Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

Feasibility Study of Condition Monitoring for Some Event Around the Crosshead in a Reciprocating Compressor

2018 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Natural Frequency ◽  
Error Function ◽  
Measurement Data ◽  
Reciprocating Compressor ◽  
Connecting Rod ◽  
Monitoring Method ◽  
Actual Measurement ◽  
Proposed Model ◽  
Before And After ◽  
Parameter Values

The purpose of this study is to establish a new monitoring technique to quantitatively detect the states of the sliding and connecting portions, where it could be found that failures often occur. We proposed a monitoring method wherein a mathematical model and actual measurement data for the moving parts of the reciprocating compressor were used to construct a system that (i) monitors the state while the reciprocating compressor operates and (ii) predicts and diagnoses signs of damage. This paper reports on a case study involving experimental data acquired before and after failures occurred in the connecting parts of the connecting rod. The purpose is to assess how the parameter values differed between the two operating states. To equate (i) each natural frequency calculated from eigenvalue analysis based on the proposed model with (ii) each resonant frequency during operation corresponding to the natural frequency of bending, we define an error function for the identified problem, namely, the optimum problem. In this paper, it is assumed that the crosshead pin that attaches the connecting rod to the crosshead wears out, and the dimensions of the crosshead pin are processed. In the observational results, it was found that some parameter values had large differences, and the corresponding state change could occur around the crosshead. We demonstrated the possibility of detecting both types of changes in the parameter values and the deterioration in the parts for two different operating states by the proposed method.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Mass and momentum transfer by solitary internal waves in a shelf zone

2012 ◽  
Vol 19 (2) ◽  
pp. 265-272 ◽  
Author(s):  
N. Gavrilov ◽  
V. Liapidevskii ◽  
K. Gavrilova
Keyword(s):  
Mathematical Model ◽  
Internal Waves ◽  
Solitary Waves ◽  
Large Amplitude ◽  
Shelf Zone ◽  
Swash Zone ◽  
Second Mode ◽  
Before And After ◽  
The Mathematical Model ◽  
Solitary Internal Waves

Abstract. The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of solitary waves symmetric with respect to the unperturbed interface is constructed. It is shown that, taking into account the friction on interfaces in the mathematical model, it is possible to describe adequately the change in the phase and amplitude characteristics of two solitary waves moving towards each other before and after their interaction. It is demonstrated that propagation of large amplitude solitary internal waves of depression over a shelf could be simulated in laboratory experiments by internal symmetric solitary waves of the second mode.

Exact Solutions of the Vibration Problem of Beam Structures

2013 ◽  
Vol 390 ◽  
pp. 242-245 ◽  
Author(s):  
Alexander V. Chekanin
Keyword(s):  
Mathematical Model ◽  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Displacement Method ◽  
Actual Problem ◽  
Beam Structures ◽  
The Mathematical Model

The article deals with the actual problem of improving the accuracy of determining the dynamic characteristics of beam structures. To solve such problems the displacement method is used. Defining matrices are calculated with the Godunovs scheme. Numerical solutions in this case can be obtained practically with any accuracy within accepted hypotheses of the mathematical model of the calculated object. This suggests that the resulting solutions are standard. The examples of determining the natural frequencies of vibrations of beam structures that demonstrate an extremely high accuracy of the proposed algorithm are given.

Research on the Effects of Roughness on the Tactile Properties of Rice Straw Particleboard Surface

2020 ◽  
Vol 12 (6) ◽  
pp. 795-801 ◽  
Author(s):  
Xian-Qing Xiong ◽  
Ying-Ying Yuan ◽  
Yi-Ting Niu ◽  
Liang-Ting Zhang
Keyword(s):  
Surface Roughness ◽  
Rice Straw ◽  
Interior Design ◽  
Roughness Parameter ◽  
Chemical Properties ◽  
Mesh Size ◽  
Design Guidelines ◽  
Before And After ◽  
The Difference ◽  
Parameter Values

To explore the effects of roughness on the tactile properties of rice straw particleboard (RSP), the surface roughness and psychological tactile and visual experiments were conducted for RSP substrates with 0.76 g/cm3 and 0.55 g/cm3 densities after sanding with sandpaper (mesh 180#, 360#, and 600#). The effects of different sandpaper types, sanding time, and density of RSP on the surface roughness were analyzed. The experimental results are as follows. The sanding treatment had significant influence on the surface roughness characterization parameters Ra and Rpv of the RSP specimens. Surface roughness differences between the 180# and 360# mesh-prepared samples were obvious. The tactile and visual psychological values of the 360# and 600# mesh-sanded specimens were higher, and the psychological quantities of untreated and 180# mesh-sanded specimens were lower. After comparing the samples with sanding treatment of sandpaper 0∼180#, the change in surface roughness of RSP with a density of 0.76 g/cm3 was smaller than that of the specimen with a density of 0.55 g/cm3. The psychological quantity difference of RSP specimens with a density of 0.55 g/cm3 was evident. When the sanding time was 1 min., the values of the roughness characterization parameters Ra and Rpv increased slightly. After 3 min. sanding, the Ra and Rpv values stabilized. When the sanding time was 5 min, the roughness was essentially unchanged. With the change in sanding time, the measured values of the tactile psychological quantity varied greatly and the measured values of the visual psychology were very close. For the RSP substrates with higher density, the surface roughness was less after sanding with a smoother surface and better tactile properties. There were significant differences between the surface roughness of the RSPs before and after sanding. After manual sanding over the same time span, the surface roughness evaluation parameter values decreased with an increase of mesh size of the sandpaper, and the tactile properties were improved. The longer the sanding time, the smaller the difference in the surface roughness parameter values, and the smaller the difference between the tactile psychological quantity and the visual psychological quantity. To expand the research scope of RSP products, this study investigates not only the physical and chemical properties but also the subjective feelings when using the RSP products. This will provide analytical methods and design guidelines for the consideration of environmental factors in furniture and interior design.

Updating the Mathematical Model of a Structure Using Vibration Data

2005 ◽  
Vol 11 (12) ◽  
pp. 1469-1486 ◽  
Author(s):  
Ashutosh Bagchi
Keyword(s):  
Mathematical Model ◽  
Model Updating ◽  
Three Dimensional ◽  
Field Tests ◽  
Mode Shapes ◽  
Actual Structure ◽  
Shell Elements ◽  
Vibration Data ◽  
The Difference ◽  
The Mathematical Model

Model updating is an important step for correlating the mathematical model of a structure to the real one. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper concentrates on the model updating techniques using the natural frequencies or frequencies and mode shapes of a structure. An iterative technique is developed based on the matrix update method. The method hasbeenappliedtothefiniteelement models of a three span continuous steel free deck bridge located in western Canada. The finite element models of the bridge have been constructed using three-dimensional beam and facet shell elements and the models have been updated using the measured frequencies. From the study it is clear that the initial model needs to be built such that it represents the actual structure as closely as possible. The results demonstrate that the difference between the modal parameters from the model and field tests affect the quality of the model updating process.

scholarly journals DEVELOPMENT AND RESEARCH OF PROMISING SCHEMES FOR DIVIDING PIPES INTO DIMENSIONAL BILLETS

2021 ◽  
pp. 30-37
Author(s):  
Sergii Karnaukh
Keyword(s):  
Mathematical Model ◽  
Experimental Studies ◽  
Connecting Rod ◽  
High Quality ◽  
Cutting Knife ◽  
3D Software ◽  
The Mathematical Model ◽  
Cut Surface ◽  
Deform 3D

The purpose of this work is to study the known method of division of pipes by introducing a figure knife and the development of promising designs of equipment for division of pipes into measured workpieces. Based on the analysis of the actuating crank-slider mechanisms used in the equipment for division of pipes into measured workpieces, promising schemes of short-connecting rod mechanisms have been discovered that provide a local pipe section along the perimeter. The developed design of the device for dividing pipes into dimensional workpieces by the eccentric twisting method, which contains a wedge-joint mechanism in combination with a compact circular actuator, also allows to reduce energy and power costs for separation, reduce the consequences of instantaneous unloading of equipment and ensure high quality workpieces. A mathematical model of the proposed equipment was developed and the modeling of the cutting process was carried out using the DEFORM-3D software package. The analysis of the results obtained showed that in the extreme positions of the knives, jamming of the knives is possible. To eliminate jamming, it is necessary that the knives do not reach the extreme position. The adequacy of the mathematical model is confirmed by experimental studies. The error of the calculated and measured values of the torque on the cutting knife does not exceed 10%. This is due to the need for a more correct accounting of friction on the contact surfaces of the equipment. Cut tubular blanks have high geometric accuracy and high quality of the cut surface.

Study of Forward Connecting Rod Combined Lifting Mechanism Based on Linear Transformation and Vector Algebra

2012 ◽  
Vol 155-156 ◽  
pp. 505-508
Author(s):  
Ming Qing Wu
Keyword(s):  
Mathematical Model ◽  
Rigid Body ◽  
Linear Transformation ◽  
Plane Motion ◽  
Connecting Rod ◽  
Vector Algebra ◽  
Lift Mechanism ◽  
Four Bar Linkage ◽  
The Mathematical Model

By adopting the method of block analysis,the paper analyzes and calculates the forward connecting rod combined lift mechanism by broking up it into a four-bar linkage and the plane motion of an arm triangle rigid body, constructs the kinematic equations of four-bar linkage and arm triangle and the static equations of four-bar linkage based on linear transformation and vector algebra and establishes the mathematical model of lift mechanism based on linear transformation and vector algebra.

An optimized mathematical model for cancer patient care planning in the COVID-19 era.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e18663-e18663
Author(s):  
Isabel Blancas ◽  
David Martínez-Rodríguez ◽  
Fernando Rodríguez-Serrano ◽  
Rafael Jacinto Villanueva ◽  
Jose Manuel Garrido
Keyword(s):  
Mathematical Model ◽  
Demographic Data ◽  
Real Data ◽  
Oncologic Surgery ◽  
Number Of Patients ◽  
Oncologic Patients ◽  
Hospital Resources ◽  
The Difference ◽  
Using Data ◽  
The Mathematical Model

e18663 Background: The COVID-19 pandemic has threatened to collapse hospital and Intensive Care Unit (ICU) services, and it seems to limit the care of oncologic patients. The objective was to develop a mathematical model designed to predict the hospitalization and ICU admission demands due to COVID-19 to forecast the availability of hospital resources for the scheduling of oncological surgery and medical treatment that require hospitalitation or possible use of ICU services. Methods: We have implemented a SEIR model designed to predict the number of patients requiring hospitalization and ICU admissions for COVID-19. We evaluated the model using the number of cases registered in the hospitals of the province of Granada (Spain), that altogether cover 914,678 inhabitants. Calibration was performed using data recorded between March 15 and September 22, 2020. After that, the model was validated by comparing the predictions with data registered between September 23 and November 7, 2020. Besides, we performed a predictive analysis of scenarios regarding different possible sanitary measures. Results: Using patient registered data we developed a mathematical model that reflects the flow among the different sub-groups related to COVID-19 pandemics (Table). The best algorithm that fitted the disease dynamics was Particle Swarm Optimization, that minimized the difference between model output and real data used to calibrate the model. The validation phase showed the accuracy of the predictions, especially concerning trends in hospitalizations and ICU admissions. The different scenarios modelled on November 10, 2020 allowed us to predict the evolution of the pandemic until July 1, 2021, and to detect the peaks and valleys of disease prevalence. Conclusions: The mathematical model presented provides predictions on the evolution of COVID-19, the prevalence and hospital or ICU care demands. The predictions can be used to detect periods of greater availability of hospital resources that make it possible to schedule the oncologic surgery and intensify the care for oncologic patients. Furthermore, our model can be adapted to other population by recalibrating the model according to demographic data, the local evolution of the pandemic and the health policies. [Table: see text]

Adjustment of a Rotor Model to Achieve Agreement between Calculated and Experimental Natural Frequencies

1979 ◽  
Vol 21 (6) ◽  
pp. 389-396 ◽  
Author(s):  
G. T. S. Done
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Turbine Rotor ◽  
Beam Elements ◽  
Stiffness Properties ◽  
Standard Values ◽  
Lumped Masses ◽  
The Mathematical Model ◽  
Best Fit ◽  
Rotor Model

This paper is concerned with the problem of adjusting the mathematical model of a system such that the computed natural frequencies coincide with those measured experimentally. The particular system considered is a laboratory turbine-rotor model, modelled mathematically by 42 Timoshenko beam elements and lumped masses. Model adjustments are made by assuming, firstly, Young's modulus and the modulus of rigidity to be variable, a change from standard values representing overall stiffness deficiencies in the mathematical model. In this case, a best fit to the lowest six natural frequencies, as measured experimentally, is made. Secondly, stiffness diameters are assumed variable, thereby allowing for deficiencies in the model near discontinuous changes of section, and in this case, the lowest six natural frequencies are matched exactly, but an overall measure of the differences between the actual and the stiffness diameters is minimized. An analysis for the rates of change of natural frequency with the various stiffness properties (i.e. the sensitivities) is presented, and the results of the manipulation discussed.

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