Planet Load Sharing and Carrier Compliance in Epicyclic Travel Drives

2. The epicyclic arrangement in a travel drive

2.1 Configuration

The dominant configuration in a tracked travel drive is the fixed-ring epicyclic: the ring gear is held stationary against the hub housing or is cut directly into it, the sun gear is the input and is driven by the hydraulic motor shaft, and the carrier — which holds the planet pins — is the output and drives the sprocket. Three planets is the most common count in the high-torque output stage; four, five and six appear in larger units and in the lighter, faster upstream stages of a compound train.

For a fixed ring, the reduction from sun to carrier is

where z_s and z_r are the tooth counts of sun and ring. The planet tooth count does not appear: the planets are idlers in the torque sense, transmitting load from sun to ring without altering the ratio. Planet size is set by the center distance, z_p = (z_r − z_s) / 2 for a standard train, and by the tooth loading each planet must carry.

A single stage of this form is practically limited to a ratio of roughly 3:1 to 8:1 — below about 3:1 the planets become small relative to the sun (at 3:1 a standard planet already has only half as many teeth as the sun), leaving little room for the planet bearing and pin; above about 8:1 the sun becomes too small to carry the torque or to accommodate a bore. Travel drives commonly need 40:1 to 80:1 overall, so two or three stages are compounded, the carrier of one stage driving the sun of the next.

2.2 Why the planetary form is used

The reason a final drive is planetary rather than a simple offset reduction is power density. Torque divides between n planet meshes, so for the same tooth load each mesh is a fraction of the size a single mesh would need. The reaction forces at the sun are nominally balanced — for equally spaced planets the radial components cancel — so the sun needs no bearing to react a net side load, and the whole train is concentric, which suits a drive that must fit inside a sprocket hub.

Every one of those advantages is conditional on the load actually dividing as assumed. If one planet of three takes half the torque instead of a third, that mesh sees 1.5 times its design tooth load, the radial forces no longer cancel, and the sun is pushed sideways against whatever restrains it. Load sharing is therefore not a refinement in epicyclic design; it is the assumption the architecture rests on.

3. Ideal sharing and the mesh load factor

3.1 Nominal division

For a train with n planets carrying input torque T_s at the sun, ideal sharing gives each sun–planet mesh a tangential load

with d_s the sun pitch diameter. The same tangential load appears at each planet–ring mesh, so the ring mesh sees the same force on a larger radius and, being an internal mesh with a conforming tooth pair, a substantially lower contact stress. This is why in practice the sun–planet mesh governs surface durability in most travel drives, and why sun gears are the member most often found pitted in a stripped unit.

3.2 The mesh load factor

Rating standards handle unequal sharing by an explicit multiplier applied to the nominal per-mesh load. The epicyclic-specific treatment is set out in ANSI/AGMA 6123⁵. In ISO 6336¹ the symbol is K_γ; AGMA's epicyclic design practice uses a mesh load factor with the same meaning. It is defined as the ratio of the load on the most heavily loaded mesh to the average load per mesh:

so K_γ = 1.0 is perfect sharing and higher values are worse. It multiplies the load used in both the bending and the contact calculation, alongside the application, dynamic and load distribution factors. Because contact stress varies with the square root of load, a K_γ of 1.25 raises contact stress by about 12 % and, on a curve where life varies with a high power of stress, that is not a small effect. Bending stress varies directly with load, so the same factor costs a full 25 % there.

The values published in the design literature depend chiefly on the number of planets and on whether any member is allowed to float. Table 1 gives magnitudes of the kind quoted in the epicyclic design practice; they are illustrative rather than prescriptive, and a specific design with measured pin positions and a known floating arrangement may do considerably better.

3.3 Three planets and static determinacy

With one member floating, the difference between three planets and four is not a point on a gradual trend; it is a change of kind. A sun gear restrained only by its meshes has three planar degrees of freedom available to it: two translations and, trivially, rotation. With three equally spaced planets the sun can translate in the plane to equalize the three mesh deflections, and there is exactly one position at which it does. The problem is statically determinate: whatever the pin position errors, a floating sun finds the position that shares the load, and it does so passively.

With four or more planets even a floating sun has more constraints than freedoms. There is in general no position of the sun at which all four mesh deflections are equal, and the load division is then set by the relative stiffnesses of the members and by the manufacturing errors, not by a self-centering geometry. This is why the published mesh load factors deteriorate with planet count, and why designers who want the load capacity of five or six planets must invest in the compliance arrangements of section 5 to get it.

Determinacy is a property of the floating arrangement, not of the planet count alone. With every member located, the sun's bearing reactions join the mesh loads as unknowns and a three-planet train is statically indeterminate too, so the wider gap between three planets and four in the all-members-fixed column of Table 1 is not the determinacy boundary; the bands are illustrative, and neither column isolates it.

The practical corollary matters for anyone assessing a drive: a three-planet unit that is sharing badly is almost always telling you that the sun is not free to float — a seized spline, a bottomed thrust face, a sun trapped by a bearing that was never meant to locate it.

4. Sources of unequal sharing

4.1 Planet pin position error

The dominant manufacturing contributor is the tangential position error of the planet pins in the carrier. If one pin is displaced tangentially from its nominal position, the backlash at that planet's two meshes changes: the mesh closes early on one flank and late on the other. Under load, the planet whose mesh closes first begins to take load before the others engage, and it continues to carry more until the elastic deflection of the members brings the remaining planets into contact.

The sensitivity is high because gear mesh stiffness is high. A mesh deflection under full load is typically on the order of ten to thirty micrometers; a tangential pin position error of ten micrometers is therefore a large fraction of the total elastic take-up, and pin position is held to single-digit micrometers in carriers built for good sharing. Radial pin position error matters less: it changes the center distance, and hence the operating pressure angle and backlash, but does not directly advance or retard the engagement in the way a tangential error does.

Pin bore position in the carrier is normally produced in a single setup on both carrier plates together, or by line-boring an assembled carrier, precisely so that the two ends of each pin agree and so that the pins agree with each other. A carrier repaired by welding and re-boring one plate is a carrier whose sharing behavior is no longer known. Flank accuracy itself is classified under ISO 1328-1⁷ and inspected per ISO/TR 10064-1⁸.

4.2 Carrier torsional windup

The carrier is not a rigid body. Torque enters it at the planet pins, distributed around the pin pitch circle, and leaves through the output spline or flange at the center. Between those two the carrier twists. In a two-plate carrier the twist is taken by the connecting webs or posts between the plates, and if those posts are not symmetric — and in a carrier with three posts between three planets they are — the twist is not uniform around the circumference.

The consequence is that the pin at one angular position is displaced tangentially relative to the pin at another, which is exactly the error of section 4.1 but produced elastically and in proportion to torque. It follows — and DIN 3990¹⁰, the ancestor of the ISO method, makes the same point — that sharing measured at low torque may not represent sharing at rated torque, and that a carrier design is a sharing decision as much as a strength decision. Single-plate ("cantilever") carriers, in which the pin is supported at one end only, are compact and cheap but add pin bending to the same error budget; they are common in the light, high-speed first stage of a compound drive and rare in the output stage.

4.3 Ring gear and housing compliance

A ring gear cut into a relatively thin hub, or bolted into a housing that is itself supported at discrete points, deflects radially under the planet loads into a lobed shape with as many lobes as there are planets. This compliance is in part beneficial: a ring that yields at the most heavily loaded planet transfers load to its neighbors, which is a passive sharing mechanism, and some designs deliberately thin the ring behind the teeth to exploit it. It is harmful when the ring's stiffness varies around the circumference — for instance where a bolt boss, an oil port or the housing's own mounting feature stiffens one sector — because then the compliance itself is unequal.

4.4 Planet bearing clearance and planet tilt

Planets run on needle roller bearings, on plain bushings, or on tapered or cylindrical roller sets, in every case with a working clearance. That clearance permits the planet to move radially and, more importantly, to tilt about an axis perpendicular to the pin. Tilt does not much affect how much load a planet takes; it affects where across the face width that load acts, which is the subject of section 6. Bearing clearance also permits a small tangential shift, which does contribute to sharing, and a planet bearing that has worn its clearance open is a planet that engages later than its fellows.

5. Recovering sharing by design

5.1 The floating sun

The commonest and cheapest sharing arrangement is to let the sun float. The sun is connected to its input shaft by a loose-fitting or crowned spline with generous clearance and no radial location, and is supported radially by nothing except its three planet meshes. Under load it moves the few tens of micrometers needed to equalize them. For a three-planet train this is nearly a complete solution, which is why so many travel drives are three-planet trains with a floating sun.

The arrangement has consequences of its own. A floating sun is unconstrained at rest and can rattle at light load; it relies on a spline that must transmit full torque while permitting radial motion, so the spline sees combined sliding and load, and spline fretting is a recognized wear mode in these drives. The spline, specified under ISO 4156-1¹², is usually crowned and generously lubricated for that reason. Any repair that replaces a floating spline connection with a tighter or piloted one removes the sharing mechanism the design depends on.

5.2 Floating ring and floating carrier

Where the sun cannot float — because it must be piloted for another reason, or carries a bearing — the ring may be allowed to float instead, mounted on a spline or in a compliant carrier ring rather than pinned rigidly to the housing. Floating the carrier is rarer, since the carrier is the output and must be located to drive something.

Only one member need float, and floating more than one does not help: once the train has enough freedom to equalize, further freedom only removes location the drive needs elsewhere.

5.3 Flexible pins

For trains of four or more planets, where floating a single member cannot equalize all meshes, the established alternative is to make the pins themselves compliant in a controlled way. In the flexible-pin arrangement, the planet is carried on a sleeve that is supported from one end of a cantilevered pin, so that the planet can translate tangentially under load while remaining parallel to its nominal axis. The pin's bending compliance is large compared with the mesh's, so a heavily loaded planet deflects away and sheds load onto its neighbors.

The point that distinguishes a flexible pin from a merely undersized one is the parallel motion: a simple cantilevered pin bends into a slope, tilting the planet and destroying the face load distribution, whereas the sleeve arrangement converts that slope into a translation. This is the mechanism by which epicyclic trains of five and more planets are built with mesh load factors approaching those of three-planet trains, and it is found in large industrial and wind-turbine gearing more often than in mobile travel drives, where three planets and a floating sun usually suffice.

6. Face load distribution — a separate problem

6.1 Why it is not the same question

Load sharing asks how the total torque divides between planets. Face load distribution asks how the load carried by one planet distributes across the width of that mesh. They are independent: a train can share perfectly between three planets and still concentrate every one of those three loads on one end of the tooth. ISO 6336-1¹ treats them with separate factors — the mesh load factor K_γ for the first, and the face load distribution factors K_Hβ and K_Fβ for contact and bending respectively for the second.

In a well-built travel drive the face factors are frequently the larger of the two, and it is worth noting that they are also the ones most easily wrecked by a repair. A planet bearing with excess clearance, a bent pin, a carrier plate distorted by heat, a planet pin pressed in out of square: each of these tilts a planet and moves its load to one end of the face while leaving sharing between planets essentially unchanged.

6.2 Sources and remedies

The geometric sources of mesh misalignment are pin non-parallelism relative to the sun and ring axes, planet bearing clearance and tilt, elastic deflection of the pin under load, and thermal distortion of the carrier. Analytical methods for the face factors are given in AGMA 927⁶. The standard remedies are lead crowning of the planet or sun teeth, so that a small misalignment moves the contact patch rather than concentrating it at an edge; end relief, which removes the last fraction of a millimeter at each end of the face where edge contact would otherwise occur; and helix angle modification, in which a deliberate lead correction is cut to cancel a predicted deflection at the design load.

The third of these is load-specific by construction: a helix modification designed to cancel deflection at rated torque leaves a residual misalignment at low torque, in the opposite sense. This is one reason a drive can show contact marking at one end of the face at light load and central marking at working load, and why marking inspection is only meaningful against a stated load condition.

7. Consequences for rating and observed damage

The factors of Table 2 multiply. A drive with K_γ = 1.25 and K_Hβ = 1.4 is running its worst mesh at 1.75 times the nominal tooth load on the contact side, which on a Hertzian basis is about a 32 % increase in contact stress. Against the shape of the surface durability curve reviewed in DYCO-TP-102, an increase of that order is not a marginal reduction in life; it moves the component to a different part of the curve.

This is the mechanism behind a damage pattern that is familiar to anyone who has opened a number of failed travel drives: the damage is not uniform around the planet set. One planet is pitted and its fellows are serviceable; one planet bearing has spalled and the other two are within limits; the sun shows heavier wear on the flanks that face one particular planet. Uniform damage across all planets suggests a cause acting on the whole train — contamination, lubricant failure, sustained overload. Damage concentrated on one planet suggests the load was never divided in the first place, and points at pin position, carrier condition, or a sun that was not free to float.

The diagnostic value of that distinction is high and it costs nothing to observe. It should be recorded before a set is disassembled far enough to lose the angular relationship between the parts.

8. Implications for replacement practice

Three consequences follow for anyone selecting or fitting replacement planetary components.

Planets are a matched set. Because sharing depends on the relative timing of the meshes, and because that timing depends on the planets' tooth thickness and their bearing clearance as well as on pin position, replacing one planet of three with a new part of nominal dimensions in a set whose other two have run for thousands of hours re-introduces a timing difference between the new planet and its fellows. The new planet is dimensionally tighter and engages earlier. Where no member can float, it then takes a disproportionate share; where the sun floats freely, the sun runs off-center to absorb the difference instead (section 3.3), spending float that also has to cover pin position error, and a sun that runs out of float puts the train back into unequal sharing. Planetary sets are replaced as sets for these reasons and not merely as a commercial convention.

The carrier is a precision component, not a bracket. Its pin bore positions are part of the gear geometry. A carrier that has been welded, straightened, or had a pin bore repaired is outside the tolerance the rating assumed, and no inspection of the gears themselves will reveal it. Where a carrier is reused, pin bore position and parallelism are the measurements that matter, not visual condition.

Floating members must remain free. A sun spline that has fretted, corroded or been assembled with an interference it was never designed for will not float, and a three-planet train that cannot float its sun has lost its sharing mechanism while looking entirely correct on the bench. Spline condition and free radial movement of the sun are worth confirming explicitly.

Each of these is a reason why a drive assembled from individually correct parts can still be a drive that does not last. Interchangeability at the level of the part number is necessary but it is not the whole of fitment; the set has to be consistent as a set.

9. Summary

The load capacity of an epicyclic travel drive is the capacity of its most heavily loaded mesh, not the sum of its meshes. Rating standards recognize this in the mesh load factor, whose published magnitude depends primarily on planet count and on whether a member is free to float. Three equally spaced planets with a floating sun is a statically determinate arrangement that shares passively and is for that reason the dominant configuration in mobile travel drives; four or more planets require deliberate compliance, most effectively the flexible-pin arrangement, to achieve comparable sharing. Sharing between planets and load distribution across the face width are separate problems with separate causes and separate remedies, and both multiply into the rated stress. In service, damage concentrated on one planet of a set is evidence about sharing that uniform damage does not provide; in repair, the practical consequences are that planetary sets are replaced as sets, that carrier geometry is part of the gear geometry, and that a floating member which has ceased to float has removed the mechanism the whole architecture depends on.