3.3.3. Rod-End

Another important element of mechanical transmission that has been an object of study is the spherical rod-end, which connects the actuator to the airframe and the aerodynamic surface, performing a critical safety function at the aircraft level. Rod-ends are subjected to different failure modes, such as crack openings, lubricant degradation, surface denting, and so forth. However, the most common failure is represented by the wear of the internal surface of the spherical joint, with the consequent increase of backlash, which, if outside the acceptable range, could result in a significant accuracy reduction in surface positioning. Furthermore, a significant rise in friction forces within the spherical joint, due to lubricant degradation and improper lubrication regimes, can lead to excessive bending stress on the actuator. This component has been studied in conjunction with a high-fidelity model of a complete actuator to also investigate the effect on its expected performance [40]. To simplify the model definition and prepare for more complex models, some simplifying assumptions were made. This involved reducing the 3D spherical joint geometry to a 2D cylindrical approximation, ignoring misalignment and lubricant leakages. The rod-end model considered 3 different operating conditions based on the relative position between

the shaft and bush. As the clearance decreased, the system transitioned from hydrodynamic lubrication to mixed and then to direct metal-on-metal contact. As for the ball screws, grease lubrication was considered and, therefore, the lubricant media was represented by its base oil. Conducting a PHM study on aerospace rod-ends requires defining models that are both computationally efficient and accurately reflect the component's physics; for this reason, a finite difference scheme has been selected as a resolution method of the simplified Reynolds equation. To streamline the simulation and avoid the need for iterative solvers, the Half-Sommerfeld solution was chosen to describe cavitation regions, while the viscosity was computed at each FDM node, dependent on the temperature and local pressure according to the Vogel-Barus equation [31]. Depending on the operative conditions, the model was able to represent the variation of the lubrication regime from full film to mixed and boundary lubrication, monitoring the local Tallian parameter and weighting the results from the hydrodynamic and direct contact models.

Figure 9 illustrates the effect of the rod-end backlash on the final surface positioning when the control surface is moved by 2 parallel servo-actuators according to the activestandby control strategy. It can be observed in Figure 9a how the backlash in the rod-end due to excessive wear causes important variation in the deflection of the control surface, which can lead to increased surface vibration, damage, and controllability issues. In particular, it can be seen from Figure 9a that the equivalent surface displacement considering surface kinematics in the presence of backlash (green line) differs from that with no backlash (red line) by approximatively 2 mm, which corresponds to half the width of the imposed backlash for the current simulation for the fully deflected surface condition; while the surface position varies by about 0.6 mm for null commands of the active actuator, mainly due to the presence of external aerodynamic loads, internal damping, and the attachment with the second stand-by actuator.

**Figure 9.** Simulation results of a rod-end with a high backlash of 2 mm connecting 2 servo-actuators to the control surface: (**a**) Pin trajectory within the rod-end housing during the simulation; (**b**) Comparison between the surface position obtained with (green) and without (red) backlash in the rod-end (© 2021 ASME. Reprinted, with permission, from [40]).

Figure 9b depicts the motion of the internal sphere within the rod-end housing during the simulation and shows how it impacts the bushing's race, contributing to damage progression and rod-end degradation. The model gives in the output the normal and frictional contact forces and the wear information, which are useful insights to understand the component's behavior under various working conditions, helping in the definition of a suitable PHM framework.

#### *3.4. Real-Time Modeling*

The abovementioned high-fidelity models are accurate, metaphysical, and extremely detailed, based on the physical descriptions of the involved phenomena. However, the high level of detail counterposes the computational constraints required to run PHM routines. In fact, such models are very computationally intensive and are not suitable for prolonged simulations of a complete servosystem. With the aim of streamlining the computational time to make them available to generate a large dataset of nominal and degraded system responses and to be used in real-time simulations on the iron bird, several reduction techniques were applied to the models to obtain a simplified EMA model capable of reproducing the main features required by the iron bird to enable the simulation of a complete flight, i.e., the position of the actuator and control surface. The various considered degradations were then inserted into the model with equivalent simplified models; they aimed to simply reproduce the effects of each fault progression on the relative signals which were seen as being affected by such degradations during the offline phase, according to the detailed results obtained with high-fidelity models. Because of the practical implementation of the iron bird and the performance of its hardware components, the real-time (RT) model must comply with the time constraint of a maximum integration frequency of 12 kHz.

Hence, only the more important dynamics were considered in the RT model to balance the need for realism with the computational effort. It is worth highlighting that not only 1, but multiple EMA models should be run simultaneously to enable the correct functionality of the iron bird; therefore, the actual model complexity must remain as low as possible to avoid CPU overloads. Furthermore, jitter usually occurs in the RT hardware, so a certain amount of security margin must be considered.

Following these constraints, the RT model was assembled, as shown in Figure 10. It was composed of several subsystems, each representing an interconnected subcomponent reflecting the physical arrangement. The main blocks represent the Power Drive Unit, controller, electric motor, mechanical transmission, and control surface. A number of simplifying assumptions were made to speed up the simulations. The 3-phase electric motor was modeled with the equivalent d-q axes representation, exploiting the Clarke-Park transformation. Also, the PDU was represented by a 3-leg inverter with conduction losses dependent on the temperature. The ball screw and rod-ends were contained in the mechanical transmission subsystem, describing the motion transformation from rotational to linear considering mechanical efficiency, stiffness, and friction. The latter was modeled with the fast and simple Karnopp model to maintain the computational requirements as low as possible. The surface's block enclosed the description of the variable lever arm which allowed the linear displacement of the actuator to create a controlled rotation of the aerodynamic surface. The system was then basically reduced to a 2-body lumped mass model: 1 representative of the control surface and the other of the entire mechanical drive from the rotor to the translating part of the ball screw. The rod-end connection stiffness was considered in the connection point between the 2 lumped masses. All the sensors were represented with dynamic transfer functions and, together with the controller states, were sampled at the various control loops' frequencies. A simple single-body thermal model was used to estimate the global temperature change of the EMA during the simulation.

The RT model was created according to the following principles:


As stated in the previous paragraphs, 7 faults were considered, 5 of which described a progression in time, and 2 (i.e., motor's static eccentricity and PDU's MOSFET base drive open circuit) were imposed a priori before the simulation started. The introduction of the selected failure modes within the real-time models was achieved in 2 separate ways, depending on the model modifications required to adapt the high-fidelity model to the

real-time framework requirement. The 1st type was represented by those failure modes whose progression could be successfully described by the reduced-order model, such as the magnet degradation, the occurrence of rotor eccentricity, and the degradation modes affecting the mechanical transmission. In such cases, the very same models adopted for the high-fidelity model were ported within the real-time simulation with minimal adjustments. For other failure modes, including the turn-to-turn short and the MOSFET base drive open circuit, a different approach was needed; the physics-based representation of such degradation process required a 3-phase dynamic model of the motor, while the real-time representation worked on a streamlined d-q axis description.

**Figure 10.** Main screen of the RT model.

Starting with the latter case, the approach was to map the effects that the degradation mode had on the quantities represented in the real-time model through the high-fidelity environment, then proceeding to modify the signals of the real-time model according to such maps. To better explain this approach, please consider the case of the turn-to-turn short and the scheme provided in Figure 11. The real-time model described the nominal health behavior of the motor according to a d-q axis description, computing the expected windings temperature *Tw*, according to a streamlined thermal model of the motor. Such temperature was then used to feed the turn-to-turn short model, which computed the expected variations on each of the 3-phase currents according to the fault mapping.

**Figure 11.** Implementation of the turn-to-turn short in the real-time model.

Such variations were then applied to the 3-phase currents (*ia*, *ib*, and *ic*) derived from the direct, quadrature currents computed by the real-time model. Once the variations were applied, the updated d-q axis currents were obtained through the inverse Park transformation.

The faults of the mechanical transmission included the wear of ball screw and rod-end and the lubricant degradation. The latter, as seen, also caused an increment in the wear rate, but, as previously stated, mutual excitations of different failure modes were ignored in this work for being outside the original scope of the research project. Wear was considered by means of the Archard equation. The effect of wear is a backlash increase that was modeled by means of a double-sided elasto-backlash with hysteretic damping based on the relative position of the 2 bodies. Since only 2 bodies represented the mechanical dynamics of the system, the backlash models for both the ball screw and the rod-end were condensed into

a single backlash located in the rod/surface joint. A smart approach was implemented to differentiate the 2 situations, consisting in sending the actual rod position back to the controller if no ball screw backlash was considered, while conveying the linear position on the surface's side of the backlash if the degradation was introduced. Despite this, the backlash of the rod-end is normally taken into consideration in the model. As a result, the effective backlash seen by the RT model, concentrated in the rod/surface connection, was the sum of the 2 backlashes in series. The effect of lubricant degradation was obtained with a mechanical efficiency reduction in the RT model.

Figure 12 shows the results obtained with the RT model when a surface position command is imposed to the EMA with aerodynamic loads dependent on the surface deflection. To highlight the effect of 1 of the selected degradations, 2 simulations with low and high levels of backlash in the rod-end are shown; for the second case, the surface position exhibits flutter oscillations for little commands due to the excessive backlash under the action of the external loads. The discrepancies between the detailed and simplified models emphasized during the highly dynamic phases of the simulation, i.e., the first part, while tending toward 0 for steady conditions, assumes an RMS value of the absolute error between the results of the RT model and the detailed model, shown in Figure 12, of 0.23 deg, which is a reasonably small value and an acceptable compromise when considering the computational constraint imposed by the hardware implementation. The presence of the backlash model does not introduce substantial variations to the RMS error.

**Figure 12.** Comparison between detailed model and RT model with low and high levels of backlash.
