Vibration Analysis of a Vertical Roller Mill: Modeling and Validation

2014 ◽  
Author(s):  
Engin H. Çopur ◽  
Metin U. Salamci ◽  
Selahattin Gülbeyaz
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Physical Parameters ◽  
Roller Mill ◽  
Vibration Tests ◽  
Working Parameters ◽  
The Mathematical Model ◽  
Vertical Roller

In this paper, vibration characteristics of a Vertical Roller Mill (VRM) are studied by using physical parameters of an operating VRM. The mathematical model is derived and simulated for a set of working parameters. Mechanical properties of the grinding material and the physical properties of the mechanical construction are used in the vibration model in order to obtain more realistic results. Simulation results are presented which give critical frequencies of the VRM. The effects of the hydraulic compressive force to the vibration characteristics are investigated. The effects of the material feeding rate (which affects the mineral thickness to be grinded) to the vibration characteristics are also simulated. In order to validate the mathematical model, a set of experimental vibration tests are performed on the VRM. Vibrations are measured during the run-down procedure of the VRM in order to determine natural frequencies of the mill as well as excitation frequencies of the system. The measurements showed the validity of the proposed mathematical model for the vibration analysis of the VRM.

Simplified Adaptive Nonlinear Robust Controller for Linearized Pantagraph-Type Manipulator

1995 ◽  
Vol 7 (3) ◽  
pp. 242-249 ◽  
Author(s):  
Kiyotaka Izumi ◽  
◽  
Keigo Watanabe ◽  
Masatoshi Nakamura ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Physical Parameters ◽  
Additional Mass ◽  
Robust Controller ◽  
End Effector ◽  
Linear Controller ◽  
The Mathematical Model ◽  
Nonlinear Robust

If physical parameters are adjusted suitably in the pantagraph-type manipulator, the mathematical model becomes linear so that we can apply a linear controller. However, when the manipulator has an additional mass as an end-effector, the linear controller does not work well because the resultant model becomes nonlinear. In this paper, we propose a simplified adaptive nonlinear robust controller which we can apply to the manipulator, irrespective of the system linearity or nonlinearity. The effectiveness of the controller is illustrated by some simulations.

Analysis of Vibrating Natural Frequency of Pressure Pipeline

2011 ◽  
Vol 421 ◽  
pp. 98-101
Author(s):  
Ting Yue Hao
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Flow ◽  
Physical Parameters ◽  
Beam Model ◽  
Instability Condition ◽  
Coupling Vibration ◽  
Critical Flow Velocity ◽  
Pressure Pipeline ◽  
The Mathematical Model

The pressure pipeline is simplified as the beam model with two simple supported ends. The mathematical model is established, considering influence of the fluid-solid coupling vibration. Then the critical flow velocity is obtained by calculation and solving. By analyzing the practical numerical example，the influence of physical parameters on the first three-order natural frequency is discussed. Using Matlab software for programming, the instability condition of pressure pipeline is obtained, which is consistent with the result of numerical calculation.

Study on Torsional Vibration Characteristics of Cross Shaft Universal Coupling

2020 ◽  
pp. 1-11
Author(s):  
Nengqi Xiao ◽  
Xiang Xu ◽  
Ruiping Zhou ◽  
Baojia Chen
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Torsional Vibration ◽  
Vibration Characteristics ◽  
Mass Point ◽  
Parameter Method ◽  
System Matrix ◽  
Ship Propulsion ◽  
Universal Coupling ◽  
The Mathematical Model

In this work, the ship propulsion shaft system with cruciform universal coupling is studied. First, based on the analysis of the structure and characteristics of the cross-axis universal coupling, the motion relations and expressions between the components of the universal coupling are established by using the coordinate transformation method. Second, the characteristics of the four submodels of the head mass point element, the end mass point element, the universal coupling mass point element, and other mass point elements are discussed, and the corresponding torsional vibration differential equations of the four submodels are established. On this basis, the mathematical model of the propulsion shafting system and the differential equations of torsional vibration are established by using the modularization method and lumped parameter method. Finally, the torsional vibration modes and response characteristics of the shafts are calculated and analyzed by using the system matrix method when the external load driving torques of the universal coupling, propeller, and diesel engine are considered. At the same time, the correctness of the mathematical model and calculation method is verified by the test and comparative analysis of ship propulsion shafts. It lays a theoretical foundation for further research on torsional vibration characteristics and mechanisms of the ship propulsion shafting system based on universal coupling.

Multi-objective storage location allocation optimization and simulation analysis of automated warehouse based on multi-population genetic algorithm

2018 ◽  
Vol 26 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Yu-ling Jiao ◽  
Xiao-cui Xing ◽  
Peng Zhang ◽  
Liang-cheng Xu ◽  
Xin-Ran Liu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Dynamic Simulation ◽  
Population Genetic ◽  
Physical Parameters ◽  
Location Allocation ◽  
Multi Objective ◽  
Storage Location ◽  
Population Genetic Algorithm ◽  
The Mathematical Model

Aiming at the requirement of working efficiency and security of automated warehouse and taking the operation time of outbound–inbound, the equivalent center of gravity of overall shelf and the degree of relative accumulation of related products as the multi-objective functions, the mathematical model is constructed for multi-objective storage location allocation optimization. According to the simple weighted genetic algorithm, it is easily prone to the problem of immature convergence when solving multi-objective programming problems. So, the multi-population genetic algorithm is proposed to solve the mathematical model of storage location allocation optimization. Combining with the experiment data of toy car assembly and automated warehouse, the results of the automated warehouse storage location allocation are obtained. FlexSim dynamic simulation model is established based on the storage location allocation solution, the physical parameters of automated warehouse and the experimental requirements plan of vehicle model assembly. The operation effect of the model and the utilization rate of the equipment are analyzed. The result of multi-population genetic algorithm is more reasonable and effective. It is proved that the result of multi-population genetic algorithm is superior to the result of simple weighted genetic algorithm, which provides an effective method for storage location allocation optimization and outbound–inbound dynamic simulation.

Vibration Analysis Based on the Mathematical Model of the Air-Suction Device Tillage Seeder Seeding

2014 ◽  
Vol 1061-1062 ◽  
pp. 794-798
Author(s):  
Xu Zhang ◽  
Man Quan Zhao ◽  
Fei Liu ◽  
Shuai Dong ◽  
Yue Qin Liu
Keyword(s):  
Mathematical Model ◽  
Working Condition ◽  
Seed Quality ◽  
Surface Soil ◽  
Soil Surface ◽  
Vibration Characteristics ◽  
Forward Speed ◽  
Suction Device ◽  
The Mathematical Model ◽  
Gas Suction

In order to study air-suction when tillage planter in the field farming, Vibration due to the surface roughness of the resulting excitation tillage effects on seed planter of the device, Derivation of the air-suction device tillage planter seeder vibration characteristics of the mathematical model, Vibration characteristics of the mathematical model derived gas suction device tillage seeder seed planter primarily by structural properties, Forward speed when operating, Seed row distance between the soil surface, Soil roughness and soil sticky decision. Can predict and analyze working condition tillage planter seed quality through the establishment of the vibration characteristics of the mathematical model.

Mathematical model used for predicting arc-flash protective performance of fabrics based on physical parameters

2021 ◽  
pp. 004051752110226
Author(s):  
Wen Zhu ◽  
Hong Tang ◽  
Qilong Sun ◽  
Zhen Huang ◽  
Chengjiao Zhang
Keyword(s):  
Mathematical Model ◽  
Raw Materials ◽  
Principal Component ◽  
Thermomechanical Properties ◽  
Physical Parameters ◽  
Weave Structure ◽  
Arc Flash ◽  
Protective Fabrics ◽  
Protective Performance ◽  
The Mathematical Model

In this study, parameters that may affect the performance of arc-flash protective fabrics were systematically analyzed. Sixteen different commonly used fabrics with different configurations and grammage were produced and investigated, namely four raw materials with different configurations (93:0:5:2, 70:23:5:2, 46:47:5:2, and 23:70:5:2) and four with different grammage (180, 210, 240, and 270 g/m2). It was found that factors had different effects on the arc protective performance. Principal component analysis showed that the four plain weave fabrics of 180 g/m2 behaved differently compared with other samples, which was ascribed to the related differences in weave structure. In addition, a predicting mathematical model was developed based on the parameters that have the greatest influence on arc protective performance. The prediction parameters were not added to the structure, but replaced with physical parameters such as air permeability and thermomechanical properties. The adjusted R2 was 0.867, which demonstrated the rationality of using multiple linear regression to accurately predict arc protective performance. It was hypothesized that the construction of the mathematical model could contribute to the arc protective fabric evaluation and future researches in this field.

scholarly journals VIBRATION ANALYSIS OF THE TOOL BEARING SPINDLE IN CASE OF SUPERFINISHING TECHNOLOGIAL PROCESSES ESTABLISHMENT OF THE GENERAL MOVEMENT EQUATIONS

2020 ◽  
Vol 8 (5) ◽  
pp. 339-347
Author(s):  
Daniel Popescu
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Matrix Form ◽  
Simplifying Assumptions ◽  
General Movement ◽  
The Mathematical Model

The paper presents a mathematical model for determining the general movement equations that describe the vibration movement of the tool bearer spindle at superfinishing operations. There are presented the specific problems and the work schematics. The mathematical model uses the axioms of kinetic impulse and moment derivatives. At superfinishing, the spindle is eccentric and its working position is vertical. A series of simplifying assumptions are used, such as: Bernoulli’s hypothesis, the movement is without shocks, there are no remnant tensions, the strains are of elastic nature only. There are emphasized the components of the movement equations under restricted matrix form. The effect of transversal contraction and the torsion vibrations are neglected.

scholarly journals NUMERICAL METHOD OF VIBRATIONS RESEARCH IN LARGE FLEXIBLE SYSTEMS

2014 ◽  
pp. 52-59
Author(s):  
Olena Mul ◽  
Delfim Torres
Keyword(s):  
Mathematical Model ◽  
Communication Network ◽  
Numerical Method ◽  
Frequency Spectrum ◽  
Elastic System ◽  
Physical Parameters ◽  
Flexible Systems ◽  
The Real ◽  
Fundamental Systems ◽  
The Mathematical Model

The mathematical model of the real flexible elastic system is considered with the distributed and discrete parameters, which presents the equation at derivative parts with non-classical maximum terms. Complication of maximum terms makes impossible finding of exact analytical decision of such maximum task, in connection with what for researches the numerical method of the normal fundamental systems of decisions is used. Dependence of frequencies of possible vibrations is explored on different physical parameters of system. It is shown, that introduction to reverse communication network after speed with the defined values of the reverse communication coefficient allows controling the frequency spectrum in which excitation of vibrations are possible.

scholarly journals Measurement of low frequency mechanical vibrations based on an inverted magnetic pendulum

2019 ◽  
Vol 9 (5) ◽  
pp. 3480
Author(s):  
Susana V. Awad ◽  
Joaquin F Orozco ◽  
Fredy E Hoyos
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Low Frequency ◽  
Physical Parameters ◽  
Model Design ◽  
Frequency Meter ◽  
Adjustable Range ◽  
The Mathematical Model ◽  
Considerable Period ◽  
The Magnetic Field

<span>In this paper is presented the mathematical model, design and construction of a prototype of a  vibration frequency meter in an adjustable range of 2 Hz to 30 Hz; The experimental results and their analysis are also presented, making a comparative evaluation with the theoretical model. The device is based on the principle of resonance applied in an inverted magnetic pendulum whose natural frequency can be modified by variations of physical parameters. The oscillation of the pendulum is recorded detecting variations in the magnetic field using hall effect sensors; the data recorded with a microprocessor is analyzed and the results are simultaneously plotted in a computer interface. The data obtained were processed to be plotted in the frequency domain, facilitating its analysis. It was proved that the prototype can be used as a frequency meter and that the adjustable character of the device works according to the mathematical model. Finally, The effect of the friction force was studied, it was concluded that the friction force affects the measurement after a considerable period of time of oscillation, but not in the first moments.</span>

scholarly journals Modeling and Analysis of Energy/Exergy for Absorber Pipes of Linear Parabolic Concentrating Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Reza Alayi ◽  
Mahdi Mohkam ◽  
Hossein Monfared ◽  
Alibek Issakhov ◽  
Nima Khalilpoor
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Solar Collectors ◽  
Matlab Software ◽  
Modeling And Analysis ◽  
Parabolic Collector ◽  
The Mathematical Model

In this paper, the physical parameters of the absorber pipe of a linear parabolic collector have been investigated. The types of solar collectors, specifically the linear parabolic collector, have been comprehensively studied. Then, the mathematical model of heat transfer in the absorber pipe of the collector has been presented based on valid references. Numerical solutions of the equations related to the absorber pipe were performed by MATLAB software, and the effects of the physical parameters of the absorber pipe on its efficiency were investigated. The results show that increasing the length of the absorber pipe causes a nonlinear decrease in the efficiency of the absorber pipe. One of the important results is the increase in fluid temperature due to the increase in the diameter of the adsorbent tube, which increases the diameter of the fluid temperature by 60 K, in which the parameter increases the efficiency by 0.38%.

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