Transcript Drive Train Components

Drive Train Components
Chains and pinions and gears, Oh my!
ROBOTICS ACADEMY: Drive Train Components
Drive Trains: Energy source  useful work
Energy sources

Animals


Stored potential energy


steam engine, internal combustion, gas/steam turbine,...
Chemical


waterwheel, windmill, sail, hydroelectric, warp drive…
Combustion


gravity, spring, compressed air…
Momentum transfer


transportation, direct work, treadmill, manual labor…
battery, fuel cell, gas generator, …
Nuclear

heat for steam turbine, solar, radiometer, …
ROBOTICS ACADEMY: Drive Train Components
Drive Trains: Energy source  useful work
FIRST® Energy sources

Animals


transportation, direct work, treadmill, manual labor…
Stored potential energy

gravity, spring, compressed air…
Momentum transfer
 waterwheel, windmill, sail, hydroelectric, warp drive…

Combustion



Chemical


steam engine, internal combustion, gas/steam turbine,...
battery, fuel cell, gas generator, …
Nuclear

heat for steam turbine, solar, radiometer, …
ROBOTICS ACADEMY: Drive Train Components
Connecting drive components
Rotational to rotational
 Gears
 spur, helical, bevel, worm, planetary
 Pulleys and belts
 toothed, flat, round, V
 Sprocket and chain
 Hydraulic pump and motor
 Couplers
Rotational to linear
 Pinion & rack, cam & follower, crank & rod
 Solenoids and magnets
 Air and hydraulic cylinders
ROBOTICS ACADEMY: Drive Train Components
Gear basics – torque, speed, power & efficiency
Gear teeth are designed for rolling contact along the
pitch circle. The rolling contact provide by the
involute shape minimizes sliding and power loss.
If the center distance is not set correctly, teeth slide
and wear, and efficiency drops.
Basic statics relations:
Sum of forces on a body
N
=0
r
 Fi  0
i1
N
Sum of moments on a body = 0
r
 Mi  0
i1
Efficiency in terms of power: 
For gears, efficiency, h, is
typically between 90% and98%

Pinput h  Poutput
ROBOTICS ACADEMY: Drive Train Components
Forces and torques on gears and shafts
Drive gear
Output gear
Free body diagram to compute forces and moments
 input Moment (torque) on input shaft (N-m)
r
Fin gear Resistive force from mating gear (N)
r
Fin shaft Reaction force on shaft (units N)
r

 input  Fin gear  rin gear  0
Sum of moments

r
r
Sum of forces on input gear
Fin gear  Fin shaft  0

r
r
Sum of forces between gears Fin gear  Fout gear  0
r
r

Sum of forces on output gear Fout shaft  Fout gear  0
r

 output  Fout gear  rout gear  0
Sum of moments

 output rout gear N teeth out gear


Ideal torque ratio
 input rin gear N teeth in gear


FBD
of
output
gear
Resistive torque of output is
opposite rotation direction



ROBOTICS ACADEMY: Drive Train Components
Gear speed and power calculations
Drive gear
Output gear
Pitch circles of mating gears must have same speed
 in gear Rotation rate (units of s-1)
rin gear Radius of input gear (units of m)
r
v in pitch circ Velocity pitch circle (units of m/s)
Power transmission



 in gear  rin gear   out gear  rout gear
Speed ratio
 input   input
 output rin gear N teeth in gear


 input rout gear N teeth out gear


rout gear  
rin gear 
Out  output   output  


 input r
 
 input r


in gear  
out gear 
In
  input   input + losses
Pinput h  Poutput
ROBOTICS ACADEMY: Drive Train Components
Other gears and gear reductions
Helical:
Smoother running
Change shaft
directions
Worm gear:
Considerable
reduction;
Only driven
by the worm
Bevel gear:
Used to change axis;
More efficient than
helical
 output  input N output


 input  output
1

High friction with
direction change
Planetary
gears:
Low forces on
shafts;
Rugged and
smooth
Stackable units

 output  input
N ring
rring

1
1
 input  output
N sun
rsun
ROBOTICS ACADEMY: Drive Train Components
Belt and pulley drives
Belt drives suppress noise transmission and mitigate jerk and shock
Mechanics follows from continuous
velocity at the outside of both pulleys
 input  rinput   output  routput
Maximum belt tension
V-belt: high traction,
limited curvature
 output  input routput


 input  output rinput
T( units of N)  Tpre tension   output /routput



Flat leather: release and
apply tension to engage
as a clutch
mechanism
Serpentine: staple
on modern cars
Round belts: can
be used to drive
shafts set along
skew axes
Toothed: Positive
drive applications
similar to chains,
but teeth are not as
robust
ROBOTICS ACADEMY: Drive Train Components
Chain and sprocket drives
Chains provide a robust connection between drive components
Velocity and torque relations are
the same as belts. At very high
speeds, inertial effects should
be considered
Rollers sit in seat of
sprocket and pins
spin inside of the
rollers
 output  input routput


 input  output rinput

Dual chain: high
torque applications
Reverse: shaft direction
using idler gears
Transmission chains: higher
efficiency, longer life less noise
ROBOTICS ACADEMY: Drive Train Components
Bushings
Rotating or sliding contact surfaces to
control friction and component wear.
Various shapes for rotation and thrust
Hydrodynamic lubrication
theory operates at high
speeds. It’s much the
same as a car
hydroplaning on a wet
roadway.
Low to moderate loads, wide range of
speeds. Shaft must have polished surface.
Often either grooved or made from porous
metal (e.g. sintered brass) to facilitate
lubrication. Groves
are fed through oil
holes. Porosity
releases oil during
operation.
The load offsets the shaft vertically.
Shaft rotation brings oil into a
converging wedge geometry.
More fluid cannot fit into the smaller
gap, so pressure builds.
The pressure acts counter to the
load, keeping the gap open.
ROBOTICS ACADEMY: Drive Train Components
Bearings
Provide low friction over entire range of loads for low to
high velocities. May not be suitable for very high velocities.
Ball bearing: Moderate
load and some thrust.
Double ball: Flanks
designed to tolerate
moderate thrust.
Roller bearing: high
load and some thrust.
Tapered roller: High
load and thrust in one
direction.
Thrust bearings:
Designed to
support axial loads
Needle bearing:
High load, often ride
directly on the shaft.
Polished shaft.
ROBOTICS ACADEMY: Drive Train Components
Flexible shaft couplers allow misalignment
Accommodate
small alignment
errors
Universal joint
Allow modest
changes in shaft
direction
Constant velocity joint
Allow substantial
changes in shaft
direction
ROBOTICS ACADEMY: Drive Train Components
Flexible shaft mounts allow misalignment
Pillow block bearings allow mounts at ends of
a shaft to be misaligned by several degrees
Bearings with a concave race
permit dynamic alignment for
oscillating components
ROBOTICS ACADEMY: Drive Train Components
Converting circular motion to linear motion
Cam and follower: Can design
circular to cyclic linear mapping.
Requires force to keep follower
on cam.
Crank shaft and connecting rod: Nearly
sinusoidal linear motion. End of rod
must be confined to track or sleeve.
Rack and pinion: Non-cyclic,
linear relation between shaft
rotation and rack motion.
 shaft  rgear  v rack
A worm gear will also work

ROBOTICS ACADEMY: Drive Train Components
Inertial considerations: eccentricity & vibrations
m
r
Consider a wheel with a mass distribution that deviates
from perfect axisymmetry. Assume all of the out-of-balance
mass is replaced by an equivalent mass, m, at the outer
radius, r. The eccentric mass creates an unbalanced force:
F  mr 2
The force is transmitted to the structure, which
has a natural frequency of vibration.
 of structure response
Amplitude
T=
Amplitude if only driving force is considered
Why worry?
How bad can it be??
ROBOTICS ACADEMY: Drive Train Components
Inertial considerations: Flywheels
Flywheels are used on rotating machinery to smooth out jerky power sources
or provide a more constant speed during impulse loads.
Stored energy
Hoop stress
1 2
2
E  I ; I  mrmean
2
  r 2 2
(Safety consideration)


Downsides:
a) The energy stored by the flywheel has to come
from the motor at some point. Motors need to
accelerate more slowly.
b) Rotating machinery cannot be stopped as quickly.
Typical automotive flywheel
ROBOTICS ACADEMY: Drive Train Components
Basic calculations and unit conversions
N
r
 Fi  mvÝ
Forces on a component, including weight, must balance
Inertial forces are negligible for most FIRST robotic applications
Moments on a component must balance
Rotational inertial forces are negligible for many FIRST applications
i1
N
r
 M i  IÝ
i1
Torque=Moment=Force acting orthogonal to lever arm from 
center of rotation
Motor torque unit conversion example
f
M
= 5 lb x 1.2 ft
Motor torque
=5 lb
d
M =f x d
16 oz
1 lb
x
1.2 ft
12 in
1 ft
Conversion factors equal one (1.0)
=5 lb
16 oz
1 lb
x
1.2 ft
12 in
1 ft
Set so old units cancel top to bottom
Use the orthogonal force and distance
6.0 ft-lb = 80 oz x 14.4 in = 1152 oz-in