Algebraic Self-Similar Renormalization in Theory of Critical Phenomena

We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several different examples. The advantage of the method is in combining simplicity with high accuracy.Comment: 1 file, 44 pages, RevTe

Dynamic Modeling of a 3D Printer Based on a Four Arms Scara Mechanism

This work presents the dynamic simulation of a four arms SCARA (Selective Compliance Articulated Robot for Assembly) mechanism used in 3D printers in a multidisciplinary free software. Different extruder heads and motor supply voltage 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 kinematics analysis, motion translation, and dynamic analysis. After accomplishing these steps, the computation of the positioning error completes the analysis. The simulation showed that the supply voltage has the greater influence on the construction of the part. The extruder mass becomes relevant when the voltage is 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

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.6247048110. International Conference on Rotor Dynamic

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.6351853010. International Conference on Rotor Dynamic

Identification Of A Rotating Machine Support Structure Through Mimo Technique

Large turbine sets are supported by several bearings, and these are connected to the structure foundation, which is usually made of steel and concrete. Besides, the structure is embedded in soil by concrete blocks or pillars, and the bearings work as dampers absorbing the vibration transmitted from rotor to foundation. This interaction affects both subsystems (rotor and foundation), and it is important to determine their dynamic behaviour. This work presents the application of a time domain method to calculate the modal parameters of a support structure of rotating machinery, used to include its influence on the dynamic behaviour of the rotor through the application of the Mixed Coordinates method, which uses modal coordinates of the structure and physical coordinates to the rotor-bearings subsystem. In order to test the modal analysis techniques, three techniques of excitation of the support structure were employed in a theoretical model: a single point excitation force applied by a shaker; a multi-point excitation where a set of shakers are connected to the structure; and a multi-point excitation generated by the unbalance of a rotor during its run-up and run-down. The MIMO techniques were also applied in a test rig that consists of a small rotor supported by a couple of plain journal bearings. Load cells were placed around the bearing cases to measure the forces applied to the structure, and there are accelerometers applied to the surface of the bearing case. This experimental data were used to calculate the modal parameters of the structure connection nodes, which were added to a rotor-bearings subsystem, where the rotor is represented by a Finite Element model, and the bearing coefficients are determined by the Finite Volume Method. A comparison was made between the experimental and simulation results of the identification techniques. © IMechE 2008.1331344Weber, H., (1961) Über das gemeinsame Schwingungsverhalten von Welle und Fundament bei Turbinenanlagen, (48), pp. 55-62. , VDI-BerichteGasch, R., Vibration of Large Turbo-Rotors in Fluid-Film Bearings on an Elastic Foundation (1976) Journal of Sound and Vibration, 47 (1), pp. 53-73Bachschmid, N., Bernante, R., Frigeri, C., Dynamic Analysis of a 660 MW Turbogenerator Foundation (1982) Proceedings of the International Conference Rotordynamic Problems in Power Plants, pp. 151-161. , Rome, Italia, ppDiana, G., Cheli, F., Vania, A., 1988, A method to identify the foundation modal parameters through measurements of the rotor vibrations, ImechE paper C300/88, Proceedings of the 5th International Conference on Vibrations in Rotating Machinery, Cambridge, UK, pp. 217-222Feng, N., Hahn, E.J., Experimental Identification of the Pedestals in a Rotor-Bearing-Pedestal System (1998) Proceedings of the 5 th International Conference on Rotor Dynamics, pp. 734-745. , IFToMM, Darmstadt, Germany, ppEdwards, S., Lees, A.W., Friswell, M.I., Experimental identification of excitation and support parameters of flexible rotor-bearings-foundation system from a single run-down (2000) Journal of Sound and Vibration, 232 (5), pp. 963-992Bachschmid, N., Pennacchi, P., Vania, A., Gregori, L., Zanetta, G. A., 2004, Unbalance identification in a large steam turbogenerator using model-based identification and modal foundation, ImechE paper C623-081, Proceedings of the 8th International Conference on Vibrations in Rotating Machinery, Swansea, UK, pp. 383-392Cavalca, K.L., Cavalcante, P.F., Okabe, E.P., An investigation on the influence of the supporting structure on the dynamics of the rotor system (2005) Mechanical Systems and Signal Processing, 19, pp. 157-174Okabe, E.P., Cavalca, K.L., Analysis of a theoretical-experimental model of a rotor-bearing-foundation system (2007) Proceedings of the 19th International Congress of Mechanical Engineering - COBEM, , Brasilia, Brazil, Paper DSS15-0732Gontier, C., Smail, M., Gautier, P.E., A time domain method for the identification of dynamic parameters of structures (1993) Mechanical Systems and Signal Processing, 7 (1), pp. 45-56Fassois, S.D., Lee, J.E., On the problem of stochastic experimental modal analysis based on multiple-excitation multiple-response data, part II: The modal analysis approach (1993) Journal of Sound and Vibration, 161 (1), pp. 57-87Moore, S.M., Lai, J.C.S., Shankar, K., ARMAX modal parameter identification in the presence of unmeasured excitation - I: Theoretical background (2007) Mechanical Systems and Signal Processing, 21, pp. 1601-1615Moore, S.M., Lai, J.C.S., Shankar, K., ARMAX modal parameter identification in the presence of unmeasured excitation - II: Numerical and experimental verification (2007) Mechanical Systems and Signal Processing, 21, pp. 1616-1641Fassois, S.D., MIMO LMS-ARMAX identification of vibrating structures - part I: The method (2001) Mechanical Systems and Signal Processing, 15 (4), pp. 723-735Florakis, A., Fassois, S.D., Hemez, F.M., MIMO LMS-ARMAX identification of vibrating structures - part II: A critical assessment (2001) Mechanical Systems and Signal Processing, 15 (4), pp. 737-758Ljung, L., (1999) System Identification: Theory for the User, , Prentice Hall, New Jersey, USA, 609 pNelson, H.D., A finite rotating shaft element using Timoshenko beam theory (1980) Journal of Engineering for Industry - Transactions of the ASME, 102, pp. 793-803Maliska, C.R., (2000) Heat transfer and computational fluid mechanics, , in Portuguese, Editora LTC, Rio de Janeiro, Brazil, 468 pPatankar, S.V., (1980) Numerical Heat Transfer And Fluid Flow, , Hemisphere Publishing, Washington DC, USA, 210 pEwins, D.J., (1995) Modal Testing: Theory and Practice, , Research Studies Press, Somerset, UK, 313 pPetsounis, K.A., Fassois, S.D., Parametric time-domain methods for the identification of vibrating structures - a critical comparison and assessment (2001) Mechanical Systems and Signal Processing, 15 (6), pp. 1031-106

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

Modeling of 3D Printer Based on a Flexible Cartesian Mechanism

This work presents the computational modeling of a three dimensional printer based on a flexible Cartesian mechanism using a multidisciplinary open source software. The dynamic simulation of the flexible mechanism was compared to that of a rigid one to highlight the differences between both approaches. The flexible components of the printer were modeled using beam elements. The simulation showed that the flexibility of the deposition mechanism contributes to its error positioning and vibration

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 Butenschön. 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 Butenschön model was implemented in C and Fortran 95 and integrated to OpenModelica as an external library.6030732

Modeling and Simulation of a Wind Turbine Gear Set with Hydrodynamic Bearings Attached to an Induction Generator

This work presents the numerical modeling and simulation of a wind turbine gearset with hydrodynamic bearings and an induction generator. Transmissions based on epicyclic gear trains applied to wind turbines have some advantages, i.e., compactness, robustness and low maintenance requirement. The early stages of the development of such mechanism need numerical results in order to design it properly. The complexity of this machine requires a multidisciplinary approach to model and simulate a system comprising of mechanical, fluid and electrical components. The bearing model is integrated to the kinetics of the gearbox, allowing a precise evaluation of the journal bearing's movements. Through a multidisciplinary multibody dynamics software, the gearbox dynamics, the bearing behavior and the induction generator are calculated in a single system. The numerical solution of the hydrodynamic lubrication problem of a finite bearing is achieved using the finite element method. The hydrodynamic bearing and the induction generator are implemented as a user module in MBDyn software, which makes them available to model and simulate other types of rotating machinery. Simulations of two different conditions showed a better damping property when compared to rolling bearings, in this gearset