Image made using the COMSOL Multiphysics® software and is provided courtesy of COMSOL.
The pressure distribution in the lubricant of the bearings (rainbow color plot), von Mises stresses (blue color plot), and displacement of the bearings (Orbit plot) resulting from a rotordynamics analysis.
The study of rotordynamics is important in application areas that involve rotating machinery, such as the automotive and aerospace industries, power generation, and the design of electrical products and household appliances. The physical behavior of rotating machines is greatly influenced by vibrations, which are exacerbated by the rotation and structure of the machines themselves. Perfectly symmetrical rotor assemblies exhibit different natural frequencies as a function of rotational speed, while imperfections and unbalances can excite these frequencies in intricate ways. When designing machinery with rotating parts, you need an efficient way to consider these behaviors and optimize operation and performance.
You can use the Rotordynamics Module, which is an expansion to the Structural Mechanics Module, to analyze the effects of lateral and torsional vibrations of rotating machinery in order to study rotor vibrations and contain their levels within acceptable design limits. Among the different design parameters you can evaluate with this module are critical speeds, whirl, natural frequencies, stability thresholds, and the stationary and transient responses of a rotor due to mass unbalances. You can also see how rotational behavior may lead to stresses in the rotor itself, as well as additional loads on and vibration transmissions to other parts of the rotating machine’s assembly.
With the Rotordynamics Module, you can take into account the effects of various stationary and moving rotor components, including disks, bearings, and foundations. You can also easily postprocess your results directly within the software environment, presenting them as Campbell diagrams, modal orbits, harmonic orbits, waterfall plots, and whirl plots.
See how to perform a vibration analysis of the crankshaft of a 3-cylinder reciprocating engine in this tutorial model. Due to the eccentricity of the crank-pin and balance masses on the crankshaft, it undergoes self-excited vibration under rotation. The crankshaft is modeled using solid elements to accurately capture the effects of the eccentricity of the crank-pin and balance masses.
The objective with this tutorial model is to demonstrate how you can study the transient response of the rotor and the orbits of the balance masses on the shaft. The simulation results include the stress and pressure profile in the crankshaft, orbits of the center of the journals, and lateral displacement components of a journal.
Note that the Solid Rotor interface is used to model the rotor, while the bearings are modeled using the Hydrodynamic Bearing interface.
In this tutorial model, learn how to model multiple rotors connected through helical gears using the Rotordynamics Module, an add-on product to the Structural Mechanics Module and COMSOL Multiphysics®. When modeling geared rotors, the presence of gears in the system induces the lateral and torsional vibrations in the rotors. The gear mesh is assumed to be elastic, having a constant stiffness value.
We demonstrate an eigenfrequency analysis to compute the eigenfrequencies of the system for different speeds of the driving rotor. A transient analysis is also performed for the given speed of the driving rotor and the load torque on the driven rotor. With these analyses, we can compute the orbits of gear centers and forces on the bearings. The transient analysis is performed for both rigid and elastic gear mesh in order to analyze the effect of gear mesh stiffness on the rotor vibrations.
The simulation results for this tutorial model include a Campbell diagram showing the variation of eigenfrequencies with the rotational speed, critical speeds of the rotor, frequency response curves for the gear displacement and rotation, the von Mises stress distribution in the shafts, orbits of the gear centers in the rotating and fixed frames of reference, and the dynamic transmission error when transferring rotation from one shaft to another.
This example demonstrates how you can use modeling to investigate the performance of different hydrodynamic journal bearings. The model uses the Hydrodynamic Bearing interface, which solves the Reynolds equation to compute the pressure developed in a thin fluid film for four different bearing types: plain, elliptic, split-halves, and multilobe.
Results include the fluid pressure profile on the bearings, plots of journal eccentricity versus load, the steady-state position of the journals, and the fluid thickness profile when the journal is concentric with the bearing.
In the tutorial, we compare variations in the equilibrium journal position and thickness profile of the fluid film. By comparing these quantities, we can find the optimal bearing under similar operating conditions.
The Whirling of a Uniform Shaft tutorial model shows you how to perform a transient analysis of a uniform shaft under gravity. The shaft is supported by two hydrodynamic bearings at its ends. The gyroscopic effect causes the rotor to whirl about its initial axis and the rotor eventually reaches a steady orbit.
Results include the stress profile on the rotor with the maximum bending stress, the bearing fluid pressure, and the orbit of the journal. In the last result, the journal spirals outwards to eventually reach a steady orbit.
Also analyzed in this example is the frequency spectrum of the journal acceleration, which confirms that the half-frequency whirl is the dominant mode of whirling.
In this tutorial model, you will see how to set up eigenfrequency and transient analyses (using FFT) of a rotor with various mountings and bearing supports. The example illustrates how to use Campbell and Waterfall plots to find the critical speed. It also demonstrates the range of stability of the rotor.
The rotor is modeled using the Beam Rotor interface in the Rotordynamics Module, an add-on to the COMSOL Multiphysics® software. Inertial properties and offset of the rotor components are modeled using the Disk node. The bearing support is modeled by an equivalent stiffness-based approach using the Journal Bearing node provided in the interface. The FFT analysis uses the Time dependent with FFT study sequence.
In this example, learn how to model two rotors connected by a spline coupling. The first rotor is a fixed cantilevered rotor and the second rotor is supported. The model assumes that only translational motion is coupled between the rotors through the coupling, while the rotations of both rotors are uncoupled.
The tutorial demonstrates how to perform an eigenfrequency analysis at different speeds of the rotor, where the gyroscopic effects in the rotor stiffen the forward modes and soften the backward modes. The simulation results are illustrated in a Campbell plot and the critical speeds are compared and found close to those obtained in references.