Gear ratios gear types bearings materials lubrication interfaces etc. Epicyclic gear train problems and solutions pdf best of all, they are entirely free to find, use and download, so there is no cost or stress at all. In terms of coupled pgts, the torque equilibria at the cut free couplings are to be consi. For convenience, lets denote r, s, and p as the number of teeth on the gears. Planetary gear trains provide high power density in comparison to standard parallel axis gear trains. A carrier connected to a drive shaft holds the planet gears. Planetary gear boxes chapter 10 3 index technical information 4 size 100 1. Pdf relations between size and gear ratio in spur and planetary. The planetary gearbox is one of the most used mechanical transmission.
One of the planetary gearsets from our transmission has a ring gear with 72 teeth and a sun gear with 30 teeth. Ability to calculate the gear ratios, torques, and effective inertia for simple, compound. The compound planetary gear block represents a planetary gear train with composite planet gears. Internet searches for how to proved fruitless and dare i say information is being withheld, so this programmer set out to demystify the methods for calculating the widely used equations of. Their number of teeth depends on the demultiplication of the gearbox. The exponent to use in the calculation of equivalent load depends on. How to derive the formula for the planetary mechanism gear ratio duration. Pdf program design for the 3k planetary gear mechanism with. How to i design a planetary gear with a gear ratio of 2. This does not generate planetary gears, and im also unclear as to how design a planetary gear with a 2. The planets are merely seen as a bridge between the sun gear and annulus gear.
Equation and calculators to determine ratios of planetary or epicyclic gear assemblies. If desired, find the gear ratios for the intermediate gears. Calculate gear ratio by dividing the number of teeth on the driven gear by the number of teeth on the driving gear. Planetary gear boxes chapter 10 4 technical information table 1 thermal power adjustment factor fk work time % room temperature c 10 20 30 40 50 100 1. For example, if the sun gear has 20 teeth and the ring gear has 60, the planetary gear has 80 teeth. This block models a gear train with sun, planet, and ring gears. Two inputs are needed to obtain a predictable output. Intro planetary gears also refer as epicyclic gearing consisting three elements sun. The first solutiona single branch, twostage helical gear sethas two identical ratios, derived from taking the square root of the final ratio 7. The stepped planet gears enable a larger speed reduction ratio in a more compact geometry than an ordinary planetary gear can provide t r. Jan 09, 2018 the gear ratio formula for two meshing gears is simple and intuitive, while the gear ratio formula for the planetary mechanism is not. According to mueller, two fundamental planetary gear trains are kinematically equivalent if one gear ratio of a transmission is equal to. This section introduces planetary gear systems, hypocycloid mechanisms, and constrained gear systems, which are special gear systems which offer features such as compact size and high reduction ratio.
Calculate the input and outputs speeds and torques of gear boxes. Planetary kinematics note that point 1 on the planet gear is stationary zero velocity due to noslip assumption note that point 2 on the planet gear has the same velocity as point 2 on the sun gear also due to noslip assumption, which is given by. Modal analysis is a widely used technique to calculate the frequency. Two forms of planetary gears of the bevel type are shown in figures 23 and 24. Understanding, selecting and applying planetary gearheads. You can click on any of the images for a larger view. Provided that the ring gear has a constant size, different ratios can be realized by varying the number of teeth of the sun gear and the number of teeth of the planetary gears. Planetary gears gsa the easytomount highend economy gearbox for high power transmissions. The software enables calculation of the system gearbox in one step, including a complete documentation into a pdfa document, according to iso 190051. Ports c, r, and s represent the shafts connected to the planet gear carrier, ring gear, and sun gear. The angular speed of the planet carrier can be found since we know.
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. Planetary gear ratio calculations this article also available in spanish. The larger gear engages a centrally located sun gear, while the smaller gear engages the ring gear. The sun gear is located at the center, and transmits torque to the planet gears. We can get lots of different gear ratios out of this gearset. Reduction ratios not listed in chart 1 require special design. Each planet gear system has a reduction state, a direct coupling and an acceleration mode.
Ground, helical toothed precision components inside the gear ensure low running noise and high running smoothness. The basic form of a planetary gear system is shown in figure 17. Consider a simple schematic of a gear box with an input and output shaft. Since, i am working in the metric unit every dimension will be in mm. Gear ratio, torque and speed calculations smlease design. The conventional gear trains described in the previous sections are all onedegreeof free dom dof devices.
It allows us to find a gear ratio without actually having to build a gear train and turn the gears. In an epicyclic gear train, the axes of the shafts, over which the gears are mounted, move relative to a fixed axis. Gear ratio is the ratio of output and input number of teeth on a shaft. In terms of coupled pgts, the torque equilibria at the cutfree couplings are to be consi. Gear train with sun, planet, and ring gears matlab. In mathematical terms, the smallest reduction ratio is 3. The first constraint for a planetary gear to work out is that all teeth have the same pitch, or tooth spacing. Abstract it has been said that deriving the formulas for the ratios between the various gears of an epicyclic planetary gear system is nonintuitive and taxes the human intellect to say the least. Typically, the planet gears are mounted on a movable arm or carrier, which itself may rotate relative to the sun gear. How to derive the formula for the planetary mechanism. Pdf this paper deals with the gear matching of 3k planetary gears. We can find the ratio of any two gears if we know the number of teeth on each of the gears. A question that i often get is how to work out planetary gears using the gear template generator working out the tooth counts for planetary gears is actually not that complicated, so.
Another class of gear train has wide application, the epicyclic or planetary train. In the past ive had luck using this site to create an illustrator file that i can extrude in rhino. The number of teeth of the planets has no effect on the ratio. Bear in mind the difference between the standard reduction ratio fo framenumbers under 315 and over 355. How to derive the formula for the planetary mechanism gear ratio.
Planetary epicyclic gear ratios equations and calculators. Planetary gear design a planetary gear system, also referred to as epicyclic gearing, consists of three elements a sun gear, one or more planet gears, and a ring gear. In other words, the gear ratio is the ratio between the number of teeth on two gears that are meshed together, or two sprockets connected with a common roller chain, or the circumferences of two pulleys connected with a drive belt. Gear optimization macrogeometry the following shows the gear optimization in some case studies. This is a c o mp li c a t e d m e c h a n ism to solve. The comparison of planetary gear system over helical gears systems is done on the basis of volume, weight and torque density keywords. Depending on the ratio the gearbox will either have one, two or three stages. The overall demultiplication of multi stage planetary gear units is calculated by multiplying the ratios of the single stages. Please start with the tutorial for shaft calculation to see how to introduce geometry and supports for single shafts.
The lowbacklash planetary gearheads of the gsa series are designed for high positioning accuracy and highly dynamic cycle operation. Planetary gears, gear train, is 4460, torque density. Reduction ratio i 833 808i 1,500 examplesof selection select the nearest reduction ratio from among the ratios of the standard reduction ratio chart see chart 1. Design of machinery an introduction to the synthesis and. The gear ratio is defined as gr input speedoutput speed.
Planetary gear train with stepped planet gear set matlab. They are used to increase or decrease the speed or torque of the output shaft. Selecting gears in metric unit the gear tooth profile of the spur gear will be in module. High efficiency in combination with high transmission ratios. This means that the driver gear has to turn about 4.
Pdf calculation of torque performance of a novel magnetic. Also, locking any two of the three components together will lock up the whole device at a 1. At a ratio of less than 3, the sun gear becomes too big against the planet. In our example, we would find the gear ratio by dividing the thirty teeth of the driven gear by the seven teeth of our new driver. In this article we will discuss how to calculate gear ratio, speed and torque for various gear train. Pdf in this report equations for the minimum gear sizes necessary to. L where a gear a and the arm c have a common axis at o 1 about which they can rotate. Calculation of torque performance of a novel magnetic planetary gear.
The gsb090 planetary gear, with a gear ratio of i10, is used as a machine axis. N is usually in revmin but the ratio is the same whatever units of speed are used. Relations between size and gear ratio in spur and planetary gear. This relationship between the tooth ratio and the gear ratio is very important. A question that i often get is how to work out planetary gears using the gear template generator. All the components are modelled in catia to check the assembly and the. Working out the tooth counts for planetary gears is actually not that complicated, so i initially neglected to mention how to do it. Epicyclic gearing or planetary gearing is a gear system consisting of one or more outer, or planet, gears or pinions, revolving about a central sun gear or sun wheel. In this tutorial, we will show you an original and easyto.
The gear ratio is the ratio of the number of turns the output shaft makes when the input shaft turns once. Design and optimization of planetary gears considering all. Choosing which piece plays which role determines the gear ratio for the gearset. One of the two gears engages the centrally located sun gear while the other engages the outer ring gear. A point on the pitch circle of the planet gear traces an eppicyclic curve. Epicyclic gearing planetary gearboxes neugart gmbh. So ive found the following formula for calculating the gear ratio of a planetary gear. The sun gear is located at the center, and transmits torque to the planet gears that orbit around it. The number of teeth for spur gears is given by where k 1f fll1 for fulld tht th08f tbt th d ldepth teeth, 0. The gear b meshes with gear a and has its axis on the arm o 2, about which the gear b can rotate. Calculation of a planetary gear train this tutorial shows the usage of mesys shaft calculation with shaft systems.
Also the case study to determine the reduction ratio of two stage gear box is discussed. To understand gear ratio we suggest you first read. Internet searches for how to proved fruitless and dare i say information is being withheld, so this programmer set out to demystify the methods for. For the predefined gear ratios, one negativeratio drive and two structurally different positiveratio drives will be designed and compared fig. Each of these three components can be the input, the output or can be held stationary.
Can transmit high torque are very compact provide high torsional rigidity offer a wide variety at the input are variable in their reduction gear ratio can be combined with the planetary gear unit in helical or bevelhelical gear version. Question about calculation of planetary gear ratios. The planet gear in figure 23 rotates about a fixed bevel gear at the center of which is the driven shaft. Epicyclic gearing systems also incorporate the use of an outer ring gear or annulus, which. A twostage planetary gear stage is defined using the program. For a threespeed hub, a onestage planetary gear system is used, for a fivespeed hub a 2stage.
Show students how the gear ratio can be expressed as a fraction. Calculating gear ratios within a planetary gear set. Each composite planet gear is a pair of rigidly connected and longitudinally arranged gears of different radii. Nov 08, 2012 the overall demultiplication of multi stage planetary gear units is calculated by multiplying the ratios of the single stages. Special issue of the 3rd international conference on. Experimental characterization of the coupling stage of a. The next steps depend on the state of the planetary gears connected to the carrier, although all use the same formula. Calculate the number if teeth required in the ring gear for the ratio 5. The main purpose of this planetary was to see if i could make it with hand cut gears and how smoothly it would operate.
Technically, a meaningful ratio range for a planetary stage is approx. It is stated that the simple planetary gear train consisting of two central gears, one or more planet gears and one arm, has 34 different types. Figure 3 gear box ratio the ratio of the gear box is defined as 2 1 n n output speed input speed g. Let us compare a planetary gear train with a conventional one, with fixed gear axes, designed for the same gear ratio of angular velocities of the input and output mechanism links. The gear ratio formula for two meshing gears is simple and intuitive, while the gear ratio formula for the planetary mechanism is not. Now consider that b is free to rotate on its shaft. Planetary gears are common in transmission systems, where they provide high gear ratios in compact geometries. It has been said that deriving the formulas for the ratios between the various gears of an epicyclic planetary gear system is nonintuitive and taxes the human intellect to say the least. The median conk tact stiffness from the load gradient calculation is used for the analysis, as well as wheel body stiff ness sun, ring gear, bearing stiffness and bear ing clearances sun, planet, ring gear and planet carrier. All 34 types can be derived from one general form of the simple planetary gear train. In order to achieve the above objective, methodology of design used is explained in next point. D rotation of driver per revolution of follower or the driven gear or pulley. Lightweight design for planetary gear transmissions. Ronald walters multilayer planetary drive ronald walters sent me some pictures and a description of a very complicated planetary gear drive that he built.
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