Gear Train

Gear Train Assembly

Design Overview

The gear train subsystem transmits power from the weights and winding subsystem to the rest of the clock. The pendulum and escapement help regulate the rate at which the weights transmit power to the rest of the gearbox, thus maintaining a speed at which the shafts of the gearbox spin. The gear train needed to have the correct gear ratios to help the system correctly tell the time given our overarching functional requirements of accurately keeping time. This page outlines the decisions, process, and outcomes of the gear train subsystem.

Background Research

We first began researching how clocks function and looking into the gears required to make the clock operate. We gained much inspiration from these pictures and resources on how to overlay the hour hand with the minute hand while still integrating with the other subsystems of the clock. From these images, we determined having multiple shafts inside a gearbox would be the best way to help transmit power.

We also ended up taking apart a small pendulum cuckoo clock to inspect how the gearbox was organized in layout and the size of the components in the gearbox. The gearbox and shafts looked similar in organization to the images below.

Since our escapement wheel does one revolution every 30 seconds, we had to make sure we could have our main shaft revolve once every hour (3600 seconds) and our hour hand shaft revolves once every 12 hours (43200 seconds). This in turn affects our gear ratios. As opposed to the usual gear ratio of 720:1 for a standard 2-second period (or rather an escapement that does one rotation every 60 seconds), we had to double the gear ratio to adjust for our 1-second period. Thus, our gear ratio needed to be 1440:1.

Design

Creating the Gear Ratios

As stated earlier, we knew that we needed to achieve a 1440:1 gear ratio between the escapement wheel and the clock face to track time. The issue was on what gears we would use for transmitting power between the other subsystems of the clock. We first looked into gears that we would be able to buy online to reduce manufacturing time and imprecision. This started to become a problem as we determined the smallest gear we could buy was 15 teeth, which would mean other gears in the system would be bigger than what is possible to buy. As a result, we decided to manufacture our own gears. Even though our gears were smaller than if we had bought them online, the biggest gear we had was a 60-teeth gear with a diameter of 7.5". While our gear train originally used 2 plates, because of shafts interfering with gears on other shafts, a third plate was necessary to take advantage of the 3D space and allow the centers of our gears to be the correct distance from each other.

To determine the placement of the shafts we used the gear center distance equation shown below:

The equation gives the distance the centers of the meshing gears should be in inches. The additional 0.008" is used to reduce friction between the gears to make them more efficient and avoid grinding between the gears. Placing the escapement, main, and winding shafts was also informed by the necessity of centering them in the clock. For the escapement shaft, the pendulum needs to be centered to give it the most area to swing in and thus needs to be centered. Centering the main shaft is necessary because we wanted the clock face to be in the center of our structure. The winding shaft is centered because we wanted the distance of the ropes from the winding shaft to their corresponding pulley to be equal.

We wanted to minimize the number of shafts in our gearbox to simplify the system and not introduce new areas of complexity. Mimicking the images and other clock gearboxes resulted in us needing 7 shafts, 1 main shaft, 1 escapement shaft, 1 cannon tube countershaft, 2 shafts for the winding mechanism, and 3 countershafts. We selected hex shafts to turn the gears as opposed to using clamping hubs, keyed gears, or another locking method. To secure the gears along the shaft and make sure they mesh properly, we cut divots into the shaft and used retaining rings, additionally because of their small size to reduce the chance of accidentally creating interference.

To integrate the winding mechanism we included a coupling shaft to transmit power from the winding shaft to the main shaft, and a bearing at the top of the back plate to mount the winding shaft at the correct distance to mesh with the coupling shaft. We placed the escapement shaft at the bottom of our geartrain because beneath our gear train is where the pendulum swings and this allowed for the escapement to mesh with the escape wheel.

Feasibility

After designing the gear train, we had to determine what to use to physically build it. With a budget of $300 and knowing some of it would be spent on the structure, pendulum, and winding mechanism, we were constrained by cost. Additionally, we wanted our gear train to fit in the structure while leaving enough space for the pendulum to swing and weights to fall on the sides so the geartrain was constrained to 6" x 12" x 14".

While we wanted to use manufactured metal gears for their efficiency we quickly found that they were way out of our budget. Also, the smallest gears we found had too many teeth. Therefore, to get the desired gear ratio, some of our gears would be too big to satisfy the size constraint. From this, we determined it would be better to manufacture our own gears since we could dictate the number of teeth and the diametral pitch of the gears. This allowed us to make the gears smaller to satisfy the size constraint.

Since we decided to manufacture our own gears, the question remained of how we were going to manufacture our gears. We looked at a variety of different materials for our gears. Metal was unnecessarily heavy and hard to work with because our largest torque is low at ~2lb-in meaning our gears didn't need to be too strong and the water jet in our shop can be inaccurate depending on stock thickness. Since we wanted our gears to be 1/4" thick for them to consistently mesh, our shop's waterjet would make inaccurate cuts affecting our gears' ability to mesh. We didn't want to use wood because of the high friction of wood on wood. We considered acrylic but we would have to laser cut the gears which would cause microfractures and cause sudden breaks if we were to use it in our gear train. Delrin seemed to be a good material however our shop prefers we don't laser cut delrin. Finally, we settled on 3D printing our gears. In our research, we saw that hobbyists and other clockmakers make their own custom gears by woodworking or 3D printing. From our experiences, we were taught not to 3D print our gears, but in this instance, to manufacture our own custom-sized gears, this seemed like the most feasible option available to us. To print our gears, we used a Stratasys printer, a precise printer that is able to print using ABS a lightweight and durable plastic.

Determining Failure Points

While ABS is a durable material, we were concerned about our gears, specifically gear teeth, breaking. Using the Lewis equation, we determined the stress on the gear teeth based on the most torque experienced by one of the gears. Since the torque is based on the winding shaft, and the only gear reductions after the winding shaft are on the cannon tube countershaft and cannon tube gear, the cannon tube gear experiences the greatest torque in our gearbox system.

We used a Matlab script to calculate the stress experienced by the cannon tube gear. Firstly, we found the torque from the winding barrel. Then using the gear reduction of the cannon tube itself and its countershaft, we found the max torque in the system (the torque on the cannon tube gear). From the max torque, we found the tangential force on the cannon tube gear by dividing it by the radius. Through research, we found the Lewis form factor to use in our equation. We already knew the face width, or gear thickness, of our gears and the diametral pitch. Using all these variables and the tangential force, we found the maximum stress experienced by a gear tooth in our gear train. We then compared this against the ultimate tensile strength of ABS and found that the max stress experience was well under it. The calculated factor of safety is 1865.

Manufacturing

Breaking down the in-house manufactured components of our geartrain, we have the gears, gear plates, shafts, and clock hands. We 3D printed all our gears on the Stratasys printers. The gear plate profiles as well as the standoffs, support, and preliminary bearing holes were waterjet. We press-fit the bearings so the bearing holes had to be precise and we didn't want to depend on the water jet for accuracy because of the varying kerf due to material thickness.  To get the bearing holes within tolerance we used the CNC functions on the manual mills. For the other gear plate holes, we used the manual mill to drill them to size. We decided to fasten the plates together by threading the holes in the middle plate because the longest bolts we had were 2"; the gear plates were 0.25" thick and the spacing between each plate was 1.5". To cut our hex shafts to size and create divots for retaining rings to lock our gears along the shaft, we used the lathe. Finally, we also waterjet the clock hands.

Outcomes and Conclusions

While we thoroughly thought out the design and manufacturing methods, we realized there are some things that could be improved or done with more time. Since our gears are 3D printed, they're less efficient. If we were able to design around or had access to smaller metal gears we could purchase, our gear train would be more efficient. When assembling the gear train, we realized we could have paid more attention to the CAD. The escape gear was not fully contained in the gear plate so when we tested the gear train it rubbed against the surface we were resting it on. Finally, if given more time we could have run FEA on the gears to see if they would have failed because of stress or strain. However, this seemed redundant after creating our Matlab script which already identified when the gears would fail under stress.

Overall, we were able to sufficiently create the gear train with the correct gear ratio and were able to connect well with the other subsystems of the clock. Since the gear train was the subsystem that served as the point of integration, the gearbox was vital in making sure that the clock could function regardless of correctly keeping time or not.