Planetary gear systems, also known as epicyclic gear systems, are important components in modern engineering. They are useful for speed variation and can be found in everything from automatic car transmissions and industrial food mixers to operating tables and solar arrays. With four core components — the ring gear, the sun gear and the planetary gears connected to the carrier — the idea of calculating the gear ratio of a planetary system may sound daunting.
However, the single-axis nature of the system makes it easy. Just be sure to note the state of the carrier in the gear system. When calculating planetary or epicyclic gear ratios, first note the number of teeth on the sun and ring gears. Add them together to calculate the number of planetary gear teeth.
Following this step, the gear ratio is calculated by dividing the number of driven teeth by the number of driving teeth — there are three combinations possible, depending on whether the carrier is moving, being moved or standing still. You may require a calculator to determine the final ratio. To make calculating planetary gear ratios as simple as possible, note the number of teeth on the sun and ring gears.
For example, if the sun gear has 20 teeth and the ring gear has 60, the planetary gear has 80 teeth. The next steps depend on the state of the planetary gears connected to the carrier, although all use the same formula. Calculate gear ratio by dividing the number of teeth on the driven gear by the number of teeth on the driving gear.
If the carrier is acting as the input in the planetary gear system, rotating the ring gear while the sun gear is still, divide the number of teeth on the ring gear the driven gear by the number of teeth on the planetary gears the driving gears. If the carrier is acting as the output in the planetary gear system, being rotated by the sun gear while the ring gear stays still, divide the number of teeth on the planetary gears the driven gear by the number of teeth on the sun gear the driving gear.
If the carrier is standing still in the planetary gear system while the ring gear rotates the sun gear, divide the number of teeth on the sun gear the driven gear by the number of teeth on the ring gear the driving gear. Blake Flournoy is a writer, reporter, and researcher based out of Baltimore, MD. Working independently and alongside professors at Goucher College, they have produced and taught a number of educational programs and workshops for high school and college students in the Baltimore area, finding new ways to connect students to biology, psychology, and statistics.
They have never seen Seinfeld and are deathly scared of wasps. About the Author. Copyright Leaf Group Ltd.Documentation Help Center. The Compound Planetary Gear block represents a planetary gear train with composite planet gears.
How to Calculate Gear Ratios and Torque
Each composite planet gear is a pair of rigidly connected and longitudinally arranged gears of different radii. One of the two gears engages the centrally located sun gear while the other engages the outer ring gear. The figure shows the equivalent circuit for the structural component.
To increase the fidelity of the gear model, specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed to be negligible. The block enables you to specify the inertias of the internal planet gears only.
To model the inertias of the carrier, sun, and ring gears, connect Simscape Inertia blocks to ports CSand R. You can model the effects of heat flow and temperature change by exposing an optional thermal port. To expose the port, in the Meshing Losses settings, set the Friction parameter to Temperature-dependent efficiency. The Compound Planetary Gear block imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel planet :.
N R is the number of teeth on the ring gear. N P2 is the number of teeth on planet gear 2. N P1 is the number of teeth on planet gear 1. N S is the number of teeth on the sun gear.
The four degrees of freedom reduce to two independent degrees of freedom. The gear ratio g RP must be strictly greater than one. For more information, see Model Gears with Losses. Coulomb friction slows down simulation.
For more information, see Adjust Model Fidelity. Thermal conserving port associated with heat flow. Heat flow affects gear temperature, and therefore, power transmission efficiency. This port is exposed when, in the Meshing Losses settings, the Friction parameter is set to Temperature-dependent efficiency. Fixed ratio, g RPof the ring gear to the planet gear. This gear ratio must be strictly greater than 1. Fixed ratio, g PSof the planet gear to the sun gear.
This gear ratio must be strictly greater than 0. Temperature-dependent efficiency — Transfer of torque between gear wheel pairs is defined by table lookup based on the temperature.
Constant efficiency — Related parameters are exposed.But what if you need more than 7x faster? Or what if you need a really strong moving part? You can achieve this by stacking the gears in a certain way, called compound gears. Below is a slightly-modified diagram of our Nothing But Net flywheel, which used compound gears to get the flywheel spinning fast enough to launch the NBN balls:.
The drive axle on the left had 2 motors, top and bottom, with a tooth gear; the output axle on the right has a tooth gear and the flywheel. The magic happens on the axle s in the middle of the sandwich. The key to compound gears is putting 2 gears of different sizes on the same axle, as shown above a tooth gear on top, being driven by the tooth gear, and an tooth gear below it, driving the tooth gear on the flywheel axle.
For compound gears, we just calculate this same gear ratio for each pair of gears however many pairs you haveand then multiply them together, achieving the same answer as shown in the example above:. The nifty thing about compound gears is that you can stack them up in many different combinations, and by using even more than 3 axles, you can achieve very high speed or very high torque.
Notice I said high speed OR high torque. And, as I mentioned in my previous post about how motors workeven when you pick one of these, there is a limit to how far you can go. What will happen if you try to push the motors too far? Motor Overload aka Motor Stall. They will just stop, or they will work for a short period of time, and then fail. My next post is going to be about motor overload, so stay tuned!
Coach's CornerMechanical. Renegade Robotics. Below is a slightly-modified diagram of our Nothing But Net flywheel, which used compound gears to get the flywheel spinning fast enough to launch the NBN balls: The drive axle on the left had 2 motors, top and bottom, with a tooth gear; the output axle on the right has a tooth gear and the flywheel. Share this post:. Coach's CornerMechanical gears mechanics. Generic selectors.
Exact matches only. Search in title. Search in content.Related Resources: gears. Gear Design and Engineering. S is negative when secondary and initial drivers rotate in opposite directions. Formulas in which S is used, give speed relationship between follower and the initial driver. All Calculators require a Premium Membership.
Direction of Rotation.
Iif the calculated result is negative, the driver and follower will rotate in opposite directions; otherwise, a non-negative answer means tha both will rotate in the same direction. Figures 19 - 22 are used to obtain the speed ratios when there are two driving members rotating at different speeds. These are Compound Drive types. Planetary Bevel Gears.
The planet gear in Figure 23 rotates about a fixed bevel gear at the center of which is the driven shaft. Figure 24 illustrates the Humpage reduction gear. This is sometimes referred to as cone-pulley back-gearing because of its use within the cone pulleys of certain types of machine tools.
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Gear ratios and compound gear ratios
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Gear Ratio Calculator
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By joining you are opting in to receive e-mail. Promoting, selling, recruiting, coursework and thesis posting is forbidden. Students Click Here. Related Projects. I am trying to calculate the first gear ratio of a compound Simpson gear set. Power is transmitted thru the front planetary ring gear 66 tooth. The output shaft is splined to the rear planetary ring gear 66 tooth and the front planetary carrier. The sun gear is common 34 Tooth on each end.In the theory of mechanics, torque is a twisting force applied to an object.
The force is applied by a lever which can be real or imaginary; the longer the lever or greater the force, the greater the torque. You express the units of torque as the length of the lever times force, with examples being foot-pounds or newton-meters. Gears are useful for multiplying or dividing torque, whether the gears mesh directly or through a belt or chain; the ratio of the size of the gears determines whether they increase or decrease torque.
Multiply the force acting on the first gear by the first gear's radius. If, for instance, a force of 4, newtons acts on the gear, and it measures 0. The gear turns with newton-meters of torque. Divide the second gear's radius by the first gear's. If the second gear, for instance, measures 0. The system's gear ratio is 2-to This is the gearbox's output torque. This article was written by the It Still Works team, copy edited and fact checked through a multi-point auditing system, in efforts to ensure our readers only receive the best information.
How to Calculate Planetary Gear Ratio
To submit your questions or ideas, or to simply learn more about It Still Works, contact us. Step 1 Multiply the force acting on the first gear by the first gear's radius. Step 2 Divide the second gear's radius by the first gear's. About the Author This article was written by the It Still Works team, copy edited and fact checked through a multi-point auditing system, in efforts to ensure our readers only receive the best information.The gear ratio refers to the number of times the ring gear spins compared to the number of times the pinion gear spins.
This sounds easy, but when it comes to figuring out the gear ratio, how can you be sure you have the right numbers for your calculations? The surefire way is to go inside, wash your hands, and use our free online calculatorand take out all the hassle!
If the gear ratios are off, that can lead to engine trouble, seizure of the engine, increased fuel consumption and other road hazards. Therefore, it is important to know your proper gear ratios, not only at low gears but also as you get the engine to higher gears.
If the gears spin too fast, what could happen could spell total disaster. While you are at it, take a look at our RPM Calculator. Gas powered engines are loud, so instead of risking having ear trouble while calculating or possibly dropping your calculator into the engine and watching it shatter, instead do it in the safety of sitting at your computer desk and write in the numbers instead.
Calculations are simple. Within seconds, you will have your proper gear ratio in hand. Why not take our gear ratio calculator and introduce it to all of your do-it-yourselfer friends by posting it on Facebook, Twitter or Digg and having them figuring out their gear ratios from visiting your page?
Another option is to download a widget and paste it on your website, which would be a nice bonus for people who already like fixing up cars and making sure that their gear ratios are correct. So use our free calculator and get the results you need with no mess and no oily hands. Let's be honest - sometimes the best gear ratio calculator is the one that is easy to use and doesn't require us to even know what the gear ratio formula is in the first place!
But if you want to know the exact formula for calculating gear ratio then please check out the "Formula" box above. You can get a free online gear ratio calculator for your website and you don't even have to download the gear ratio calculator - you can just copy and paste! Click the "Customize" button above to learn more! Calculator Pro Calculators. Ring Gear:. Pinion Gear:. Thank us with a "Like":. Need multiple calculators? Not what you're looking for?
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