Eduardo Paiva Okabe

On the Analysis of Rotor-Bearing-Foundation Systems

This work presents a methodology to analyse the influence of the foundation or supporting structure on the rotor-bearings system. A frequency response analysis of the complete system was accomplished by considering physical co-ordinates for the rotor-bearings system and principal co-ordinates for the foundation. The mathematical procedure applied a modal approach to the supporting structure, using modal parameters of generalised mass, damping ratio and natural frequency, which were calculated from the frequency response functions (FRF) of an actual structure. Convergence of the method was verified and the effect of the flexible foundation on the complete system response was analysed. A new formulation for the Mixed Co-ordinates method was presented to evaluate the influence of the supporting structure on the directional response of a rotor. An analysis of the directional frequency response function (dFRF) of the complete system was accomplished considering directional co-ordinates for the rotor-bearings system and principal co-ordinates for the foundation. These results were compared to the conventional FRF procedure.

Detailed Modeling of Wind Turbine Gear Set by General-Purpose Multibody Dynamics

This work presents the development of a kinematic model of a spur gear pair and the implementation of a hydrodynamic bearing in a multidisciplinary multibody dynamics software. Both models are employed to simulate the behavior of a planetary gear set typically adopted in wind turbines. Geared transmissions have been a popular choice to transmit the rotation of the main rotor to the electrical generator in this type of turbine. Compared to other kinds of transmission, a gearbox is more compact, robust and require low maintenance over its lifetime, which is interesting, since these turbines are usually installed in remote places. The gearbox of a wind turbine is normally composed by a set of spur gears and bearings, assembled in arrangement known as epicyclic. Spur gears generally have an involute profile, which allows a constant transmission of the angular speed. This kinematic constraint between gears is defined by the angle that the surface of their teeth is in contact with. This angle is known as pressure angle and, by design, it should remain constant during operation. However, a variation of the distance between gears changes this angle, which also changes the direction of the transmission of the movement. To account for this effect, the joint is described by the projection of the absolute velocity of the contact point of each gear on the line of action, which is calculated from their position. Another important group of elements are the bearings that support gear and shafts. They can absorb part of the vibration, and compensate misalignments and teeth surface failures. Hydrodynamic bearings are widely employed in turbomachinery, due to their simplicity, long life and good damping properties, which are features that wind turbines can benefit from. Most of the hydrodynamic bearing models are two dimensional, so they have to be adapted to be implemented in a multibody dynamics software. The development of these modifications is also described in this work, so any other hydrodynamic bearing model can be easily adapted using the same procedure. Finally, a model of the wind turbine gearbox is presented, and some of the features of using the aforementioned elements inside a multibody dynamics software can be highlighted.Copyright

Modeling and Simulation of the Drivetrain of a Metal Lathe

Vibrations in turning machining are one of the most common sources of problems. Bad quality finishing, decrease of the tool life, dimensional errors, and noise are some of the issues generated by these vibrations. To understand the role of each component, this work presents a model of a metal lathe including its drivetrain, and simulates it during the internal turning operation. The drivetrain is composed by an electric motor connected to the spindle through a pulley and belt transmission. The spindle was modeled as a rotor supported by rolling bearings, while the chuck with jaws and the workpiece were considered to be rigidly attached to the spindle. The interface between the workpiece and the tool was modeled considering their relative displacement and the machining condition, thus generating a set of cutting and drag forces that varies during the operation. The tool holder was modeled by three-node finite volume beam elements that are attached to the turret. The turret was connected to the machine frame through a total joint (configured as prismatic). This model was implemented in the dynamic simulation software MBDyn and a module was developed in C++ to mimic the interaction between workpiece and tool. Different configurations of the machine were tested, such as the diameter of the tool holder and the rotation speed of the spindle, and their influence on the drivetrain is reported.

Simulation and Analysis of the Influence of the Support Structure on a Wind Turbine Gear Set

This work presents the numerical modeling, simulation and analysis of a wind turbine gearset supported by a flexible structure model. Gearboxes based on epicyclic gear trains applied to wind turbines have some advantages, i.e., compactness, robustness and low maintenance requirements. The gearbox is one of its main components because it is responsible for transforming the low angular speed of the rotor into the higher operation speed of the induction generator. Failures in this component cause loss of efficiency and directly impact the energy generated. The gearbox is attached to the nacelle, which is supported by the wind turbine tower. Wind gusts and shear can cause vibration that affects the tower and the nacelle and, therefore, all the components attached to them. To model these phenomena, a detailed model of a 600 kW turbine was built using the MBDyn software. The bearing, gear and the induction generator models were implemented as user-defined modules and were further integrated into the complete model of the wind turbine. Results showed that the gearbox components were affected by the dynamic behavior of the support structure and, therefore, its influence should be accounted for in the design of wind turbines.

Analysis of Analytical Hydrodynamic Bearing Models on a Reciprocating Compressor

Reciprocating compressors are one of the most common machines, as they are usually found in household refrigerators and air conditioners. The reciprocating compressor is a rotor-crankshaft-piston machine supported by lubricated bearings. They are sealed to retain and store the refrigerating gas, therefore, the maintenance of the compressor is difficult and expensive. Thus reciprocating compressors should be designed to last the life span of the appliance. Most models of reciprocating compressors considers rigid bearings, which completely neglects the influence of the hydrodynamic bearings on the dynamic behavior of the compressor. This work shows the modeling and analysis of a reciprocating compressor with flexible bearings. The rotor which is part of the motor is supported by a pair of hydrodynamic bearings that are modeled using three different analytical models: Capone, Vance and Butenschon. Analytical models of bearing are much faster than numerical ones, such as the ones that use the finite difference (FDM) or finite element method (FEM). The three models have different approaches to solve the Reynolds equation and, therefore, distinct results were found using each one of them. The model was developed in the OpenModelica software using the elements of the Mechanics.Multibody library. The Butenschon model was implemented in C and Fortran 95 and integrated to OpenModelica as an external library.

Modeling and Simulation of a 3D Printer Based on a SCARA Mechanism

This work presents a dynamic simulation of four arms SCARA (Selective Compliance Articulated Robot for Assembly) mechanism used in 3D printers in an multidisciplinary free software. Different extruder heads, motor supply voltage and microstepping strategies were simulated to show their impact on the construction of the printed part. To do the complete analysis of the printer, it is necessary to simulate the workflow to print a part. The steps of this workflow are part modeling, G-code generation, G-code translation, inverse kinematic analysis, motion translation and dynamic analysis. After accomplishing these steps, the computation of the positioning error completes the analysis. The simulation showed that the microstepping strategy had the greater influence on the construction of the part. The extruder mass became particularly relevant when the voltage was reduced. Simulation of the complete system also showed that electrical and mechanical components can be integrated in one model, although the behavior of components of one domain can restrict the simulation performance of the entire system.