Multi-mass Model Research Articles

Robust Speed Control of a Multi-Mass System: Analytical Tuning and Sensitivity Analysis

The regeneration of highly dynamic driving maneuvers on vehicle test benches is challenging due to several influences, such as power losses, vibrations in the overall system that involves the vehicle with the test bench, uncertainties in the model parameterization, and time delays from both the test bench and the measurement systems. In order to improve the dynamic response of the vehicle test bench and to overcome system disturbances, we employed different types of control algorithms for a mechanical multi-mass model. First, those controllers are extensively investigated in the frequency domain to analyze their stability and evaluate the noise rejection quality. Then, the expectations from the frequency analysis are confirmed in a time-domain simulation. Furthermore, sensitivity analysis tests were conducted to evaluate each controller’s robustness against the modeling parameters’ uncertainty. The linear quadratic controller with integral action demonstrated the best compromise between performance and robustness.

Step-by-step simulation of wear of working surfaces in roller bearings

The purpose of this work was to develop effective methods for calculating the wear rate of raceways and roller bearings under dynamic loads. The wear of the working surfaces of rolling bearings in many practical cases is an important critical factor affecting their performance and durability. However, only a limited number of publications are devoted to this issue. In most of them, Archard's law, which has been experimentally confirmed during hydrodynamic friction of bearing steels, is used to calculate the wear rate of the contacting surfaces. Based on this law, the article presents a method of direct step-by-step calculation of the wear rate at variable contact loads and sliding speeds. In accordance with it, the change in the normal force, sliding speed and thickness of the oil film in contact is determined in the dynamic calculation of the bearing, and the finite element method is used to calculate the contact pressure field. The multi-mass model of bearing dynamics includes a contact friction model that allows adequately reproducing the conditions of hydrodynamic contact of solids. The direct calculation method involves a large number of calculations that make the impact of individual factors on the wear rate opaque. Therefore, along with it, a method for calculating the wear rate by averaged parameters is proposed. Using these two methods, the wear calculations of the raceway of the inner ring and the rollers of a double-row tapered roller bearing were performed. The comparison of the results confirms the acceptable accuracy of the calculation according to the averaged parameters.

Multimass modelling of Milky Way globular clusters – I. Implications on their stellar initial mass function above 1 M⊙

ABSTRACT The distribution of stars and stellar remnants (white dwarfs, neutron stars, and black holes) within globular clusters holds clues about their formation and long-term evolution, with important implications for their initial mass function (IMF) and the formation of black hole mergers. In this work, we present best-fitting multimass models for 37 Milky Way globular clusters, which were inferred from various data sets, including proper motions from Gaia EDR3 and HST, line-of-sight velocities from ground-based spectroscopy and deep stellar mass functions from HST. We use metallicity-dependent stellar evolution recipes to obtain present-day mass functions of stars and remnants from the IMF. By dynamically probing the present-day mass function of all objects in a cluster, including the mass distribution of remnants, these models allow us to explore in detail the stellar (initial) mass functions of a large sample of Milky Way GCs. We show that, while the low-mass mass function slopes are strongly dependent on the dynamical age of the clusters, the high-mass slope (α3; m > 1 M⊙) is not, indicating that the mass function in this regime has generally been less affected by dynamical mass loss. Examination of this high-mass mass function slope suggests an IMF in this mass regime consistent with a Salpeter IMF is required to reproduce the observations. This high-mass IMF is incompatible with a top-heavy IMF, as has been proposed recently. Finally, based on multimass model fits to our sample of Milky Way GCs, no significant correlation is found between the high-mass IMF slope and cluster metallicity.

Tracing the Evolution of SMBHs and Stellar Objects in Galaxy Mergers: A Multi-mass Direct N-body Model

By using direct N-body numerical simulations, we model the dynamical coevolution of two supermassive black holes (SMBHs) and the surrounding stars in merging galaxies. In order to investigate how different stellar components evolve during the merger, we generate evolved stellar distributions with an initial mass function. Special schemes have also been developed to deal with some rare but interesting events, such as the tidal disruption of main-sequence stars, plunging low-mass stars, white dwarfs, neutron stars and stellar-mass black holes, and the partial tidal disruption of red giants or asymptotic giant branch stars. Our results indicate that the formation of a bound SMBH binary will enhance the capture rates of stellar objects by SMBHs. Compared to the equal stellar mass model, the multi-mass model tends to result in a higher average mass of disrupted stars. Instead of being tidally disrupted by the SMBH, roughly half of the captured main-sequence stars will directly plunge into the SMBH because of their small stellar radii. Giant stars, on the other hand, can be stripped of their envelopes if they are close enough to the SMBH. Though most remnants of the giant stars can survive after the disruption, a small fraction still could plunge into the SMBH quickly or after many orbital periods. Our results also indicate significant mass segregation of compact stars at the beginning of the merger, and then this effect is destroyed as the two SMBHs form a bound binary.

Automatic Driving Research of Cloud Model High-Speed Train based on Genetic Algorithm Optimization

High-speed train is a complex nonlinear system with strong coupling, which is easily disturbed by uncertain factors. The traditional model of single-mass point train does not consider the influence of train length and interaction force between trains. Given that high-speed train is vulnerable to time-varying disturbance in the complex and changeable external environment, and the traditional single-mass point train model does not consider the train length and interaction force between vehicles, a genetic algorithm (GA) optimised cloud model proportion integration differentiation (PID) speed controller based on a rigid multi-mass point model was designed. The numerical features of the cloud model are first optimized by the global optimization capability of the GA, then the cloud model reasoner corrects the parameters of the PID controller in real time through the corresponding reasoning rules. Moreover, the PID controller with adjustable parameters completes the control output of the speed controller. The rigid multi-mass point model of the train is established, and CRH3 train is selected to simulate the selected line to prove the feasibility of the cloud model PID control algorithm based on GA optimisation. Under the same conditions, PID and fuzzy PID controllers are set for speed-tracking performance comparison, which verifies that the cloud model PID controller based on GA optimisation has small speed-tracking error and strong robustness. It can more effectively reduce the influence of interference caused by uncertain factors on the automatic driving operation speed controller of high-speed train and has better control effect.

The dynamic loads of mobile continuous earthmoving machine during the working body lock

working body is locked significant dynamic loads appear that influence the drive shaft and might lead to the machine breakdown. Preliminary approximate calculation of these loads is made according to oneor two-mass dynamic loads. For more detailed and precise analysis of dynamic load in drive shaft elements of the earth moving machines it is necessary to review the multimass model machine element movement. Goal. The aim of research is definition of the dynamic load and working out methodology that appears in the continuous earth digging machine elements during working body lock. Methodology. The discreet dynamic system dynamic and mathematical model construction is performed by means of the programming language Modelica. The model relevance is assessed via a two-mass model analytical solution. Results. Drive shaft element loading is assessed via the dynamic coefficient, which depends on kinematic, flexible and inertial machine parameters. Originality For the first time the continuous earth digging machine dynamic model that enables the automobile chassis drive shaft to interact with the continuous digging chain is constructed. It was determined that the drive shaft dynamic loading parameter correlation change upon the earth digging machine working body meaningful parameters. With designed model usage, the input data for transmission element engineering calculation was defined and the automobile basic chassis construction, equipped with the continuous digging chain. Practical value. The obtained dynamic factor value and developed methodology can be applied during continuous earth moving machine designing and calculation. Dynamic load decrease is possible through shaft stiffness and rotating mass inertia adjustment, and also by introducing elastic protecting frictional coupling with a controlling device.

Condition Monitoring of Ball-Screw Drives Based on Frequency Shift

Ball-screw drives are one of the common wear parts in machine tools. The wear will affect the positioning accuracy of motion axes and can cause a high rejection rate in production. Therefore, it is interesting to develop a method, which can detect the wear condition of ball screws at an early stage. Stiffness loss and backlash in ball-screw drives are often associated with wear. This article proposes a novel method to detect stiffness loss and backlash for ball-screw drives without preload based only on machine internal data. To simulate the wear of a ball screw, a spacer sleeve has been designed, which effectively reduces the axial stiffness of the feed axes. This design allows a quick modification of the wear status of the machine axes and can be utilized to test if the wear status is detectable by analyzing the machine internal data. A multimass model is developed and validated by experimental data, which is used to simulate the dynamic behavior of the machine axis dependent on wear.

Light Duty Truck Rear Axle Thermal Modeling

<div class="section abstract"><div class="htmlview paragraph">More stringent Federal emission regulations and fuel economy requirements have driven the automotive industry towards more sophisticated vehicle thermal management systems to best utilize the waste heat and improve driveline efficiency. The final drive unit in light and heavy duty trucks usually consists of geared transmission and differential housed in a lubricated axle. The automotive rear axle is one of the major sources of power loss in the driveline due to gear friction, churning and bearing loss affecting vehicle fuel economy. These losses vary significantly with lubricant viscosity. Also the temperatures of the lubricant are critical to the overall axle performance in terms of power losses, fatigue life and wear. In this paper, a methodology for modeling thermal behavior of automotive rear axle with heat exchanger is presented. The proposed model can be used to predict the axle lubricant temperature rise. It also can be used to study the effect of coolant temperature on the axle warm-up and efficiency for a typical EPA fuel economy driving cycle.</div><div class="htmlview paragraph">Thermal axle consists of automotive rear axle with a heat exchanger added to the axle housing to control the axle lubricant temperature using energy from coolant. The proposed multi-mass model allows an assessment of the effect of operating parameters (heat exchanger effectiveness, coolant flow rate, coolant temperature, lubricant viscosity) on the axle performance and driveline efficiency. The model represents a useful tool to optimize coolant energy distribution between axle and other vehicle thermal system devices. The model can be used to develop more sophisticated thermal system control strategies with variable coolant flow control devices. The model will also be helpful to select axle lubricant for optimum axle performance. The model is validated by comparing its results with experimental data obtained from EPA fuel economy driving cycle vehicle tests.</div></div>

Mitigation of Subsynchronous Interactions in Hybrid AC/DC Grid With Renewable Energy Using Faster-Than-Real-Time Dynamic Simulation

Transmission line capacity enhancement by series compensation is commonly used in power systems, which consequently faces potential subsynchronous interaction (SSI). In this work, faster-than-real-time (FTRT) simulation based on the field-programmable gate arrays is proposed to mitigate the disastrous SSI in a hybrid AC/DC grid integrated with wind farms. Dynamic simulation is applied to the AC system to gain a high speedup over real-time, and a detailed multi-mass model is specifically introduced to the synchronous generator to show the electrical-mechanical interaction. Meanwhile, the DC grid undergoes electromagnetic transient simulation to reflect the impact of power converters' control on the overall grid, and consequently, the EMT-dynamic co-simulation running concurrently due to FPGA's hardware parallelism is formed. As the two simulations are inherently distinct, a power-voltage interface is adopted to separate them which enables their coexistence in one program. It shows that following the detection of a contingency, the FTRT hardware platform can generate an optimum solution with precisely quantified power flow changes in advance to keep the hybrid AC/DC grid stable. The FTRT efficacy is proven by a number of cases where the accuracy is validated by offline simulation tool Matlab/Simulink.

A Modeling Method for the Driving Process of Heavy-Haul Train Based on Multi-Mass Model

Unlike the locomotive, heavy-haul trains have large carrying capacity and consist of hundreds of carriages; the longitudinal impulse in the train has significant coupled nonlinear characteristics during its operation. With the continuous increase in traction weight, problems with the existing control models gradually appear, vehicle decoupling and derailment occur, and the trains often fail to operate on schedule. Using the coupler characteristic curve, this paper comprehensively considers uncertain factors such as the train loading weight, line ramps, vehicle dynamic performance differences, and changeable operating environment to accurately model the heavy-haul train coupling force and train longitudinal dynamic multiple points. We optimize the target curve of the ideal running speed of the train and design the corresponding running tracking control strategy. The simulation results show that the ideal target speed curve optimization method designed in this paper can effectively improve key indicators such as safety, punctuality and energy saving in train operation to make trains more safely and efficiently run.

Understanding the multi-mass model and sound generation of vocal fold oscillation

When a speaker speaks, the vocal fold oscillates, generating a voice. The voice resonating in the vocal tract and in the mouth is converted to speech when the speaker changes the shapes of the mouth and tongue. When the vocal fold oscillates, a voice is generated because the vocal fold oscillation vibrates the air in succession, and the vocal fold oscillation triggers the generation of the fundamental frequency of the vocal fold as well as that of the harmonic sound at the same time. It is not easy to understand these sound generation principles acoustically, however, unless one is equipped with deep knowledge in the fields of physics and acoustics. In this paper, therefore, the vocal fold will be simplified as a multi-mass model, and a way to easily understand the principle that the fundamental frequency and harmonic sound are generated simultaneously by vocal fold oscillation will be presented.

Validation of analytical methods for the estimation of the torsional vibrations of ship power transmission systems

The propulsion system is one of the main sources of ship vibrations. A typical propulsion system consists of an engine, a shaft line and a propeller. In order to estimate the vibration levels of a ship propulsion system, analytical methods are still relevant in the preliminary ship design stage. In this paper, three analytical procedures for the vibration analysis of a ship shafting system are presented. The shafting system dynamic behaviour is simulated by reducing the problem to two-, three-, and multi-mass models. Propeller and engine damping is taken into account. Differential equations of motion for the two- and the three-mass models are solved analytically. In the case of the multi-mass model, Rayleigh's quotient and the Galerkin method are used for free and forced vibration analysis, respectively. Since the first natural mode of the shaft line is dominant, the problem can be reduced to a single d.o.f. in the modal space and solved analytically. For all three models, relatively simple formulae for the engine torque transfer factor to the intermediate shaft are derived. The presented procedures are validated by a comparison with measurements. The comparison indicates the high accuracy of the proposed procedures.

SUBSYNCHRONOUS RESONANCE MITIGATION USING WIDE AREA MEASUREMENT SYSTEM

This paper presents the wide area measurement based controller for subsynchronous resonance mitigation in two machine system. The dq0 model of the two machine system.is considered in this paper. Generator 1 is multimass model as per given in IEEE first bench mark model and genereator 2 is considered as lumped model. The computation of frequency from voltage phasor of each generator is used for SSR mitigation. The difference of frequency of two machine is used as control signal . This control signal modulate the firing angle of thyristor controlled reactor through controller .As the control signal is global signal ,it will give damping to almost all torsional modes of oscillation and eliminates local controller for each torsional modes. This paper shows application of wide area controller in dq0 model mitigates subsynchronus oscillation in system.

The hunt for self-similar core collapse

Context. Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, ρ ∝ r−α. Aims. We aim to find the characteristics of core collapse in N-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify. Methods. We developed a method that identifies the core collapse in N-body models of star clusters based on the assumption of their homologous evolution. Results. We analysed different models (equal- and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of α : the equal-mass models have α ≈ 2.3, which agrees with theoretical expectations, the multi-mass models have α ≈ 1.5 (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example from 100 kT to 104 kT in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of ∼104 kT to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.

UNSTEADY OPERATING MODES OF THE MAIN DRIVE UNIT OF A MACHINE-TOOLS FOR SOLID RAILWAY WHEELS PROCESSING

Purpose. The paper deals with determining the conditions of the dynamic overload formation for a drive unit in the wheel-processing machine in various unsteady operating modes and suggests ways to reduce it. Methodology. The problem was solved by creating a dynamic computational multi-mass chain model followed by modeling of its loading by external force options, the values of which were obtained by analytical and experimental methods. The solution to equations of motion with determining the load of the drive unit in the transient acceleration mode and in the tie-in one was carried out by means of MathCad. Findings. The design scheme for the drive unit of the rotational movement of the machine faceplate is represented by a linear three-mass row system with two elastic connections and with three absolute degrees of freedom. The analytical determination of the cutting force moments takes into account changes in the kinematic parameters of the cutting regime when machining the different sections of the profile with cup-tip tool. The worst case of load application is accepted with simultaneous insertion of tools. The equivalent torque of the cutting forces is defined as the sum of the moments from each of the tools at multi-cut machining. The moments of elasticity of bonds in the steady state of the machine drive unit are determined. Dynamic loads with coefficients of dynamism in the bonds Kd12 = 1.13 and Kd23 = 1.04 are insignificant in the tie-in mode and rapidly decrease their value. Absolute values of the twisting elastic moment in the C23 bond in the start-up mode are insignificant and much less than the values of the steady load. Using the method of calculation and experimental research, a significant dynamic overload of the machine drive unit in the mode of rheostat start-up by a directcurrent motor was established. The reactive elastic moment with the periodic change is 2.7 times higher than the nominal moment of steady processing regime. Originality. Authors created the elastic dynamic model of the machine drive unit for the processing of railway wheels. In accordance with the model, the equations of mass motion and bond loading are compiled and solved. The theoretical conditions for reducing the drive unit loading are determined. Practical value. Based on the simulation of the transient drive start-up process, significant overloads of its elements have been determined. They are several times higher than the response of elastic bonds during cutting. To prevent this, it is recommended to change the mode of multistage starting of the engine with a decrease of the starting current by at least two times up to a value of not more than 1 200 A.

Reduction of SSR oscillations in power system network with STATCOM and UPFC

SSR is a complex issue in electric power transmission network because of which the mechanical arrangement of a multi mass model encounters shaft harms. To keep away from this issue the mechanical oscillations which for the most part happen amid a balanced short circuit fault on the transmission network ought to be moderated by a few means. This paper delineates about the IEEE second benchmark framework which is demonstrated and simulated in MATLAB Simulink. The outcomes are compared when Static Synchronous Compensator (STATCOM) is incorporated and furthermore with those when Unified Power Flow Controller (UPFC) included for their viability in moderating the Subsynchronous Resonance motions.

The Influence of Multi-terminal MMC-HVDC on the Subsynchronous Oscillation Characteristics of the Unit

The five-terminal MMC-HVDC in Zhoushan can bring the risk of SSO to the units in the neighbouring Zhoushan power plant. This paper illustrates the five-terminal MMC-HVDC on the topology structure and the working principle of the three-layer control system (the system level, the convert level and the valve level, etc.); the shaft multi-mass model of steam turbine generator in the Zhoushan power plant is established, too. Finally, the simulation model based on the actual power grid in Zhoushan area is established in the RTDS, and the influence of different control methods and operation modes on SSO characteristics of Zhoushan power plant unit is analyzed. This paper reveals the influence of different control methods on SSO characteristics of the units, and the influence of different operation modes on the initial values of the SSO modal

多質点系モデルを用いた自動車タイヤの安定性解析

多質点系モデルを用いた自動車タイヤの安定性解析

未知の斜面における4脚歩行ロボットのZMPに基づくトロット歩容

We focus on a quadruped robot as a mobile platform which would work at various environment such as disaster sites, offices and factories. In this paper, we assume that terrain consists of slopes and we propose a walking gait for a quadruped robot on unknown slopes. In this method, the robot basically walks in trot gait because trot gait has both high stability and practical walking speed in order to walk stably on steep slopes. At first, robot estimates slant of the slope by using body attitude and foot positions on the slope. Then it generates walking pattern for the robot to walk stably on the slope by using inverted pendulum model and multi-mass model of the robot. The proposed method was verified through experiments with a quadruped robot TITAN-VIII walked on slopes where a step or other slope exist halfway.

Effect of Different Turbine-generator Shaft Models on the Sub-synchronous Resonance Phenomenon in the Double Cage Induction Generator Based Wind Farm

This paper focuses on the turbine-generator shaft models of double-cage Induction Generator (IG) based wind farm and its influence on the sub-synchronous resonance phenomenon. For this purpose, six different shaft models as 6-mass, 4-mass, 3-mass I, 3-mass II, 2-mass and 1-mass models are considered for double-cage IG wind-turbine. By using the linear modal analysis method, the effects of the different multi mass model of double-cage IG wind-turbine on the SSR phenomenon are studied. The results obtained by eigenvalue analysis show that the model of double-cage IG wind-turbine has an important effect on the detecting of Subsynchronous Resonance (SSR) phenomenon. The analytical results are validated by detailed electromagnetic transient simulation using PSCAD/EMTDC software.