Gears

Hello and welcome to my second blog on gears!

In this blog, 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 gears to lift the water bottle

5. My learning reflection on the gears activities.

Definition of gear module, pitch circular diameter and the relationship between gear module, pitch circular diameter and number of teeth

Gear module: refers to the size of the gear teeth. It has a unit of mm and the larger a module number, the larger the size of the teeth. Gears that mesh together have the same module.

Pitch cicular diameter: refers to the imaginary circle that passes through the contact point between two meshing gears. It represents the diameters of two friction rollers in contact and moves at the same linear velocity.

Relationship between gear module (m), pitch circular diameter (PCD) and number of teeth (z) can be represented using the equation m= PCD/z

Relationship between gear ration (speed ratio) and output spped for a pair of gears

Gear ratio = speed of output gear / speed of input gear

Relationship between gear ratio and torque for a pair of gears

As the gear ratio increases the torque for the pair of gears increases

This relationship helps us in activity 1 where we lift water using gears. With faster moving output gear speeds, the torque generated by the output gears increase too, allowing us to use lesser effort to raise the bottle of water.

Proposed design to make the hand-squeezed fan better

One slightly more obvious improvement in the design on the fan can be to decrease the gear ratio.This means that the input gear would be bigger while the output gear will be smaller. When more force is applied, the fan would be spinning at higher speeds due to the output gear being the smallest.

Adding lubrication, like grease, would also help the gears to spin faster and thus sppin the fan blades faster.

Description on how my practical team arranged the gears provided in the practical to raise the water bottle

a. Calculation of the gear ratio (speed ratio)

Essentially, the gear ratio can be calculated by multiplying the fractions together, giving us a relatively high gear ratio of 8.89!

b. The photo of the actual gear layout

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

Number of total revolutions = 61

Length of rope = 105cm

61(2ℼR) = 105

R=0.274

Measured winch radius = 5.7/ 2 = 2.85cm

d.Video of the turning of gears to lift the water bottle

As seen in the video the gears are able to rotate relatively smoothly and are rarely obstructed by other factors such as the gears being 3D printed or due to wear and tear of the gears after some use.

Learning reflection on gear activities

Learning gears was slightly more challenging as compared to laser cutting. There were many more calculations and meanings of words that we had to learn and understand. For example, we learnt that a group of gears can be used to change each other's speed, torque and rotation. We also learnt terms such as teeth, pitch circular diameter and torque.

Furthermore, there was much confusion on several equations such as how to calculate gear ratio or how to find out the relation of speed ratio with torque, number of teeth and pitch circular diameter. While trying to calculate the gear ratio for some of the activities and questions, a few groups did not know if the formula was number of teeth of driver gear divided by the number of teeth of follower gear or the other way around. After Dr Noel went through on the white board on how to simply calculate gear ratio, our doubts were all clarified and we could do the questions given to us, including the quiz with ease.

I felt that activity 1 was definitely the biggest challenge for us in the practical. It took us several tries to calculate the highest gear ratio that we possibly could. We had to think of reasons such as why can or why can't we put several gears in specific positions, maybe the handle would be obstructed by other gears or it might lower the gear ratio. 

There were also some points where we resulted in trying our luck on calculating the gear ratio by doing it randomly as we felt so helpless while trying to figure out how these equations worked. However, we pressed on and found out different methods in which we could increase our gear ratio. One such method was understanding how the gear works. While being so engaged in trying to find the highest gear ratio, we were definitely mind blocked to a certain extent which prevented us from discovering the solutions that were right beneath our noses. When we decided to stop for a moment and let our minds rest, we found out that the gear ratio can simply be increased by flipping the gears around! This made a huge difference as the compound gears made a huge impact on the gear ratios due to the fact that we can place pretty much the smallest gear followed by the largest gear that we have. I felt that my group did a decent attempt at calculating the gear ratio, however, I believe that with stronger knowledge in this "subject", we will be able to calculate the highest possible gear ratio with ease in the future.

Lastly, the gears practical was interesting and engaging as it helped us to apply mathematical concepts to gears with more meaning. It has also allowed me to see my difficulties in a different perspective. When I am stuck on a problem, I learnt that there are only 2 ways I can go. One, to take a break and two, to look at the big picture. If I am going to try and solve a problem without taking any initiative, the problem will simply never be solved. Thats all for my reflection, hopefully I will be able to somehow apply these concepts to any future or upcoming projects.