Design Strategy for Geared Rotary Actuators: Challenges and Opportunities

Example of a geared rotary actuator with five planet shafts.

Geared rotary actuators (GRAs) are compound planetary gear drives with a high gear ratio that can provide a high power density along a motor shaft. They can work basically as a motorized hinge and can find multiple applications such as in robotics, electric vehicles or even as aerospace gears. The question is, are GRAs reliable to be used in increasingly electrified transportation systems? Challenges and opportunities arise on the horizon for this type of reducer, especially in flight support systems for near-future airplanes.
 

State of art

Geared rotary actuators eliminate the need for a planet carrier thanks to the precise integration of their components offering a very compact mechanical transmission. One of the most used GRA is the center-hinge compound planetary gear set (as the one illustrated in the image above), which could be applied in flight support systems to get a significant reduction in aircraft weight [1]. Determination of their reliability and efficiency is very important to guarantee its effective application [2,3]. However, one of their main drawbacks is related to mounting feasibility. As a compound planetary gear drive, many design conditions must be fulfilled [4].
 

Challenges of design

The presence of floating rings in the structure of a GRA offers significant advantages to the transmission as the tangential forces at each planet shaft must be in equilibrium. Just the radial forces are transmitted through the rings and mutually balanced. However, this simplicity represents a challenge from a design perspective due to the complications it entails during assembly.

One of these complications is that the ring gear A must be shifted during the mounting operation to engage with the planet gears A and, at the same time, avoid any collision with planet gears B. Otherwise, the mounting would not be possible. Another challenge is to keep all the planet shafts at the required center distance and equally spaced around the sun gear shaft, requiring special tooling for mounting. Finally, the design must foresee the reliability of each component and other general aspects of the transmission, such as efficiency (both forward and backward), volume, torque density, and inertia.

An optimal design of a GRA should ensure an objective gear ratio while maintaining size constraints and keeping efficiency as high as possible. Numerous design conditions must be considered during the search of possible solutions: avoiding of undercutting, pointing and interferences, conditions for equally spaced planets with enough space between them, ensuring of partial and/or complete tooth hunting, ensuring of non-synchronous meshing of the planets, feasibility of mounting or avoid clocking angles between planet gears A and B to facilitate the manufacturing of the planet shafts. In this context, there is a clear need for a design strategy capable of generating multiple solutions that satisfy the numerous design constraints and classify them in terms of reliability and efficiency.

Figure 1: Scheme of a geared rotary actuator.

Strategy of design

The design strategy takes as input a range of standardized modules [5] for each stage: stage A, composed of the sun gear, planet gears A and the output ring gear; and stage B, composed of planet gears B and the fixed ring gears (Figure 1). Additionally, it considers as input a range of profile shift coefficients and tooth numbers for both planet gears A and B. The output of the methodology consists of the tooth numbers for the sun gear and both ring gears, as well as the profile shift coefficients of these gears. In this process, the operating center distances in stages A and B are constrained to match a specified center distance, and no backlash is considered between the gear pairs at this initial step of the design. Furthermore, the ring gears are constrained to align the gear tooth spaces at the planet positions, and the same number of teeth is used for both planet gears A and B, enabling the absence of clocking angles between them. Flank and root safety factors are determined for each solution and for each gear component using the Standard ISO 6336 [6,7]. Mean efficiencies are also estimated for each solution, based on references [2,3].

Figure 2: 2D finite element model: (a) stage A and (b) stage B.

Subsequent analyses

The design strategy enables the classification of the obtained solutions based on their reliability and efficiency. A subsequent analysis using a 2D finite element model (Figure 2) would allow for a more accurate estimation of contact and bending stresses in the selected solution. To achieve this, an input torque is applied to the sun gear reference node, while the reference node of ring gear A is fixed for each contact position. The results also include the functions of loaded transmission errors and the efficiency variation throughout the meshing cycle, considering a mean value of the friction coefficient. This model enables the definition of the macro-geometry design and requires subsequent analyses through 3D models to adjust the micro-geometry deviations of the tooth surfaces.
 

Conclusion

The development and availability of advanced design tools for GRAs, aimed at enhancing reliability and efficiency, can provide new opportunities for this type of gear reducer across a wide range of industrial and technological sectors. This work is part of the research project PID2023-152913NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by FEDER, UE.

About the Authors:

Prof. Dr. Ignacio Gonzalez-Perez, 
Professor, Department of Mechanical Engineering, Materials and Manufacturing, Universidad Politécnica de Cartagena, Cartagena (Región de Murcia), Spain.

Prof. Dr. Alfonso Fuentes-Aznar, 
Professor, Department of Mechanical Engineering, Rochester Institute of Technology, Rochester NY, USA.

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References

[1] Wang A., El-Bayoumy L., Venables N., “Preliminary design considerations on epicyclic gears in aircraft high-lift systems”, Proceedings of the ASME 2011 International Design Engineering Technical Conferences, DETC2011-48462, Washington D.C., USA (2011).
[2] Bertucci A., Jacazio G., Sorli M., “Performance study and mathematical model of aerospace geared rotary actuators”, International Journal of Applied Engineering Research 13, 167-174 (2018).
[3] Wang A., Gitnes S., El-Bayoumy L., “The instantaneous efficiency of epicyclic gears in flight control systems”, Journal of Mechanical Design 133, 051008 (2018).
[4] Arnaudov K., Karaivanov D.P., Planetary Gear Trains, CRC Press Taylor & Francis Group, Boca Raton (2019).
[5] DIN 780-1:1977-05, Series of Modules for Gears; Modules for Spur Gears (1977). https://doi.org/10.31030/1076231.
[6] ISO 6336-2:2019, Calculation of Load Capacity of Spur and Helical Gears, Part 2: Calculation of Surface Durability (Pitting) (2019)
[7] ISO 6336-3: 2019, Calculation of Load Capacity of Spur and Helical Gears, Part 3: Calculation of Tooth Bending Strength (2019)

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