foundations of physical science workshop: gears. gears cpo science
TRANSCRIPT
Foundations of Physical Science
Workshop: Gears
GearsCPO Science
Key Questions
How do gears work?
What is the Law of Gearing?
How can Gear Ratios be used to design machines?
Overview Build gear machines
Deduce the rule for calculating the number of turns for each gear in a pair of gears
Apply ratios to design machines with gears
Design a gear machine to solve a specific problem
Simple Machines Include: rope and pulley
wheel and axle systems
gears
ramps
levers
screws
Gears as Simple Machines
Simple machines can change the direction and/or magnitude of an Input Force
What are the variables? Teeth – Each sized
gear has a particular # of teeth. How many does each size have?
Turns – Each gear turns an exact amount of times, which we can count. How many times does each one turn?
Gear Investigation #1 Build 3 Gear
machines Top Gear – Input
Gear
Bottom Gear – Output Gear
Looking at the Results Can you derive a mathematical
formula which relates the # of turns of the Input Gear to the # of Turns of the Output Gear?
What is the relationship?
Use the # of Turns
Use the # of Teeth
Mathematical Relationship (Input gear turns x Input gear teeth) = (Output
gear turns x Output gear teeth)
Make the equation easier to use by substituting 1.Let Ni = # of turns of the Input gear2.Let Ti = # of teeth of the Input gear3.Let No = # of turns of the Output gear4.Let To = # of turns of the Output gear
5.Ni x Ti = No x To
The Law of Gearing
Ni x Ti = No x To
Can we write it another way?
Complex Gear Machines Make a machine that
uses at least 2 pairs of gears- Not this one--- make your own
Record the position and # of teeth on each gear in the Data Table
Record and count how all the gears rotate
Use what you have learned and the table to work out the gear ratios
Gear Assembly for Complex Machine
Looking at the Pairs of Gears Use Table 2 to figure out how to
calculate the final gear ratio
Final Gear Ratio Each pair of
gears has a gear ratio
This ratio (fraction) can be reduced
There can be more than two pairs of interfacing gears in total
Find the Gear Ratios of all pairs
Final Gear Ratio Reduce each Gear Ratio fraction from Table 2
12:24 = 12/24 = 1/2
Multiply all Gear Ratio fractions
½ x ½ = ¼ = 1:4
This is the Final Gear Ratio
1:4 or 4:1? The gear ratio depends on what gear you use as
input and what gear you use as output.
If the final gear ratio fraction is less than 1, like 1:2 = ½, the output gear turns less than the input gear. This is used for power, like when using a low gear to go uphill on a bike.
If the final gear ratio fraction is more than one, like 4:1 = 4/1, the output gear will turn more than the input gear. This is used for speed, like using a high gear when going really fast downhill on a bike.
Designing Gear Machines What is the objective? Speed vs. Power
What is the desired Final Gear Ratio? – factor it to lowest possible values
Look at the gears you have to work with
Use the available ratios to get the final gear ratio you need
How about spin direction?
Factoring Gear Ratios Example
Gear Ratio Desired – 6:1
1.Factor 6/1 3 x 2 = 62.Check Available Ratios – 1:3, 1:2, 2:3,
3:1, 2:1, 3:23.Is it possible? Yes 3/1x 2/1= 6/1= 6:14.Attach Gear pairs that give desired
Final Ratio
5.It may require more than two pairs of gears
How Can You Make-9:1
4:1
18:1
The highest possible ratio with the gears provided
3/1 x 3/1 = 9/1
2/1 x 2/1 = 4/1
3/1 x 3/1 x 2/1 = 18/1