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Planetary gear rule correction
- 1. For every symmetry in nature there is a corresponding law of conservation Emmy Noether It is about the conservation of energy. With one input at ‘a’ on the lever: The energy would be equal to ‘a’ at any point on the lever. The force would be inversely proportional to the velocity, and the torque is always equal at these points. d c b a "a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. Max Planck I would rather hear from you people, I’m 76. John
- 3. The planetary gear set is used in most automatic transmissions. The latest applications are in the development of CVTs. We are using them when we need a power- split scheme. When all 3 members are moving, the error becomes very observable. It is time we correct our analysis of torque and power distribution on a planetary gear set.
- 4. The current rule is: The torque ratio between the ring and sun is directly proportional to their radius. This is true for all rpm ratios. Wrong
- 5. Input Planet Carrier Output Sun Output Ring Planet set Planet carrier Planet gear Sun Ring I put a planet set from a 1972 Chrysler Torque Flight together with a pulley on the ring and sun shaft, and a parallel shaft to drive the planet carrier. Ring 62 teeth and sun 28. The object is to prove my theory that the torque is not always at the same ratio, but varies inversely with the rpm ratio.
- 6. Between the sun and ring are the planet gears. The planet gears are carried on their axis by the planet carrier. The sun, ring and carrier all share the same axis. The planet gears carry all the energy from one or two members to the other one or two members, depending on the application. I will be putting energy into the planet carrier. The energy will flow to the ring and sun via the planet gears. I will prove that you can vary the rpm ratio of the ring and sun by varying the torque ratio of the ring and sun. By adding and subtracting force on the ring and sun outputs you can vary their rpm. You can’t do it any other way.
- 7. Video of Torque vs RPM Torque Ratio is Not Constant Click the link to view my video John Marsha jammarsha@myfairpoint.net 603-826-9741 https://www.youtube.com/watch?v=PMk- ZDxJdHg Four more slides
- 8. The profession went astray with the equal force on the two sides of the planet gear, the ring side and the sun side. The force is equal relative to the pin on the carrier, the source. It was assumed to be equal on the ring and sun relative to their axis as well. Wrong. This false rule looks OK when we are using the planet set with one member fixed. Hence the false rule was certified. It will take a lot of thinking to shift this paradigm.
- 9. Force distribution at one to one. All three members are turning together and the planet gears are not turning on their axes. The force on the planet gear axis is equally split to its sides. The force on the ring and sun is equal relative to the axis of the planet gear, not the ring and sun axis. Thinking about a lever, the force is inversely proportional to the distance from the pivot. More important and germane to this issue is that the force is inversely proportional to the velocity ratio of the points. Conservation of Energy. Half of the force at the planet axis is worth less on the ring and more on the sun relative to their axis. At one to one, on the ring and sun, it’s equal torque not equal force.
- 10. 2 1 4 11 8 3 s p r This is a simple lever. If we put 3 lbs force at b, we should be able to measure 21 /4 lbs at a, and 11 /8 lbs at c. The arc at a, is ½ the arc at c. The velocity at a, is ½ the velocity at c. 3 c a b 11 8 21 4
- 11. The analysis becomes a lot simpler and easier to understand. 𝑓 𝑓𝑜𝑟𝑐𝑒, 𝑣 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝜔 𝑟𝑝𝑚, 𝑡 𝑡𝑒𝑒𝑡ℎ, 𝑒 𝑒𝑛𝑒𝑟𝑔𝑦, 𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 𝑅 𝑅𝑖𝑛𝑔, 𝐶 𝐶𝑎𝑟𝑟𝑖𝑒𝑟, 𝑃 𝑃𝑙𝑎𝑛𝑒𝑡, 𝑆 𝑆𝑢𝑛, 𝑇 𝑇𝑜𝑟𝑞𝑢𝑒, ℎ𝑝 𝑝𝑜𝑤𝑒𝑟 Power ℎ𝑝 𝐶 ℎ𝑝 𝑅 + ℎ𝑝 𝑆 ℎ𝑝 𝑅 ℎ𝑝 𝑆 Torque 𝑇𝑅 𝑇𝑆 ∗ 𝜔𝑠 𝜔𝑟 𝑇𝑆 𝑇𝑅 ∗ 𝜔𝑟 𝜔𝑠 𝑇 𝑓 ∗ 𝑟 Rpm 𝜔𝑃 𝜔𝑅 ∗ 𝑡𝑅 𝑡𝑃 ∗ 1 2 − 𝜔𝑆 ∗ 𝑡𝑆 𝑡𝑃 ∗ 1 2 − 𝜔𝐶 , 𝑣 𝜔 ∗ 𝑟 𝜔𝐶 𝜔𝑅 ∗ 𝑡 𝑅 𝑡 𝑠+𝑡 𝑅 − 𝜔𝑆 ∗ 𝑡 𝑆 𝑡 𝑠+𝑡 𝑅 𝜔𝑅 𝜔𝐶 ∗ 𝑡 𝑅+𝑡 𝑆 𝑡 𝑅 − 𝜔𝑆 ∗ 𝑡 𝑆 𝑡 𝑅 𝜔𝑆 𝜔𝐶 ∗ 𝑡 𝑅+𝑡 𝑆 𝑡 𝑆 − 𝜔𝑅 ∗ 𝑡 𝑅 𝑡 𝑆 Energy 𝑒𝑅 𝑓𝑅 ∗ 𝑣𝑅 , 𝑒𝑆 𝑓𝑆 ∗ 𝑣𝑆 , 𝑒𝑃 𝑓𝑃 ∗ 𝑣𝑃 , 𝑒𝐶 𝑓𝐶 ∗ 𝑣𝐶 , 𝑒𝑅 𝑒𝑆 𝑒𝑃 2 𝑒𝐶 2 Ring force 𝑓𝑅 𝑓𝐶 2 ∗ 𝑣𝐶 𝑣𝑃 ∗ 𝑣𝑃 𝑣𝑅 𝑓𝐶 2 ∗ 𝑣𝐶 𝑣𝑅 Sun force 𝑓𝑆 𝑓𝐶 2 ∗ 𝑣𝐶 𝑣𝑃 ∗ 𝑣𝑃 𝑣𝑆 𝑓𝐶 2 ∗ 𝑣𝐶 𝑣𝑆 Planet force 𝑓𝑃 𝑓𝐶 2 ∗ 𝑣𝐶 𝑣𝑃 , 𝑓𝑃 𝑓𝑅 ∗ 𝑣𝑅 𝑣𝑃 + 𝑓𝑆 ∗ 𝑣𝑆 𝑣𝑃 , 𝑓𝑅 ∗ 𝑣𝑅 𝑣𝑃 𝑓𝑆 ∗ 𝑣𝑆 𝑣𝑃 𝑓𝑃 2 Carrier force 𝑓𝐶 𝑓𝑆 ∗ 𝑣𝑆 𝑣𝑃 ∗ 𝑣𝑃 𝑣𝐶 + 𝑓𝑅 ∗ 𝑣𝑅 𝑣𝑃 ∗ 𝑣𝑃 𝑣𝐶 𝑓𝑆 ∗ 𝑣𝑆 𝑣𝐶 + 𝑓𝑅 ∗ 𝑣𝑅 𝑣𝐶