Week 9 - Analysis for the Top Gripper Sub-assembly

Note: This section was updated after week 12&13 to include the appropriate sub-assembly drawings for visual reference.

To reiterate, the purpose of this sub-assembly is to apply a torque to the lid of the jar/bottle to twist it off. It was determined earlier in the project, from a study of ergonomics (see Ref. 1 below ), that the necessary amount of torque required to twist off any lid (on beverages or food jars/bottles) is approximately 10 N-m. The way this sub-assembly functions to achieve that purpose is through a set of planetary gears that allow for the inner housing of the sub-assembly to rotate about the central axis, which causes the planet gears to rotate about their axis' and in turn allows the grippers to close in the on the lid and twist it off. The planetary gear system for our sub-assembly consists of one sun gear (input), three planet gears (idlers), and one ring gear (output). The grippers for our sub-assembly consist of three-Grade 8 steel hex head screws with a coupling nut on each one - this is to prevent the threads of the screws from scratching and damaging the lids of bottles/jars.

Motor Choice

To being the analysis for this sub-assembly, we started with choosing an appropriate motor. Originally, we were going to choose a high speed, low torque motor because we discovered those were the motors that were used in similar products. However, the reason we didn't go that route was that it was difficult obtaining one of those types motors because they were either (1) sold only through wholesale or (2) we'd have to buy a used one from an unaccredited seller i.e., random seller on eBay. Instead we chose a readily available motor from Amazon (Item 16 in BOM) because it already came with a gearbox, thus higher torque, but lower speed and one of our team members had experience using these types of motors. The motor we chose has a no-load speed of 220 RPM and a rated torque of 0.5 N-m.

Torque Analysis

Initial Torque from motor: T_1 = 0.5 N-m

Torque increase from gearbox (consists of one pair of spur gear - 96T & 12T - G.R. = 8 ): T_2 = 8*T_1 = 4 N-m

Torque increase from the planetary set of gears (sun gear - 24T, planet gear - 72T, ring gear - 168T - G.R. = 7): T_3 = 7*T_2 = 28 N-m

Taking into consideration a motor efficiency of 70% and gear efficiency of 90%, the final output torque is about 17 N-m, which exceeds the minimum required torque of 10 N-m. We didn't want to have too much of a significant torque difference because that would also cause our speed to decrease significantly.

Speed Analysis

Initial no-load speed from motor: n_1 = 220 RPM

Using the results from the torque analysis, the final speed of our sub-assembly, taking into consideration motor and gear efficiencies, is about 2.5 RPM. It should be noted that it might be a bit less than this due to friction between the gears (assuming there is friction even with the application of grease) and friction between the bottom gear plate (Item 4 on BOM) and the lid gripper housing bottom (Item 12 on BOM) (however, there is only 0.58 inches of contact between those two parts).

Gear Analysis - Forces and Stress

To determine the forces and stresses on the gears for this sub-assembly, Shigley's Mechanical Engineering Design 10th Ed., was referenced.

Gear Set 1 - 96T and 12T Gears with a diametrical pitch of 24 teeth/in (0.94 teeth/mm) Calculations

Note: That the transmitted load on 12T Gear is the same, but in the opposite direction.

Note: We did not attempt to use the AGMA Stress Equations because the book only provides the K-factors for certain types of metal gears and the AGMA standards for plastic gears does not list any K-factors, at least not any that we we're able to find.

Gear Set 2 - Planetary Gear Set - 24T, 72T, and 168T Gears with a diametral pitch of 28 teeth/in (1.1 teeth/mm)

Note: The SF on the sun gear is a bit concerning, so to increase its value, the face width will have to be increased to 33 mm to obtain a SF of 1.3.

Contact Ratio Analysis

Pages referenced for determining contact ratio from Shigley's Mechanical Engineering Design 10th Ed.

To determine the length of path of contact, the following reference was used:

https://www.kggear.co.jp/en/wp-content/themes/bizvektor-global-edition/pdf/1.9_Contact-ratio-and-Specific-sliding_TechnicalData_KGSTOCKGEARS.pdf

From these results, its evident that there is a minimum of 3 to 4 teeth in contact, thus the stress isn't just distributed to one tooth.

Analysis on the Planet Gear

The reason for this analysis on this specific gear is because when the gripper is applying the torque to twist off the lid, it has a normal that it applies to said lid and an equal opposite force on said gripper. Because of how the gripper is inserted through an off-center hole on the planet gear, there is the possibility that the force transmitted throughout the surface area of that hole will cause the gear to break. To determine if this was an actual concern, an FEA on the planet gear was conducted using Autodesk Inventor.

To begin the analysis, the force on the gripper must first be determined. This was achieved by dividing the torque of the planetary gear (17 N-m) by the distance from the off-center hole to the gear’s axis of rotation (0.023 m), giving us a force of 740 N. To convert this force to a pressure, the surface area of the off-center hole needed to be determined. The diameter of the hole is 0.00508 m and the height of the gear is 0.0254 m, thus its surface area is 4.05E-04 m^2.

Here are the results of the FEA on the planet gear from Autodesk Inventor:

The stress analysis indicated that the maximum stress on the off-center hole is 0.5 ksi, which would not be enough to cause any concern for the design and material option of the gear. Similarly, the displacement analysis indicated that the maximum displacement on the off-center hole is 1.8E-04 inches.

Reference 1: journal.iehfs.ir/article-1-268-en.html