EPICYCLIC GEAR SYSTEM
Cross Reference To Related Applications This application is a continuation-in-part of U.S. patent application serial no. 10/680,043, filed October 7, 2003, from which priority is claimed. Technical Field This invention relates in general to gear systems and, more particularly, to an epicyclic gear system. The typical epicyclic or planetary gear system basically has a sun gear provided with external teeth, a ring gear provided with internal teeth, and several planet gears located between the sun and ring gears and having external teeth which mesh with the teeth on the sun and ring gears. In addition to its gears, the typical system has a carrier to which the planet gears are coupled. Either the sun gear, the ring gear, or the carrier is held fast, while power is delivered to and taken from the remaining two components, and thus power is transferred through the planetary system with a change in angular velocity and an inverse change torque. The sun and ring gears for all intents and purposes share the same axis - a central axis - while the planet gears revolve about radially offset axes that are parallel to the central axis - or at least they should be. Often the offset axes and the central axis are not parallel, and as a consequence the planet gears skew slightly between sun and ring gears. This causes excessive wear along the teeth of the planet, sun and ring gears, generates friction and heat, and renders the entire system overly noisy. The problem certainly exists in straddle-designed planetary carriers. With this type of carrier the pins on which the planet gears rotate extend between two carrier flanges in which the pins are anchored at their ends. The carrier experiences torsional wind up which causes
one carrier flange to rotate slightly ahead of the other flange. Not only does this skew the pin for each of the planet gears such that one end lies circumferentially ahead of the other end, but it also causes the leading end of the pin to dip toward the central axis and the other end to draw away from the central axis. The end result is a poor mesh between the planet gears and the sun and ring gears, and of course the friction, wear and noise associated with poorly meshed gears. To counteract this tendency, some planetary systems rely on gears that are wider than necessary with lead correction and thus offer greater tolerance to skewing along the gear contact. But these systems can occupy excessive space and can be quite heavy. Another type of epicyclic gear system uses a single flange carrier and a double cantilever arrangement at the pins for the planetary gears to insure that the planet gears and the sun and ring gears remain properly meshed. In this arrangement the single carrier flange is offset axially from planet gears, and the carrier pins project from that flange into, and indeed through, the planet gears. Each carrier pin has one end anchored in the carrier flange and at its other end is fitted within a sleeve which returns back over the pin, yet is spaced radially from the pin, to support the planet gear. U.S. Patent 3,303,713 to R.J. Hicks shows a double cantilevered arrangement. Sometimes an antifriction bearing is fitted between the sleeve and the planet gear. But antifriction bearings consume space, making the planet gears excessively large in diameter, which in turn makes the entire gear system too large and heavy. Summary of the Invention Figure 1 is an exploded perspective view of an epicyclic gear system constructed in accordance with and embodying the present invention; Figure 2 is a fragmentary sectional view of the gear system at one of its planet gears;
Figure 3 is an exploded perspective view, partially broken away and in section, of one of the planet gears and the carrier pin and inner race for that planet gear; Figure 4 is a fragmentary sectional view of the gear system similar to the system of Fig. 2, but with its carrier provided with a modified pin and inner race; Figure 5 is a fragmentary sectional view of the gear system similar to the system of Fig. 2, but with its carrier provided with another modified pin and inner race; and Figure 6 is a fragmentary sectional view of the gear system with its carrier provided with still another modified pin and inner race. Brief Description of Drawings Referring now to the drawings, an epicyclic gear system A (Fig. 1 ), which is in effect a planetary transmission, has a sun gear 2, a ring gear 4 which surrounds the sun gear 2, and planetary gears 6 located between and engaged with the sun gear 2 and ring gear 4. In addition, the gear system A includes a carrier 8 on which the planet gears 6 rotate. The typical epicylic gear system has a sun gear, a ring gear, planet gears, and a carrier, but the gear system A is highly compact and for its size has a greater power density. Moreover, the planet gears 6 mesh better with the sun gear 2 and ring gear 6, causing less wear, diminishing friction, and reducing noise. The gear system A has a central axis X. The sun gear 2 lies along the axis X with its center being the axis X. Thus, should it rotate, it will rotate about the axis X. It has external teeth 10 and is attached to a shaft 12 or some other supporting structure. The ring gear 4 surrounds the sun gear 2, with which it is concentric and thus shares the axis X. It is attached to a housing 14 or some other structure which may or may not rotate. Should it rotate, it will rotate about the axis X. It has internal teeth 16.
The planet gears 6 occupy the annular space between the sun gear 2 and ring gear 4 and have external teeth 18 which mesh with the teeth 10 of the sun gear 2 and the teeth 16 of the ring gear 4. They rotate about axes Y that are offset from, yet parallel to, the central axis X. Each planet gear 6 has (Figs. 2 & 3) tapered raceways 20 and 22 which are presented inwardly toward its axis Y and taper downwardly toward an intervening surface between the small ends of the raceways 20 and 22. The large ends of the raceways 20 and 22 open out of the gear 6 at end faces 26 and 28 which extend out to the teeth 18 and may be squared off with respect to the axis Y. The carrier 8 is attached to another shaft 30 (Fig. 1 ) or other structure, and has its center along the axis X. Should it rotate, it will rotate about the axis X. The carrier 8 includes a carrier flange 32 and carrier pins 34 (Fig. 2) which project all in the same direction from the flange 32, there being one pin 34 for each planet gear 6. More specifically, the carrier flange 32 lies opposite the end faces 26 of the planet gears 6, while the pins 34 project into the gears 6 to establish the axes Y about which the gears 6 rotate. The carrier flange 32 contains bores 36, with each pin 34 at one of its ends being fitted into one of the bores 36 with a interference fit and secured by a weld 38 at the very end of the pin 34 or otherwise attached firmly to the flange 32. Thus, the pins 34 have fixed ends which are anchored in the carrier flange 32 and free ends located remote from the carrier flange 32. Actually, each pin 34 has (Figs. 2 & 3 ) a shank 40 at and leading away from its fixed end, a head 42 at its free end, and an intervening segment 44 forming a groove 46 between the shank 40 and head 42. The shank 40 typically projects beyond the carrier flange 32 a distance equal to or slightly less than the length of the groove 46. It extends out of one of the bores 36 of the flange 32 and into the planet gear 6 for the pin 34 and has a cylindrical surface of uniform diameter. The head 42 also has a cylindrical surface of uniform diameter, and that diameter may
be slightly greater than the diameter of the shank 40. While the head 42 may be somewhat shorter than the shank 40, it still is long enough to lie partially within the planet gear 6. The intervening segment 44 also possesses a cylindrical surface of uniform diameter, except at its ends where it merges into the shank 40 and the head 42 at fillets 48. That diameter, of course, is less than the diameters of the shank 40 and head 42. The planet gears 6 rotate around their respective carrier pins 34 on antifriction bearings 50, each lying within its gear 6 and around its pin 34. Actually, each bearing 50 includes (Figs. 2 & 3) the tapered raceways 20 and 22 on its planet gear 6. Each also includes an inner race 52 which is mounted on the head 42 of its pin 34 and projects over the pin 34 and into the gear 6. The inner race 52 includes a unitary race sleeve 54 and a separately formed rib ring 56 at one end of the sleeve 54. Also, each bearing 50 has tapered rollers 58 organized in two rows, one along the raceway 20 and the other along the raceway 22. The rollers 58 surround the inner race 52. Each carrier pin 34, being anchored in the carrier flange 32 at its fixed end and otherwise projecting beyond the flange 32, is cantilevered from the flange 32. The race sleeve 54 that surrounds the pin 34 is fitted to the head 42 at opposite or free end of the pin 34 and doubles back over the pin 34, so that the sleeve 54 and the inner race 52 of which it is apart is cantilevered from the free end of the pin 34. To this end, the race sleeve 54 has a through bore 60, which at its one end receives the enlarged head 42 on the pin 34. An interference fit exists between the head 42 and the surface of the bore 60 in the sleeve 54 and the end of the head 42 lies flush with the end of the sleeve 54. Here the pin 34 and sleeve 54 are joined together along a circular weld 62 (Fig. 2). Beyond the head 42 the surface of the bore 36 is spaced from the shank 40 of the pin 34, thus providing the second cantilever. The sleeve 54 projects through the interior of the planet gear 6 and here is provided with two
tapered raceways 64 and 66, and an intervening surface 67 between the raceways 64 and 66. The raceway 64 is located farthest from the head 42, while the raceway 66 is located generally around the head 42, with its small diameter end and the beginning of the head 42 being at generally the same axial location. The raceway 64 is presented toward the raceway 20 on the gear 6 and tapers in the same direction, whereas the raceway 66 is presented toward the raceway 22 on the gear 6 and tapers in the same direction as that raceway. Thus, the two raceways 64 and 66, like the raceways 20 and 22, taper downwardly toward each other. The intervening surface 67 is larger than the small ends of the raceways 64 and 66 and enhances the rigidity of the sleeve 54. At the large end of the raceway 64, the race sleeve 54 has a thrust rib 68 which is formed as an integral part of the sleeve 54. It projects axially slightly beyond the end face 26 of the gear 6 and radially to provide a rib face along the large end of the raceway 20. The other raceway 66 at its large end merges into a short cylindrical surface 70 of no greater diameter. The surface 70, in turn, leads out to a rabbet in the opposite end of the sleeve 54, that rabbet being formed by a cylindrical end surface 72 of lesser diameter and a shoulder 74 located between the two cylindrical surfaces 70 and 72. The rib ring 56 fits over the cylindrical surface 72 and against the shoulder 74. It projects radially outwardly past the other cylindrical surface 70 where it is provided with a rib 76 (Fig. 2) which projects axially over the cylindrical surface 70 to present a rib face at the large end of the raceway 66. The opposite ends of the rib ring 56 and the end face on the head 42 of the carrier pin 34 are generally flush, and here the rib ring 56 is joined to the sleeve 54 along another circular weld 78. Both the race sleeve 54 and the rib ring 56 are formed from a low carbon bearing grade steel which is case carburized. Then the sleeve 54 may be ground along its end face out of which the rabbet opens and likewise the rib ring 56 may be ground along its corresponding end face,
this to remove the hard case and expose the lower carbon core beneath it. Only after the hard case is removed in these areas, are the circular welds 62 and 78 made. On the other hand, one may mask these areas during the carburizing process to prevent carbon penetration, and thus eliminate the need for subsequent material removal. Within each planet gear 6, the tapered rollers 58 occupy the annular space between the gear 6 and the inner race 52. Here they are organized in two rows - one between the raceways 20 and 64 and the other between the raceways 22 and 66. The rollers 58 that are between the raceways 20 and 64 have their tapered side faces in contact with those raceways - there being generally line contact - and their large end faces against the face of the integral thrust rib 68. The rollers 58 that lie between the raceways 22 and 66 along their tapered side faces are generally in line contact with those raceways, and along their large end faces contact the face of the rib 76 on the rib ring 56. The rollers 58 of each row are on apex, meaning that the conical envelopes in which their side faces lie have their apices at a common point along the axis Y. This produces pure rolling contact between the rollers 58 and the raceways 20, 22, 64, 68. Moreover, the bearing 50 is preferably set to light preload, so no clearances exist between the raceways 20 and 64 and their rollers 58 and the raceways 22 and 66 and their rollers 58, and this is perhaps best achieved by grinding a surface of the rib ring 56 so as to control the axial position of the rib face for the rib 76 on the ring 56. As a consequence of the preload, the axis Y remains stable with respect to the gear 6. However, the bearing 50 may be set with a slight end play, in which event clearances will exist in it. In each row of rollers 58, a cage may separate the rollers 58 of that row, so that they do not contact each other. But the cage may be eliminated to increase the load capacity of the bearing 50 and thereby make the gear system A even more compact. When bearing 50 operates without a cage in its rows its rollers 58, adjacent rollers 58 can
contact each other along their tapered side faces. To retard metal adhesion at contacting side faces, the rollers 58 along at least their tapered side faces should have a tribological coating that retards adhesion or at least every other roller 58 should have such a coating in it. Actually, a coating is applied only when speeds, loads, and lubrication are such that metal adhesion becomes possible. One suitable coating includes particles of noncrystalline metal carbide and an amorphous hydrocarbon matrix in which the particles are embedded. The tribological coating may be applied to the rollers 70 by physical vapor deposition, by chemical deposition, or by a combination of the two. U.S. patent application 10/114,832, filed 2 April 2002, for the invention of G. Doll and G. Fox entitled "Full Complement Antifriction Bearing", which invention is assigned to The Timken Company, discloses other tribological coatings, which will suffice for the rollers 70, and procedures for applying them. That application is incorporated herein by reference. The assembly of the gear system A begins with the carrier 8, particularly the pin 34 and the race sleeve 54 of the inner race 52. The head 42 of the pin 34 is forced into the sleeve 54 from the ground end of the sleeve 54 until the end face of the head 42 is flush with ground end face of the sleeve 42. Thereupon, rollers 58 are installed along the raceway 64 of the race sleeve 54 to provide one row of rollers 58. Next the gear 6 is advanced over the sleeve 54 with its end face 26 leading. Its raceway 20 comes against the row of tapered rollers 58 that exists around the raceway 64. By rotating the gear 6 relative to the sleeve 54, the rollers 58 along their side faces seat along the raceways 20, 64 and further move up those raceways until their large end faces seat against the face of the integral thrust rib 68. This leaves the remaining raceways 22 and 66 exposed. More rollers 58 are installed between these raceways 22 and 26. With the rollers 58 of this row seated along the raceways 22 and 66, measurements are taken to determine the distance between the large end faces of those rollers 58 and a reference surface
on the race sleeve 54. A rib ring 56 is selected having a rib 76 which positions the rollers 58 such that the bearing 50 has the desired preload or clearance in it. The rib ring 56 is installed over the cylindrical surface 72 on the race sleeve 54 and against the shoulder 74. While the rib ring 56 is held against the shoulder 74, the weld 78 is made, and the weld 62 may be made at this time as well. This completes the assembly of the bearing 50. Once the bearing 50 is assembled and the pin 34 is attached at its head 42 to the inner race 52, the opposite end of the pin 34, which is on its shank 40, is forced into one of the bores 36 in the carrier flange 32. Indeed, each bore 36 in the flange 32 is fitted with a carrier pin 34 that supports a planet gear 6 and bearing 50 installed on the pin 34 in the same manner. With the carrier 8 complete, its planet gears 6 are fitted around and engaged with the sun gear 2 and also fitted into and engaged with the ring gear 4. In the operation of the epicyclic gear system A, torque is applied to the carrier 8 at its shaft 30 and resisted by the planet gears 6 which engage the sun gear 2 and ring gear 4. Each carrier pin 34, being cantilevered from the carrier flange 32, deflects relative to the flange 32 under the torque. The inner race 52, being cantilevered from the pin 34 at is opposite end where the deflection of the pin 34 is the greatest, deflects in the opposite direction so as to compensate for the deflection caused by the pin 34. As a consequence of the two deflections, the axis Y for the planet gear 6 remains essentially parallel to the center axis X, and the planet gear 6 remains properly meshed with the sun gear 2 and ring gear 4. The groove 46 in the pin 34 facilitates the flexure of the pin 34 immediately before its head 42, and this enables the inner race 52 to achieve the correct deflection without extending the pin 34 and inner race excessively beyond the end face 28 of the planet gear 6. The two deflections afforded by the double cantilever enables the planet gears 6 to be shortened and the groove 46 prevents excessive projection of the
pin 34 and inner race 52 beyond the gear 6. The presence of the outer raceways 20 and 22 on the gear 65 itself and the inner raceways on the race sleeve 54 which is attached directly to the pin 34 further contributes to the compactness of the system A. The carrier pin 34, when provided with the groove 46, operates most effectively when the following dimensional relationships exist for a pin 34 formed from medium carbon, heat treated steel: Diameter and length of the head 42 depends upon the bearing selection to support the tapered raceway 66.
Length of the groove 46 is usually 50 to 60 percent of the sum of the length of shank 40 beyond the carrier flange 32 and the length of the groove 46. This may vary due to the carrier flange 32 stiffness.
Diameter of the intervening segment 44 at the groove 46 is usually 70 to 71 percent of diameter shank 40, based on stress concentration factors. Diameter of shank 40 is designed such that the maximum von Mises stress under the carrier flange 32 is below the infinite fatigue limit of the material during nominal loading conditions. This is typically dependent on the material properties, microstructure, strength, hardness and heat treatment. For example, in one case the stresses did not exceed 100-Mpa under nominal loading conditions for medium content alloy steel.
The radial gap between outer diameter of the shank 40 and inner diameter of the race sleeve 54 is greater than the radial deflection of the pin 34 at the extreme load conditions.
The diameter of the intervening surface 67 on the race sleeve 54 should be greater than the mean diameter of the raceways 64 and 66 to rigidity the sleeve 54.
The radius of the fillets 48 should reduce stress concentrations associated with an abrupt change in section as described in well- known textbook techniques. For example, the radius may be a value equal to half the difference between the outer diameter of shank 40 and outer diameter of intervening segment 44.
Width of carrier flange 32 is usually 90 to 150 percent of outer diameter of shank 40.
The geometry of the groove 46 is dependent upon the required radial deflection for improved load sharing of the planet gears 6 with the sun gear 2 and ring gear 4. Preferably the nominal deflection of the pin 34 along the axis Y should be greater than the backlash between the gears 2, 4 and 6 in the epicyclic system A under nominal loading, this to insure that the load is equalized among the planet gears 6 and over the widths of those gears 6. Another carrier 80 (Fig. 4) likewise establishes axes Y about which planet gears 6 revolve, and it also has a carrier flange 32 provided with bores 36. However, the gears 6 rotate on modified carrier pins 82 and modified inner races 84. Each pin 82 has a shank 40 and an intervening segment 44 beyond the shank 40 where it creates a groove 46 in the pin 82. Beyond the segment 44 and groove 46 the pin 82 has a modified head 86 provided with a large diameter surface 88 immediately beyond the groove 46 and a small diameter surface 90 extended beyond the large diameter surface 88 at a shoulder 92. The small diameter surface 90 leads out of the end of the pin 82.
The inner race 84 for each pin 82 has in its race sleeve 54 an elongated bore 94 which at one end opens out of the race sleeve 54 through the thrust rib 68 and at its other end opens into a short reduced bore 96 which opens out of an end face 98 at the opposite end of the sleeve 54. The two bores 94 and 96 are separated by a shoulder 100. The head 86 of the pin 82 fits through the elongated bore 94, there being an interference fit between the large diameter surface 88 of the head 86 and the surface of the bore 94. The head 86, at its small diameter surface 90 projects through the reduced bore 96 and beyond the end face 98 of the race sleeve 54. Indeed, the head 86 of the pin 82 is advanced through the elongated bore 94 of the race sleeve 54 until its shoulder 92 comes against the shoulder 100 in the race sleeve 54. In addition, the modified inner race 84 has a modified rib ring 102 that fits around the small diameter surface 90 on the head 86 with an interference fit and bears against the end face 98. The rib ring 102 has a rib 104 which projects toward the integral thrust rib 68 and beyond the end face 98. The rib ring 102 is attached to the head 86 along a circular weld 106. The race sleeve 54 for the modified inner race 84 has tapered raceways 64 and 66 which lead up to the thrust rib 68 and rib 104, respectively. One row of tapered rollers 58 lies between the raceway 64 on the inner race 84 and the raceway 20 in the patent gear 6 and another row of tapered rollers 58 lies between the raceways 22 and 66, all to form a bearing 108 that is set to preload. The race sleeve 54 of the modified inner race 84 is formed from high carbon bearing grade steel that has been through hardened. The rib ring 102 is formed from low carbon bearing grade steel which has been case carburized. However, the case does not exist at the outer end of the race 84, it having been removed by grinding or, by reason of masking, having never formed, so that the weld 106 is made in the low carbon steel.
Still another carrier 110 (Fig. 5) is similar to the carriers 8 and 30 in that it supports planet gears 6 that rotate on bearings 50 including inner races 52 or 84. But the carrier 110 has a grooved pin 112 that differs somewhat from the grooved pins 34 and 82 of the carriers 8 and 30. In this regard, the pin 112 has a shank 114 that lies entirely or almost entirely within the bore 36 of the carrier flange 32. Typically, the length of the shank 114 is equal to or less than the diameter of the carrier bore 36. The pin 112 also has a head 116 that fits within the through bore 60 of the race sleeve 54, to which it is secured by a weld 62 or 106. Between its shank 114 and its head 116, the pin 112 has a reduced intermediate segment 118 formed by a conical surface 120 and a cylindrical surface 122. The surfaces 120 and 122 produce the groove 46 in the pin 112. The conical surface 120 at its large end possesses a diameter equal to that of the shank 112 and here merges with the shank at a fillet 124. The surface 120 tapers downwardly away from the shank 114 and at its small end merges with the cylindrical surface 122 along another fillet 124. The cylindrical surface 122 extends toward the head 42 or 84, into which it merges along still another fillet 126. The section having the cylindrical surface 122 facilitates flexure circumferentially with respect to the axis X of the gear system A, whereas the section having the conical surface 120 facilitates flexure radially with respect to the axis X. The length of the conical surface 120 measured along the axis Y should be greater than one-half the distance between the faces of the thrust rib 68 and the rib ring 76. The length of the cylindrical surface 122, measured along the axis X, is typically one-half or less the length of the length of the conical surface 120, likewise measured along the axis X. The fillets 124 and 126 reduce stress concentrations associated with abrupt changes in diameter. Actually the geometry of the intermediate segment 118, with its conical surface 120 and cylindrical surface 120 and fillets 124 and 126,
is dependent upon the required radial deflection for improved load sharing of the planet gear 6 with the sun gear 2 and the ring gear 4. Preferably the nominal deflection of the pin 112 along the axis Y should be greater than the backlash between the gears 2, 4 and 6 in the epicyclic system. Under nominal loading, this to insure that the load is equalized among the planet gears 6 and over the widths of those gears 6. The fillet radius 124 values are related to stress level capacity of the planet carrier 32 at the face of the carrier flange 32 from which the pin 112 emerges as well as the yield strength limit of the pin 112. Yet another carrier 130 (Fig. 6) is similar to the carriers 8, 30 and
110 in that it supports planet gears 6 that rotate on bearings 50, but the bearing 50 for each has a somewhat different inner race 132 which fits over and accommodates a different carrier pin 134. Indeed, the inner race 132 and carrier pin 134 are configured such that the pin 134 experiences generally uniform stress between the flange 32 and that portion of the inner race 132 in which the pin 134 is received and anchored. This enables the pin 134 to have a minimum cross section. Considering the pin 134 first, it has at one end a cylindrical shank 136 which is anchored, almost entirely, within the bore 36 and at its opposite end a cylindrical head 138 which is essentially the same diameter as the shank 136. Between the shank 136 and the head 138 the pin 134 has an intervening portion 140 formed from two approximately conical surfaces 142 which taper downwardly toward each other and merge at a fillet 144. The conical surfaces 142 and fillet 144 provide the carrier pin 134 with an annular groove 146. The inner race 132 includes a race sleeve 150 and a rib ring 152. The race sleeve 150 has through bore 60 where it receives the pin 134. It also has the two raceways 64 and 66 as well as the integral intervening surface 67 and rib ring 68. It also has the cylindrical surface 72 that leads away from the large end of the raceway 66 at a reduced diameter. The rib ring 152 fits over the cylindrical surface 72 of the race
sleeve 150 and is joined to the race sleeve 150 at the weld 78. It has the rib 76 against which the large ends of the rollers 58 along it bear. The race sleeve 150 fits over the head 138 of the carrier pin 130 with an interference fit and is attached to the carrier pin 130 at a weld 62. It extends over the groove 146 where it is spaced from the intervening portion 140 of the pin 134, and at its opposite end is beveled so as to remain spaced from the underlying conical surface 142 - indeed, for enough to permit the race sleeve 150 to deflect radially with respect to pin 134. The head 138 lies axially beyond the face of the rib 76 on the rib ring 152 so that it does not underlie the raceway 66. The carrier 130 operates most effectively when the pin 134 is formed from median carbon, heat treated steel and flowing relationships exist: Diameter and length of the head 138 depends upon the bearing selection to support the tapered raceway 66.
The length of the intervening portion 140 of the pin 134 is about equal to the length of the teeth 10 for the planet gear 6 that is around the pin 134.
The diameter variation of the intervening portion 140 is such that the maximum von Mises stress at the carrier flange 32 is below the maximum von Mises stress in the portion of the pin 134 that is received in the bore 36 of the carrier flange 32 and is below the infinite fatigue limit of the material of the pin 134 during nominal loading conditions and remains substantially consistent along the intervening portion 140. This is typically dependent on the material properties, microstructure strength, hardness and heat treatment.
The minimum radial gap between the intervening portion 140 of the pin 134 and the bore 40 of the race sleeve 150, that is the gap at the free end of the race sleeve 150, is greater than the radial deflection of the pin 34 at extreme load conditions.
The diameter of the intervening surface 67 on the race sleeve 150 should be at least as great and preferably greater than the mean diameter of the raceways 64 and 66, this to rigidity the race sleeve 150.
The width (thickness) of the carrier flange 32 and the length of each bore 36 within it should be between about 90 and 150 percent of the diameter of the shank 136 each pin 134. The small diameter of the tapered raceways 64 and 66 and the diameter of the bore 60 are such that large bending deflections and stresses in the inner race are under acceptable limits that typically depend on the material properties. The minimum diameter of the bore 60 should be the difference divided by 2 between the small diameters of the raceway 64 and 66 (either) and the bore 60 times 1.6 the section of an equivalent nonintegrated antifriction bearing.
The geometry of the intervening portion 140 is dependent upon the required radial deflection for improved load sharing of the planet gears 6 with the sun gear 2 and ring gear 4. Preferably the nominal deflection of the pin 134 along the axis Y should be greater than the backlash between the gears 2, 4 and 6 in the epicyclic system A under nominal loading, this to insure that the load is equalized among the planet gears 6 and over the widths of those gears 6.
Referring to Figure 6, the geometry of the intervening portion is obtained by solving the equation below for (DM) when given a stress level (VM), a load (P), and an active pin length (l_ι). The stress level (VM), load (P), and pin length (L-i) are defined as constant and the pin diameter (D(X)) becomes variable. VM = Von Mises Stress P = Load Li = Active pin length X = Distance from the end of the intervening portion 140 D(χ) = Pin diameter at a given distance X
The above equation can be solved using computer software to provide a table of values showing a pin diameter (D
(X)) for each X value. Variations are possible. For example, the rolling elements may be balls, in which event the raceways on the planet gears and on the inner races should conform in contour to them, yet remain oblique to the axis Y so as to accommodate thrust as well as radial loads. The rolling elements may also be spherical or cylindrical rollers. Also, the carrier pins 34 and 134 need not have the grooves 46 or the intervening portion 140, but instead the shank 40 and 136 of each may extend out to the head 42 and 138 or the head 86.