Influence Coefficients Method Research Articles

Analysis and optimization of junction between cylindrical part and end dome of filament wound pressure vessels using data driven evolutionary algorithms

The junction between cylindrical part and end dome is the most critical place of the filament wound composite pressure vessels because the shear forces and bending moments occur in this area. The strength analyses of junction between cylindrical part and different types of known end domes based on influence coefficients method were performed for filament wound composite pressure vessels manufactured using glass-epoxy and carbon-epoxy composites. Four known end domes were considered that is, a spherical shell, a geodesic-isotensoid shell, a shell based on minimizing of the Tsai-Hill’s strength criterion and shell designed in authors’ previous work (Hoffman 1 shell). Moreover, the study is also dealing with design of optimal end dome shape which takes account to the junction area. Finding of optimal end dome shape was based on data-driven evolutionary algorithms. Using input dataset from the analytical simulation surrogate models were created using Evolutionary Deep Neural Nets (EvoDN2) algorithm. The multicriterial optimization procedure was performed using Constrained Reference Vector Algorithm (cRVEA) optimization algorithm. Results indicates that the optimal end dome shape highly depend on material properties.

On experiments of a novel unsupervised deep learning based rotor balancing method

Rotor dynamic balancing is essential in rotor industrial. The conventional balancing methods, including the influence coefficients method and modal balancing method, are effective, but lack economy and sufficient usage of the data. To overcome the disadvantages of the conventional balancing methods, a balancing method using unsupervised deep learning without weight trails had been proposed. The proposed network could identify the unbalanced forces from the data observed from just one run of the rotor and without labels. To validate the novel balancing method, an experimental rig is well-designed and established. Experimental validation and comparison with influence coefficients method are conducted. The experimental results show that the proposed balancing method gives consideration to both cost and accuracy. Compared with influence coefficients method, no extra weight trail process is needed and balancing performances are comparative. The experimental rig can be used for proving the scheme and for further same kind of research.

A computerized method of contact pressure and load distribution for crossed beveloid gears

Exact contact pressure and load distribution are key evaluation indices for beveloid gear design. A numerical calculation approach of contact pressure and load distribution for crossed beveloid gears is proposed, as opposed to the traditional method based on a finite element modeling software package. To acquire the flexibility properties of beveloid gear tooth surfaces, an accurate finite element (FE) model about a beveloid gear tooth with root fillets is first built. A solution model for crossed beveloid gears is developed using the influence coefficients technique. An enhanced solving approach is presented to improve the robustness of the solving model by addressing the limitation of the influence coefficients method. In addition, a unique contact pressure is presented. The numerical example proposed can be used to test the proposed methodology.

Partial least squares assisted influence coefficients concept improves accuracy in X-ray fluorescence analysis

Routine application of X-ray fluorescence (XRF) spectrometry in laboratory practice requires special procedures to correct for matrix effects. One of the most popular procedures is the influence coefficients method. In this method the regression equation relating analytical signal to the target element concentration is extended with empirical terms correcting the influence from particular matrix elements. While the influence coefficients method is quite accurate, it is rather laborious as it requires individual selection of matrix terms for each element under study. The influence coefficients method is based on the least squares regression technique, thus the number of matrix correction terms is limited by the number of available standard calibration samples. Here we propose a very simple technique that can take into account an unlimited number of terms in the influence coefficients method through the employment of partial least squares regression (PLS) where spectral intensities, their ratios and squared intensities are employed as variables. Unlike traditional application of PLS in XRF studies where the regression model is built using spectral intensities only, the proposed approach inspired by classic influence coefficients allows elimination of complex specific XRF matrix effects. The paper describes the suggested method and demonstrates its' performance in two EDXRF data sets with significant matrix effects (ore and steel samples).

Investigation into the influence of bearings nonlinear forces in unbalance identification

Rotating machines are key components in several industrial sectors, mainly, in energy generation. In this way, a rotating component supported on hydrodynamic bearings creates typical problems, being high vibrations amplitudes due to unbalance, one of the most common. To avoid failures and ensure a safe operation, the rotor should be balanced, and influence coefficient methods are usually used. Since balancing by the traditional influence coefficients method requires trial masses, the machine can sometimes experience a long setup time, causing financial losses. Also, this method assumes a linear rotor response that can hamper the balancing procedure for nonlinear situations, which happens when the rotor experiences high vibrational motion. Thus, this work proposes a balancing identification that considers nonlinear bearings and avoids trial masses. For this, a mixed-integer gradient-based optimization is presented. The theoretical model of a rotor supported by hydrodynamic bearings is obtained using the Finite Element method and solving the Reynolds equation. In order to save computational time, the bearing forces are approximated by a fifth order Taylor series expansion. The presented results show that nonlinear bearing consideration can improve the machine diagnosis.

A transient characteristic-based balancing method of rotor system without trail weights

In this paper, a transient characteristic-based balancing method (TCBM) combined with dynamic load identification (DLI) technique to identify the unbalance parameters of the general rotor system is proposed. The dynamical equations of motion of general rotor system is derived by the transfer matrix method (TMM). Then the DLI technique is used to obtain the transient excitation forces, which are totally estimated by the transient vibration responses and the modal characteristics of the rotor system. Theoretical error analyses are carried out to verify the accuracy of the calculated results of the transient excitation forces and the validity of the DLI technique. The unbalance parameters are identified by calculating the results of the transient excitation forces with unbalance characteristic points. The numerical and experimental results demonstrate that the proposed method has good performance in dynamic balancing of the rotor system. The dynamic balancing accuracy of the TCBM is close to the influence coefficients method (ICM) in experimental investigations, while the TCBM balancing through transient vibration responses and without trail weights. More importantly, it will facilitate the on-site dynamic balancing process by designing a complete set of balancing system tools for rotor dynamics analysts based on the TCBM.

Impact-driven broadband piezoelectric energy harvesting using a two-degrees-of-freedom structure

Impact-driven piezoelectric energy harvesters are more capable of harvesting vibration energy at low frequency than bending-type ones. However, an impact-driven harvester usually relies on either a free moving object or a cantilevered driving beam to provide impact. The former is difficult for developing a precise model to predict its frequency responses while the latter can only achieve high power output about the first resonant frequency of the driving beam. In this paper, a novel impact-driven two-degree-of-freedom piezoelectric energy harvester is introduced to scavenge vibration energy harvesting in a wide frequency range that includes its two resonant frequencies. The proposed harvester consists a two-degrees-of-freedom beam structure and a piezoelectric diaphragm. The beam structure is designed to have two close resonant frequencies with similar amplitudes of tip displacement under excitations at a fixed acceleration magnitude. A proof mass is fixed to the end of the beam to hits and deforms the piezoelectric diaphragm to generate electricity under base excitations. The diaphragm also works as a stopper to introduces the piecewise linear hardening effect and improve the frequency range under up sweeps. The theoretical model is developed based on the stiffness influence coefficients method and validated with experimental results. The amplitudes of the voltage output at the first two resonant frequencies are similar under excitations with a fixed acceleration magnitude. Different excitation levels are tested to investigate the performance of the harvester. Parametric analysis of the beam lengths is conducted to investigate their influence on the performance of the harvester. The proposed harvester demonstrates the capability of harvesting vibration energy in a wide frequency range that covers the two resonant frequencies. The hardening effect caused by the stopper further improves the bandwidth under up sweeps.

Dynamical simulation of a CNC turning centre

This paper deals with the analysis of a CNC turning centre, more specifically the spindle system. The FEM analysis shows the natural frequencies of the spindle system and the same system was analysed by using the TMM and the influence coefficients method. These analyses pave the way to compare these three methods.

Characteristics of oil film nonlinearity in bearings and its effects in rotor balancing

Since unbalance is inherent to any rotating machine, and some effects like coupling misalignment and thermal bow, which are not taken into account in pre-balancing, can lead to changes in unbalance distribution, in-field rotor balancing is sometimes a necessary action. Traditionally, the influence coefficients method has been used as the main balancing procedure, and due to the low accessibility in assembled rotating machinery, generally only the journal displacements inside hydrodynamic bearings are available for the balancing procedure. However, influence coefficients method assumes linearity of rotor response and it is known that hydrodynamic bearings can sometimes present a strong nonlinear relationship between bearing forces and journal displacements, making balancing difficult or even impossible. Otherwise, the bearing housing vibrations are directly proportional to the bearing forces and are independent of the journal displacements, therefore avoiding problems related to oil film nonlinearities. This paper proposes the use of bearing housing accelerations as influence coefficients and verifies experimentally that balancing can be successful also in highly nonlinear oil film bearing conditions. First, the oil film nonlinear characteristics are introduced by means of a simple analytical model. Then, different behaviors have been experimentally investigated by means of a test rig rotor supported by three hydrodynamic bearings, designed to enhance oil film nonlinear effects. Nonlinear effects are quantified through deviations with respect to linear behavior and development of higher harmonics in the response of the oil film. It is shown that these effects can seriously affect the possibility of balancing with the use of influence coefficients. Finally, it has been verified experimentally that balancing with the use of bearing housing acceleration to calculate influence coefficients was successful, as expected.

Tuning of Parametric Excitation for Rotor Balancing

Residual unbalance is the primary source of vibration in rotating machines. In many cases, the time and, consequently, the cost involved in the balancing procedure is high due to the need to accelerate the rotor up to every critical speed to be balanced in every iteration of the traditional influence coefficients method. Recently, a novel method which does not need to accelerate the rotor up to every critical speed to be balanced was proposed. In this method, active magnetic bearings are used to apply a parametric excitation at the combination resonance frequencies inducing an effect similar to transferring kinetic energy from a lower mode to higher modes. Therefore, maximizing the energy transferred is mandatory to obtain a high signal-to-noise ratio and capture the correct responses of the higher modes to successfully balance the rotor. This paper study the sensibility of the kinetic energy transfer between modes to the parameters of the parametric excitation; namely amplitude, frequency, and phase. The analyses are performed via computational simulations of a flexible rotor sustained by two AMBs and with three critical speeds in its operational range.

Robust Balancing Approach for Rotating Machines Based on Fuzzy Logic

Unbalance is one of the most common malfunctions found in rotating machines generating high vibration amplitudes that can lead to fatigue and wear of rotor elements. There are several well-known balancing techniques wherein one of the most widespread approaches is the so-called influence coefficients method (IC method). Aiming to increase the robustness of the standard IC method, in this paper, a revised IC balancing methodology for rotating machines is proposed. In this sense, a preprocessing stage is applied to access the uncertainties affecting the rotating machine. In this sense, measurement data sets evaluated under the fuzzy logic approach are used. Thus, the rotor vibration responses measured over a long period are considered by means of a fuzzy transformation (defining unbalance fuzzy sets). The unbalance condition of the rotating machine is determined through a defuzzification process. This unbalance condition is then introduced in the IC method algorithm aiming at obtaining correction weights and associated angular positions that increase the balancing robustness as compared with the classical approach. Numerical and experimental studies are used to evaluate the effectiveness of the proposed methodology. The obtained results illustrate the capacity to increase the balancing overall robustness.

DESIGN AND ANALYSIS OF A THREE-STAGE CYCLOIDAL PLANETARY GEAR DRIVE FOR HIGH REDUCTION RATIO

A new compact design of three-stage differential cycloidal planetary gear drive based on the concept of the so-called RV-reducer is proposed for high reduction ratio. The aim of the paper is to explore the structural and the loading characteristics of this new design. The drive consists of an involute stage and The reduction ratio of this drive type can be positive or negative depending on the tooth numbers of the gears. The relation of transmitted torques onto each component are derived based on the relations of torque and power equilibrium. The loaded tooth contact analysis of the drive is also developed based on the influence coefficients method. The influence of the two mechanism types and the arrangement of the cranks on the shared loads and contact stress acting on multiple tooth-pairs as well as the transmitted torques are analyzed and discussed in the paper.

Optimization of unbalance distribution in rotating machinery with localized non linearity

Classical balancing techniques for rotating machinery consider that these systems are linear. However, if some nonlinearity appears in the structure, these techniques do not work properly and the results obtained regarding the correction weights and their corresponding angular positions are not satisfactory. This behavior is due to the fact that these techniques, such as the influence coefficients method, consider linear relations involving the unbalance excitations and the resulting vibration. On the other hand, the choice of the number and the repartition of the correction planes depends on the possible accessibility that varies for each machine. In this work, a new method dedicated to the identification of the rotating machinery and the unbalance distribution in linear and non linear conditions is realized through pseudorandom optimization methods and the system modeling is performed by using the well-known finite element method. The nonlinearity is introduced by using a frequency dependent bearing. Several computer simulations are performed for different rotor configurations (linear and nonlinear). The methodology is then validated through an experimental test rig. The results obtained demonstrate the effectiveness of the method developed.

Low-frequency balancing of two-bracket rotors of turbomachines

A method for balancing high-speed two-bracket turbomachine rotors, widely employed in gas-turbine engines, general-purpose air compressors, turbogenerators, and engine turbosupercharging units, is examined. A procedure is proposed for stage-by-stage dynamic balancing of turbomachine rotors, including dynamic balancing of impellers on a mandrel. The influence-coefficients method has been used to calculate disbalances. Recommendations are offered for applying low-frequency balancing of bracket rotors on the basis of their amplitude-frequency characteristics.

Employing fractals and FEM for detailed variation analysis of non-rigid assemblies

Many studies on non-rigid assemblies, or assemblies of non-rigid components, suggest that the component variation affects the assembly dimensional quality. However, little is known about how the variation of surface micro-geometry of assembly components influences the assembly dimensional quality. In this paper, a new method based on the fractal geometry and finite element method (FEM) is proposed to study such an influence. In the new method, a special fractal function, named the Weierstrass–Mandelbrot (W–M) function, is used to extract and represent the characteristics of surface micro-geometry of assembly components. FEM is applied to analyze the deformation of non-rigid assemblies by integrating the variation of component micro-geometry. The sensitivity matrix between the component variation and assembly variation is obtained by using the existing influence coefficients method. It is found that contributions of the surface micro-geometry of assembly components to the final variation of non-rigid assemblies could be substantial under certain conditions. The proposed method is illustrated through a case study on an assembly of two flat sheet metal components under different fixture-releasing conditions.

Active Balancing of Turbomachinery: Application to Large Shaft Lines

Unbalance defects are inherent to rotating machinery manufacturing and cause important vibra tions that are necessary to decrease. This work, which comes after a bibliographical study, relates to active balancing of rotors. The unbalance correction is carried out in real time, during operation in steady state and transient responses. The concept suggested consists of generating a correction force using two mobile weights situated in the same plane and running at a constant radius of the rotation axis. The balancing process is based on the influence coefficients method and includes specific measurement and control developments. Influence coefficients are determined in a first step and then used to balance the rotor at a specified speed during its transient response to minimize vibrations at critical speeds. A first experimental application is presented. A technological device designed for large-sized machines is described and used to balance a single rotor test bench. The technology and the process efficiencies are shown: vibrations at critical speed are strongly de creased. A simulation of active balancing of the rotor is then carried out to validate the simulation's procedure compared to experimental results. The second application is a numerical simulation of the active balancing of an industrial turbogenerator group passing through multiple critical speeds. Results show the active balancing of a multirotor machine's advantage compared to conventional balancing.

Automatic balancing of flexible rotors, Part II: Synthesis of system

A simple synthesis method of automatic balancing for a system of flexible rotors is proposed in this paper. In order to describe the rotating system, transfer functions with complex coefficients are adopted. The influence coefficients method is used for derivation of the control law. The relationship between the influence coefficients matrix and the system control transfer function matrix with complex coefficients is set out. Balancing heads with movable correction masses are applied for balancing. An algorithm of operation of the computer control device is given.