Machine Design

# New Finite Elements Simplify Complex Analyses

A difficult to analyze amusement-park ride lead to the invention of an actuator element, and more.

Jeffrey Wanko
Application Engineer
Algor Inc.
Pittsburgh, Pa.

Guessing the loads for a static stress analysis has always been a fly in the finite-element ointment. Most static loads poorly represent constantly changing loads of the real world. And when loads are inaccurate, the entire analysis effort can be wasted.

Recent developments in Mechanical Event Simulation software from my company, however, say good-bye to guessing at loads. For example, when it is necessary to understand shock loads on a product, engineers using the software can just model product without any supports and specify its distance above a floor. The software takes over, letting the object accelerate by gravity to the floor. It calculates the point of impact, finds the loads, how they transmit throughout the part, and determines resulting stresses.

With the capability to model real-world (and nonlinear) events, it sometimes becomes necessary to invent specialized elements to more completely model mechanical systems, their movements, and related stress conditions. For example, with the invention of an actuator element, engineers can now more easily model motion-induced stresses in structures, an event common to most every mechanism.

Inventing an element
The actuator element technology resulted from a client application in which an engineering consultant needed to analyze a hydraulically operated cinematic simulator ride. The ride is essentially a “flying” platform supported by three pairs of double-acting hydraulic cylinders connected to a base unit. The hydraulic devices are attached independently so that activating one cylinder can reposition the flying platform without budging the other five. Therefore, six independent inputs, one for each of the cylinders, produces complex motion that requires a sophisticated numerical solution.

Calculating dynamic loading created by the actuators for input into a static finite-element stress analysis would not have been feasible. Motion simulation software, on the other hand, could produce force-versus-time charts, but results could only be applied to a static stress analysis, requiring the engineer to perform multiple analysis runs to get stress results over time. Finally, the engineer would have to drastically simplify the solid model of the assembly for the simulator to perform a static stress analysis, compromising the accuracy and validity of his results.

Although software for simulating mechanical events can reproduce the motion of the machine, it has to calculate accelerations to find the inertial loads. An element was needed to act like an actuator, which would apply a force or displacement to an attached weight. Solving Newton’s second law of motion (F/m = a) would then let the software calculate accelerations.

The resulting actuator element looks like a beam element — a straight line. Users program the element by calling up its menu and typing in values to a displacement-versus-time table. For the ride, the values were based on the action of each cylinder recorded during a test run. Although the ride lasts for several minutes, the selected 12-sec input is a slice from a data profile that holds the most extreme action in which riders feel a plus or minus 2-g acceleration. Outputs from the actuator can be displacement, velocity, or acceleration versus time as well as stresses on the structure.

The application
The actuator element came out of consulting work by Edward M. Pribonic of Seal Beach, Calif., who was asked to analyze the cinematic simulator. The engineer needed to verify that bearings supporting the ride would withstand stresses over time caused by actuator movement. The ride’s developer had to produce analytical load and stress values for the bearings before it could be certified for use in Europe.

The ride from Iwerks Entertainment, Burbank, Calif., consists of 12 motion bases, each of which carries four people on a flying platform, arranged before an indoor 1808 theater screen. Riders watch a film that puts them in the front seat of a roller coaster or a jet fighter whipping around the sky. Each flying platform then pitches and rolls with the on-screen action while a sound track completes the experience. The event is highly dynamic. The assembly for the ride includes a welded space frame with many 1⁄4-in. plates to which bearings are mounted.

Algor’s Mechanical Event Simulation (MES) software seemed the candidate system in which to model and solve the problem. Users often need only apply easily obtained values for velocity or acceleration for the software to solve for motion, inertial loads, and then stresses. But inputs for the cinematic ride were not easily obtained.

Without an actuator in the system model, it was impossible to know accelerations. After examining drawings, thinking through the physics, and postulating different ways to apply loads, the engineers found that the problem lead back to the hurdle of not knowing the loads or the accelerations.

The hydraulic system, however, provided clues. An accumulator keeps the hydraulic pressure constant at 2,000 psi, and simple two-position valves are either open or closed. When a valve to a cylinder closes, it neither extends nor retracts, despite what others are doing.

It turns out that the engineer did not need to know the force in the cylinder because the pressure is constant. Hence, the output force is constant and only the acceleration changes.

An actuator element should let users eliminate force as a load application. In this case, the consulting engineer had real physical data to analyze the event over time. Doing so also required an accurate model because geometry frequently influences loads and stresses applied to a structure.

A greater hurdle became obvious after the data was laid out to the development team for the new element because it also meant developing a new solver. The math that describes independent computer-controlled motion leads to a completely unsymmetric matrix.

Most FEA strives for a symmetric matrix. Consider that as one cylinder changes, it alters the position of the other five cylinders even when they are not extending or retracting. They are coupled to the others but their motion is independent. The development of the sparse unsymmetric solver took a few months. In spite of the enormity of the task, the development of the actuator element was concurrent with the solver.

Four Algor developers shouldered the responsibility of developing the solver while a fifth programmer developed the motion-data translator, which would allow Ed Pribonic to read in Iwerks motion-data profiles to run the MES. This development effort now benefits all MES users. For example, an engineer can now import a spreadsheet containing loading-versus-time data, whereas before the translator development, the curve would be entered manually. Furthermore, on the heels of the sparse unsymmetric solver, the company is developing a new sparse symmetric solver, a faster version for general and proper matrices.

With the element and solver in place, the analysis could progress. Motion data for the simulation was the first thing needed. Although a computer drives the ride, a person must produce motion-data profiles to operate the system. It is done by an operator watching the film and using a joystick to signal the seating platform to rise, tilt, or fall. Inputs from the joystick go to a computer that creates a data file, which is stored and run by the motion simulator’s computer. This displacement-versus-time data, thousands of points, became the inputs for the analysis.

To see how well the analysis compared to an actual run, engineers with the ride developer placed accelerometers on the unit and ran the operation profile. The consulting engineer found good agreement between the recorded acceleration and those calculated by the FEA software. This means the actuator element functions as it is intended to do.

Modeling assemblies
With the FEA software ready to handle actuators, a final task was to read the assembly into the analysis software. Analysts are asked to handle assemblies more often because it is impractical to transfer calculated displacements and loads from one part to another.

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A drawback of the trend to larger models is that they can be enormous. The assembly of the ride simulator, for example, held about 100 components. Results could take days without a cluster of computers working to solve the problem.

Fortunately, two other recent developments in CAD/CAE interoperability tools and engineering elements can shorten the job. Software technology called InCADPlus, also from Algor, works within CAD solid modelers to capture the exact CAD part or assembly without translation to a neutral file format. Simplified to just a menu pick, this seamless geometry transfer is done with good order so analysts can easily assign details such as material and element type to each part or group. The interoperability tool works with widely used CAD solid modelers, such as SolidWorks, Solid Edge, Pro/Engineer, and Mechanical Desktop.

The other recent development is the kinematic element, also from my company. It transfers loads but not stresses, so its processing time is minimal.

The new technology lets analysts assign kinematic elements to large portions of complex assembly models in which stress is unimportant. Elastic elements, those that do calculate stress, are assigned to usually small areas of interest. The advantage of these later two developments means the assembly need not be defeatured. For example, the model for the ride simulator included about 140,000 elements, of which about 120,000 were kinematic. Everything but the cylinders were modeled in CAD and as an assembly. Riders were represented by simple masses. So the model included only about 20,000 elastic elements in 40 components. This is a reasonable size and solved in several hours. Results showed bearing loads well within margin and the ride earned its European certification.