scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

scholarly journals MOVEMENT STABILITY OF A SECTION OF THE MACHINE FOR BLACK FALLOW CULTIVATION IN A LONGITUDINAL-VERTICAL PLANE

2020 ◽  
Author(s):  
Volodymyr Bulgakov ◽  
Semjons Ivanovs ◽  
Volodymyr Nadykto ◽  
V. Kaminsky ◽  
L. Shymko ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Rational Design ◽  
Vertical Plane ◽  
Design Parameters ◽  
Field Investigations ◽  
Special Machine ◽  
Rational Design Parameters ◽  
Movement Stability ◽  
The Impact ◽  
Angle Of Rotation

One of the tasks of using the black fallow in agricultural production is the weed control and the moisture conservation in the soil. Application of the most advanced soil cultivation technologies ensures preservation of no more than 75% of precipitations in the soil. To improve the state of this issue, we have developed a special machine for processing the black fallow. A mathematical model has been developed that describes the dynamics of the movement of the harrow section in a longitudinal-vertical plane, and its solution is given, which allows investigation of the impact of this or that design parameter upon the dynamics of the angle of rotation in time. The adequacy of the developed mathematical model is confirmed by special laboratory and field investigations of the created experimental machine. With rational design parameters the rotation angle of the harrow section in a longitudinal-vertical plane will not exceed – 3º, and the time of its exit to the equilibrium position will not exceed 16...17 s.

THE IMPACT OF THE DIMENSION OF A MATHEMATICAL MODEL OF INTERNAL BALLISTICS ON DESIGN PARAMETERS OF A SHOT FOR GRAIN GUNPOWDER CHARGES

2021 ◽  
pp. 95-110
Author(s):  
I.G. Rusyak ◽  
◽  
V.A. Tenenev ◽  
Keyword(s):  
Mathematical Model ◽  
Powder Mixture ◽  
Thermodynamic Model ◽  
Dynamic Models ◽  
Design Parameters ◽  
Variable Cross ◽  
One Dimensional ◽  
Gas Dynamic ◽  
Wide Range ◽  
The Impact

The problem of the impact of the mathematical model dimension on the calculated intraballistic characteristics of a shot for the charges made of granulated powder is considered. Mathematical models of the shot are studied using the spatial (axisymmetric), one-dimensional, and zero-dimensional (thermodynamic) formulations. The thermodynamic model takes into account the distribution of the pressure and velocity of a gas-powder mixture behind the shot for a channel of variable cross-section. Comparison of simulation results is carried out in a wide range of loading parameters. It is shown that there is a range of the loading parameters for a thermodynamic approach to give satisfactory approximation to the parameters obtained using the gas-dynamic approach, which describes the flow of a heterogeneous reacting mixture with a separate consideration of phases and intergranular interactions between them. Notably that in the entire range of the charging parameters studied in this work, the one-dimensional and twodimensional gas-dynamic models only slightly differ from each other. Therefore, in the main pyrodynamic period, the actuation of the charge, made of granulated powder, can be simulated using a one-dimensional gas-dynamic model or a zero-dimensional thermodynamic model with allowance for spatial distribution of the pressure and velocity of the gas-powder mixture.

scholarly journals THEORETICAL JUSTIFICATION OF SOME STRUCTURAL-TECHNOLOGICAL PARAMETERS OF MILKING MACHINEWITH DRIVING DRIVING MODE

2020 ◽  
pp. 16-26
Author(s):  
Ihor Babyn ◽  
Anatoliy Hrytsun
Keyword(s):  
Milk Production ◽  
High Vacuum ◽  
Design Parameters ◽  
Theoretical Studies ◽  
Technological Parameters ◽  
Machine Milking ◽  
Mode Of Operation ◽  
Milking Machine ◽  
Technical Solutions ◽  
The Impact

An analysis of the technical solutions of milking machines with controlled vacuum mode and theoretical studies of the operation of the milking machine actuator, which allows to reduce the vacuum load on the udder and the impact on the sphincter of the cervix and prevent "idle" milking in high vacuum in the machine process. The completeness of milking cows and reducing the incidence of their mastitis depends to some extent on the operation of milking equipment. Performance indicators of the technological process of serial milking equipment do not always fully comply with the current zootechnical requirements. During their work at the beginning and at the end of the milking of the animal there may be a process of "idle" milking at high vacuum, which often leads to the disease of animals with mastitis and subsequent culling. Along with the increase in milk production, quality is becoming extremely important. The analysis of the known technical solutions of milking machines with a controlled mode of milking shows that the domestic and foreign industry do not produce milking machines with a controlled mode of milking, which fully correspond to the physiology of animals. In our opinion, the most effective one is to consider a milking machine with a low-inertial milk flow sensor, which controls the vacuum mode, both in poddyah and interstitial chambers of milking glasses. Conducted theoretical studies of the working process of machine milking allowed to systematize the engineering calculation method of milking machine with a controlled mode of operation and to determine the optimal design parameters of the actuators. The analytical expressions obtained characterize the influence of their parameters and mode of operation on the dynamics of milk production during machine milking of cows.

Solving a Planar Four-Bar Design Problem Using Continuation

1989 ◽  
Author(s):  
A. P. Morgan ◽  
C. W. Wampler
Keyword(s):  
Polynomial System ◽  
Continuation Method ◽  
Computer Time ◽  
Design Parameters ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Design Elements ◽  
Real Solutions ◽  
Time Limitations

Abstract The problem of synthesizing a planar 4-bar with given pivots such that the coupler curve passes through live precision points is considered. It is shown that the design parameters must satisfy a system of 4 fourth-degree polynomial equations in 4 unknowns which has at most 36 nonzero real solutions. This polynomial system is solved using a continuation method, which thereby generates the collection of all designs that meet the precision-point specification. A computer program that implements this continuation method has been tested on a number of problems. It is reliable and fast enough for the purposes of design. The approach to kinematic design represented by this work is completely general, subject only to computer-time limitations that may arise for problems with many design elements.

scholarly journals Mathematical Model and Data Analysis to Determine the Number of Confirmed Infections Due to Covid-19 in Spain

2020 ◽  
Vol 14 (7) ◽  
pp. 60
Author(s):  
Gaston Sanglier ◽  
Sonia Cesteros ◽  
Eduardo J. Lopez ◽  
Roberto A. Gonzalez
Keyword(s):  
Mathematical Model ◽  
Data Analysis ◽  
Mathematical Models ◽  
Polynomial Regression ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Vital Importance ◽  
The World ◽  
Speed Of Propagation ◽  
Regression Adjustment

Covid-19 initially started in China, although cases of infection by this virus are currently being identified in Europe since January and February of this year camouflaged within a strong outbreak of influenza that had not been identified before. What is certain is that in about a hundred days it has spread around the world threatening humanity. There seems to be a great need to find a rapid response to the speed at which the virus is spreading. In this work, different mathematical models are studied to accurately determine the speed of propagation or infection of people infected by Covid-19 based on data collected from the evolution of the pandemic in Spain. Several mathematical models are proposed and analyzed, but the model proposed as the most suitable is a fourth degree polynomial regression adjustment that presents an R-square statistic of 99.72% which gives a great adjustment of the model for the calculation of the number of infected confirmed by this virus in Spain.  Knowing these data is of vital importance to be able to take and undertake the most urgent health and social measures in an effective and orderly manner. This will have a great repercussion in being able to avoid a high number of possible infections.

Solving a Planar Four-Bar Design Problem Using Continuation

1990 ◽  
Vol 112 (4) ◽  
pp. 544-550 ◽  
Author(s):  
A. P. Morgan ◽  
C. W. Wampler
Keyword(s):  
Polynomial System ◽  
Continuation Method ◽  
Computer Time ◽  
Design Parameters ◽  
Polynomial Equations ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Design Elements ◽  
Real Solutions ◽  
Time Limitations

The problem of synthesizing a planar 4-bar with given pivots such that the coupler curve passes through five precision points is considered. It is shown that the design parameters must satisfy a system of 4 fourth-degree polynomial equations in 4 unknowns which has at most 36 nonzero real solutions. This polynomial system is solved using a continuation method, which thereby generates the collection of all designs that meet the precision-point specification. A computer program that implements this continuation method has been tested on a number of problems. It is reliable and fast enough for the purposes of design. The approach to kinematic design represented by this work is completely general, subject only to computer-time limitations that may arise for problems with many design elements.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Analyzing the Impact of Healthy Behavior on Weight Change with a Provable Mathematical Model (Preprint)

2020 ◽  
Author(s):  
Ayan Chatterjee ◽  
Ram Bajpai ◽  
Pankaj Khatiwada
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Health Behavior ◽  
Weight Change ◽  
Simulated Data ◽  
Negative Behavior ◽  
Healthy Behavior ◽  
Healthy Habits ◽  
Lifestyle Diseases ◽  
The Impact

BACKGROUND Lifestyle diseases are the primary cause of death worldwide. The gradual growth of negative behavior in humans due to physical inactivity, unhealthy habit, and improper nutrition expedites lifestyle diseases. In this study, we develop a mathematical model to analyze the impact of regular physical activity, healthy habits, and a proper diet on weight change, targeting obesity as a case study. Followed by, we design an algorithm for the verification of the proposed mathematical model with simulated data of artificial participants. OBJECTIVE This study intends to analyze the effect of healthy behavior (physical activity, healthy habits, and proper dietary pattern) on weight change with a proposed mathematical model and its verification with an algorithm where personalized habits are designed to change dynamically based on the rule. METHODS We developed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate (BMR), total daily energy expenditure (TDEE), and body-mass-index (BMI) to establish a relationship between health behavior and weight change. Followed by, we verified the model with simulated data. RESULTS The proposed provable mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with the proposed algorithm using simulated data following the necessary constraints. The adoption of BMR and TDEE calculation following Harris-Benedict’s equation has increased the model's accuracy under defined settings. CONCLUSIONS This study helped us understand the impact of healthy behavior on obesity and overweight with numeric implications and the importance of adopting a healthy lifestyle abstaining from negative behavior change.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Sao Paulo ◽  
The State ◽  
São Paulo ◽  
Health Authorities ◽  
The World ◽  
The Moment ◽  
The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

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