Blog 2, Gears

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:

   1. Calculation of the gear ratio (speed ratio)

   2. The photo of the actual gear layout.

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

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

5. My learning reflection of 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:

For the definition of a gear module, it is the unit size that indicates how big or small a gear tooth is. It is the ratio of the reference diameter of the gear divided by the number of teeth.

So in layman terms, a gear module refers to size of the individual teeth of a gear.

For the definition of the pitch circular diameter (PCD), It is the diameter of the imaginary circle that passes through the points where two interlocking gears touch.

The gear module, pitch circular diameter and the number of teeth are all related through the equation is

PCD = m x z

Where the m refers to the gear module & z refers to the number of teeth

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

First, gear ratio is the ratio of the number of teeth in the driven gear to the number of teeth in the driver gear (Output teeth to Input teeth).

On the other hand, the speed ratio is the ratio of the output speed to the input speed.

Therefore for a pair of gears, the lower the gear ratio, the higher the output speed. Similarly, the higher the gear ratio, the lower the output speed. Therefore, the gear ratio and the output speed have an inverse relationship.

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

Torque is the measure of twisting force, calculated as the product of circumferential force multiplied by the radius of the gear.

Therefore, a higher gear ratio would imply that the gear would produce a higher torque. Hence, the gear ratio is proportional to the torque it produces.

3. Below are the proposed design to make the hand-squeezed fan better:

This is the initial design of our hand-squeezed fan:

This is a proposed design to improve our hand-squeezed fan:

The change in this design is that the driver gear is changed to a gear with 30 teeth instead of 20. This new design is a better design as compared to our original, as the gear ratio is lower (higher speed ratio). This meant that the new fan design would rotate more times than our original ratio.

New Gear ratio = 10/30 x 9/20 x 9/20

= 0.0675

Thus, Speed ratio = 1/Gear ratio

= 14.815

Therefore, the new turbine will rotate almost 15 times when the input gear is rotated once.

4. Below are the 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).

First, my team analyzed the different types of gears provided. We were given many different gears with various amounts of teeth. We had a few idlers and come compound gears and using them, we had to calculate our gear ratio which produces the greatest torque. From our knowledge, we had learnt that the greater the gear ratio, the greater the torque. Hence, we had to make a gear ratio which is the largest possible.

These were the gears we were provided with:

1)Gear 30T with handle (1pc)

2)Gear 50T with handle (1pc)

3)Gear Compound 20T-40T (2pcs)

4)Gear Compound 20T-30T (1pc)

5)Gear Compound 12T-40T (1pc)

6)Gear Idler 30T (1pc)

7)Gear Idler 40T (1pc)

8)Gear 40T with winch (1pc)

We had to use one handle gear and all of the other gears as tasked by Mr Chua.

We calculated using the formula for gear ratio = Driven teeth/Driver teeth

40/30 + 40/20 + 40/40 + 30/20 + 40/30 + 30/40 + 40/30 = 5.33 (3 s.f.)

b. The photo of the actual gear layout.

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

Height of bottle raised = 200 mm

1 rotation of final gear = 2 π r = πD

Diameter of final gear, D = 22 mm

No. of rotations of final gear (Output RPM) = 200/π(22) = 2.9

Since Gear ratio = Input RPM / Output RPM,

5.33 = Input RPM / 2.9

Therefore, Input RPM = 15.457 = 15.5

Hence, number of revolutions required to rotate the crank handle = 15.5

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

5. Below is my Learning Reflection on the gears activities

This gears activity has actually helped me to learn a lot of things and how gears actually work. Initially before the practical, I thought that the gears are only there to help make things faster or exert more force. I had no idea that there were so many equations and principles behind these gears.

Even before the practical, we had to do the pre-prac activity which was simply watching 4 videos on how gears functioned. Although the videos were all similar, they did teach some important equations and concepts such as the gear ratio, torque, gear teeth and speed ratio. When I was watching the videos, I did not pay very good attention to them and realized I had missed out on some key information later on.

From the videos, I managed to learn that gears function based on the number of teeth they have and the size of each teeth (module). For gears with less teeth and smaller modules, they tend to turn faster with smaller torques. For gears with more teeth and bigger module, they tend to turn slower with greater torques. Gear ratio which was calculated with by the ratio of the driven gear to the driver gear, is an important relationship to determine the torque/speed of the gear. A gear with a larger gear ratio has greater torque and a gear with smaller gear ratio has greater speed.

During the practical itself, we had to go through the worksheet as a team. We had to use our knowledge from the videos we had watched and complete the worksheet together as a team. While doing the worksheet, I managed to learn some interesting concepts and relationships. I remembered about the PCD which means the Pitch Circular Diameter, which is related to the module and number of teeth, by PCD = m x z. There were many relationships we found between the qualities such as m, speed ratio, torque, PCD and z which are all related to one another, which made understanding about the gears easier. We also learnt about the difference between the simple gear train and the compound gear train. Simple gear train has an idler gear, while the compound gear train has the compound gear which serves different purposes. I also found out that the idler gear is used to make the driven gear and the driver gear turn the same direction.

After the worksheet, we began on the actual practical work, which was activity 1. Activity 1 is using the different gears given to move a water bottle of 600 ml with the least effort. For this to be done, we had to create a gear set-up with the greatest gear ratio, since a higher gear ratio produces a greater torque. Therefore, we first analyzed the different types of gears we were given and tried to segregate them as such that we obtained the greatest gear ratio. Since we had to use all of the gears, we had to think properly before carrying out the assembly. Since gear ratio is calculated by the number of teeth of driven gear/ number of teeth of driver gear, we realized that we have to ensure that the driven gear had more teeth than the driver gear. Therefore, our first calculation of the gear ratio came out to be 17.78, which we initially thought was the highest we could get. However, when we checked our calculations again, we realized it could be adjusted to be greater than before. So, after changing the positions of some of the idler gears and the compound gears, we managed to get a gear ratio of 25.8. This was indeed the highest gear ratio we could get after multiple tries and we thought it was good enough to move on with.

However, this was where we faced our first struggle. We realized that the board that we were provided with could not fit the gears properly. This was a huge problem for us as this meant that our gear ratio will have to be changed in order for the set-up to work. This would then mean we produce less torque. We had no choice, and therefore continued on with the construction of the set-up as we were running out of time. We ended up with a final gear ratio of 5.333, which was disappointing but at the same time, I am glad that we managed to finally make the set-up work. It was worth the trial and error of trying to get the optimum gear ratio and the construction of the gear ratio was a fun filled experience. Doing this activity has really made me feel more proficient in the use and concepts of how a gear works.

Finally, we moved on to activity 2, which was the construction of the fan. During this activity, we had split it up between our group. Yan Zhen and I were busy doing activity 1 while Jeremy and Anna were doing activity 2. Luckily we split the work between the team, so that we could complete it within the time period. The fan activity was also a struggle for us, as we had accidentally broken off one of the pieces while trying to assemble the fan according to the sketch. For the fan activity, we had to make the fan move as fast as possible, which meant a lower gear ratio. Following the set-up allowed us to obtain a gear ratio of 1/8, which meant that for every rotation of the driver gear, the turbine rotates 8 times. This was a good and accurate result, as it was similar to our actual gear set-up, which rotated about 7.5 times.

From both the activities, I managed to realize that the actual number of rotations for the gear is not always equal to the theoretical number of rotations calculated . When thinking about possible reasons, we realized that it is usually due to the friction that is between the teeth of the 2 interlocking gears. The loss of energy through friction is the reason why the actual and theoretical has slight differences. Overall, I am glad that I was able to do this practical as it has taught me a lot of concepts about gears. Learning about the gear ratio, speed ratio and other important factors would definitely be useful for me in my future workplace when needed.