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Background

Explore the contents of this article with a free Wolfram System Modeler trial. Rolling bearings are one of the most common machine elements today. Almost all mechanisms with a rotational part, whether electrical toothbrushes, a computer hard drive or a washing machine, have one or more rolling bearings. In bicycles and especially in cars, there are a lot of rolling bearings, typically 100--150. Bearings are crucial---and their failure can be catastrophic---in development-pushing applications such as railroad wheelsets and, lately, large wind turbine generators. The Swedish bearing manufacturer SKF estimates that the global rolling bearing market volume in 2014 reached between 330 and 340 billion bearings. Rolling bearings are named after their shapes---for instance, cylindrical roller bearings, tapered roller bearings and spherical roller bearings. Radial deep-groove ball bearings are the most common rolling bearing type, accounting for almost 30% of the world bearing demand. The most common roller bearing type (a subtype of a rolling bearing) is the tapered roller bearing, accounting for about 20% of the world bearing market. With so many bearings installed every year, the calculations in the design process, manufacturing quality, operation environment, etc. have improved over time. Today, bearings often last as long as the product in which they are mounted. Not that long ago, you would have needed to change the bearings in a car's gearbox or wheel bearing several times during that car's lifetime. You might also have needed to change the bearings in a bicycle, kitchen fan or lawn mower. For most applications, the basic traditional bearing design concept works fine. However, for more complex multidomain systems or more advanced loads, it may be necessary to use a more advanced design software. Wolfram System Modeler has been used in advanced multidomain bearing investigations for more than 14 years. The accuracy of the rolling bearing element forces and Hertzian contact stresses are the same as the software from the largest bearing manufacturers. However, System Modeler provides the possibilities to also model the dynamics of the nonlinear and multidomain surroundings, which give the understanding necessary for solving the problems of much more complex systems. The simulation time for models developed in System Modeler is also shorter than comparable approaches.

Background

Explore the contents of this article with a free Wolfram System Modeler trial. Today, many helicopters launch from and land on ships at sea. Some are conventional helicopters, both commercial and military, and some are drones. In Wolfram System Modeler, we now have a system for simulating helicopter landings and launches that includes waves and ships. The models have been used for the design of mechanical parts, autopilots, landing criteria, and operational limits.

Major components of the system

  The aim has been to develop a model with an accurate depiction of the waves, ship motion, and helicopters in such a way that the results can be used not only qualitatively but also quantitatively in real industrial applications. The first task is to calculate the motion of the landing platform mounted on the ship's deck. There is commercially available historical wave data for different seas and oceans. Since access to this data is expensive, we will instead describe the waves mathematically. A model of the forces on the ship's hull was developed with classical analytical theory. With the waves and ship hull forces, the motion of the ship's landing platform can be calculated. If we assume that the helicopter landing does not influence the landing platform motion, the system is simplified. We speed up the simulation by storing the motion in a database for the different wave heights, lengths, and directions, and the ship's speed. Typically the database will include wave heights of 1, 2, 3, and 4 m; wave directions 0, 30, 60, 90, 120, 150, and 180 degrees; wave lengths 100, 150, and 200 m; and ship speeds of 5 and 10 knots. The helicopter was modeled with the MultiBody library. It includes mechanical parts such as rotors with gyroscopic effects and landing gear with hydraulic dampers. Friction models for wheel-deck interface and flexible beams for the rotor blades have been developed. We have also developed a simple autopilot where the landing algorithm is implemented and tested. For one application, the model has been run with the actual autopilot as hardware in the loop.