The aim of this part is to provide insight on how the presented model is parametrized.
The actuators perform the important role of moving the control surfaces precisely within a permissible time and error. The high-level requirements for aileron system will come from the roll control feature requirements. The typical performance requirements are the maximum load (stall load) on the actuator and extension and retraction rates of the piston (no load speed) The model parameters come from a pre-sizing made based on the following inputs from literature:
Sizing an entire actuation system is complicated due to many couplings between the actuators and the hydraulic systems. In order to keep pre-sizing simple, these performance requirements are considered for a single actuator powered by an ideal supply pressure – without losses.
Symmetrical cylinder section computation
The stall load is the maximum force the actuator can generate. At this performance point, the delta pressure available in the cylinder chamber, to face the load, equals the supply pressure . Therefore, in steady state, we can write:
Where and are respectively pressure in the extension and retraction chambers of the cylinder and its section.
Servovalve maximum flow area
The no-load speed () enables computing the maximum flow rate () moving the cylinder:
In this scenario, the pressure in the symmetrical cylinder chambers are equal as the force to face is zero (in steady state).
Associated with a symmetrical cylinder, the servovalve shall have symmetrical orifices. Therefore, hydraulic restrictions can be modeled with a single characteristic (in this case for the extension scenario):
From here, the flow area can be calculated as , where is the flow number and the fluid density. However, Modelon Hydraulic Library can also do that for you as one way to parametrize the valve is to give the flow rate for a given delta pressure – which would be here for a pressure drop of .
Step-by-step approach for incremental model building
As a part of the blog series, we focus on modeling the entire actuator, shown in Figure 1. The modeling process is divided into two steps. First step is to come up with the simple actuator system and get it validated. The next step – covered in the next post – will be to add all other valves, enabling damping and isolation functions.
Simple/nominal actuator model
In terms of modeling the actuator in active mode, the main components are the symmetric hydraulic cylinder and the electro-hydraulic servovalve. Both these components are off-the-shelf components in the Modelon Hydraulics Library, which is the library being used for the purposes of this blog. The key things to look out for are the parameterization of the actuator and connections with other components of the circuit. The parameters for the models come from the pre-sizing that has
The hydraulic cylinder model is available as a component DoubleActingDualRod. This is a library model that has two variable hydraulic chambers along with required mechanics like end stops and mass of piston modeled. The friction between the cylinder and piston is also modeled. The main parameterization required are dimensions of the cylinder and piston.
The electro-hydraulics servovalve is modeled using a functional representation which models flow areas between different ports of the servovalve as variable orifice. The parameters to be provided are the areas of the flow ports. The supply and return pressures are connected to the servo valve as source and sink. A simple controller is built around the actuator that can command a required position of the piston by controlling the spool position of the servovalve as shown in Figure 2.
Figure 2: Simple Actuator Model
Actuator model validation
The pre-sizing of the valve and cylinder section were based on the no-load speed and stall load requirements. When plotting the speed v/s load characteristic of the modeled actuator, we can see that the model meets these actuator requirements.
Figure 3: Actuator performance characteristic – Speed vs. Force
The frequency domain validation of the actuator is done using model. This will ensure the bandwidth of the system. The model shown in Figure 2 is linearized and Bode plot is drawn as shown in Figure 4. This shows a close correlation of bandwidth of system mentioned in Table 1.
Figure 4: Bode plot showing cut-off frequency
In this blog, we introduced the aileron actuator role in the overall actuation system as well as the A320 aileron actuator architecture – enabling two modes: active and damping (stand-by). Then, we covered the pre-sizing and modeling of a similar aileron actuator in active mode. Simulation results demonstrate that the model meets the specified requirements.
Simulation models are usually built incrementally. In the case of the aileron actuator, the active mode can be separated from the damping mode.,
Stay tuned – The following blog post will increment this model with the damping mode and safety valves in order to explore non-nominal behavior of the actuator.