INTRODUCTION
Developing a lunar lander is a challenging task, as the Odysseus lander proved. Landers must be lightweight, while withstanding the stresses of the rocket launch and landing. Under ideal conditions, the lander would achieve zero velocity both vertically and laterally as the vehicle touches down. Practically, this is a very difficult challenge which requires advanced guidance, navigation, and control (GNC) systems along with a descent propulsion system. Altimeters, accelerometers, cameras, and other sensors provide feedback allowing thrusters to slow the lander. In the likely event the lander’s velocity isn’t zero, the lander must deploy legs which can absorb the shock of the landing while preventing the rover from tipping over. To further complicate the challenge, the lander experiences 1/6 of earth’s gravity and temperatures ranging from -400 ˚F to 250 ˚F depending on the time of day and location. The environmental conditions make it impossible for a test which emulates all conditions of a lunar landing. Simulation is one important approach for developing solutions to these challenges.
Lunar landers are complex multi-physics systems, which create the need for many different types of simulation. Thermal simulation can be used to analyze the effects of extreme temperatures on structural components. Computational fluid dynamics (CFD) is leveraged to analyze the thrusters and the lander’s interaction with the moon’s very thin atmosphere. Finite element analysis (FEA) is used to analyze structural members for fatigue, vibrations, and impacts. Multibody dynamics (MBD) is used to analyze the lunar lander’s dynamic response during a landing and test the integration of mechanical systems with moving parts.
Building the Model
In this example, we will focus on developing an MBD model of a lunar lander touching down on the surface of the moon. This lander uses stages of springs to increase the spring rate as the springs compress. While the springs compress, dampers dissipate the kinetic energy as heat, limiting rebound on landing. The goal of this study is to optimize the spring rates of each leg to minimize acceleration, minimize lander tilt, and minimize spring travel. The multibody dynamics model will be built in Altair MotionSolve. Co-simulation with Twin Activate, an intuitive 1D modeling software, will be used to optimize the spring rate.
In the MotionSolve model, the vehicle begins at zero velocity and falls toward the surface of the moon under the influence of gravity. Contacts between the ground and the lander feet handle the reaction force. Spring forces are calculated by the Twin Activate model.
The solution process begins in MotionSolve. Vehicle acceleration, vehicle pitch, and spring displacement for each leg are sent to the Twin Activate model. Each variable acts as an input into a cost function which weighs each variable and calculates a singular cost. Acceleration is given the highest weight because a rapid deceleration could damage sensitive equipment, the vehicle, and astronauts.
Optimization seeks to minimize this cost function and in effect the acceleration, vehicle pitch, and spring displacement. The optimization algorithm produces a set of spring rates for the front leg and rear legs. Twin Activate uses the new spring rate and displacement to create a new force vs displacement curve. The model interpolates the data set which creates the curve to find the force at the current displacement for each spring. The force is sent to MotionSolve where the MBD solver calculates the new state of the vehicle and each spring.
The process repeats for each timestep until the lander is stationary on the ground. During this process, the program tabulates the cost for each spring rate guess at each timestep. The program then repeats the simulation using this information to minimize the cost function.
SOFTWARE REQUIREMENTS
MotionView (2024 or newer)
MotionSolve (2024 or newer)
Twin Activate (2024 or newer)
MODEL FILES
MODEL SETUP & SIMULATION STEPS
- Open Crash_Box_Optimization.scm or Crash_Box_Baseline.scm in Twin Activate.
- Select an initial spring rate guess.
- Open Model to view the initialization code.
- Change the select option to change the initial spring rate guess.
- Run the model in Twin Activate.
- Open the h3d file created in the Results folder using HyperView to review the animation.
RESULTS
The model contains two initial guesses for the spring stiffness. The first profile, called crash box 1, has a gradual increase in spring rate as displacement increases. Crash box 2 begins with a low spring rate which rapidly increases as displacement increases. Optimization from these initial spring rate profiles results in different optimized spring rates. The animation does not demonstrate notable differences between crash boxes, however, there are measurable differences in acceleration, pitch, and spring displacement.
Crash Box 1
| First Stage Stiffness (N/mm) | Damping Coefficient (Ns/mm) |
|---|
| Baseline | Optimized | Baseline | Optimized |
Front Leg | 500 | 1000 | 63.2 | 89.4 |
Rear Leg | 500 | 421 | 63.2 | 58.0 |
Crash Box 2
| First Stage Stiffness (N/mm) | Damping Coefficient (Ns/mm) |
|---|
| Baseline | Optimized | Baseline | Optimized |
Front Leg | 500 | 779 | 63.2 | 78.9 |
Rear Leg | 500 | 306 | 63.2 | 49.5 |
The optimization dramatically decreases the pitch angle to keep the rover level upon landing. This decreases the travel of the front spring while increasing the travel of the rear springs. While the optimization is successful at keeping the rover level, it fails to decrease the maximum acceleration. In crash box 1, the optimization maintains a peak acceleration of approximately 19 m/s/s. In crash box 2, the maximum acceleration increases to 21 m/s/s. The optimization algorithm could be further refined to reduce acceleration by increasing the weight given to acceleration in the cost function.
CONCLUSION
Multibody dynamics is a powerful tool which allows engineers to analyze the landing of lunar modules. MBD can provide insights into vehicle acceleration, tilt during landing, and more. In combination with optimization, springs and shock absorbers can be modified to soften the landing. MBD and many other simulation tools (FEA, CFD, EDEM, etc) allow engineers to make informed decisions about complex problems. These tools are especially beneficial when a system of interest is difficult to prototype and test. Proper implementation of simulation leads to better designs in less time.
AUTHORS
John Dagg, Systems Engineering Intern
Christopher Fadanelli, Solution Engineer – Systems Integration
Ananth Kamath Kota, Global Technical Manager – Systems Integration
