How to Calculate Gear Ratios in a Planetary Gear Set

Automatic transmissions use two primary mechanical mechanisms to lock planetary gear set components. A brake band locks one component by wrapping loosely around a drum attached to that component; hydraulic pressure on the band piston compresses the band, preventing rotation. A clutch locks two components together using alternately arranged fiber discs and metal plates within a clutch pack; hydraulic pressure compresses them together, forcing the connected components to rotate as a single unit. These mechanisms enable the transmission to achieve different gear ratios by selectively locking various components of the planetary gear sets.

Control of the planetary gear set comes from two multi-plate clutches, one one-way clutch, and two brake bands. The front clutch has outer plates splined to the input shaft and inner plates splined to the primary sun gear shaft. The rear clutch has inner plates splined to the front clutch drum and outer plates connecting to the secondary sun gear. The front band wraps around the outside of the rear clutch drum, while the rear band is on the outside of the planet carrier to hold it stationary when applied. When the rear band is in release position, the one-way clutch allows the planet carrier to rotate freely for forward motion but not in reverse direction.

One-way clutches allow rotary motion in one direction only, simplifying hydraulic and mechanical control. The Spragg type has an inner race with a central spline on the stator support shaft, with the outer race as part of the stator hub. Equally spaced sprags produce wedging action to stop reverse rotation, held by a spring-loaded cage. The Roller type has an inner race splined to the stator support, with the outer race having wedge-shaped segments retaining rollers. A waved compression spring pushes rollers toward the narrow wedge end. A force against engine rotation locks the outer race onto rollers. Most automatic transmissions use epicyclic planetary gears constantly in mesh, with a Sun gear meshing with planet pinions on a planet carrier that spaces them equally around the Sun gear and locates them to mesh with an internally toothed ring gear. Planetary gear motion is described as walking (when Sun or ring gear is stationary, the alternative driving member rotates planet gears on their pins, turning the planet carrier in the same direction) or idling (when planet carrier is stationary, torque transmits from Sun to ring gear or vice versa via planet gears, with driven member turning opposite to driving member). Control is done by hydraulic servos acting on line bands or clutches, or by one-way clutches. In neutral, the planet carrier attaches to the output shaft while the Sun gear attaches to the input shaft, causing planet gears to idle on stationary carrier pins and turn the ring gear opposite to engine rotation. For low gear, a brake band holds the ring gear stationary, forcing planet gears to walk around the stationary ring gear, moving the planet carrier in the same direction as engine rotation but at slower speed with increased torque. Direct-drive (one-to-one ratio) is obtained by locking any two members together using a multi-plate clutch. For reverse, the ring gear attaches to the output shaft while the planet carrier is held stationary by a brake band, causing planet gears to idle on stationary pins and turn the ring gear opposite to engine rotation. Simple gear sets cannot obtain all required ratios, so compound planetary gear sets are used. The Ravigneaux gear set has two simple gear sets with one ring gear, with primary and secondary Sun gears meshing with short and long pinions respectively, both mounted in a common planet carrier. The Simpson gear set has two simple gear sets connected by a long Sun gear common to both, with each set having a part spline to the output shaft. Old bands are externally contracting types with friction material bonded onto spring steel backing, with one end against a stop and the other accommodating a push rod from a hydraulically operated servo. The simplest servo has a cylinder with piston, return spring, and push rod. In pressure release type servos, band application uses fluid pressure on the piston head, but release is obtained by supplying fluid at the same pressure to the opposite side, with the return spring moving the piston to release position. Diaphragm springs provide extra leverage to increase apply force while also providing release force. Multiple disc clutches couple planetary gear members and shafts together, with driving and driven plates (clutch pack) where one set has friction material bonded onto both phases (wet clutches). The plates may be dished or waved with alternate high and low segments for smooth engagement. Release is affected by coil springs or packs of small springs. The released position must retain clearance to allow plate separation and avoid premature wear. Partial application at high speed can occur if fluid is trapped in the clutch cylinder after release, with trapped fluid accumulating at the outer portion under centrifugal force. This is prevented by a pressure relief valve (reed or ball check type) that closes with apply fluid and unseats by assembly rotation to let fluid escape.

Two members in a planetary gear set can be locked together using a clutch mechanism. A clutch disc is attached to one member (such as the sun gear shaft) and can move along the shaft. Another disc is fastened securely to another member (such as the ring gear). When the movable disc is forced against the stationary disc, friction creates a connection that locks the two members together, causing them to turn as a single unit.

Automatic transmissions use a control mechanism to select which planetary gear components are driven, driven, or held stationary. This is achieved using brake bands (hold components stationary) and multi-plate clutch assemblies (connect components together). The transmission control unit determines which components to engage based on vehicle speed, throttle position, and other factors. Multiple planetary gear sets (2, 3, or 4) can be combined to produce more gear ratios. The number of planet gears affects load distribution and efficiency.

Planetary gear systems distribute torque smoothly and evenly across multiple gears, with three-planet setups distributing load among all three simultaneously. This design reduces torque loading on axle shafts by up to 80% compared to conventional axles. A four-planet system spreads torque over 2.5 times more gear tooth contact area than older designs. The enclosed planetary gears cannot separate under peak loads because they are confined within the ring gear housing, ensuring consistent engagement and preventing gear escape that occurs in open gear arrangements.

In the planetary gear system, power from the input shaft is distributed between the sun gear and the ring gear based on resistance levels. When the planet carrier rotates, the planet gears simultaneously mesh with both the sun gear and the ring gear. Power flows through whichever path offers less resistance. If the sun gear path has lower resistance, power goes to the mechanical drivetrain; if the ring gear path has lower resistance, power goes to the hydraulic system.

In systems with multiple gears, power is distributed based on removal at each gear, with each shaft segment carrying only the power passing through it. The instructor demonstrates a system where 65 kW input power is reduced to 35 kW after gear A and further to 20 kW after gear B. Torque in each segment is calculated using T = P/ω, where ω remains constant throughout the system if all gears rotate at the same frequency. This shows that different shaft segments experience different torques, and the design must account for the maximum torque in any segment. The angular speed conversion from Hz to rad/s (multiplying by 2π) is essential for accurate torque calculations.

When all components of an epicyclic gearbox are moving, power flow analysis requires constructing a free body diagram for the planet gear to determine forces and torques. The process involves: calculating input torque from power and speed (T = P/(ω)), determining gear forces using torque = force × radius, ensuring force equilibrium on the pivoted planet gear, calculating output torque from force and annulus radius, and verifying power conservation. In this example: Input power = 5 kW at 63 RPM gives input torque = 77.9 Nm; Gear force = 16.8 N; Output torque = 136.8 Nm at -21 RPM gives output power = 3 kW; Power loss = 2 kW due to inefficiencies.

The multiple planet gears in a planetary gear system allow for force distribution across several gear teeth simultaneously. This distributed load enables the system to handle significantly higher torque compared to a single gear configuration. As a result, planetary gears can generate substantial torque in compact sizes, making them suitable for applications ranging from construction equipment like excavators to automotive transmissions.

Planetary gear trains have numerous practical applications in engineering. They are commonly used in: (1) Automatic transmissions in vehicles, providing smooth gear changes without interrupting power flow, (2) Differentials in automotive applications, (3) Robotics for compact and efficient power transmission, (4) Wind turbines for speed reduction, and (5) Industrial machinery for high-torque applications. The key advantage is their ability to provide multiple gear ratios in a compact space while maintaining high efficiency and smooth operation. The first practical application was in automatic transmissions for vehicles.

Final drives in heavy equipment like bulldozers use planetary gear systems. The planet gears revolve around a central sun shaft, creating a compact and efficient power transmission design. This configuration allows for high torque transmission in a relatively small space, which is essential for heavy machinery applications.

Planetary gears are versatile mechanical components used across multiple industries including military robotics (bomb squad robots), medical equipment, oil and gas, hoists and cranes, and household appliances due to their high reliability, efficiency, and ability to handle both delicate and heavy-duty applications.

A planetary gearbox is a mechanical system comprising a central sun gear, orbiting planet gears, and an outer ring gear, which provides high torque density, compact size, and efficient power transmission through multiple stages of gear reduction, making it suitable for diverse industrial applications including wind turbines, robotics, and material handling equipment.

Internal or ring gears are commonly used as planetary gears when space and weight are issues but large speed reduction and torque are needed. Planetary gears share load among multiple planet gears, creating more contact surfaces and larger contact area than traditional parallel axis systems. Load is more evenly distributed, making gears more resistant to damage. Applications include tractors, construction equipment, helicopter transmissions, turbine engines, automatic transmissions, and electric screwdrivers.