduction
ME14
Introduction to Mechanical Engineering Design
Efficiency
• In reality gears are not 100% efficient
• Good quality spur gears are typically in the 90+ %
efficiency range
• This can be a problem with multiple (large) gear
reductions
Each a 2:1 reduction with 95% efficiency
Overall a 32:1 reduction, but only 77% efficient
ME14
Introduction to Mechanical Engineering Design
Belts and Chains
• Belts are essentially the same as spur gears
but they have the ability to have large
offsets
P1
P2
V p1  V p 2  r11  r22
1 r2
NG 

2 r1
ME14
Introduction to Mechanical Engineering Design
Slip
• Belts rely on friction and to prevent slip
tension must be maintained
• Chains and timing belts that have teeth with
positive engagement can help prevent slip
ME14
Introduction to Mechanical Engineering Design
Shafts
Energy used to
overcome the
forces resulting
from misalignment
will reduce the
overall efficiency
of your system
Parallel misalignment
Angular misalignment
This is the key to doing well in the transmission contest
ME14
Introduction to Mechanical Engineering Design
Pins
• Pins hold two parts together based upon the
shear strength of the pin
• Pins are good when the joint must take both
thrust and shear
• Pinned joints are easy to analyze and reliable
• Pinned joints can be used as a mechanical
fuse
• Pinned joints are difficult to
assemble and disassemble
because pins are typically
press fit into place
ME14
Introduction to Mechanical Engineering Design
shaft
gear
pin
18
Keys
• Keys transmit torque in shear across the
length of the key
• Keys have all the advantages of pins, but
they are easy to install in remove
• Keys do not take any axial load
Woodruff key
Used to reduce stress concentrations in the shaft
ME14
Introduction to Mechanical Engineering Design
19
Clamp Fit
• Clamps depend upon friction and the bolted
connection between two parts (or a single
part with a flexure) to develop the clamping
force
• Clamped connections can be easy and
reliable for low torque applications
ME14
Introduction to Mechanical Engineering Design
20
Press (Interference) Fits
• Two parts can be pressed together if the hole
is manufactured smaller than the shaft that is
installed
• The load between these two parts is taken in
friction developed by the strain of the press fit
• Manufacturing tolerances are very tight for
this type of connection
– For a 0.25” diameter shaft with a class FN2 fit
• Shaft 0.2510” – 0.2514”
• Hole 0.2500” – 0.2506”
• Difficult to disassemble without damage to the
parts
ME14
Introduction to Mechanical Engineering Design
21
Splines
• Splines are essentially matching internal and
external gears used to transmit torque
• Splines are extremely reliable and efficient
• Splines are difficult to manufacture
ME14
Introduction to Mechanical Engineering Design
22
Retaining Rings
• Retaining rings are used to constrain things
axially in one direction on a shaft
• Installed by machining a groove into one of
the mating parts
• Can be made external or internal
External
E-Style External
ME14
Introduction to Mechanical Engineering Design
Internal
23
Shaft Connections
Coupler transmits torque and
allows for misalignment
ME14
Introduction to Mechanical Engineering Design
Key or set screw
transmits torque
Couplers
• Bellows
• Spider Coupling
• Helical
• Universal Joint
ME14
Introduction to Mechanical Engineering Design
Bearing and Bushings
ME14
Introduction to Mechanical Engineering Design
Bushings
• Bushings have sliding contact and rely on low
friction at the point or line of contact
Ploss  F r 
r
F
ME14
Introduction to Mechanical Engineering Design
Rolling Element Bearings
• Replace sliding contact with rolling contact
which is much more efficient
Outer Race
Ball
Separator
(retainer)
Inner Race
ME14
Introduction to Mechanical Engineering Design
Image courtesy of Barden
Precision Bearing
Rolling Contact
ωb
ω1
ri
rLi
ro
rb
V
rLo
V  1rLi
b 
ME14
Introduction to Mechanical Engineering Design
V 1rLi

rb
rb
Spherical Bearings
• Allows for misalignment in all rotational
degrees of freedom
• Constrains in all translational degrees of
freedom
• Good for low speed / high load applications
ME14
Introduction to Mechanical Engineering Design
A Brief Into to Specifying
Electric Motors
ME14
Introduction to Mechanical Engineering Design
Electric Motors
• Torque is proportional to current
• Speed is proportional to voltage
• An electric motor generates an
Electromotive Force (back EMF)
as it spins
• A portion of the input voltage
goes to doing work and a portion
goes to overcome the back EMF
ME14
Introduction to Mechanical Engineering Design
T = Kt I
w = K eV
V=
w
Ke
Vin = Vemf + IR
w
T
Vin =
+
R
Ke Kt
Kt
Ke
ME14
Introduction to Mechanical Engineering Design
Electric Motors
For a given voltage
6000
80
70
5000
60
Speed (rpm)
50
3000
40
30
2000
20
1000
10
0
0
0.05
0.1
0.15
0.2
Torque (Nm)
0.25
ME14
Introduction to Mechanical Engineering Design
0.3
0
0.35
Efficiency (%)
4000
Electric Motor Power
Can’t always operate here
due to heat
50
6000
45
5000
40
Speed (rpm)
30
3000
25
20
2000
15
10
1000
5
0
0
0.05
0.1
0.15
0.2
Torque (Nm)
0.25
ME14
Introduction to Mechanical Engineering Design
0.3
0
0.35
Power Output (W)
35
4000
Continuous Operating Range
ME14
Introduction to Mechanical Engineering Design