Gears, Pulley Drives, and Sprockets

https://www.youtube.com/watch?v=D_i3PJIYtuY&feature=youtu.be

These 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 a mechanism used for transmitting rotary motion and torque through interlocking teeth. A gear train is made when two or more gears are meshed Driver gear causes motion Motion is transferred to the driven gear Gears Mating gears always turn in opposite directions. An Idler Gear allows the driver and driven gears to rotate in the same direction. Mating gears always have the same size teeth (diametric pitch). Gears

The 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 Ratios

Variables to know 4” n = number of teeth d = diameter w = angular velocity (speed) t = torque ** Subscripts in and out are used to distinguish between gears **

nin= 6 nout = 12

din = 2in. dout = 4in.

win = 40rpm wout = 20rpm

tin = 40 ft-lb tout = 80 ft-lb Gear Ratios

Equations to know GR = Gear Ratio

GR nd w t out  out in  out 1 nin d inwt out in

? 12 4in. 40rpm 80 ft  lb 1 6 2in. 20rpm 40 ft  lb 2 1 Gear Ratios

GR n 12 .6 What is the gear ratio out  between gear A and B? 1nin 20 1 5 .42 What is the gear ratio  between gear B and C? 12 1

20 4 What is the gear ratio  between gear C and D? 51 Gear Ratios Idler gears don’t affect GR!

What is the TOTAL gear 0.6 0.42 4 1    train gear ratio? 1 1 1 1

If gear A and D were directly GR n 20 1 connected to each other, what out  1n20 1 would the resulting gear ratio be? in

What would the total gear ratio be if the last gear had 40 teeth? 0.6 0.42 8 2 GRn 40 2    or out   1 1 1 1 1 nin 20 1 Gear Ratios – Compound Machines

•Used similarly to MA •Applies to torque instead of force

•In a compound machine, total MA and GR are products of components

•MA used only to calculate forces, not torques. •GR used only to calculate torques, not forces. Example Compound Machine •Here are 3 mechanisms in series: •#1 Wheel-axle •#2 Gear train •#3 Wheel-axle Example Compound Machine •Mechanism #1: Wheel-axle Example Compound Machine •Mechanism #2: Gear train Example Compound Machine •Mechanism #3: Wheel-axle Example Compound Machine Example Compound Machine Compound Gear Train

Driver 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. Compound Gear Ratios

D B C A 10 T 20 T 40 T What is the gear ratio 50 T between gear A and B? GR n 40 4 What is the gear ratio out  between gear C and D? 1 nin 10 1

GR nout 50 2.5  1 nin 20 1 What is the gear ratio of the entire gear train? 4 2.5 10  1 1 1

Pulley and Belt Systems

out in

Equations 2in. d w t outin out dinwt out in

6in. 30rpm 55ft lb 2in. 1 10rpm 18 ft lb 3

d = diameter ω = angular velocity (speed) t = torque Sprocket and Chain Systems

1.5in. 3in. in out

nd w t out out in  out ndin inwt out in

22 3in. 90rpm 120ft  lb 11 1.5in. 45rpm 60 ft  lb

n = number of teeth d = diameter ω = angular velocity (speed) τ = torque Comparing Pulleys and Sprockets

Pulley Sprocket Method of Transmitting Belt Chain Force Quiet, no lubrication No slip, greater Advantages needed, inexpensive strength Higher cost, Disadvantages Can slip needs lubrication, noisy Image Resources

Microsoft, Inc. (2008). Clip art. Retrieved January 15, 2008, from http://office.microsoft.com/en-us/clipart/default.aspx