Sun and Planetary Gears

Introduction

        You may have heard or read about a normal car gearbox, which consists of three shafts with various gear combinations on them, each of which is controlled by the driver via a gear stick to change ratios. In a manual transmission, this is the typical gearbox. When it comes to automatic transmissions, however, there is a separate system for shifting gears. The " Planetary Gearset " which has several advantages above a regular gearbox, is the key to the complete autonomous system. Nonetheless! Planetary gear sets are also utilised to distribute motor power to the wheels in Formula Student cars, particularly in Electric Vehicles. This gearset can be used in electric vehicles with both in-wheel and chassis-mounted motors.

When did the Planetary Gear first appear?

    Planetary gears, also called as epicyclic gears, were first devised by the Greeks over 2,000 years ago to aid in the prediction of planet movements in the solar system. The simplest explanation for how they came up with the gear is because planetary gears are made up of a central driving gear (i.e., the sun) and several “planet” gears that circle around it. Both the central and planet gears are surrounded by a ring gear.

        In the automotive sector, the first planetary gear gearboxes were put to the Wilson-Pilcher vehicle, which was built in the United Kingdom, in the early 1900s. In 1908, the Ford Model T featured planetary gears in its two-speed manual transmission. Moving forward a few decades, in 1937, Oldsmobile released the "Automatic Safety Transmission," an automatic transmission with planetary gears that could shift between high and low gear ranges and only required a clutch for standing starts.

Definition of Epicycloid and Hypocycloid

    First and foremost, let us define the terms Epicycloid and Hypocycloid. Their definitions cannot be any more straightforward than those found in dictionaries. Epicycloid refers to a curve drawn by a point on a circle's circumference rolling on the outside of another circle, whereas Hypocycloid refers to a curve drawn by a point on a circle's circumference rolling on the inside of another circle. The two are depicted in the diagrams below (epicycloid and hypocycloid respectively).

Fig: Epicycloid

Fig: Hypocycloid

Construction of Sun and Planetary Gear

 

    It all starts with a gearing design that is epicyclic. An epicyclic gear train is made up of two gears with the centre of one rotating around the centre of the other. The centres of the two gears are connected by a carrier, which rotates to carry one gear, called the planet gear, around the other, called the sun gear. The planet and sun gears mesh, allowing their pitch circles to roll freely. An epicycloid curve is traced by a point on the planet gear's pitch circle.

    The planetary gear can also be built such that it rolls on the inside of the pitch circle of an outer ring gear in an epicyclic gear train. In this condition, the hypocycloid is the curve traced by a point on the planetary gear’s pitch circle.

 

    By constraining the relative movements of the three gears, we may achieve a variety of various combinations of gear sets by combining the two techniques of meshing the gears stated above, i.e., a planet gear engaging the sun and ring gear and the sun gear concentric with the ring gear, all three gears being in the same plane. A carrier or arm connects the sun's and planet gears.

    The gear ratio in an epicyclic gearing system is a little peculiar, especially as there are multiple methods to convert an input rotation into an output rotation. The epicyclic gear is composed of three fundamental components:

• Sun gear: The core gear.

• Planetary Carrier: contains one or more similar-sized planet gears meshing with the sun and ring gears.

• Ring Gear: An outer ring with teeth that face inward and mesh with the planet gears.

Types

 

    One of the three components in these epicyclic gear systems is normally maintained fixed, one of the two remaining components is an input, and the last component is the output. Three fundamental epicyclic gearbox designs are feasible based on this: Planetary, Star, and Solar. We will go through these sorts in further detail later in this article. For the time being, let us run some numbers to see what we can come up with. For the time being, let us perform some calculations to derive an interesting relationship between the angular speeds and the number of teeth of the three gears. This result will be used to calculate the gear ratios of the different types of epicyclic gearbox designs and finally decide the one suitable for a Formula Student electric car.
 
    This is essentially a superposition technique for making calculations easier. As indicated below, the planetary gearset is separated into two layouts.

 +  = 

 
    Let us do calculation for separate arrangement and then sum up both.

 

Adding equation (i) and (ii):

     This is fundamental formula to calculate the gear ratios for planetary, star and solar gear sets.

    If we fixed one of three quantities, we could get four different gearsets. These four cases listed below:

As a result of the various gear ratios acquired above for various gearsets, the planetary set is the ideal one that is utilized in practically all automatic transmissions and in Electric Vehicles since it has the greatest achievable gear ratio ideal for achieving maximal acceleration due to torque multiplication all the way from the motor to the wheels.

In Formula Student EVs, a single gear ratio is sufficient for transmission needs. Compound epicyclic gear sets, on the other hand, are utilized in cars with automatic transmissions to achieve varied gear ratios by connecting numerous planetary gear sets.

Where are Planetary Gear Systems Used?

 

        When space and weight are limited, but a significant degree of speed reduction and torque is required, at that place planetary gears are frequently used. This rule applies to a wide range of sectors, including tractors and construction equipment that require a lot of torque to move the wheels. Planetary gear sets can also be found in turbine engines, automated transmissions, and even electric screwdrivers.

    Because the load is spread among numerous planet gears, planetary gear systems may generate a lot of torque. In comparison to a standard parallel axis gear system, this design provides more contact surfaces and a bigger contact area between the gears. As a result, the stress is more equally distributed, and the gears are less susceptible to damage.

Optimum number of planet gears

         As a result, three planets are always in mesh, resulting in a greater ‘'effective" number of planets sharing the load. The thick coat of oil employed in them dampens any vibrations that may occur as a result of the clearances. In a planetary gearset, the gears are not permanently fixed in relation to one another. It is intriguing! Isn't that so?

             The optimal number of planet gears to utilize in a planetary gearset is an important design consideration. The effective number of planets sharing the load and the number of planets actually used in the set are two different things. In 1970, D. L. Seager devised a set of equations to predict load sharing across planet gears after conducting a theoretical examination of loading in a simple planetary gear system.

        He discovered that as the number of planets exceeds three, the load is no longer evenly distributed among them. The sort of support that these gears have, whether fixed or floating, was considered in this analysis.

        The gears are supported in bearings which is a fixed support, and the centres of the sun, planet, and ring will not coincide owing to manufacturing flaws. As a result, there are fewer planets in mesh at the same time, resulting in a lower “effective” number of planets sharing the burden.

    One or two members of a floating support are given a modest degree of radial freedom/float, which can be as little as 0.002 inches. This permits the members to modify their postures to produce an equalizing effect, ensuring that their centres are all in the same place.

Advantages of sun and planetary gear over parallel shaft gear

 

        Until now, we have covered practically all the important factors to consider when determining the size, number of teeth, gear ratios, and relative placements of planet gears in planetary gearsets. However, these were only the quantitative aspects of planetary gearsets, which included computations and deduced facts that were utilized as design guidelines. What meaningful values can we glean from all of this? What makes these gearsets superior to their conventional gearbox counterparts? Let us have a look at the benefits that this clever gearset has to offer.

         The compact and light package is the main advantage of epicyclic gears over parallel shaft gears. Light means a high torque to weight ratio, whereas compact means a high torque to volume ratio. This is because using numerous planets allows the burden to be spread out among them. If you utilize three planet gears, each sun-planet contact will carry one-third of the total load, thus the sun gear will be about one-third the size of a parallel shaft gear designed to transmit similar torque. As the number of planets grows, so does the number of sun-planet contact points, and therefore the torque density.

        As it comes to rotating component inertia, the planetary gearbox inertia is less by the square of the number of planets when compared to a regular gearbox with the same torque rating.

        Furthermore, in a parallel shaft gearbox, the lubricant is thrown away at high shaft speeds, necessitating the usage of pressured forced lubrication. Lubricant, on the other hand, cannot escape through a planetary gearset because it is constantly dispersed among the components and mixed into the gear contacts, allowing them to be grease lubricated for the rest of their lives. Furthermore, smaller gears can be manufactured with more precision than larger parallel shaft gears.

Conclusion

         When it comes to transmission design in Formula Student cars, particularly electric vehicles, the planetary gearset is the important component to look for. These gearsets are the connecting links between the motor and the wheels, whether the engine is positioned on the chassis or in the wheel. These gears can be examined and constructed based on the traction that the road can provide, engine specs, and other factors. The planetary gearset is a key component to look for when it comes to transmission design in Formula Student cars, especially electric vehicles. Whether the engine is mounted on the chassis or in the wheel, these gear sets are the connecting links between the motor and the wheels. These gears can be evaluated and built based on the road's traction, engine specifications, and other considerations.

Vishwakarma Institute Of Technology

B-Tech Second Year

Mechanical Engineering

• Dr.(Prof.) Umesh Chavan
• Shreyas Chafodikar
• Prajyot Chatur
• Aniket Chaudhari
• Harsh Bhutada
• Pavan Chavan