Gears

Gears Documentation Blog Entry

 

In this page, I will describe:

1.     The definition of gear module, pitch circular diameter and the relationship between gear module, pitch circular diameter and number of teeth.

2.     The relationship between gear ratio (speed ratio) and output speed, between gear ratio and torque for a pair of gears.

3.     How I can design a better hand-squeezed fan, including the sketches

4.     How my practical team arranged the gears provided in the practical to raise the water bottle, consisting of:

a.     Calculation of the gear ratio (speed ratio)

b.     The photo of the actual gear layout.

c.     Calculation of the number of revolutions required to rotate the crank handle.

d.     The video of the turning of the gears to lift the water bottle.

5.     My Learning reflection on the gears activities.

 

 

1.    These are the definition of gear module, pitch circular diameter and the relationship between gear module, pitch circular diameter and number of teeth:

A gear module is the unit size indicating how big or small a gear. It can be defined as the ratio of the reference diameter of the gear divided by the number of teeth.

 

The pitch circle diameter (PCD) of a gear is the diameter of the pitch circle. A gear is a friction wheel with teeth, and the pitch circle corresponds to the outer circumference of the friction wheel and is the reference circle for determining the pitch of the gear teeth.


 

Relationship between gear module pitch circle diameter and no. of teeth

 

Gear module, m = Pitch circular diameter, PCD ÷ no. of teeth, z

 

2.    Below is the relationship between gear ratio (speed ratio) and output speed for a pair of gears.

 

Gear ratio is the inverse of speed ratio. If gear ratio increases, output speed for a pair of gears will decreases.

 

If the speed ratio is larger than 1.0, then the gear pair is operating as speed increaser. If the speed ratio is between 0.0 and 1.0, then the gear pair is operating as a speed reducer.

 

Below is the relationship between gear ratio and torque for a pair of gears.

When gear ratio increases, torque increases.

 

3.    Activity 1: lifting a water bottle using gears.

a.     Calculation of the gear ratio (speed ratio).

Since we had constructed a simple gear train,

 

Gear ratio = Number of teeth in output gear ÷ Number of teeth in input gear

                  = 40 ÷ 30

                  = 1.33

 

Speed ratio = Gear ratio ^ -1

                     = 0.752

 

b.    The photo of the actual gear layout.




 

Sketch of actual gear layout



c.     Calculation of the number of revolutions required to rotate the crank handle.

Distance travelled by the water weight = Distance travelled by the output gear = 200 mm

 

Diameter of the winch = 22 mm

                                       = 2.2 cm

 

Number of revolutions of the output gear = 20 cm ÷ (π × 2.2 cm)

                                                                        = 2.8937

 

Number of revolutions required to lift bottle = 2.8937 × 1.33

                                                                                        = 3.85

 

Actual number of revolutions required to lift bottle = 4

 

The theoretical number of rotations needed to lift the bottle 20 cm off the ground is not the same as the actual number of rotations. This is because of friction between gears, the board and screws. Other than that, the gear setup could have been further optimized to achieve better efficiency.

d.    The video of the turning of the gears to lift the water bottle.

 


 

Activity 2: Hand-powered fans

 

Sketch of the gear layout



Speed ratio

Gear ratio = (z₃/z₁) × (z₅/z₂) × (z₆/z₄)

                  = (10/20) × (9/20) × (9/20)

                  = 0.10125

 

Speed ratio = Gear ratio ^ -1

                     = (0.10125)^ - 1

                     = 9.88

 

Turbine rotations per crank

 

Theoretical no. of rotations = Speed ratio

                                               = 9.88

 

Total rotation of the turbine after 3 cranks = 29

 

Actual no. of rotations = 29 ÷ 3

                                       = 9.67

 

Hence, efficiency = (9.67 ÷ 9.88) × 100 %

                              = 97.9 %

Efficiency is not 100% as air resistance and friction create energy loss.

Video of the hand-powered fan in operation for one crank of the handle




Below is the proposed design to make the hand-squeezed fan better:

Changing the input gear to be bigger with more teeth and the output gear to be smaller with less teeth will improve the number of rotations per crank. This is because speed ratio is the inverse of gear ratio. So if the input gear has more teeth and the output gear has less teeth, the speed ratio will increase and hence increasing the number of cranks.

 


4.    Below is my Learning Reflection on the gears activities

During the practical, I learned many theories regarding gears and how different gears can be used for different scenarios. Before this lesson I merely thought of gears as objects that turn, nothing more.

 

As of the hands-on part of the practical, I mainly worked on the first activity, screwing on the screws and nuts to secure the gears to the board. Using the theories I had learned, I was able to discern if I should use the bigger or smaller input gear and what order the gears should go if I wanted the smallest gear ratio. However, I was perhaps too fixated on achieving the lowest gear ratio and overlooked the fact that it would take too much strength to turn the gear, and since the gear was 3D printed, it was not the most sturdy. As a result, I ended up breaking the handle of the gear. This, however, would not be the only thing my group would break as my groupmates in activity 2 would also break the fan blade by dropping it onto the ground.

 

When securing the gears I was constantly getting frustrated as the helen key we have been provided was too small to get a good grip on the screw. As a result the helen key will consistently move out of position when trying to screw on the screws onto the board.

 

Other than some minor issues which was resolved quickly, the practical went swimmingly for my group and I also had a blast working with gears.


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