scholarly journals Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element

2021 ◽  
Vol 6 (5 (114)) ◽  
Author(s):  
Yuriy Abramov ◽  
Oleksii Basmanov ◽  
Yaroslav Kozak
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Electric Current ◽  
Integral Transformation ◽  
A Priori ◽  
Single Pulse ◽  
Pulse Method ◽  
Time Parameter ◽  
Sensing Element ◽  
Equations Of Mathematical Physics

This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is represented as a series relative to the Bessel functions. The resulting solution is used to construct a mathematical model of a thermoresistive sensing element in the form of a transfer function, which takes the form of the transfer function of the inertial link. To trigger the thermoresistive sensing element of fire detectors, a single pulse of electric current in the shape of a rectangular triangle is used. The integral Laplace transformation was applied to mathematically describe the response of a thermoresistive sensing element to the thermal effect of such a test influence. To obtain information about the time parameter of fire detectors with a thermoresistive sensing element, the ratio of its output signals is used, which are measured in the a priori defined moments. A two-parametric expression was built to determine the time parameter of fire detectors; a verbal interpretation of the pulse method to determine it was provided. The implementation of this method ensures the invariance of the time parameter of fire detectors with a thermoresistive sensing element relative to the amplitude of a single pulse of an electric current, as well as relative to the parameter that is included in its transfer coefficient.

scholarly journals PULSE METHOD FOR DETERMINATION OF TIME PARAMETERS THERMAL FIRE DETECTOR

2021 ◽  
Vol 4 (164) ◽  
pp. 166-170
Author(s):  
Ya. Kozak
Keyword(s):  
Electric Current ◽  
Time Constant ◽  
Sensitive Element ◽  
Integral Transformation ◽  
Pulse Method ◽  
Auxiliary Parameter ◽  
Sensing Element ◽  
Fire Detector ◽  
Time Parameters ◽  
Analytical Expressions

For thermal fire detectors with a thermoresistive sensitive element, the method of determining its time parameters is justified. The time parameters of operation and the time constant of the thermal fire detector are considered as time parameters. The method is based on the use of the Joule-Lenz effect, for the implementation of which single pulses of electric current are passed through the thermoresistive sensitive element of the fire detector. Pulses having the shape of a quarter sinusoid or a quarter cosinusoid are used as such test signals. Using the Laplace integral transformation, analytical expressions are obtained, which represent the formalization of the reaction of the thermoresistive sensitive element of the fire detector to the corresponding test signals. These analytical expressions are used to obtain the functional dependences of the fire detector time constants on the pulse duration of the electric current and the auxiliary parameter. The auxiliary parameter is the ratio of the values ​​of the output signal of the thermal fire detector at two fixed points in time. This choice of auxiliary parameter allows to ensure invariance with respect to the transfer coefficient of the thermal fire detector with a thermoresistive sensing element. The fixed moments of time are chosen to be equal to half and three quarters of the duration of the pulses of electric current flowing through the thermoresistive sensitive element of the fire detector. The time of operation of the thermal fire detector is determined in the form of two additive components, one of which is a time constant of the fire detector, and the other is determined by the values ​​of normalized parameters in accordance with existing regulations. A sequence of procedures is given, which together represent a method of determining the time parameters of thermal fire detectors of this type.

scholarly journals TEMPERATURE ERROR WHEN DETERMINING THE TIME PARAMETER OF A FIRE DETECTOR WITH A THERMORESISTIVE SENSITIVE ELEMENT

2021 ◽  
Vol 6 (166) ◽  
pp. 151-155
Author(s):  
Ya. Kozak
Keyword(s):  
Electric Current ◽  
Current Pulse ◽  
Mathematical Description ◽  
Sensitive Element ◽  
A Priori ◽  
Time Parameter ◽  
Temperature Error ◽  
Electric Current Pulse ◽  
Sensing Element ◽  
Fire Detector

For fire detectors with a thermoresistive sensing element, a mathematical description of the reaction to the thermal action of an electric current pulse flowing through such a sensing element and having the shape of a right triangle is obtained. The mathematical description is constructed using the Laplace integral transformation and is shown to be a superposition of two Heaviside functions. The parameters of these functions are determined by the transmission coefficient and time constant of the thermoresistive sensitive element of the fire detector and the amplitude and duration of the electric current pulse. It is shown that the ratio of the output signals of the thermoresistive sensitive element of the fire detector at two a priori given moments of time can be used to determine the time parameter of the fire detector. The values ​​of a priori set moments of time, in which the temperature of the thermoresistive sensitive element of the fire detector is determined, are selected under the condition of simplicity of technical implementation. If there is a change in ambient temperature, it leads to a temperature error as a function of the time parameter of the fire detector. For such an error, a mathematical description is obtained in the general case, as well as for the case when the thermal influence on the thermoresistive sensitive element of the fire detector is due to the flow of an electric current pulse in the form of a right triangle. It is shown that the value of the temperature error has a minimum at the values ​​of the ratio of the output signals of the thermoresistive sensitive element of the fire detector at two a priori time points belonging to the range The value of this error does not exceed 4.9% with variations in ambient temperature, the value of which does not exceed 2.0%.

scholarly journals Mathematical model of the process of drying fine dispersed materials under the influence of alternating electric current

2021 ◽  
pp. 51-56
Author(s):  
O.V Zamytskyi ◽  
N.O Holiver ◽  
N.V Bondar ◽  
S.O Kradozhon
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Porous Material ◽  
Electric Current ◽  
Diffusion Processes ◽  
Direct Influence ◽  
Alternating Electric Current ◽  
Equations Of Mathematical Physics ◽  
Spatial Coordinates ◽  
First Time

Purpose. Establishing the dependences and determining rational parameters of the process of drying fine materials by direct influence of an electric current. Methodology. In the work, theoretical, analytical, empirical, and experimental methods as well as methods of mathematical statistics are used. Mathematical modeling of the process occurring during drying of finely dispersed materials by direct influence of alternating current is carried out. Findings. As a result of the research on the basis of physical representations of the process of drying capillary-porous material, a mathematical model is designed connecting temperature and moisture content in a plate from capillary-porous material by means of equations of mathematical physics. Originality. For the first time dependence has been obtained on the temperature and moisture content of the time and spatial coordinates of drying by passing an electric current through the layer of moist capillary-porous material, a feature which is both simultaneous accounting of thermal and diffusion processes in the material that can increase the accuracy of calculations and establish rational parameters of drying. Practical value. The obtained dependences are used when developing calculation methods and designing an industrial drying plant.

MODELING OF THE DYNAMIC PROCESS RELEASE OF STUCK DRILLING TOOLS BY HYDRO-PULSE METHOD

2019 ◽  
pp. 94-103
Author(s):  
K. H. Levchyk ◽  
M. V. Shcherbyna
Keyword(s):  
Mathematical Model ◽  
Dynamic Process ◽  
Drilling Fluid ◽  
Pulse Method ◽  
Geometrical Parameters ◽  
Technical Solution ◽  
Rock Layer ◽  
Drilling Tool ◽  
Drilling Tools ◽  
Drill Pipes

A technical solution is proposed for the elimination the grabbing of drilling tool, based on the use of energy due to the circulation of the drilling fluid. The expediency eliminating the grabbing drilling tool using the hydro-impulse method is substantiated. A method of drawing up a mathematical model for the dynamic process of a grabbing string of drill pipes in the case of perturbation of hydro-impulse oscillations in the area of the productive rock layer is developed. The law of longitudinal displacements arising in the trapped string is obtained, which allows choosing the optimal geometrical parameters of the passage channels and the frequency rotational of shutter for these channels. Recommendations for using this method for practical use have been systematized.

Pulse-Width Modulated Amplifier for DC Servo System and Its Matlab Simulation

2015 ◽  
Vol 9 (1) ◽  
pp. 625-631
Author(s):  
Ma Xiaocheng ◽  
Zhang Haotian ◽  
Cheng Yiqing ◽  
Zhu Lina ◽  
Wu Dan
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Input Signal ◽  
Pulse Width ◽  
Rotation Speed ◽  
Servo Motor ◽  
Matlab Simulation ◽  
Pulse Width Modulated ◽  
Signal Changes ◽  
The Relationship

This paper introduces a mathematical model for Pulse-Width Modulated Amplifier for DC Servo Motor. The relationship between pulse-width modulated (PWM) signal and reference rotation speed is specified, and a general model of motor represented by transfer function is also put forward. When the input signal changes, the rotation speed of the servo motor will change accordingly. By changing zeros and poles, transient performance of this system is discussed in detail, and optimal ranges of the parameters is recommended at the end of discussion.

The measuring system for monitoring the microarc heating process during surface hardening of steel products

2021 ◽  
pp. 33-39
Author(s):  
Makar S. Stepanov ◽  
rina G. Koshlyakova
Keyword(s):  
Heat Treatment ◽  
Mathematical Model ◽  
Electric Current ◽  
Measurement Method ◽  
Sample Surface ◽  
Steel Sample ◽  
Measuring System ◽  
Heating Process ◽  
Carbon Powder ◽  
Measured Temperature

The accelerated heat treatment during steel products hardening technology has been investigated. The possibility of measuring the temperature of steel products by thermoelectric platinum-platinum-rhodium thermocouple under microarc heating conditions is analyzed. During the experiments, working junctions of two S-type thermocouples: working and standard, were coined into the sample surface at the same level. The free thermocouples ends were connected to a digital multimeter and a personal computer. It was determined that 5 factors affect the measurement results: the electric current strength in the circuit, carbon powder, calibration, number of repeated measurement cycles, and a thermocouple copy. When planning the experiment, the concept of conducting a step-by-step nested experiment was used. Variance analysis method was used to process the experimental results. The measurement method precision parameters were calculated: repeatability and reproducibility. A linear mathematical model linking the measurement method reproducibility index with the measured temperature value has been obtained. A linear mathematical model is obtained that relates the reproducibility index of the measurement method to the measured temperature value. A measuring system for the experimental determination of the temperature of a steel sample is proposed and its application is justified for different electric current densities on the sample surface and varying duration of microarc heating. The possibilities of selecting and controlling the microarc heating modes depending on the required temperature of the heat treatment of the steel product are determined.

A mathematical model for the third-body concept

2017 ◽  
Vol 23 (3) ◽  
pp. 420-432 ◽  
Author(s):  
Pavel Krejčí ◽  
Adrien Petrov
Keyword(s):  
Mathematical Model ◽  
A Priori Estimates ◽  
A Priori ◽  
Dynamical Problem ◽  
Sobolev Embedding ◽  
Third Body ◽  
Embedding Theory ◽  
The Third ◽  
Galerkin Approximations ◽  
Body Concept

The third-body concept is a pragmatic tool used to understand the friction and wear of sliding materials. The wear particles play a crucial role in this approach and constitute the main part of the third-body. This paper aims to introduce a mathematical model for the motion of a third-body interface separating two surfaces in contact. This model is written in accordance with the formalism of hysteresis operators as solution operators of the underlying variational inequalities. The existence result for this dynamical problem is obtained by using a priori estimates established for Faedo–Galerkin approximations, and some more specific techniques such as anisotropic Sobolev embedding theory.

scholarly journals The effect of antimony presence in anodic copper on kinetics and mechanism of anodic dissolution and cathodic deposition of copper

2008 ◽  
Vol 44 (1) ◽  
pp. 107-114 ◽  
Author(s):  
Z.D. Stankovic ◽  
V. Cvetkovski ◽  
M. Vukovic
Keyword(s):  
Anodic Dissolution ◽  
Single Pulse ◽  
Pulse Method ◽  
Sulfate Solution ◽  
Electrode Reaction ◽  
Xrd Analysis ◽  
Lattice Parameter ◽  
Crystal Lattice Parameter ◽  
Cathodic Deposition ◽  
Anode Copper

The influence of the presence of Sb atoms, as foreign metal atoms in anode copper, on kinetics, and, on the mechanism of anodic dissolution and cathodic deposition of copper in acidic sulfate solution has been investigated. The galvanostatic single-pulse method has been used. Results indicate that presence of Sb atoms in anode copper increase the exchange current density as determined from the Tafel analysis of the electrode reaction. It is attributed to the increase of the crystal lattice parameter determined from XRD analysis of the electrode material.

Research on the influence of the discharge breakdown process on the crater formation during EDM

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenchao Zhang
Keyword(s):  
Mathematical Model ◽  
Discharge Channel ◽  
Electrical Discharge Machining ◽  
Pulse Discharge ◽  
Single Pulse ◽  
Crater Formation ◽  
Content Type ◽  
Breakdown Process ◽  
Positive Ions ◽  
Fluid Coupling

PurposeThis paper aims to study the breakdown, oscillation and vanishing of the discharge channel and its influence on crater formation with simulation and experimental methods. The experiment results verified the effect of the oscillating characteristics of the discharge channel on the shape of the crater.Design/methodology/approachA mathematical model that considers the magnetohydrodynamics (MHD) and the discharge channel oscillation was established. The micro process of discharging based on magnetic-fluid coupling during electrical discharge machining (EDM) was simulated. The breakdown, oscillation and vanishing stage of the discharge channel were analyzed, and the crater after machining was obtained. Finally, a single-pulse discharge experiment during EDM was conducted to verify the simulation model.FindingsDuring the breakdown of the discharge channel, the electrons move towards the center of the discharge channel. The electrons at the end diverge due to the action of water resistance, making the discharge channel appear wide at both ends and narrow in the middle, showing the pinch effect. Due to the mutual attraction of electrons and positive ions in the channel, the transverse oscillation of the discharge channel is shown on the micro level. Therefore, the position of the discharge point on the workpiece changes. The longitudinal oscillation in the discharge channel causes the molten pool on the workpiece to be ejected due to the changing pressure. The experimental results show that the shape of the crater is similar to that in the simulation, which verifies the correctness of the simulation results and also proves that the crater generated by the single pulse discharge is essentially the result of the interaction between transverse wave and longitudinal wave.Originality/valueIn this paper, the simulation of the discharge breakdown process in EDM was carried out, and a new mathematical model that considers the MHD and the discharge channel oscillation was established. Based on the MHD module, the discharge breakdown, oscillation and vanishing stages were simulated, and the velocity field and pressure field in the discharge area were obtained.

Data Mining for Model Identification

2011 ◽  
pp. 438-444
Author(s):  
Diego Liberati
Keyword(s):  
Mathematical Model ◽  
New Technologies ◽  
A Priori ◽  
Large Data ◽  
Point Of View ◽  
The Other ◽  
Gene Expressions ◽  
Other Hand ◽  
Hybrid Dynamics ◽  
Non Linear

In many fields of research, as well as in everyday life, it often turns out that one has to face a huge amount of data, without an immediate grasp of an underlying simple structure, often existing. A typical example is the growing field of bio-informatics, where new technologies, like the so-called Micro-arrays, provide thousands of gene expressions data on a single cell in a simple and fast integrated way. On the other hand, the everyday consumer is involved in a process not so different from a logical point of view, when the data associated to his fidelity badge contribute to the large data base of many customers, whose underlying consuming trends are of interest to the distribution market. After collecting so many variables (say gene expressions, or goods) for so many records (say patients, or customers), possibly with the help of wrapping or warehousing approaches, in order to mediate among different repositories, the problem arise of reconstructing a synthetic mathematical model capturing the most important relations between variables. To this purpose, two critical problems must be solved: 1 To select the most salient variables, in order to reduce the dimensionality of the problem, thus simplifying the understanding of the solution 2 To extract underlying rules implying conjunctions and/or disjunctions between such variables, in order to have a first idea of their even non linear relations, as a first step to design a representative model, whose variables will be the selected ones When the candidate variables are selected, a mathematical model of the dynamics of the underlying generating framework is still to be produced. A first hypothesis of linearity may be investigated, usually being only a very rough approximation when the values of the variables are not close to the functioning point around which the linear approximation is computed. On the other hand, to build a non linear model is far from being easy: the structure of the non linearity needs to be a priori known, which is not usually the case. A typical approach consists in exploiting a priori knowledge to define a tentative structure, and then to refine and modify it on the training subset of data, finally retaining the structure that best fits a cross-validation on the testing subset of data. The problem is even more complex when the collected data exhibit hybrid dynamics, i.e. their evolution in time is a sequence of smooth behaviors and abrupt changes.

Sign in / Sign up

Export Citation Format

Share Document