Lecture 2 Mechanisms & Machines · Gears, Pulleys, & Sprockets These three power train elements...
Transcript of Lecture 2 Mechanisms & Machines · Gears, Pulleys, & Sprockets These three power train elements...
Lecture 2Mechanisms & Machines
The Six Simple Machines
Lever Wheel andAxle Pulley
The Six Simple MachinesInclined Plane ScrewWedge
Simple machines:Gears
Why does a wind turbine need a
gearbox?
By the way…• Where is the safety harness• No fall protection• No eye or hearing protection• This subcontractor would be
removed from the site & possibly terminated
This person has a fun job
The gearboxes are big and they weigh a lot
Gears, Pulleys, & SprocketsThese three power train elements transfer energy through rotary motion.
• Change the speed of rotation• Change the direction of rotation• Change the amount of torque available to do work
Gears
A gear train is made when two or more gears are meshed
A gear train is a mechanism used for transmitting rotary motion and torque through interlocking teeth.
Driver gear causes motion
Motion is transferred to the driven gear
Gears
Mated gears always turn in opposite directions.An Idler Gear allows the driver and driven gears to rotate in the same direction.Mated gears always have the same size teeth (diametric pitch).
GearsThe rpm of the larger gear is always slower than the rpm of the smaller gear.Gears locked together on the same shaft will always turn in the same direction and at the same rpm.
Gear RatiosVariables to know
n = number of teethd = diameter
ω = angular velocity (speed)τ = torque
** Subscripts in and out are used to distinguish between gears **
4”
nin=din =ωin =τin =
62in.40rpm40 ft-lb
nout =dout =ωout =τout =
124in.20rpm80 ft-lb
Gear Ratios
out out outin
in in out in
n dGR1 n d
τω= = = =
ω τ
Equations to knowGR = Gear Ratio of the gear set
lbftlbft
−−
4080
rpmrpm
2040
.2
.4inin
6122
1
Gear Ratios
= =out
in
nGR1 n
What is the gear ratio between gear A and B?
=5 .42
12 1What is the gear ratio between gear B and C?
=20 45 1
What is the gear ratio between gear C and D?
=12 .620 1
= =out
in
nGR1 n
= =out
in
nGR1 n
Input gear
Gear Ratios
• • =0.6 0.42 41 1 1
What is the TOTAL gear train gear ratio?
What would the total gear ratio be if the last gear had 40 teeth?
• • =0.6 0.42 8 21 1 1 1
11
If gear A and D were directly connected to each other, what would the resulting gear ratio be?
=20 120 1
or = = =out
in
nGR 40 21 n 20 1
= =out
in
nGR1 n
Idler gears don’t affect GR!
Compound Gear Trains
The two middle gears share a common axle, so they rotate at the same speed.
This allows the final gear to rotate slower and produce more torque than if it were connected only to the driver gear.
Driver
Here, the two middle gears are connected to a common axle and rotate together
50 T40 T
20 T 10 T
40 410 1
=
AB
C
D
What is the gear ratio between gear A and B?
50 2.520 1
=
What is the gear ratio between gear C and D?
What is the gear ratio of the entire gear train?4 2.5 101 1 1
• =
1= =out
in
GR nn
1= =out
in
GR nn
out out outin
in in out in
n dGR1 n d
τω= = = =
ω τ
Pulley and Belt Systems
out outin
in out in
dd
τω= =
ω τ
.2
.6inin
rpmrpm
1030
d = diameter ω = angular velocity (speed) τ = torque
out
lbft
lbft
−
−
3118
55
What is the purpose/effect of each of these pulleys below?
Do you see something wrong with this pulley/belt arrangement below?
Sprocket and Chain Systems
out out outin
in in out in
n dn d
τω= = =
ω τ
1122
.5.1.3
inin
n = number of teeth d = diameter ω = angular velocity (speed) τ = torque
3in.
out1.5in.in
rpmrpm
4590
lbftlbft
−−
60120