Three-mass Model Research Articles

Dynamic Models of Mechanical Seals for Turbomachinery Application

One of the primary causes of mechanical face seal failure is rotor vibration. Traditional dynamic seal models often cannot fully explain failure mechanisms. The dynamic models of seals proposed in this paper, including those developed by the authors, are valuable for predicting seal dynamics during operation in specific turbomachinery and for explaining the causes of seal failure. The single-mass dynamic model is suitable for analyzing the dynamics of contact mechanical face seals and simply designed dry gas seals. The two-mass dynamic model is used to investigate the operational dynamics processes of classical dry gas seals under complex loading conditions. The three-mass dynamic model is used to study various complex types of mechanical face seals. This model can determine the normal operating condition range and explain leakage mechanisms in the presence of excessive rotor vibrations.

Vibrating roller with compacted soil interaction modelling

Introduction. Vibrating rollers are the most common means of compacting soils in construction. The nature of stress development on the contact surface of the roller with the ground depends on the technical characteristics of the vibrating roller (the mass of the roller, the mass of the roller frame, the frequency and driving force of vibrations, the number and characteristics of the roller shock absorbers) and the properties of the soil.Materials and methods. Simulation of the interaction of a vibrating roller with compacted soil was carried out using a three-mass rheological model of the frame-roller-soil system. Differential equations of mass motion in contact and separation modes were solved numerically. To determine the numerical values of the loading time (increase in contact stresses from zero to the maximum value) and the unloading time (decrease in contact stresses from the maximum value to zero), as well as the maximum reaction force of the soil, a computational experiment was conducted on a rheological model. The mass of the vibrating roller module (the mass of the front axle) and the relative driving force were used as independent parameters of the vibrating roller. The coefficients of elastic and viscous resistance of the soil were chosen as independent parameters of the soil. The total number of combinations of factors was 192. The values of the time of loading and unloading of the soil, as well as the maximum strength of the soil reaction, were determined by oscillograms of changes in the strength of the soil reaction over time.Results. Using the STATISTICA program, regression equations, to calculate the numerical values of the loading and unloading time of the soil, as well as the maximum reaction force of the soil and the corresponding values of the reliability coefficients of the multiple approximation, were obtained.Discussion and conclusion. The rheological model reproduces the asymmetric nature of changes in contact stresses during soil compaction by a vibrating roller, observed in experimental stress oscillograms obtained during field experimental studies. The results obtained are important for calculating the depth of stress propagation in the ground and the distribution of stresses in the ground after the passage of a vibrating roller using a wave approach to describing stress propagation in the ground. In the future, it is advisable to conduct a computational experiment with an expanded list of independent parameters of the roller, including the oscillation frequency.

Belt conveyor starting mode optimization

The work is aimed at increasing the efficiency of belt conveyors by choosing the drive mechanism movement mode. During the operation of belt conveyors, significant energy and dynamic loads occur in the elements of the drive mechanism and traction body. The available loads significantly affect the energy losses and the reliability of the drive mechanism and the traction body. Energy and dynamic loads during transient processes (starting, braking, changing speed or performance and emergency stop) are especially dangerous. At this moment, high-frequency oscillations of both the traction body and the drive elements arise. With such fluctuations in the traction body (belt) of the conveyor, significant breaking forces arise, which create additional unwanted stresses in it and, as a result, contribute to premature destruction. In addition, the stator and rotor windings of the electric motor are heated, which accelerates their wear and failure. In order to reduce dynamic loads, it is proposed to optimize the movement mode of the drive mechanism. For this purpose, the conveyor is presented in the form of a three-mass dynamic model, based on which a mathematical model was created. From the conducted dynamic analysis of the belt conveyor, it was established that during the start-up process, significant power and energy overloads occur in the elements of the drive and the traction body, which depend on the driving force of the drive. In addition, high-frequency oscillations of the tape are observed. Since the undesirable properties of the belt conveyor largely depend on the magnitude of the driving force of the drive, it should form the basis of the optimization criterion. In addition, the driving force of the drive must be reflected in the optimization criterion during the entire movement process, that is, the optimization criterion must be presented in an integral form. To eliminate the possible compensation of negative and positive values of the driving force on the conveyor, the latter should be represented in the integral criterion in quadratic form. Therefore, the rms value of the driving force of the drive during the start-up time was chosen as the criterion for optimizing the motion mode of the belt conveyor. Optimization of the conveyor movement mode was carried out by minimizing the integral dynamic criterion. As a result of the optimization, the start-up mode of the belt conveyor was determined, which minimizes the effect of dynamic loads. This start-up mode makes it possible to increase the reliability of the conveyor and reduce the energy consumption of the drive.

Active damping of torsional vibrations in the drive train of a DFIG wind turbine

Torsional vibrations in the drive train of the doubly-fed induction generator (DFIG) based wind turbine can cause large mechanical stress and reduce the life cycle of the components. They can be easily induced by sudden changes from the turbine rotor side or grid side. In this paper, a model-based active damper of the torsional vibration designed with the linear quadratic-Gaussian (LQG) algorithm is proposed. The modelling of the drive train takes the flexibility of the rotor blades into account and utilizes a three-mass model. A combination of different simulation packages, namely FAST (Fatigue, Aerodynamics, Structure, Turbulence) and Matlab/Simulink describing important dynamics of both the mechanical and electrical side, is applied to analyse the vibrations in the drive train and test the algorithm. Simulation results show that the proposed active damping can suppress the torsional vibrations in the drive train effectively even if a gird fault occurs.

Deep Learning for Neuromuscular Control of Vocal Source for Voice Production.

A computational neuromuscular control system that generates lung pressure and three intrinsic laryngeal muscle activations (cricothyroid, thyroarytenoid, and lateral cricoarytenoid) to control the vocal source was developed. In the current study, LeTalker, a biophysical computational model of the vocal system was used as the physical plant. In the LeTalker, a three-mass vocal fold model was used to simulate self-sustained vocal fold oscillation. A constant/ǝ/vowel was used for the vocal tract shape. The trachea was modeled after MRI measurements. The neuromuscular control system generates control parameters to achieve four acoustic targets (fundamental frequency, sound pressure level, normalized spectral centroid, and signal-to-noise ratio) and four somatosensory targets (vocal fold length, and longitudinal fiber stress in the three vocal fold layers). The deep-learning-based control system comprises one acoustic feedforward controller and two feedback (acoustic and somatosensory) controllers. Fifty thousand steady speech signals were generated using the LeTalker for training the control system. The results demonstrated that the control system was able to generate the lung pressure and the three muscle activations such that the four acoustic and four somatosensory targets were reached with high accuracy. After training, the motor command corrections from the feedback controllers were minimal compared to the feedforward controller except for thyroarytenoid muscle activation.

The use of PI-algorithm for high-speed electric rolling stock automatic control system

The article is devoted to analysis of automatic control systems used to optimize current collection on high-speed railway electric rolling stock. A classification of automatic control systems has been developed. The use of automatic control systems that change the pantograph static force can significantly improve the quality of the current collection. However, their use changes the compression of the elastic elements of the panhead suspension, which can ultimately lead to its complete compression and breakaways. To solve this problem, authors propose using intra-spring pneumatic elements in panhead suspension. The automatic control system must simultaneously control the pantograph static force and the panhead suspension static characteristics. The authors proposed and described an automatic control system of the pantograph contact force and the panhead suspension static characteristics. To test the prospects of the proposed automatic control system, a three-mass mathematical model of a pantograph equipped with intra-spring pneumatic elements in panhead suspension has been developed and implemented in the MATLAB Simulink software package. The obtained results indicate the possibility of using intra-spring pneumatic elements in panhead suspension when using an automatic control system. It allows you to avoid vertical impacts causing a sharp increase in contact force and breakaways of the panhead.

Using a vertical three-mass computational model of the vocal folds to match human phonation of three adult males.

Computer models of phonation are used to study various parameters that are difficult to control, measure, and observe in human subjects. Imitating human phonation by varying the prephonatory conditions of computer models offers insight into the variations that occur across human phonatory production. In the present study, a vertical three-mass computer model of phonation [Perrine, Scherer, Fulcher, and Zhai (2020). J. Acoust. Soc. Am. 147, 1727-1737], driven by empirical pressures from a physical model of the vocal folds (model M5), with a vocal tract following the design of Ishizaka and Flanagan [(1972). Bell Sys. Tech. J. 51, 1233-1268] was used to match prolonged vowels produced by three male subjects using various pitch and loudness levels. The prephonatory conditions of tissue mass and tension, subglottal pressure, glottal diameter and angle, posterior glottal gap, false vocal fold gap, and vocal tract cross-sectional areas were varied in the model to match the model output with the fundamental frequency, alternating current airflow, direct current airflow, skewing quotient, open quotient, maximum flow negative derivative, and the first three formant frequencies from the human production. Parameters were matched between the model and human subjects with an average overall percent mismatch of 4.40% (standard deviation = 6.75%), suggesting a reasonable ability of the simple low dimensional model to mimic these variables.

Enhancing a Three-Mass Vehicle Model with Wheel-Size Effect for Scanning Bridge Frequencies

An advanced miniature vehicle model is proposed by incorporating size of two wheels in a three-mass vehicle model to consider the offset of contact points due to the presence of pavement irregularity. In this proposed vehicle–bridge system, each wheel has its own dimension in addition to the mass related to the degree-of-freedom while it is assumed to be rigid. In the theoretical formulation, the real contact points and contact displacements turn to be unknown parameters. As such, a numerical framework is established by proposing a procedure in the time integration scheme to determine these parameters and deriving explicit coding structure to locate the two wheels on the bridge during simulation. The parametric study investigates the size effect of wheels, effect of vehicle damping, and pitching effect as a result of wheel size on the identification of frequencies. The results show that using larger wheels leads to smaller dynamic responses of the bridge and smaller vertical responses of the vehicle by the present vehicle model. Furthermore, higher accuracy is observed in the proposed vehicle model in comparison with the traditional three-mass vehicle model. The first three bridge frequencies can be identified distinctly under the most severe pavement irregularity.

Dynamic Analysis of the Thermo-Deformation Treatment Process of Flat Surfaces of Machine Parts

Thermo-deformation treatment refers to methods of strengthening during which strengthened layers with a nanocrystalline structure are formed in the surface layers by modifying the metal surface layer, which changes its phase and structural and chemical compositions, reduces grain size, and improves performance. Grinding of the metal structure was achieved by combining two methods simultaneously during this treatment: the action of a highly concentrated energy source on the surface layer and intense plastic deformation. The source of highly concentrated energy was generated in the contact zone of the tool-disc, which rotates at high speed during friction on the treated surface. Intense deformation was achieved due to the grooves on the tool’s working surface. Dynamic analysis of the thermo-deformation treatment process of flat surfaces of machine parts and a calculation scheme of the surface grinder machine’s elastic system, which is the three-mass model, were developed. When the groove width increased from 4 mm to 8 mm, the force amplitude in the contact zone increased from 10 N to 75 N. Accordingly, the thickness of the nanocrystalline layer increased from 190–220 μm to 250–260 μm, and its hardness increased from 9.3 GPa to 11.1 GPa.

SIMULATION OF VIBRATORY PLATE INTERACTION WITH THE GROUND SURFACE

The paper presents a three-mass rheological model of the system "soil – vibration plate base – vibration plate frame". The rheological model makes it possible to reproduce different modes of interaction between the vibratory plate base and soil: with different types of plate decoupling and without decoupling. We verify this model by comparing the experimental values of the vertical oscillation span of the base and frame of the Zitrek CNP 20 vibrating plate with the previously calculated values. As a whole, the calculated values of the span of vertical oscillations of the base and frame of the Zitrek CNP 20 vibrating plate correlate with the experimental data in the range of the dynamic modulus of soil deformation of 13…30 MPa. During the experiment we used the rheological model and obtained results are as follows: the mass of the vibrating plate (50; 150; 250; 350; 450; 550; 650; 750 kg), the coefficient of the elastic resistance of soil (30; 60; 90; 120 MN / m), and the coefficient of viscous resistance of soil (100; 200; 300 kN • s / m). The total number of combinations of parameters was 96. The processed results of the computational experiment provide the regression dependences for calculating the maximum soil reaction force, the time of soil loading (increasing the values of the reaction force of soil) t1, and the time of soil unloading (decrease the values of the reaction force of soil) t2. The simulation results show that, within one exposure cycle, the soil loading time t1 is less than the soil unloading time t2. The ratio t1/t2 is influenced by the weight of the vibratory plate, as well as the factors of elastic and viscous resistance of soil. This feature (t1/ t2  1) is typical for both vibratory rollers and rammers, which is confirmed by the results of the relevant experimental studies. The obtained regression dependences of parameters Fs, t1, and t2 on the vibratory plate mass and the factors of elastic and viscous resistance of soil are important for calculating the distribution of stresses and strains on the depth of the compacted soil.

Interaction of vibroimpact lattice and screen sieve in anti-phase oscillation mode

Introduction. One of basic technological operations in construction technology is a process of classification of fine grained mineral materials, for example, natural sand. The related actual problem is connected with increasing performance and effectiveness of screening of sand medium, in particular reducing the contamination of screening surface of vibrating screens from seal particles and sticking in sieve holes wedge-shaped grains. The solution of this problem concludes in performing by the use of vibroimpact screens of various operating principle. One of innovative vibroimpact screen constructions is a screen with vibroimpact lattice, mounted under sieve with a gap on spring elements, which provides an impulse impact on all sieve surface area. Such construction provides increasing the effectiveness of sieve cleaning due to the transfer to sieve impact impulse in each screen oscillation period and reducing its excessive damage and abrasion by increasing the area of vibroimpact lattice and sieve interaction. The purpose of the work is to determinate functional relationships of dynamical interaction between elements of three-mass vibroimpact ‘screen body – vibroimpact lattice – sieve’ system for providing the necessary value of impact impulse transferred to sieve in relation to screen body oscillation frequency and amount of gap between lattice and sieve.Materials and methods. The research is based on a method of mathematical modelling. On the first stage the research is being conducted with using two-mass ‘screen body – vibroimpact lattice’ model without consideration the impact between lattice and sieve for determination the oscillation frequency range of in-phase oscillation regime and gap values providing an impact between lattice and sieve. For the calculation of displacement of screen elements and for research the relationships of its parameters in selected range the three-mass model of vibroimpact model of screen with one impact pair is used on a second stage of research.Results. As a result of calculation obtained the functional relationships of correlation of the gap between vibroimpact lattice and screen sieve and oscillation frequency on the impact impulse transferred to sieve and sieve double amplitude were obtained. The developed recommendations for practical using of obtained relationships for adjustment operating regimes of vibroimpact screen which allow to establish the screen operating oscillation frequency and value of gap between lattice and sieve for providing high effectiveness of sieve holes cleaning from contaminating particles.Discussion and Conclusions. Performed mathematical modelling allowed to obtain dependencies of influence of gap between sieve and vibroimpact lattice and screen elements oscillation frequency on impulse transferred on screen sieve and sieve double amplitude. Developed practical recommendations of obtained dependencies allow to perform an effective adjustment of vibroimpact screen operating regimes and reduce the labor intensity of works being performed during its starting-up and maintenance.

Modeling the influence of COVID-19 protective measures on the mechanics of phonation.

In an effort to mitigate the 2019 novel coronavirus disease pandemic, mask wearing and social distancing have become standard practices. While effective in fighting the spread of the virus, these protective measures have been shown to deteriorate speech perception and sound intensity, which necessitates speaking louder to compensate. The goal of this paper is to investigate via numerical simulations how compensating for mask wearing and social distancing affects measures associated with vocal health. A three-mass body-cover model of the vocal folds (VFs) coupled with the sub- and supraglottal acoustic tracts is modified to incorporate mask and distance dependent acoustic pressure models. The results indicate that sustaining target levels of intelligibility and/or sound intensity while using these protective measures may necessitate increased subglottal pressure, leading to higher VF collision and, thus, potentially inducing a state of vocal hyperfunction, a progenitor to voice pathologies.

Three-Mass Structural-Isolating-Damping Model Subjected to Near- and Far-Fault Earthquakes

ABSTRACTSeismic base isolators and dampers are commonly used as control tools in building frames to mitigate earthquake damage. This study proposes and investigates a structural system consisting of a central fixed core and an isolated section, the two parts of which are connected to each other by a damper. In new structures, called partially isolated (PI) structures, the interaction between conventional frames with fixed bases and frames equipped with control tools including isolators and dampers is measured using a three-mass model by three simplified differential equations of motion. Validating the proposed model provided good results. The model with various modes of partial isolation and certain mass ratios was subjected to seven near-fault and seven far-fault earthquakes to be evaluated. The mean displacement, acceleration, and shear responses of the structural-isolating-damping model were compared with those of fully isolated (FI) and fully fixed (FF) structures. The results showed that by connecting the two parts, responses of the fixed part to FF structure and those of the isolated part to FI structure significantly improved. Under near-fault earthquakes, the displacement response reduction of the fixed part to FF model was estimated to be about 20% and the response of the isolated part to FI model was about 50%. Due to the functional weaknesses observed in FI structures including large displacement of the structure base, poor performance of the isolator in near-fault earthquakes, and high costs of preparing and installing the isolation system, these points were significantly resolved in PI structures.

DYNAMICS OF A CIRCULAR KNITTING MACHINE WITH A DEVICE OF REDUCTION OF DYNAMIC LOADS WITH TWIN SPRINGS

The issue of improving the efficiency of circular knitting machines remains relevant, so the task of research is to develop a new design of circular knitting machine with a device to reduce dynamic loads with torsion springs, engineering method of choosing rational parameters of the device, and evaluate its efficiency. The aim of the work is to analyze the feasibility of using a device with torsion springs to reduce the dynamic loads in the drive of circular knitting machines, to develop a method for selecting rational parameters of the device and evaluate the effectiveness of its use. The article uses modern methods of the theory of dynamics of mechanical systems in order to assess the feasibility of using a device with a torsion spring to reduce the starting dynamic loads in the drive of machines. Based on the analysis of the dynamics of mechanical systems with elastic ties, an algorithm for calculating the dynamic loads that occur during the start of circular knitting machines, the calculated dynamic model of which is reduced to a three-mass dynamic model with an average leading mass. A new design of the device is proposed to reduce the dynamic loads that occur during the start of circular knitting machines. In contrast to the known devices, the proposed device is made in the form of two cylindrical torsion springs and bypass couplings, which increases its efficiency. The new design of the drive of the circular knitting machine with the device of reduction of dynamic loadings with torsion springs, a method of a choice of rational parameters of the device and results of an estimation of efficiency of its use are presented. A scientific novelty is the development of scientific bases and engineering methods for designing devices for reducing dynamic loads in the drive of knitting machines. The practical significance lies in the development of a new design of the device for reducing dynamic loads in the drive of circular knitting machines and an engineering method for selecting its rational parameters.

Vehicle-Bridge Interaction System with Non-Uniform Beams

Since the bridge is often treated as the uniform beam for simplicity in most numerical studies of vehicle-bridge interaction, this study proposes a non-uniform vehicle-bridge interaction system by incorporating a three-mass vehicle model in a non-uniform bridge for wider applications, in which non-uniform beam elements of constant width and varying depth are considered. For clarity, the inclined ratios of the entire bridge and one beam element are separately defined in order to describe the non-conformity in computation while both mass and stiffness matrices are re-formulated to comply with the finite element sign convention. As the natural frequencies of a non-uniform bridge cannot be accessed directly, the vehicle scanning method is first adopted to obtain the bridge frequencies. Then, the parametric study is conducted by considering vehicle damping, bridge damping, and pavement irregularity. In addition to the vehicle frequency, the numerical results show that the proposed vehicle-bridge interaction system is able to scan the first four bridge frequencies with desired accuracy subject to pavement irregularity. Concerning the pitching effect of the vehicle, it is shown that the locations for installing sensors are actually affected by both the geometry and the cross-sectional geometry of the bridge in the concern of achieving high resolution of frequency identification.

Theoretical Formulation of Three-Mass Vehicle Model for Vehicle–Bridge Interaction

The vehicle–bridge interaction (VBI) is studied using a semi-analytical approach based on a three-mass vehicle model. As most work analyzes vehicle–bridge interaction numerically and/or analytically by treating the vehicle as a simplified lumped mass, to the best of the author’s knowledge, this work first presents the theoretical formulation of the three-mass VBI system, where a more realistic vehicle model equipped with a rigid mass and two unsprung mass-spring-damper systems is considered. By assuming the first modal vibration of beam, the semi-analytical solutions are derived, which can be served as the reference solutions for calibrating VBI analyses using different models or methods.

A three-mass viscoelastic plastic model used for studying mechanics and dynamics of shock interaction of solid bodies in determining the mechanical characteristics of building materials

Shock and vibration processes play an important role in engineering. Therefore, the study of mechanics and dynamics of the impact interaction of bodies by modeling these processes is an urgent task. To study dynamic processes, a mechanorheological three-mass viscoelastic plastic model was developed. Differential equations for various stages of motion were obtained. The conditions of transformation during the transition from elastic to plastic deformations, from the loading stage to the unloading one under the impact interaction with the surface were described. The functioning method was studied; the results of experimental studies were presented.

Energy-Efficient Bipedal Walking: From Single-Mass Model to Three-Mass Model

SUMMARYThe work aims to realize energy-efficient bipedal walking by employing the three-mass inverted pendulum model (3MIPM) and compare its energy performance with linear inverted pendulum model (LIPM). To do this, a general optimal index on center of mass (CoM) acceleration is first derived for energetic cost evaluation. After defining the equivalent zero moment point (ZMP) motion, an unconstrained optimization approach for CoM generation is extended for 3MIPM, which can track different ZMP references and address the height variation as well. To make use of the allowable ZMP movement, a constrained optimization method is also employed, contributing to lower energetic cost. Simulation and hardware experiments on a humanoid robot demonstrate that the 3MIPM could achieve higher energy efficiency.

Effect of Supraglottal Acoustics on Fluid-Structure Interaction During Human Voice Production.

A hydrodynamic/acoustic splitting method was used to examine the effect of supraglottal acoustics on fluid-structure interactions during human voice production in a two-dimensional computational model. The accuracy of the method in simulating compressible flows in typical human airway conditions was verified by comparing it to full compressible flow simulations. The method was coupled with a three-mass model of vocal fold lateral motion to simulate fluid-structure interactions during human voice production. By separating the acoustic perturbation components of the airflow, the method allows isolation of the role of supraglottal acoustics in fluid-structure interactions. The results showed that an acoustic resonance between a higher harmonic of the sound source and the first formant of the supraglottal tract occurred during normal human phonation when the fundamental frequency was much lower than the formants. The resonance resulted in acoustic pressure perturbation at the glottis which was of the same order as the incompressible flow pressure and found to affect vocal fold vibrations and glottal flow rate waveform. Specifically, the acoustic perturbation delayed the opening of the glottis, reduced the vertical phase difference of vocal fold vibrations, decreased flow rate and maximum flow deceleration rate (MFDR) at the glottal exit; yet, they had little effect on glottal opening. The results imply that the sound generation in the glottis and acoustic resonance in the supraglottal tract are coupled processes during human voice production and computer modeling of vocal fold vibrations needs to include supraglottal acoustics for accurate predictions.

Construction of physical model of jib crane rotation mechanism, program and description of experimental studies

This article outlines the main provisions of the program, methodology, description of the object of experimental studies and construction of a physical model of the jib crane rotation mechanism. A real QTZ 80 crane has been chosen for the study, which differs from the laboratory installation (physical model) of the jib crane rotation mechanism by structural, power and energy parameters, for this reason, experimental studies used physical modeling, which usually changes the scale and leaves the physical nature of phenomena. Therefore, similarity theory is used to determine the characteristics of the physical model. A physical model (laboratory unit) of the jib crane rotation mechanism was designed to conduct experimental studies on the similarity theory. This model is prepared for experimental studies of the dynamics of the rotation mechanism during the start-up process. To determine the similarity criteria, equations of motion were used that reflect the operation of the jib crane rotation mechanism, namely the three-mass dynamic model of the rotation mechanism, which is a system of three second-order differential equations. Using the obtained ratios of similarity criteria, the numerical values of the similarity coefficients of the real rotation mechanism of the jib crane and its physical model are determined. Based on the parameters obtained, a physical model of a full-scale jib crane rotation mechanism was constructed. The results obtained in this study can be further used to refine and improve existing engineering methods for calculating the mechanisms of rotation of cranes, both at the stages of their design/construction, and in real operation.