Dynamic analysis of aircraft landing gear is generally complex due to it being a multi-degree-of-freedom (DOF) system. Setting up and solving equations of motion to understand its behaviours is not an easy task – Differential equations, Integrations, Lagrange equations and Laplace transformations are some of the well-known methods used. Fortunately, this can be streamlined using the Dymola native approach – Object Oriented Modelling. This blog post will familiarise you with this modern technique and provide an analysis example of a two DOF landing gear system.
Dymola or Dynamic Modelling Laboratory is a Multiphysics and Mathematical based simulation tool that has Modelica as an underlying modelling language. It is typically used within automotive, aerospace, robotics, process and other industries to understand the behaviours of integrated and complex systems. Dymola comes with standard libraries of components from various Physics domains such as mechanical, electrical, control, thermal, fluid and more. These are utilised and further developed by researchers and engineers to create and license advanced libraries including battery, engine, powertrain and so on. One great example of industry usage of Dymola is that it was used to develop BMW i3 and i8 drivetrain in 2009.
Dymola uses Object Oriented Modelling as a native modelling approach to create integrated systems. This works by, firstly, dragging components from available libraries and dropping them into a blank model or system. Each component represents Physics and Mathematical formulas. Secondly, connect all components in the model together and define input parameters for each component. In doing so, Physics and Mathematical formulas from each component are mathematically connected to generate a system. The components in the model are to be connected in the same sequence as how they would be physically connected in the real world. Thirdly, run the simulation and view the results. With these three simple, yet effective and intuitive steps, a system has now been created. This system is now considered a new component in the library in which if the mentioned steps are repeated, systems of systems would be created.
Let’s have a look at the example below of how this method can be applied to model and simulate a two DOF landing gear system.
In this example, a drop test of a typical nose landing gear system is modelled and simulated. The drop test is assumed to be simulated for a nose landing gear of weight similar to that of Lockheed XV-4B Hummingbird (~5,445 kg design gross weight, Norman S. Currey1). According to FAR23 requirements, the drop or impact velocity for an aircraft weighing less than 8,629 kg is about 3 m/s. The landing gear is simplified to have two lumped masses, being an effective aircraft weight sitting on the nose landing gear while being an unsprung mass or a combined mass of every other component positioned below . The masses are connected via a shock-absorbing strut which has air spring (spring constant ) and oil damper (damping coefficient ) components. The other end of is connected to the unmovable ground plane via a tyre (spring constant ) which is allowed to bounce off the ground. The table below summarises the parameters used in the simulation, and the image below illustrates how the landing gear is simplified.
As earlier mentioned, typical approaches used to study and understand dynamic behaviours of the system are to set up equations of motions and solve using various Mathematical methods. This can be quite complicated although the system has only two DOF. NACA Technical Note 2743, a 90-page Landing-Gear Impact report, provides great examples of how advanced and complicated the solution could be. Object Oriented Modelling can be used instead to streamline the analysis approach. The following example is explained using the above methodology.
Step 1) – Drag and drop the required components from the available libraries. The required components are inserted into the model as shown in Figure 2 which shows every component as a simplified system and also includes physical constants such as constant gravitational force.
Step 2) – Connect all components in the same sequence as they are physically connected in the real world, and assign input parameters as listed in Table 1. The model now looks like below and is shown in Figure 3. (Note that drop velocity value is not shown here but it is embedded in the background of the model).
Step 3) – Run the simulation and view the results. Typically, the timeframe of interest is the first second after impact occurs. Therefore, the simulation is run for one second, and the computation finishes immediately after the simulation starts. The initial simulation report shows that there are 54 unknown parameters and 54 equations being simultaneously solved, and the CPU time used to complete the simulation is about 0.001 seconds for 500 result points per parameter. Figure 4 shows a set of crucial results used to assess the behaviour of the landing gear during impact. The overall results show that the landing gear quickly stabilises itself after the bounce (i.e. when the spring force from is zero). If such behaviours are desired, further assessment can include, for example, structural load path analyses and stressing using obtained spring and damping forces as inputs.
Behavioural dynamic analyses performed using Object Oriented Modelling approach in Dymola is shown to be a time-efficient approach. It can be used to effectively and quickly model and find solutions to multi DOF systems such as aircraft landing gear. The sample case study provided is only one simple example of how Dymola can be utilised. However, solutions to much more intricate problems such as complex multidomain multiphysics systems can also be simulated by Dymola. For example, this case study could be expanded to incorporate an advanced oil damper model and landing surface profiles.
If you’d like to learn more about Dymola and how it can be implemented in your business, don’t hesitate to get in touch to speak to a product expert or book a free demo session.
Bright is a PhD graduate (Aerospace Engineering) from RMIT University. He holds a Bachelor of Engineering (Aerospace Engineering) (Honours) and Bachelor of Business (Management).
During his PhD, Bright developed a great understanding and unique research skills in composite materials and Lithium-ion batteries. He presented his work at renowned international conferences and was the main author of several scientific articles in leading academic journals. Bright has experience with mechanical and thermal simulations of composite structures using Abaqus. He also has experience in CAD software including Catia V5 and programming languages such as Python and Matlab.
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