RATIONAL DISPOSAL OF PET CONTAINING WASTE AND PROSPECTS FOR THE SYNTHESIS OF NEW POLYMERS

2021 ◽  
pp. 12-20
Keyword(s):  
Mathematical Model ◽  
Ethylene Glycol ◽  
Polyethylene Terephthalate ◽  
Diethylene Glycol ◽  
Household Waste ◽  
Polyester Polyol ◽  
Unsaturated Polyesters ◽  
New Type ◽  
The Difference ◽  
The Mathematical Model

As a result of the research on the utilization of polyethylene terephthalate-containing household waste, a promising direction was identified in the production of a new type of secondary polyethylene terephthalate (SPET) - unsaturated polyesters. It was revealed that the final product, which formed when the alcoholization process is complete in any proportion of of glycol and secondary polyethylene terephthalate, is the bisalkylent terephthalate of terephthalic acid; the content of the alcoholysis product consists of bisalkylent terephthalate, different molecule mass, functionally hydroxyl-containing complex polyester polyol and free diols. The laws of alcoholization of secondary polyethylene terephthalate have been studied and the mechanism has been established. Studies have shown that, in contrast to existing theories, such as the formation of ethylene glycol in the polycondensation of phthalic anhydride bisalkylene glycol derivatives, the increase in ethylene glycol in the process was found to be due to the exchange of diethylene glycol in the macrochain. The formation of unsaturated polyesters goes stage by stage, first ethylene-, diethylene glycol acid esters are formed, then they are exposed to hydroxyl-containing oligomers - secondary polyethylene terephthalate alcohol products. A mathematical model of the process of alcoholization of SPET and diethylene glycol was created, studies showed that the difference between the values obtained as a result of the mathematical model and experiments are less than 5%. The unsaturated polyesters were synthesized on the basis of SPET alcoholization products. Many of them have shown their superiority over unsaturated polyesters PN-1, PN-3, PN-15, which are used in industry for general purposes. By developing unsaturated polyesters on the basis of secondary polyethylene terephthalate alcohol products, it was found that the structure of these polyesters is close to that of imported resins "Body", 196, 196A, used in industry.

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.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Valve Gear Refinement

2000 ◽  
Vol 124 (1) ◽  
pp. 86-90 ◽  
Author(s):  
Jurij Avsec ◽  
Milan Marcic ◽  
Maks Oblak
Keyword(s):  
Mathematical Model ◽  
Cam Design ◽  
Cam Follower ◽  
New Type ◽  
Cam Profile ◽  
Profile Design ◽  
Comparison Of The Results ◽  
The Mathematical Model ◽  
Valve Gear ◽  
Lubrication Properties

This paper describes a new type of valve gear cam—MULTICAM—which consists of seven curves and allows an optimum cam profile design. In order to calculate the cinematic and dynamic values and to assess the minimum oil film thickness in the valve gear, the mathematical model of an ideal valve gear was used. In addition, the comparison of the results between the polysine cam and the new MULTICAM cam design was made. By means of the new cam design the Hertz pressures were reduced at the point of contact between the cam and the cam follower and the lubrication properties at the top of the cam improved.

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.

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]

Mathematical Model and Error Analysis of Coordinate Measuring Arm with Revo Revolving Body

2011 ◽  
Vol 52-54 ◽  
pp. 156-161 ◽  
Author(s):  
Lei Zhao ◽  
Shu Gui Liu
Keyword(s):  
Mathematical Model ◽  
Measurement Accuracy ◽  
System Model ◽  
Error Sources ◽  
Spherical Domain ◽  
New Type ◽  
Space Coordinate ◽  
Improving Accuracy ◽  
Revolving Body ◽  
The Mathematical Model

A new type of coordinate measuring arm with a Revo revolving body which can realize quick measuring in spherical domain has high stability, fast measuring speed and high accuracy compared with common coordinate measuring arm. We use the method of space coordinate transformation to solve the problem that the transformation matrix can’t be got from Revo body to test head by DH method, and apply DH theory to build the mathematical model of system. The system model is verified right by sketching. The error model is built and the effect of measurement accuracy from all error sources is deeply analyzed. It presents a theory foundation for further researching on improving accuracy of this new type of coordinate measuring arm.

scholarly journals Measurement of the effect of chromaticity and intensity on colour representation parameters of a CRT display

2015 ◽  
Vol 2 (1-2.) ◽  
Author(s):  
Klára Wenzel ◽  
Ágnes Urbin
Keyword(s):  
Mathematical Model ◽  
The Difference ◽  
The Mathematical Model

The aim of the measurement detailed in this paper was to measure the just-noticable stimuli of the participating subjects. The stimuli were defined by chromaticity and intensity as the main parameters of the mathematical model. The results show correlance between intensity and the just-noticable stimuli, as described in the Weber-Frechner Law but a contradiction was shown after the analysis in the function of chromaticity. This contradiction can be explained by the difference between the sensitivity of the three cones of the eye.

AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

2021 ◽  
pp. 2150033
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha sohail ◽  
Andleeb Zafar ◽  
Rana Talha ◽  
Sadiq M. Sait
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Ethylene Oxide ◽  
Ethylene Glycol ◽  
Exothermic Reaction ◽  
Plug Flow ◽  
Material Balance ◽  
Chemical Species ◽  
Future Research ◽  
The Mathematical Model

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198[Formula: see text]C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129[Formula: see text]C and freezes at [Formula: see text]C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

Dynamics and Stability of Non-Planar Rigid Rotor Equipped with Two Ball-Spring Autobalancers

2019 ◽  
Vol 19 (02) ◽  
pp. 1950001 ◽  
Author(s):  
Mousa Rezaee ◽  
Mir Mohammad Ettefagh ◽  
Reza Fathi
Keyword(s):  
Mathematical Model ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Rigid Rotor ◽  
Out Of Plane ◽  
New Type ◽  
Nonlinear Equations Of Motion ◽  
The Mathematical Model ◽  
System Time

Recently, a new type of automatic ball balancer (ABB), called the ball-spring autobalancer (AB), has been proposed, which substantially eliminates the drawbacks of the traditional ABBs. In previous studies, the dynamics of the Jeffcott planar rotor equipped with ball-spring AB has been investigated. In the Jeffcott model, it is assumed that the ABB is located on the plane of the unbalance disk. However, for the non-planar rigid rotor with distributed imbalances, out-of-plane motions may occur, and the Jeffcott model becomes unreliable as the tilting motion cannot be explained. To this end, the aim of this paper is to analyze the capability of the ball-spring AB in balancing non-planar rotors and to reconfirm its pre-claimed advantages over the traditional ABBs for balancing non-planar rotors. To start, the mathematical model of the rigid rotor with two ball-spring ABs is established, based on which the nonlinear equations of motion are derived. Then, the system time responses are computed numerically and the balanced stable regions are acquired by the Lyapunov’s first method. The results of this study show that the ball-spring ABs can balance the non-planar rotors and the tilting motion does not impair the pre-claimed advantages of the ball-spring AB.

Fixture Optimization for Robotic Belt Grinding System

2011 ◽  
Vol 121-126 ◽  
pp. 2030-2034
Author(s):  
Dong Zhang ◽  
Chao Yun ◽  
Ling Zhang
Keyword(s):  
Mathematical Model ◽  
Optimization Methods ◽  
Belt Grinding ◽  
Robotic Grinding ◽  
The Monte Carlo Method ◽  
New Type ◽  
Set Up ◽  
Robotic Belt Grinding ◽  
The Mathematical Model ◽  
Grinding System

The precision is impacted when the robotic grinding path is discontinuous and the gripper needs to be replaced during manufacturing. In order to solve this problem, a new type PPPRRR grinding robot was proposed. The mathematical model for the robotic grinding paths was set up. The factors including the pose of the workpiece respect to the end joint and the position of contact wheel respect to the robot base frame {O}were analyzed to influence the grinding ability of the system. Base on the Monte Carlo method the posture and position factors above had been optimized, and the grinding ability of the system was increased. The optimization methods were proved right and workable by grinding golf head experiment.

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