The high lift system of an aircraft, including trailing and/or leading edge slats/flaps, increases lift for takeoff, controls flight during cruise, and reduces landing distance for touch-down.
This flight control system is usually composed of power drive units (PDUs), torque tubes, bevel gear boxes, offset gearboxes, leading edge (LE) geared rotary actuators (GRAs), trailing edge (TE) GRAs, and leading edge sector gears and pinions (Figure 1). The system also includes other components, such as torque limiters, slip clutches, noback drive devices, and wing tip brakes to provide system protection from overloading. Many of these components contain different types of gears that are usually highly loaded to increase the power to weight ratio. Because of the requirements on weight or envelope and consideration of cost, the gears in a high lift system are always designed with minimal margins.
The structure that supports the gear is limited in size or simplified, and the gear material and heat treatment are selected for easy manufacturing. Deflections and misalignments between meshing gears cause edge loading which generates noise and high bending and contact stresses. The deflection emanates from the high loading and the misalignment comes from wing bending or the deflection of gearshafts and housings. Irrespective of the load, once the misalignment and/or deflection cause the contact area to shift and diminish, the stress becomes large enough to cause problems.
AGMA publishes an atlas of failure modes [1] that identify some common types of wear. Bajpai et. al. [2] combines a contact analysis model and a wear prediction model to describe the evaluation of tooth surface wear of spur and helical gear pairs. In these previous papers, the focus is on the outcome of failures, and not the reasons and sources of gear wear. Drago [3] discussed spalling caused by tip interference and showed that a contact failure can lead to a more severe tooth fracture. Drago et. al. [4] also discussed the relation between micropitting to specific lubrication additive package combinations, gear quality and surface finish, which can be resolved by profile modifications. Errichello et. al. [5] investigated that the root cause of macropitting is the geometric stress concentration caused by tip-to-root interference. All these previous three papers deal with failures caused by tooth geometries and quality of gears. Errichello [6] investigated a gear set which failed due to lubrication breakdown.
The main objective of this presentation is to find out how to solve these problems if the cause is due to edge loading from the misalignment of gear mounting and/or deflection of supporting structure. In this article, several different gear failure cases in the development phase of high lift systems are presented, including leading edge geared rotary actuators, and trailing edge geared rotary actuators, sector gears and pinions, and offset gearboxes. The failure modes can be classified as spalling or pitting at the location of concentrated loads. Most of the problems can be resolved by providing correct lead modifications to alleviate the concentrated loading, while some can only be corrected by increasing the gear diameters, design modifications, or introduction of materials with higher allowable. Detailed analyses to predict deflections and misalignments on system and component levels is the key to the amount of lead modification, from which increased local contact stresses can be calculated.
The cases presented in this paper are from the pre-production risk mitigation units (RMUs). Normally the RMUs were designed with little margin to achieve minimum weight. Most system or component deflections can be predicted by analyses during the design phase. If there are any unanticipated misalignments or deflections, then failures will show up and the situation can be improved with corrections in the production units. In this way designs are optimized for minimum weight.
Leading Edge Rotary Geared Actuators
The cross section of a typical leading edge geared rotary actuator is shown in Figure 2. There are three gear meshes on each one of the planet gears. The output is on the left side of the actuator. The output planet gears are overhung and balanced by the planet gears on the right. The center planet gears act as a pivot point. Because the output planet gears are overhung, it is called a cantilever GRA.
Trailing Edge Geared Rotary Actuators
The cross section of a typical trailing edge geared rotary actuator is shown in Figure 3, and the gear schematic is shown in Figure 4. The output consists of two load paths from two end ring gears. The sun gear drives the right end planet gears. The stiffness difference between the right and left load paths causes the compound planet gear to tilt. Thus, not only the planet gear loads due to meshing with the ring gears have to be considered, but also the misalignment from the two load paths needs to be included for selecting the optimum crowning which also reduces load mal-distribution across the gear tooth faces and increases local contact stresses. Therefore, excessive crowning must be avoided.
Leading Edge Sector Gears and Pinions
A typical leading edge sector gear and pinion set is shown in Figure 5. The pinion has to be crowned to allow for wing bending if a spherical bearing mount is not possible. This gear set is exposed to outside environment and grease or dry film lubrication may be depleted between service intervals. Crowning radii have to be optimized so that contact stresses can be minimized and the risk of running dry can be mitigated.
From all the above applications in a high lift system, we can understand the importance of a good face load distribution between mating gear teeth. If misalignments become excessive, gears will suffer edge loading. Five different failure examples from pre-production risk mitigation units are the subject of the next section.
Failure Examples
Example 1: Offset Idler Gear Set
An offset gear set with one bearing very close to one end of the gearbox and another support far at the other end is shown in Figure 6. This is a very special layout, and is not the normal offset gearbox straddle mounted between two bearings. One can calculate the face load distribution according to AGMA [9]. Because of the deflection, gears are edge loaded and pitted as shown in the figure. To solve the problem, the gears need to be crowned to accommodate this misalignment. The face width is 0.80 inch. The total slope including the deflection and manufacturing errors is 0.0048 in/in. After solving the equations as discussed in [7], the crowning radius is 91 inch, and the crowning center is at the end of the tooth. A contact stress of 266 ksi is calculated under the max tangential load of 1000 lbf. From Figure 7, we can see that the crowning has eliminated the pitting problem, so that the full tooth is now sharing the load.
Lessons Learned
The lesson learned in this case is that the location of bearing supports has significant impact on the load distribution of gears. Of course, it is better to have gears straddle mounted and sit just in the middle of two rigid supporting bearings. But sometimes, because of the restriction from the structure of gearboxes, it is unavoidable to have lead modifications to relieve the situation.
Another lesson learned is that if there is a large chamfer (Figure 8) on any member of the gears in mesh, the net face width at the lowest point of single tooth contact (LPSTC) should be used to calculate the contact stress, not the face width at the root. Using this net face for contact stresses is very easy to overlook at the early stage of design process. When the design is so critical, a small percentage can make a significant difference on life calculations. The increased contact stress should be recalculated considering the localized load distribution from the crowned teeth.
Example 2: Sector and Pinion Gear Set
A sector and pinion gear set in Figure 5 must accommodate wing deflections. Because of being exposed to outside environment, the contact stress must be low enough so that running the gears without grease is possible.
The baseline design is regularly lubricated, and maximum allowable misalignment is 0.0015 in/in. The calculated contact stress is 312 ksi with crowning under maximum operating loads. However, the test was done with no re-grease between service intervals. It is clear from the gear and pinion shown in Figure 9 and Figure 10 that although the contact pattern is localized, yet because of the higher contact stress due to crowning, initial lubrication is gone after a while and soon after micro-pitting and rusting will result. Therefore, the goal is to make it lube-free. For a given misalignment, a new crowning radius and face width are proposed so that the stress is low enough to eliminate the need for re-lubrication in service. The increased face width comes with a weight penalty, though. Another solution is to change to a material that has a higher contact allowable.
Lessons Learned
A common engineering practice for calculating fatigue life is to use the mean load of a load spectrum. The mean load is the time averaged load of a spectrum which contains multiple load sets (load vs. time) and is given by equation 1. The exponent m establishes the relationship between load (i.e., stress) vs. cycles to fail. Various exponents may be used to determine the mean load, but the most common are the followings: m = 3 for bearing wear analysis [8] and m = 9 for gear contact fatigue [9].
Equation 1 is known as the Lundberg-Palmgren equation used in the mean load calculation [8] for rolling bearings. This method can be extended to gear contact life analyses, where m = 9 is derived from the slope of pitting S-N logarithmic curves [9], and the square relation between loads and contact stresses. However, this mean load method may not be correct for the sector and pinion gear set, because the high load at one tooth cannot be shared by other teeth due to the limited stroke range. The lesson learned in this failure study is that unlike other types of gears the teeth get multiple hits from mating members, the sector gear gets certain loading with specific load conditions. A cumulative damage analysis, Equation 2 [9] recommended by AGMA, is more suitable.
Example 3: Cluster Pinions in TE GRAs
The cluster pinions in the input stage of a trailing edge GRA (Figure 3) failed at the pinion gear which mated with the ring (Z) gear. A free body diagram showing the force (red dashed line with arrows) acting on the gears is shown in Figure 11. Due to the deflection and internal clearances between bearings and the mounting housing, the cluster pinions tilt downwards and inwards on the pinions at the left. Therefore, the forces between the gear mesh of cluster pinions and ring (Z) gears are concentrated at the end of the cluster pinions. The evidence of tilting gears is also shown on the input sun pinion (Figure 12).
Shown in Figure 13 is the spalling failure caused by edge loading on the end of the cluster pinions. Portions of the teeth then broke away from the origin of the spalling in a way very similar to what was described in [3]. It starts from the inner bottom end of the teeth, then pitting/spalling propagates up along the profile in the direction of sliding. The crack then turns in the direction of the line of action into the material, resulting in a chunk of metal separating from the teeth. Because the damage is only at one end of the teeth, the cause of failure is edge loading, instead of tip interference.
The solution to this problem is to provide lead modifications on the cluster pinions similar to Example one, so that the load concentration can be alleviated. Another option is to use carburized materials, so that even with undesired load distribution the design can still hold the load. Other possible options are to preload the bearings to reduce the clearance or to increase the span of bearing supports to reduce the effect of the clearance. However, the latter modification will increase the length of the actuators.
Lessons Learned
1. The effect of bearings internal clearances on overhung gears cannot be neglected, especially when the bearing span is relatively small;
2. The deflection from the supporting carrier needs to be considered in the misalignment;
3. Do not underestimate the loading in the input stage. Although the load is relatively low compared to the output stage, once the gears are tilted and the contact shifts to the edge, then the stress becomes very large.
4. There are more teeth hits on the input stage than on the output, so the de-rating factors need to be adjusted accordingly.
Example 4: Simplified Compound GRAs in LE
The triple planet gears shown in Figure 2 can be simplified to simple planet gears but still mesh with two ring gears. A degenerate version of the cantilever GRAs is shown in Figure 14 which is called simplified compound GRAs. When diametral envelope is available on the leading edge of an airplane, the cost saving on using simplified compound planetary gears could be beneficial. It has the same advantage and disadvantage of the cantilever actuator with a larger diameter but shorter length.
Risk Mitigation Testing:
1. At 50% of life teardowns, signs of spalling are shown in the root area of the housing ring gear at the interface between two ring gears (Figure 15 and Figure 16).
2. The failed unit exhibited chipped housing ring gear teeth, initiating from the root of the edge facing the output ring gear (at the interface between the two ring gears) (Figure 17).
3. The end of the sun gear also shows sign of interference near the start of active profile (Figure 18). This confirmed that the planet gears are tilted under equal and opposite loads from both ring gears.
4. Upon magnetic particle inspection, both the fixed ring gear and the output shaft ring gear exhibited fatigue cracks in the tooth root area (Figure 19 and Figure 20).
5. The failure of the fixed ring gear (Figure 20) indicates an edge loading condition in excess of what was used in the gear calculation on face load distribution.
Proposed Improvements Based on Risk Mitigation Testing Results:
1. Shot peening the ring gear teeth on the production unit provides improved bending fatigue performance over the risk mitigation unit, which was not shot peened.
2. Tapered ring gear teeth (via tilting the part in the shaper cutter) or plunge hobbing the planets can improve the face load distribution and prevent hard edge loading (Figure 21 and Figure 22). Another option is to increase the diameter so that the gears can take the extra load mal-distribution.
3. Improvement can be made without increasing the diameter by built-in slope on the ring gears. The load mal-distribution of the gears before the proper lead modification is shown in Figure 21 in which the planet gears are tilted. When the lead modification is implemented as shown in Figure 22 on both housing ring gears and output ring gears, the face load distribution becomes uniform.
Lessons Learned
1. The tilting from bearings internal clearances and carrier deflections cannot be reduced enough to solve the load mal-distribution.
2. There is more weight benefit by increasing the diameter and reducing the face width, if the envelope allows.
Example 5: Cantilever Compound GRAs in LE
A prototype cantilever (unbalanced) compound geared rotary actuator similar to the one in Figure 2 is shown in Figure 23. The major difference between these two is the location of the supporting rings.
Figure 24 shows a free body diagram in the normal section through the gear pitch in the XZ plane. For a correct design where the left separator ring is at the end shown in Figure 2 and Figure 25, the tangential force bends the planet gears in the way that the radial load and bell mouth effect on output ring gears compensate the deflection. Therefore, the left end planets have a better face load distribution (combining the Y-deflection from Figure 24 and Figure 25). The center planet gears have minimum deflections and the right end planet gear is far from the center with a shorter face width. Therefore, there is no need to crown even with both deflections in the same direction caused by tangential and radial loads.
On the other hand, Figure 26 shows a free body diagram in the cross section in the XY plane of a poor design where the deflection caused by radial load acting on the end planet gears is in the same direction as the tangential load does shown in Figure 24.
Lessons Learned
This unit failed because there is too much deflection and tilting due to wrong separator ring locations and chattering due to synchronous and low efficient designs. The output planet gear NBP should be as close to the center planet gear as possible and the left supporting ring should be at the end of whole planet gears. By doing this, the deflection and tilting will be smaller to mitigate the edge loading. The right planet gears need to be extended far enough to reduce the tilting and the loads. By controlling the diametral tolerance of the separator rings, the backlash can be minimized as well as the tilting.
Other Differences and Lessons Learned
1. The geared rotary actuators should be non-synchronous [10];
2. Sun gears need to be crowned to accommodate the tilting of planet gears;
3. It should have higher efficiency so that it will not chatter under aiding loads [10].
Because of the gear ratio requirement, the average forward efficiency becomes very close to 50%. The risk mitigation unit was a synchronous gear set, and the instantaneous efficiency varies plus/minus 20%. Therefore, at the aiding load condition, the unit chatters because it is not back drivable when the instantaneous forward efficiency falls below 50% (Figure 27 and Figure 28).
The methods to resolve this failure include:
1. Lower the gear ratio by adding an input stage;
2. Move the separator rings to the end of the planet gear, NBP;
3. Change from synchronous to non-synchronous designs;
4. Reduce the number of planets gears so that each planet is larger and deflection is smaller;
5. Improve the quality of the gears so that the backlash and tilting can be minimized.
Conclusions
Deflections and misalignments in a gear set can be detrimental when the gears are edge loaded, generating noise and high bending and contact stresses. Tooth deflections usually result from highly loaded gears and misalignments come from wing bending or deflections of the gear housings.
In this paper, several gear failure cases in the development phase of high lift systems were presented, including leading edge geared rotary actuators, trailing edge geared rotary actuators, sector gears and pinions, and offset gearboxes. The failure modes can be classified as spalling or pitting at the location of concentrated loads. Most of the problems can be mitigated by providing correct lead modifications to alleviate the concentrated loadings, while some need increase of the gear diameters, design modifications, or introduction of materials with higher allowable.
Acknowledgements
The authors would like to thank MOOG management for the approval of publication of this paper.
References
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** Printed with permission of the copyright holder, the American Gear Manufacturers Association, 1001 N. Fairfax Street, Suite 500, Alexandria, Virginia 22314. Statements presented in this paper are those of the authors and may not represent the position or opinion of the AMERICAN GEAR MANUFACTURERS ASSOCIATION.
