Blog entry 2: Gears

This week, we learned about everything gears. I'm sure everyone is familiar with these wheels of teeth, chances are, everyone have seen and have an idea of how they work before, if you have ever seen a bicycle, you have definitely seen gears in action.

In a bicycle, the pedal is connected to the front gear and used to turn it. a chain connects the front gear to the back gear, or the cassette. So when the pedal is turned, it turned the back wheel and drive the bicycle forward. The cassette is an example of a compound gear, as you can see it is actually many gears, small to big, but only one gear is used at any one time. By changing the size of the gear used, we can adjust how many rotation of the back wheel will result from one rotation of the pedal.

That is only one of countless examples of gears in our life.

Okay, sure, so the cassette can change the ratio of rotations of back wheel : pedal, but by how much exactly? How does the people designed the bike determine how big the cassette should be? Or how many individual gears the cassette should have?

That's what we will find out in this blog.

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:

Gear module: the size of individual gear teeth, measured in mm. The larger the module, the bigger the gear. On a gear with constant perimeter, increasing the gear module will decrease the number of gear teeth, as each teeth are bigger. For two gears to be meshed together, they must have the same gear module, so the teeth can fit into each other.

Pitch Circular diameter: an imaginary circle that passes through the contact point between to meshing gears. The larger the pitch circular diameter, the bigger the gear. Another way the visualize pitch circular diameter is that it is the perimeter of two smooth wheels in contact with each other, with the same center as the gears, and the same point of contact.

The relationship between gear module (m), pitch circular diameter (PCD) and number of teeth (z):

m x z = PCD

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

Gear ratio = Number of teeth on output (follower) gear / Number of teeth on input (driver) gear

Gear ratio = z input / z output

Speed ratio = Speed of follower gear / Speed of driver gear

The lower the gear ratio, the higher the speed ratio.

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

Torque is the spinning force, calculated by multiplying the force applied on the gear and the radius of said gear.

A higher gear ratio on a pair of gears will result in a higher torque.

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

better:

While using the hand fan, one of the main problem we noticed is that the handle tends to get locked in place after 1 rotation, as the piece connecting the handle to the gear (black color piece in the sketch), is only the same length as the diameter of the gear plus the space in-between the gear and the handle.

When the handle is pushed all the way in, the input gear turn exact one rotation, resulting in the handle getting locked in place as the connector piece rests in a horizontal position. Since the piece is horizontal and there is quite a lot of friction between the gears, it is very hard to push or pull on the handle to push the connector piece up or down to continue spinning.

To counter this problem, we can make the connector piece slightly longer, so the input gear rotate a bit more than one rotation and the connector piece rests in a diagonal position so it is easier to continue turning.

Another way we can improve the fan is by increasing the gear ratio, which can be achieved by making Z1, Z2, and Z4 bigger, with more teeth and make Z3, Z5, and Z6 smaller, with less teeth. So the gear ratio increase, resulting in the fan blades rotating more times for every full rotation of the input gear.

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).

Available gears for us to use:

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 were only allowed to use one gear with handle, so we decided to use the 30T gear, because we want to maximize the gear ratio, so z input need to be as small as possible.

After trying several combinations, this is our final gear ratio

Gear ratio = 40/30 x 40/20 x 40/40 x 30/20 x 40/30 x 30/40 x 40/30 = 5.333333

Gear ratio = 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 the bottle needed to be raised = 200 mm

1 full rotation of final gear = 2 π r = πD = π(22)

No. of rotations of final gear = 200/π(22) = 2.894

Gear ratio = Input rotations / Output rotations

5.333 = Input rotations / 2.894

Input rotations = 5.333 x 2.894

Therefore, Input rotations = 15.433 = 15.4

Number of rotations needed by the input gear (gear with handle) for the bottle to be raised 200mm: 15.4 rotations

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

5. Below is my Learning Reflection on the gears activities

Before we do the Gears practical, we need to watch a series of 4 videos going through all the related concepts, including driver, follower, and idle gears, gear ratio, speed ratio, simple and compound gear train, etc. The videos are quite useful as it also cleared up some commonly misunderstood concepts and teaches useful methods to calculating certain things like gear ratio. So the videos really helped us to be more prepared for the practical.

The main part of the practical consists of 3 main parts: Completing a worksheet testing us on various concepts of gears, constructing a gear system to pull up a water bottle, and constructing a hand fan.

The first part was quite easy and didn't take us very long to go through the worksheet, as most of the questions can be found right in the videos which we have watched the night before. The worksheet also reinforce on some concepts we might have missed out watching the video and give us a chance to actually practice doing questions to test our understanding and clarify any doubts.

The second part of the practical is the most challenging, as we were giving various gears with different number of teeth, and we must use all of them to construct a system that will lift a bottle of water up 200mm using the least rotation of the input gear with a handle. This means we must achieve the highest gear ratio possible, so one rotation of the input gear will result in the most number of rotation of the final follower gear, lifting the bottle the largest distance. As we need to utilize all the gears, we struggled to come up with a configuration that will give us the highest gear ratio. After many tries, initially we come up with a configuration that give us a 17.78 gear ratio. We checked with Mr Chua but he said we could get even higher, so we went back to the drafts and try even more combinations. Our method is mainly a process of guesstimating, semi-randomly arranging the gears first, calculate the gear ratio, then see what changes we can make to increase the gear ratio, and recalculate again, then make some more changes and recalculate again, repeat until we felt we can't get any higher. Finally we come up with a gear ratio of 25.8, after which we tried a few more times and couldn't get any higher number so that's what we went with.

Little did we know our final gear ratio will be nowhere near the calculated gear ratio, as we forgot to account for the fact that our configuration may not be possible to install onto the provided board, as some compound gears do not fit into each other very well due to the other gear attached to it being an obstruction. The string tied to the final follower gear to tie the water bottle onto also proved to be an obstacle as it get caught into the gear before the final gear. As we were running out of time since we spend so much time trying to get the highest gear ratio, we could not take everything apart and re-design the entire thing, so we had to make do and try our best to re-fit the gears into a configuration that will at least work. So that's how we ended up with a gear ratio of only 5.33, a faaaaar cry from the original 25.8, which ended up requiring us to turn the driver gear a lot more to lift the water bottle 200mm. Even though this part did not went as expected, I still learn alot and most importantly, we recalculated the gear ratio so many times trying to optimized it I'm pretty sure we will see them in our nightmares now.

After we get started on the first experiment, we realized we need to split our manpower to complete everything on time. So me and Jeremy get started on assembling the hand fan while Jeevan and Yan Zhen finish the rest of the first experiment. The hand fan was quite easy as we were given a specific model to follow. The only problem comes when we get to the final step, putting the fan blades into the motor, which is when we realized the hole in the fan blades is way too small to insert into the turbine. After some quick panicking, we decided to very quickly assemble the spare set available, and by a miracle we managed to fit the fan blades into the motor just enough to make it run for a video.

The calculated gear ratio for the fan is 1/8, meaning for each rotation of the input gear, the output gear, connected to the fan blades, will rotate 8 times. In the slow-mo video we filmed, we counted about 7.5 rotations, which is abit lesser than the calculated value. We suspect it might be because of the friction between the gears, so turbine did not make a full 8 rotations.

Overall, I find this practical very useful, despite us achieving a pathetic gear ratio at the first experiment. It will definitely be useful in the future when we need to construct our project.