Computer-Aided Engineering Tools

David Beale

Contents

Multibody Dynamic Simulation of the Digging Process

Modeling is often used in the formulation phases of Systems Engineering, and it is particularly applicable to lunar excavator design because prototypes cannot be tested on earth under the exact operational conditions expected on the moon. Lunar gravity, radiation, wide temperature fluctuations and regolith are factors that drive excavator design, and it is all but impossible to test a new product under these lunar conditions. However, simulations can be performed that impose the lunar conditions, then hopefully the simulation’s output will be representative of how the product will perform under lunar conditions.

Since each university will have its preferred software suite, this presentation is meant to show potential applications rather than be a tutorial for a specific software.

Graphical design of hardware is performed with a Computer-Aided Design (CAD) drawing package capable of graphically representing parts based on part features. Next the designer can assemble the parts to make a component or a system by applying assembly relationships. Next the assembly can be examined for fit and function by testing a “virtual” prototype before producing a physical prototype.

Figure 1‑1. Excavator assembly in Solid Edge

To demonstrate the process, a CAD package (Solid Edge V20) was used to draw and assembly an excavator shown in Figure 1-1. Individual parts were created first, and then assembly relationships applied. The excavator would be pinned at three points on the left side of the figure to a rover (for this demonstration they are attached to ground part 1). The figure shows 12 pin (or revolute) joints and 2 translational joints in the cylinders. Each joint removes 2 degrees of freedom. With 10 moving parts, Gruebler’s equation calculates this system to have 2 degrees of freedom. Hence two actuators (e.g. linear motors) will be able to operate this system, and obvious locations for these would be inside the cylinders, between parts 4 and 5, and 7 and 8.

The design of this and similar systems can be enhanced by a series of useful simulations that can be performed on the individual parts and/or the assembly. These simulations could be used to determine:

· Actuator power and force requirements, and link dimensions sized for the intended lifting and digging operation. The digging force mathematical model (Chapter 5) can be added as an applied force. Use a multibody dynamics simulation software here like ADAMS.

· Stresses throughout the mechanism parts induced by digging, from combined multibody dynamic simulation and finite element analysis.

· The temperature of any material point on a part (created by solar radiation and the environment), by finite element analysis.

· Thermal stresses and strained induced by temperature differences within a part, and across part joints, again using finite element analysis. Input boundary conditions determined by methods presented in “thermal control” chapter 7.

· Control laws that define actuator motion based on sensor input, to automate and/or monitor the digging operation. Use a multibody dynamics and/or a control system design software like MATLAB.

This presentation will demonstrate the potential and application of a multibody dynamics simulation.

Multibody Dynamic Simulation of the Digging Process

The parts and assembly of Figure 1-1 were built using Solid Edge V20. Dynamic Designer is a multibody simulation dynamics software interface that is an add-on software to Solid Edge. It is offered at no cost to students through Dynamic Simulation Technologies at http://interactivephysics.design-simulation.com/DDM/SolidEdge/faq.php (however you will need to make sure your particular CAD package will support it). The multibody dynamic simulation engine of Dynamic Designer is ADAMS, which could be directly accessed by importing your CAD assembly into ADAMS, without using Dynamic Designer. Other commercial software is available that could perform the tasks of this tutorial. ADAMS is a product of MSCSoftware and described at http://www.mscsoftware.com/products/adams.cfm?Q=131&Z=396&Y=397 . Working Model could have been used here, however it is limited to planar motion.

The assembly process in the CAD software requires that the relationships between parts be defined; these relationships are translated to particular joint types in the multibody dynamic simulation software. For example, an “axial align” and a “mate” between two parts will create a revolute joint. The multibody dynamic simulation softwares offer a wide variety of joints, including revolute (pin), translational (sliding), universal, spherical (ball), etc. They also include contact forces, prescribed time-dependent motions, finite element discretization of parts, control forces, etc. This demonstration is meant to be brief exposure and will not apply all the features of the software that are relevant and available.

It is not necessary to leave the Solid Edge Environment to check the range of motion. Many CAD packages have the ability to “move” a kinematic assembly through its range of motion, into the positions required to dig and unload. The shovel should be able to reach deep enough below the surface, it should be able to reach high enough per the mission requirement to reach over the top of a bin wall, and the shovel should be able to rotate enough to drop the regolith (greater than the angle of repose, see Chapter 5). This should all be accomplished in less than 5 seconds.

Mass properties (mass, center of mass and mass moments of inertia) are calculated by the software based on a material density and the part volume and geometry. Links were made of aluminum, the shovel of steel and a lunar rock of density 3.0E-6kg/mm³ was added. Units in the simulation are kg, mm, sec and N. Gravity is set to 1635 m/starting coordinates of the revolute joints are listed in Table 1-1, and the mass properties and link lengths are shown in Table 1-2.

Table 1‑1. Revolute Joint Coordinates

Joint		Revolute Joint Coordinate
part	part	X	Z
1	4	0	0
1	2	85	230
1	6	85	330
2	3	139.84	178.84
3	6	202.82	275.06
3	7	265.8	371.28
5	6	520.03	127.14
6	9	683.07	51.07
6	11	955.38	-75.71
8	9	689.15	171.92
8	10	695.13	292.78
10	11	918.36	74.8

Table 1‑2. Mass, Moment of Inertia and link lengths

Part	Mass(kg)	Moment of Inertia (Iyy)	Length(mm)
1(Grnd)	---	---	---
2	0.1319	82.0992	90
3	0.3502	1700.14	250
4	1.5791	17795.5	360
5	1.0355	7700.33	300
6	4.0360	335710	1000
7	1.5791	17795.5	360
8	1.0355	7700.33	300
9	0.5541	2661.06	250
10	0.7654	6434.71	330
11	14.8510	254919.	---
12 (Rock)	9.0551	44458.	---

Figure 1‑2. Starting position, side view

Figure 1‑3. Starting position, isometric view

The objective of the simulation is to pick up, lift and drop a rock into a bin without dropping the rock on the way up (bin not shown). Functions of cylinder displacements versus time were created with a spline function, and through trial and error an optimal set of cylinder travels were chosen. These were plotted in Figure 1-4 and 1-5. The total length of the lower cylinder is plotted in Figure 1-6.

Figure 1‑4. Prescribed splined displacement vs. time, top cylinder

Figure 1‑5. Prescribed splined displacement vs. time, bottom cylinder

Figure 1‑6. Bottom cylinder length vs. time

The simulation starts by lifting a rock already in the shovel. A “contact force” (Figures 1-7 and 1-8) is defined between the rock and the shovel since no joint exists between the rock and the shovel. The important parameter values here are the stiffnesses of the contacting elements, i.e. the steel shovel and the rock. Similarly a contact force is created between the rock and the ground. Sharp spikes in Figure 1-8 are often numerical error, and can be reduced by increasing accuracy of the numerical integration and increasing damping in the contact. The spike near t=0 is due to an impact as the shovel moves upward and contacts the rock. The full sequence of motions is shown in Figure 1-11 through 1-16.

The force in the cylinders is also needed to select the actuator, plotted in Figure 1-9. The Z force in the shovel-long beam revolute joint is plotted in Figure 1-10. Future improvements to the model could include attaching the excavator to a rover, incorporating the force characteristic of the regolith on the shovel, the force characteristic of the actuators replacing the prescribed motions, and importing to finite element analysis.