Posts

Calculating idler gear shaft deflection angle using Castigliano's theorem

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  During my work on tractor transmission development, I frequently used formulas from engineering textbooks to evaluate shaft deflection and angular rotation. Castigliano's theorem was particularly useful because many common loading configurations had already been covered in my university textbooks. However, I encountered a loading configuration during idler gear development that I could not directly find in my reference materials. I needed to calculate the angular deflection at a bearing location, so I derived an expression using the principles of Castigliano's theorem. This post documents the engineering problem, the calculation process, and why the resulting angular deflection was important for the bearing design. 1. Why Was Deflection Angle Important? The idler gear shaft had to fit into a limited space within the tractor transmission. The idler gear received an external force from its mating gear while transmitting power through the gear train. The shaft was supported by b...

How profile shift affects gear addendum and tip diameter

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During my work in transmission research and development, I often studied engineering formulas to understand how they were derived rather than simply memorizing them. When I encountered a formula in a technical reference book, I liked to work through the derivation myself whenever possible. This approach helped me understand the underlying principles, remember the relationships more effectively, and apply them to different engineering problems. While studying profile-shifted gears, I became curious about why the addendum and tip diameter of one gear could depend on the profile shift coefficient of its mating gear, as well as the center distance correction coefficient. Instead of accepting these relationships as given formulas, I used basic gear geometry to investigate why they occur. This post documents that derivation and the geometric relationship behind the result. 1. Understanding the Gear Geometry A profile-shifted gear is generated with a profile shift that changes the position of...

Deriving the working pressure angle of a gear

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During my work in transmission research and development, I often tried to derive engineering formulas myself rather than simply memorizing them from reference books. When I understood how a formula was derived, I found it easier to remember and apply the underlying principle to other engineering problems. I therefore encouraged junior engineers in R&D to work through formulas themselves whenever possible. The working pressure angle of a gear was one example that interested me. Gear design references provide formulas for calculating the working pressure angle, but I wanted to understand the geometric relationship behind them. In this post, I explain how the working pressure angle can be derived from the relationship between the base diameter, reference diameter, and working pitch diameter. 1. Reference pressure angle and working pressure angle When two gears mesh, it is important to distinguish between the reference pressure angle and the working pressure angle. The r...

Ads not showing and debugging

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One day, all the ads in my K-Pop Sudoku app suddenly stopped working. The day before, everything had been working normally. But when I tested the app again, the banner area was empty, and the rewarded ad button remained disabled because the ad had not loaded. I had not changed the code or installed any new packages. Banner, interstitial, and rewarded ads had all been working before, so I initially had no idea what had gone wrong. In this post, I will share how I investigated the problem, created a minimal test app, compared the error logs, and eventually got the ads working again. My development environment The project used the following environment: Expo SDK: 54.0.23 React Native: 0.81.5 react-native-google-mobile-ads : 16.0.0 Expo bare workflow, using the TypeScript template and npx expo prebuild The screenshot below shows what I saw when the ads stopped working.  Banner area empty, rewarded ads not loaded (if not loaded, gray inactivated button)  Starting with the obvious c...

Rewarded Ads logic and debugging

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While developing and debugging my K-Pop Sudoku app, I implemented a hint feature that lets users reveal one hidden Sudoku number after watching a rewarded ad. The app was built with Expo's bare workflow and React Native. I used react-native-google-mobile-ads to integrate Google AdMob rewarded ads. The basic idea was straightforward: when a user taps the Watch Ad button in the hint modal, the app displays a rewarded ad. After the user earns the reward, the hint modal closes and one randomly selected empty cell reveals its correct Sudoku number. However, getting this flow to work reliably took more debugging than I expected. I encountered two main problems: the first reward was not applied correctly, and the rewarded ad instance needed to be recreated before another ad could be shown. My development environment This was the environment I used for the project: Expo SDK: 54.0.23 React Native: 0.81.5 react-native-google-mobile-ads : 16.0.0 Expo bare workflow, using the TypeScript temp...