Patent Publication Number: US-2019186598-A1

Title: Apparatus and system for thin rim planet gear for aircraft engine power gearbox

Description:
BACKGROUND 
     The field of the disclosure relates generally to systems and methods for managing loads on a gearbox in aviation engines and, more particularly, to an apparatus and system for a thin rimmed planet gear in a gearbox in aviation engines. 
     Aircraft engines typically include a fan, a low pressure compressor, and a low pressure turbine rotationally coupled in a series configuration by a low pressure shaft. The low pressure shaft is rotationally coupled to the low pressure turbine and a power gear box. The power gear box includes a plurality of gears and is rotationally coupled to the low pressure fan and low pressure compressor. Aircraft engines may generate significant torsional loads on the low pressure shaft. Torsional loads on the low pressure shaft can exert torsional forces on the gears within the power gear box. Additionally, if not optimally designed these torsional loads transferred through the planet gears can exert unevenly distributed loads on bearing elements within the planet gears. These unevenly distributed loads result in higher peak roller loads which will induce higher contact stresses between the planet gear, the planet rolling elements, and the planet inner race and reduce the reliability of the planet bearings as well as the power gear box. 
     BRIEF DESCRIPTION 
     In one aspect, a planet gear includes an annular planet gear rim and a rolling element bearing assembly. The annular planet gear rim has a constant inner radius along a complete axial length and an outer radius defined as the radial distance to the root of the gear teeth. The constant inner radius and the outer radius define a gear rim thickness therebetween. The annular planet gear rim further has an average rim radius defined at a point halfway between the constant inner radius and the outer radius where transverse components of a plurality of gear tooth forces are applied to the planet gear rim, and wherein a ratio of the average rim radius divided by the rim thickness is in a range of 4 to 9. The rolling element bearing assembly comprises an inner annular bearing ring and a plurality of rolling bearing elements disposed circumferentially around the inner annular bearing ring. The annular planet gear rim is disposed circumferentially about the plurality of rolling bearing elements, and wherein the plurality of rolling bearing elements are axially retained by the inner annular bearing ring. 
     In another aspect, a gear assembly includes a sun gear, a ring gear and a plurality of planet gears coupled to the ring gear and the sun gear. Each planet gear of the plurality of planet gears comprises an annular planet gear rim and a rolling element bearing assembly. The annular planet gear rim has a constant inner radius along a complete axial length and an outer radius defined as the radial distance to the root of the gear teeth. The constant inner radius and the outer radius define a gear rim thickness therebetween. The annular planet gear rim further has an average rim radius defined at a point between the constant inner radius and the outer radius where stresses and strains within the planet gear rim are zero when radial and transverse components of a plurality of gear tooth forces are applied to the planet gear rim, and wherein a ratio of the average rim radius divided by the rim thickness is in a range of 4 to 9. The rolling element bearing assembly comprises an inner annular bearing ring and a plurality of rolling bearing elements disposed circumferentially around the inner annular bearing ring. The annular planet gear rim is disposed circumferentially about the plurality of rolling bearing elements. The plurality of rolling bearing elements are axially retained by the inner annular bearing ring. 
     In yet another aspect, a turbomachine includes a power shaft and a gear assembly. The power shaft is rotationally coupled to the gear assembly. The gear assembly comprises a sun gear, a ring gear and a plurality of planet gears coupled to the ring gear and the sun gear. Each planet gear of the plurality of planet gears comprises an annular planet gear rim and a rolling element bearing assembly. The annular planet gear rim has a constant inner radius along a complete axial length and an outer radius defined as the radial distance to the root of the gear teeth. The constant inner radius and the outer radius define a gear rim thickness therebetween. The annular planet gear rim further has an average rim radius defined at a point between the constant inner radius and the outer radius where stresses and strains within the planet gear rim are zero when radial and transverse components of a plurality of gear tooth forces are applied to the planet gear rim, and wherein a ratio of the average rim radius divided by the rim thickness is in a range of 4 to 9. The rolling element bearing assembly comprises an inner annular bearing ring and a plurality of rolling bearing elements disposed circumferentially around the inner annular bearing ring. The annular planet gear rim is disposed circumferentially about the plurality of rolling bearing elements. The plurality of rolling bearing elements are axially retained by the inner annular bearing ring. 
    
    
     
       DRAWINGS 
       These and other features, aspects, and advantages of the present disclosure will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a schematic longitudinal cross-sectional view of an exemplary gas turbine engine, in accordance with one or more embodiment of the present disclosure; 
         FIG. 2  is a schematic cross-sectional view of an exemplary epicyclic gear train that is used with the gas turbine engine shown in  FIG. 1 , in accordance with one or more embodiment of the present disclosure; 
         FIG. 3  is a longitudinal cross-sectional view of an exemplary planet gear that is used with the epicyclic gear train shown in  FIG. 2 , in accordance with one or more embodiment of the present disclosure; 
         FIG. 4  is a schematic cross-sectional view of the exemplary planet gear of  FIG. 3  and taken along line  4 - 4  of  FIG. 3 , in accordance with one or more embodiment of the present disclosure; and 
         FIG. 5  is a schematic cross-sectional view of the planet gear shown in  FIG. 3  with resultant tangential and radial forces causing the planet gear rim to deflect, in accordance with one or more embodiment of the present disclosure. 
       Unless otherwise indicated, the drawings provided herein are meant to illustrate features of embodiments of the disclosure. These features are believed to be applicable in a wide variety of systems comprising one or more embodiments of the disclosure. As such, the drawings are not meant to include all conventional features known by those of ordinary skill in the art to be required for the practice of the embodiments disclosed herein. 
     
    
    
     DETAILED DESCRIPTION 
     In the following specification and the claims, reference will be made to a number of terms, which shall be defined to have the following meanings. 
     The singular forms “a”, “an”, and “the” include plural references unless the context clearly dictates otherwise. 
     “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where the event occurs and instances where it does not. 
     Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about”, “approximately”, and “substantially”, are not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be combined and/or interchanged, such ranges are identified and include all the sub-ranges contained therein unless context or language indicates otherwise. 
     Embodiments of the thin rimmed planet gear described herein manage resultant tangential and radial loads in a power gearbox in a turbomachine, e.g. an aircraft engine. The thin rimmed planet gear includes a planet gear rim, a plurality of gear teeth, an annular inner bearing ring, and a plurality of rolling elements. The rolling elements are disposed circumferentially around the annular inner bearing ring. The planet gear rim circumscribes and rotates about the rolling elements. The gear teeth are disposed circumferentially about an outer radial surface of the planet gear rim. A sun gear and a low pressure power shaft are configured to rotate the thin rimmed planet gear through a plurality of complementary teeth circumferentially spaced about a radially outer periphery of the sun gear. The low pressure power shaft exerts torsional forces on the sun gear which exerts forces through the planet gear balanced by equal and opposite forces on the ring gear and creates a reaction force through the rolling elements, the inner ring and the pin/shaft. The planet gear rim of the thin rimmed planet gear deflects and more evenly distributes the forces across the rolling elements. Better distribution of the forces across a maximum number of rolling elements reduces the contact stresses on the planet gear bearing surface, the rolling elements, and the inner race and increases the reliability of the planet bearing and the power gear box. A planet gear with the proper planet gear rim thickness will deflect enough, but not too much, such that the reliability of planet bearing is increased. 
     The planet gear described herein offers advantages over known planet gears in aircraft engines. More specifically, the thin rimmed planet gear described herein deflects as resultant radial and tangential forces are applied to it from the sun gear and from the ring gear. Planet gear rim deflection more evenly distributes the forces across the rolling elements which decreases the contact stresses on the planet gear bearing surface, the rolling elements, and the inner race and increases the reliability of the planet bearing and the power gearbox. Furthermore, the thin rimmed planet gear described herein reduces the weight of the aircraft by reducing the amount of material in the planet gear. 
     Referring now to the drawings, it is noted that like numerals refer to like elements throughout the several views and that the elements shown in the Figures are not drawn to scale and no dimensions should be inferred from relative sizes and distances illustrated in the Figures.  FIG. 1  is a schematic cross-sectional view of a gas turbine engine  110  in accordance with an exemplary embodiment of the present disclosure. In the exemplary embodiment, gas turbine engine  110  is a high-bypass turbofan jet engine  110 , referred to herein as “turbofan engine  110 .” As shown in  FIG. 1 , turbofan engine  110  defines an axial direction A (extending parallel to a longitudinal centerline  112  provided for reference) and a radial direction R. In general, turbofan engine  110  includes a fan section  114  and a core turbine engine  116  disposed downstream from fan section  114 . 
     Exemplary core turbine engine  116  depicted generally includes a substantially tubular outer casing  118  that defines an annular inlet  120 . Outer casing  118  encases, in serial flow relationship, a compressor section  123  including a booster or low pressure (LP) compressor  122  and a high pressure (HP) compressor  124 ; a combustion section  126 ; a turbine section including a high pressure (HP) turbine  128  and a low pressure (LP) turbine  130 ; and a jet exhaust nozzle section  132 . A high pressure (HP) shaft or spool  134  drivingly connects HP turbine  128  to HP compressor  124 . A low pressure (LP) shaft or spool  136  drivingly connects LP turbine  130  to LP compressor  122 . The compressor section  123 , combustion section  126 , turbine section, and nozzle section  132  together define a core air flowpath  137 . 
     For the embodiment depicted, fan section  114  includes a variable pitch fan  138  having a plurality of fan blades  140  coupled to a disk  142  in a spaced apart manner. As depicted, fan blades  140  extend outwardly from disk  142  generally along radial direction R. Each fan blade  140  is rotatable relative to disk  142  about a pitch axis P by virtue of fan blades  140  being operatively coupled to a suitable pitch change mechanism  144  configured to collectively vary the pitch of fan blades  140  in unison. Fan blades  140 , disk  142 , and pitch change mechanism  144  are together rotatable about longitudinal axis  112  by LP shaft  136  across a power gear box  146 . Power gear box  146  includes a plurality of gears for adjusting the rotational speed of fan  138  relative to LP shaft  136  to a more efficient rotational fan speed. In an alternative embodiment, fan blade  140  is a fixed pitch fan blade rather than a variable pitch fan blade. 
     Also, in the exemplary embodiment, disk  142  is covered by rotatable front hub  148  aerodynamically contoured to promote an airflow through plurality of fan blades  140 . Additionally, exemplary fan section  114  includes an annular fan casing or outer nacelle  150  that circumferentially surrounds fan  138  and/or at least a portion of core turbine engine  116 . Nacelle  150  is configured to be supported relative to core turbine engine  116  by a plurality of circumferentially-spaced outlet guide vanes  152 . A downstream section  154  of nacelle  150  extends over an outer portion of core turbine engine  116  so as to define a bypass airflow passage  156  therebetween. 
     During operation of turbofan engine  110 , a volume of air  158  enters turbofan engine  110  through an associated inlet  160  of nacelle  150  and/or fan section  114 . As volume of air  158  passes across fan blades  140 , a first portion of air  158  as indicated by arrows  162  is directed or routed into bypass airflow passage  156  and a second portion of air  158  as indicated by arrow  164  is directed or routed into core air flowpath  137 , or more specifically into LP compressor  122 . The ratio between first portion of air  162  and second portion of air  164  is commonly known as a bypass ratio. The pressure of second portion of air  164  is then increased as it is routed through HP compressor  124  and into combustion section  126 , where it is mixed with fuel and burned to provide combustion gases  166 . 
     Combustion gases  166  are routed through HP turbine  128  where a portion of thermal and/or kinetic energy from combustion gases  166  is extracted via sequential stages of HP turbine stator vanes  168  that are coupled to outer casing  118  and HP turbine rotor blades  170  that are coupled to HP shaft or spool  134 , thus causing HP shaft or spool  134  to rotate, thereby supporting operation of HP compressor  124 . Combustion gases  166  are then routed through LP turbine  130  where a second portion of thermal and kinetic energy is extracted from combustion gases  166  via sequential stages of LP turbine stator vanes  172  that are coupled to outer casing  118  and LP turbine rotor blades  174  that are coupled to LP shaft or spool  136 , thus causing LP shaft or spool  136  to rotate which causes power gear box  146  to rotate LP compressor  122  and/or rotation of fan  138 . 
     Combustion gases  166  are subsequently routed through jet exhaust nozzle section  132  of core turbine engine  116  to provide propulsive thrust. Simultaneously, the pressure of first portion of air  162  is substantially increased as first portion of air  162  is routed through bypass airflow passage  156  before it is exhausted from a fan nozzle exhaust section  176  of turbofan engine  110 , also providing propulsive thrust. HP turbine  128 , LP turbine  130 , and jet exhaust nozzle section  132  at least partially define a hot gas path  178  for routing combustion gases  166  through core turbine engine  116 . 
     Exemplary turbofan engine  110  depicted in  FIG. 1  is by way of example only, and that in other embodiments, turbofan engine  110  may have any other suitable configuration. It should also be appreciated, that in still other embodiments, aspects of the present disclosure may be incorporated into any other suitable gas turbine engine. For example, in other embodiments, aspects of the present disclosure may be incorporated into, e.g., a turboprop engine. 
       FIG. 2  is a schematic diagram of an epicyclic gear train  200 . In the exemplary embodiment, epicyclic gear train  200  is a planetary gear train. In one embodiment, epicyclic gear train  200  is housed within power gearbox  146  (shown in  FIG. 1 ). In other embodiments, epicyclic gear train  200  is located adjacent to power gearbox  146  and is mechanically coupled to it. As an example, the epicyclic gear train  200  is for use in an aircraft engine geared drive fan system. 
     Epicyclic gear train  200  includes a sun gear  202 , a plurality of planetary gears  204 , a ring gear  206 , and a carrier  208 . In alternative embodiments, epicyclic gear train  200  is not limited to three planetary gears  204 . Rather, any number of planetary gears may be used that enables operation of epicyclic gear train  200  as described herein. In some embodiments, LP shaft or spool  136  (shown in  FIG. 1 ) is fixedly coupled to sun gear  202 . Sun gear  202  is configured to engage planetary gears  204  through a plurality of complementary sun gear teeth  210  and a plurality of complementary planet gear teeth  212  circumferentially spaced about a radially outer periphery of sun gear  202  and a radially outer periphery of planetary gears  204  respectively. Planetary gears  204  are maintained in a position relative to each other using carrier  208 . Planetary gears  204  are fixedly coupled to power gearbox  146 . Planetary gears  204  are configured to engage ring gear  206  through a plurality of complementary ring gear teeth  214  and complementary planet gear teeth  212  circumferentially spaced about a radially inner periphery of ring gear  206  and a radially outer periphery of planetary gears  204  respectively. Ring gear  206  is rotationally coupled to fan blades  140  (shown in  FIG. 1 ), disk  142  (shown in  FIG. 1 ), and pitch change mechanism  144  (shown in  FIG. 1 ) extending axially from ring gear  206 . LP turbine  130  rotates the LP compressor  122  at a constant speed and torque ratio which is determined by a function of ring gear teeth  214 , planet gear teeth  212 , and sun gear teeth  210  as well as how power gearbox  146  is restrained. 
     Epicyclic gear train  200  can be configured in three possible configuration: planetary, star, and solar. In the planetary configuration, ring gear  206  remains stationary while sun gear  202 , planetary gears  204 , and carrier  208  rotate. LP shaft or spool  136  drives sun gear  202  which is configured to rotate planetary gears  204  that are configured to rotate carrier  208 . Carrier  208  drives fan blades  140 , disk  142 , and pitch change mechanism  144 . Sun gear  202  and carrier  208  rotate in the same direction. 
     In the star configuration, carrier  208  remains stationary while sun gear  202  and ring gear  206  rotate. LP shaft or spool  136  drives sun gear  202  which is configured to rotate planetary gears  204 . Planetary gears  204  are configured to rotate ring gear  206  and carrier  208  is fixedly coupled to power gearbox  146 . Carrier  208  maintains planetary gears  204  positioning while allowing planetary gears  204  to rotate on their respective bearings. Ring gear  206  is rotationally coupled to fan blades  140 , disk  142 , and pitch change mechanism  144 . Sun gear  202  and ring gear  206  rotate in opposite directions. 
     In the solar configuration, sun gear  202  remains stationary while planetary gears  204 , ring gear  206 , and carrier  208  rotate. LP shaft or spool  136  can drive either the ring gear  206  or carrier  208 . When LP shaft or spool  136  is coupled to carrier  208 , planetary gears  204  are configured to rotate ring gear  206  which drives fan blades  140 , disk  142 , and pitch change mechanism  144 . Ring gear  206  and carrier  208  rotate in the same direction. 
     In the solar configuration where LP shaft or spool  136  is coupled to ring gear  206 , ring gear  206  is configured to rotate planetary gears  204  and carrier  208 . Carrier  208  drives fan blades  140 , disk  142 , and pitch change mechanism  144 . Ring gear  206  and carrier  208  rotate in the same direction. 
     Referring now to  FIGS. 3 and 4 , illustrated is a longitudinal cross-sectional view of the exemplary planet gear  204  of the epicyclic gear train shown in  FIG. 2 , and a schematic cross-sectional view of the exemplary planet gear  204  of  FIG. 3 , taken along line  4 - 4  of  FIG. 3 , respectively. The planet gear  204  is rotatable about an axis  300  via a pin  301 . It should be noted that the terms pin and shaft are used interchangeably herein as they refer to the component that the planet gear  204  rotates about. The planet gear  204  includes a planet gear rim  306 , a plurality of teeth  212 , and a rolling element bearing assembly  320 , comprising an inner annular bearing ring  302  and a plurality of rolling elements  304 . The plurality of rolling elements  304  are disposed circumferentially around the annular inner bearing ring  302 . The carrier  208  (shown in  FIG. 2 ) is coupled to the inner annular bearing ring  302  and the pin  301 . The planet gear rim  306  circumscribes the plurality of rolling elements  304 . The teeth  212  are disposed circumferentially about an outer radial surface  312 . The plurality of teeth  212  are configured to mesh with the sun gear teeth  210  and ring gear teeth  214 . More specifically, each planet gear  204  is meshed with the sun gear  202  and the ring gear  206  while being rotatably attached around an outer circumference of the inner annular bearing ring  302 , which is used as a rotational shaft, via the plurality of rolling elements  304 . 
     As best illustrated in  FIG. 3 , the pin  301  has mounted to an outer surface  303 , the inner annular bearing ring  302  comprising a plurality of inner races  305  defining a plurality of raceway grooves  307 . In the illustrated embodiment, the inner annular bearing ring  302  is configured for mounting to the outer surface  303  of the pin  301  and within the carrier  208  of the gear assembly using any suitable fastening mechanisms. For example, the rolling element bearing assembly  320 , and more particularly, the inner annular bearing ring  302  may be coupled to the outer surface  303  of the pin  301  and within the carrier  208  utilizing known coupling means such as, but not limited to, press fit, wedge, and/or a combination of known coupling means. The plurality of rolling elements  304  are disposed within the inner races  305 , and more particularly the plurality of raceway grooves  307 , so as to provide axial restraint of the plurality of rolling elements  304 , thus maintaining alignment of the rolling elements  304  relative to the planet gear  204 . A fastener  313 , such as a spanner nut, couples the pin  301 , the inner annular bearing ring  302  and the carrier  208  together. 
     During assembly, the planet bearing assembly, and more specifically, the inner annular bearing ring  302 , the plurality of rolling elements  304 , the carrier  208  and the geared planet gear rim  306 , is disposed within a space. Next, the pin  301  is inserted through the carrier  208  into a center of the bearing assembly and held in place by the interference fit between the pin  301  and the carrier  208  at the ends. Subsequently, the fastener  313  is positioned on the pin  301  and is drawn up against the carrier  208  to pull the bearing component tight and securely tying the assembly together. 
     The planet gear rim  306  includes a planet gear bending stress neutral axis  309 , a planet gear bending stress neutral axis radius  310 , a planet gear average rim axis  308 , a planet gear average rim radius  311 , the outer radial surface  312 , or gear root diameter  315 , a constant inner radial surface  314 , and a gear rim thickness  316 . The planet gear bending stress neutral axis radius  310  is the radius where the stresses and strains within planet gear rim  306  are zero when bending forces are applied to planet gear  204 . The gear rim thickness  316  is the radial distance between the outer radial surface  312  and the inner radial surface  314 . The halfway point between the inner radial surface  314  and the outer radial surface  314  defines the location of the average rim axis  308  and the average rim radius  311 . The planet gear average rim radius  311  and the rim thickness  316  define a ratio including values in a range from and including about 4 to and including about 9. 
     As illustrated, the annular planet gear rim bending stress neutral axis radius  310  is defined at a point near an average of a radius  317  of the constant inner radial surface  314  and a radius  318  of the outer radial surface  312  where stresses and strains within the planet gear rim  306  are zero when radial and transverse components of a plurality of gear tooth forces are applied to the planet gear rim  306 , and more particularly near the planet gear average rim radius  311 . 
     As previously alluded to, and as best illustrated in  FIG. 3 , the inner radial surface  314  has a constant radius  317  along a complete axial length. As such language indicates, this type of configuration is typically referred to as an inner land guided bearing design whereby the constant inner radius  317  of the planet gear rim  306  defines a straight or plain raceway without guide flanges. For an inner land guided bearing design, the shoulders or flanges are defined by the races  307 , as previously described, and serve to guide the plurality of rolling elements  304 . 
     This inner land guided bearing design, and more particularly the design including the planet gear rim  306  having a constant inner radius  317 , provides a plurality of benefits over known configurations. The constant inner radius  317  of the planet gear rim  306  results in the constant average rim radius  311 . In contrast, a design with guide flanges would result in step changes in the average rim radius with every thickness change along the axis of the gear. The resulting changes in thickness and stiffness would cause variations in the raceway contour and may result in local variations in surface contact forces and stresses. Furthermore, in a variable radius gear bore design, the neutral axis (near average radius) would not be a constant. The bending stiffness will not be as readily calculated and the effect of whatever section is taken to define rim thickness ratio will be highly different. 
     The constant radius or straight bore design as disclosed herein, provides a uniformity that minimizes variations and promotes reliability. A significant reliability benefit of the constant radius or straight bore design is that is can more easily shed debris that may collect in the system. With an outer land guided bearing design and a rotating gear, centrifugal forces would tend to trap particles within an artificial gravity well formed by the guide flanges. With a constant radius design, particles have a chance to escape axially to either side with the flow of oil and splash. Shutdown periods provide a reduced and zero g-field where particles may flow out with the residual oil. In addition, the inner land guided bearing design disclosed herein has manufacturing benefits, keeping the more complex machining on the easily accessible outer surface  304  of the inner annular bearing ring  302 . 
     Planet gear  204  includes at least one material selected from a plurality of alloys including, without limitation, ANSI M50 (AMS6490, AMS6491, and ASTM A600), M50 Nil (AMS6278), Pyrowear 675 (AMS5930), Pyrowear 53 (AMS6308), Pyrowear 675 (AMS5930), ANSI9310 (AMS6265), 32CDV13 (AMS6481), ceramic (silicon nitride), Ferrium C61 (AMS6517), and Ferrium C64 (AMS6509). Additionally, in some embodiments, the metal materials can be nitrided to improve the life and resistance to particle damages. Planet gear  204  includes any combination of alloys and any percent weight range of those alloys that facilitates operation of planet gear  204  as described herein, including, without limitation combinations of M50 Nil (AMS6278), Pyrowear 675 (AMS5930), and Ferrium C61 (AMS6517). 
     During operation, depending on the configuration of epicyclic gear train  200  (shown in  FIG. 2 ), sun gear  202  (shown in  FIG. 2 ), ring gear  206  (shown in  FIG. 2 ), or LP power shaft  136  rotates the planet gear  204 . The planet gear rim  306  rotates around the rolling elements  304  and the inner annular bearing ring  302 . The inner annular bearing ring  302  rotates the carrier  208 . 
       FIG. 5  is a schematic diagram of the planet gear  204  (shown in  FIGS. 3 and 4 ) with resultant radial and transverse forces  402  causing a wraparound effect of the bending planet gear rim  306 . Torsional movement of the LP power shaft  136  causes the sun gear  202  (shown in  FIG. 2 ) and the ring gear  206  (shown in  FIG. 2 ) to exert resultant radial and transverse components of the gear tooth forces  402  on the planet gear rim  306 . Resultant radial and transverse components of gear tooth forces  402  are equal in magnitude and represent the load through the teeth  212  from the sun gear  202  (shown in  FIG. 2 ) on one side and from the ring gear  206  (shown in  FIG. 2 ) on the other side. 
     Resultant radial and transverse components of the gear tooth forces  402  include resultant radial component forces  404  and resultant tangential component forces  406 . The resultant radial component forces  404  are equal and opposite respective radial components of the resultant radial and transverse components of the gear tooth forces  402 . The resultant tangential component forces  406  are equal the respective tangential components of the tooth contact forces  402 . The resultant radial and transverse components of the gear tooth forces  402  cause a wraparound effect of the bending planet gear rim  306 . The wrap around effect of the bending planet gear rim  306  is caused by both the resultant tangential component forces  406  pulling down and the resultant radial component forces  404  pushing in. The wrap around effect of the bending planet gear rim  306  distributes loads to more rolling elements  304  and, to a point, reduces the peak load on any single rolling element  304 . The reduced peak load on the plurality of rolling elements  304  improves the reliability of the rolling elements  304  and the planet gear rim  306 . In an embodiment, the planet gear rim  306  deflects to distribute gear tooth forces uniformly to the maximum rolling bearing elements. 
     Enhanced results are achieved when the gear rim thickness  316  is thick enough to maintain physical integrity but thin enough to deflect. If the gear rim thickness  316  is too low, the planet gear rim  306  wraps around and strains the teeth  212  by adding hoop stress to the tooth bending load, and driving high peak roller loads directly inboard of the gear mesh. Enhanced results are achieved when the planet gear average rim radius  311  and the gear rim thickness  316  define a ratio including values in a range from and including about 3 to and including about 10, and more particularly in a range from and including about 4 to and including about 9. The stated ratio of the planet gear average rim radius  311  to the gear rim thickness  316  provides enhanced distribution of the resultant radial and transverse components of the gear tooth forces  402  over the rolling elements  304 . 
     The above-described thin rimmed planet gear provides an efficient method for managing torsional forces in a turbomachine. Specifically, the planet gear rim deflects as resultant tangential and radial forces are applied to it from the sun gear and the low pressure power shaft and countered by the equal and opposite forces from the ring gear. Planet gear rim deflection more evenly distributes the forces across the rolling elements which reduces the peak load on any single rolling element and improves the reliability of the inner race, the rolling elements and the planet gear rim, which increases the reliability of the inner race, the rolling elements and the planet gear rim. Finally, the thin rimmed planet gear described herein reduces the weight of the aircraft by reducing the amount of material in the planet gear. 
     An exemplary technical effect of the methods, systems, and apparatus described herein includes at least one of: (a) decreasing the stress and strain on the planet gear rim; (b) decreasing the peak load on rolling elements; (c) increasing the reliability of the planet gear bearings; and (d) decreasing the weight of the aircraft engine. 
     Exemplary embodiments of the thin rimmed planet gear are described above in detail. The thin rimmed planet gear, and methods of operating such units and devices are not limited to the specific embodiments described herein, but rather, components of systems and/or steps of the methods may be utilized independently and separately from other components and/or steps described herein. For example, the methods may also be used in combination with other systems for managing torsional forces in a turbomachine and are not limited to practice with only the systems and methods as described herein. Rather, the exemplary embodiment may be implemented and utilized in connection with many other machinery applications that require planet gears. 
     Although specific features of various embodiments of the disclosure may be shown in some drawings and not in others, this is for convenience only. In accordance with the principles of the disclosure, any feature of a drawing may be referenced and/or claimed in combination with any feature of any other drawing. 
     This written description uses examples to describe the disclosure, including the best mode, and also to enable any person skilled in the art to practice the disclosure, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the disclosure is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.