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For reduced mechanical stress, some chains with links made of metallic materials could be replaced by chains made of polymeric materials. A lower weight and a higher corrosion resistance would characterize such chains. From this point of view, research on the behavior of chain links made of polymeric materials under the action of tensile stresses can become important. Modeling by the finite element method highlighted some specific aspects of the behavior of a chain link subjected to tensile stresses. Later, we resorted to the manufacture by 3D printing of some chain links from four distinct polymeric materials, with the modification of the size of the chain link and, respectively, of the values of some of the input factors in the 3D printing process. The tensile strength of the chain links was determined using specialized equipment. The experimental results were processed mathematically to determine some empirical mathematical models that highlight the influence of the values of the input factors in the 3D printing process on the tensile strength of the samples in the form of chain links. It thus became possible to compare the results obtained for the four polymeric materials considered and identify the polymeric material that provides the highest tensile strength of the sample in the form of a chain link. The results of the experimental research showed that the highest mechanical resistance was obtained in the case of the links made of polyethylene terephthalate glycol (PETG). According to experimental results, when tested under identical conditions, PETG links can break for a force value of 40.9 N. In comparison, polylactic acid links will break for a force value of 4.70 N. Links printed in the horizontal position were almost 9-fold stronger than those printed in the vertical position. Under the same test conditions, according to the determined empirical mathematical models, PETG links printed in a horizontal position will break for a force of 300.8 N, while links printed in a vertical position will break for force values of 35.8 N. [ABSTRACT FROM AUTHOR]

Cam mechanisms, covering a large structural variety, are widely used in machinery, mainly as components of automated systems. Their functioning behavior is affected by negative dynamic phenomena determined by specific high velocities and acceleration rates. Within the various types of research on the dynamic behavior of cam mechanisms, this study addresses the need to clarify the influence of geometrical parameters and technological conditions on some indicators of the jump phenomenon in contact loss for a cam-follower mechanism. This particularly developed case study referred to a mechanism with a profiled grooved disk cam and oscillating follower. To highlight the influence of the cam-follower contact elasticity on the jump phenomenon, two dynamic models were developed: one considering rigid elements in contact and the second considering elastic cam-follower contact. The models were tested within a virtually simulated experiment, and the numerical simulation results evidenced the influence of input factors like the applied load on the mechanism, the clearance in the cam-follower kinematic pair, and the rotational speed of the cam, and the inertia moment was reduced to the follower on some indicators of the jump phenomenon. Validation FEA and experiments were performed, proving the reliable appropriateness of the dynamic model based on elastic cam-follower contact. [ABSTRACT FROM AUTHOR]

Waviness is a parameter used to complete information on the machined surface state. There is little scientific and technical information on the influence exerted by the cutting conditions and the workpiece material hardness on the values of some parameters that define the waviness of milled surface. No works have been identified to present such information for dry high-speed face milling applied to hard steel workpieces. A factorial experiment with four independent variables at three variation levels was planned to model the influence of milling speed, feed, cutting depth, and steel hardness on the total heights of the profile and surface waviness for dry high-speed face milling. Mathematical processing of experimental results was used to identify the power type function and empirical mathematical models. These models highlight the direction of variation and the intensity of influence exerted by the considered input factors on the values of two waviness parameters in the case of dry high-speed face milling of samples made of four hard steels. It has been observed that the increase in steel hardness increases the total heights of the profile and surface waviness. In the case of two types of steel, a good correlation was identified between the values of the total profile waviness height and the total surface waviness height, respectively, using the Pearson correlation coefficient.

Cam mechanisms, covering a large structural variety, are widely used in machinery, mainly as components of automated systems. Their functioning behavior is affected by negative dynamic phenomena determined by specific high velocities and acceleration rates. Within the various types of research on the dynamic behavior of cam mechanisms, this study addresses the need to clarify the influence of geometrical parameters and technological conditions on some indicators of the jump phenomenon in contact loss for a cam-follower mechanism. This particularly developed case study referred to a mechanism with a profiled grooved disk cam and oscillating follower. To highlight the influence of the cam-follower contact elasticity on the jump phenomenon, two dynamic models were developed: one considering rigid elements in contact and the second considering elastic cam-follower contact. The models were tested within a virtually simulated experiment, and the numerical simulation results evidenced the influence of input factors like the applied load on the mechanism, the clearance in the cam-follower kinematic pair, and the rotational speed of the cam, and the inertia moment was reduced to the follower on some indicators of the jump phenomenon. Validation FEA and experiments were performed, proving the reliable appropriateness of the dynamic model based on elastic cam-follower contact.

Complex surfaces such as helical ones are commonly used in machinery. Such surfaces can be obtained by various machining processes, one of these processes being thread whirling. The influence of machining conditions needs to be better understood to develop a more precise prediction of the specific resulting errors involved in thread whirling. This paper firstly presents the theoretical conditions which generate micro-deviations on whirled surfaces. A theoretical model which considers the geometrical parameters describing the whirling head and cutters and the process's whole kinematics was developed. The threaded surface was described as a complex compound surface resulting from intersecting successive ruled helical surfaces corresponding to the cutting edges of the set of cutters from the whirling head. Numerical simulation results were exemplified and validation experiments were both designed and performed. Empirical mathematical models were established to highlight the influence of the input factors such as thread pitch and external diameter, the ratio between the diameter of cutters' top edge disposal and the thread's external diameter, the rotary speed of the whirling head, and the rotary speed of the workpiece on some accuracy elements and roughness parameters of the threaded surface. [ABSTRACT FROM AUTHOR]

The thermal properties of parts obtained by 3D printing from polymeric materials may be interesting in certain practical situations. One of these thermal properties is the ability of a material to expand as the temperature rises or shrink when the temperature drops. A test experiment device was designed based on the thermal expansion or negative thermal expansion of spiral test samples, made by 3D printing of polymeric materials to investigate the behavior of some polymeric materials in terms of thermal expansion or contraction. A spiral test sample was placed on an aluminum alloy plate in a spiral groove. A finite element modeling highlighted the possibility that areas of the plate and the spiral test sample have different temperatures, which means thermal expansions or contractions have different values in the spiral areas. A global experimental evaluation of four spiral test samples was made by 3D printing four distinct polymeric materials: styrene-butadiene acrylonitrile, polyethylene terephthalate, thermoplastic polyurethane, and polylactic acid, has been proposed. The mathematical processing of the experimental results using specialized software led to establishing empirical mathematical models valid for heating the test samples from −9 °C to 13 °C and cooling the test samples in temperature ranges between 70 °C and 30 °C, respectively. It was found that the negative thermal expansion has the highest values in the case of polyethylene terephthalate and the lowest in the case of thermoplastic polyurethane. [ABSTRACT FROM AUTHOR]

Wire electrical discharge machining (WEDM) is a process that is used when it is necessary to manufacture small-width slots with a micrometer accuracy or to precisely detach parts with complex contours from metal workpieces in the form of sheets or plates. The fact that the wire electrode rests only in the working zone in two of its guides allows it to achieve micrometric oscillations, leading to the generation of an error from the flat shape of the slot surfaces that gradually develops into the workpiece. The slot widths are influenced by several factors, such as the workpiece thickness, pulse-on time, pulse-off time, the wire tension force, the current, and the wire movement speed along its axis. Some theoretical assumptions about the behavior of the wire electrode were first considered. An experimental research plan was then designed to obtain additional information on the influence of the mentioned factors on the slot width in different positions of the cross-section through the slot. The statistical processing of the experimental results led to the elaboration of empirical mathematical models that highlight the order of influence and the intensity of the influence exerted by the factors mentioned above. [ABSTRACT FROM AUTHOR]

Photosynthesis is a process that indicates the productivity of crops. The estimation of this variable can be achieved through methods based on mathematical models. Mathematical models are usually classified as empirical, mechanistic, and hybrid. To mathematically model photosynthesis, it is essential to know: the input/output variables and their units; the modeling to be used based on its classification (empirical, mechanistic, or hybrid); existing measurement methods and their invasiveness; the validation shapes and the plant species required for experimentation. Until now, a collection of such information in a single reference has not been found in the literature, so the objective of this manuscript is to analyze the most relevant mathematical models for the photosynthesis estimation and discuss their formulation, complexity, validation, number of samples, units of the input/output variables, and invasiveness in the estimation method. According to the state of the art reviewed here, 67% of the photosynthesis measurement models are mechanistic, 13% are empirical and 20% hybrid. These models estimate gross photosynthesis, net photosynthesis, photosynthesis rate, biomass, or carbon assimilation. Therefore, this review provides an update on the state of research and mathematical modeling of photosynthesis. [ABSTRACT FROM AUTHOR]

Waviness is a parameter used to complete information on the machined surface state. There is little scientific and technical information on the influence exerted by the cutting conditions and the workpiece material hardness on the values of some parameters that define the waviness of milled surface. No works have been identified to present such information for dry high-speed face milling applied to hard steel workpieces. A factorial experiment with four independent variables at three variation levels was planned to model the influence of milling speed, feed, cutting depth, and steel hardness on the total heights of the profile and surface waviness for dry high-speed face milling. Mathematical processing of experimental results was used to identify the power type function and empirical mathematical models. These models highlight the direction of variation and the intensity of influence exerted by the considered input factors on the values of two waviness parameters in the case of dry high-speed face milling of samples made of four hard steels. It has been observed that the increase in steel hardness increases the total heights of the profile and surface waviness. In the case of two types of steel, a good correlation was identified between the values of the total profile waviness height and the total surface waviness height, respectively, using the Pearson correlation coefficient. [ABSTRACT FROM AUTHOR]

Wire electrical discharge machining (WEDM) is a process that is used when it is necessary to manufacture small-width slots with a micrometer accuracy or to precisely detach parts with complex contours from metal workpieces in the form of sheets or plates. The fact that the wire electrode rests only in the working zone in two of its guides allows it to achieve micrometric oscillations, leading to the generation of an error from the flat shape of the slot surfaces that gradually develops into the workpiece. The slot widths are influenced by several factors, such as the workpiece thickness, pulse-on time, pulse-off time, the wire tension force, the current, and the wire movement speed along its axis. Some theoretical assumptions about the behavior of the wire electrode were first considered. An experimental research plan was then designed to obtain additional information on the influence of the mentioned factors on the slot width in different positions of the cross-section through the slot. The statistical processing of the experimental results led to the elaboration of empirical mathematical models that highlight the order of influence and the intensity of the influence exerted by the factors mentioned above.

Photosynthesis is a process that indicates the productivity of crops. The estimation of this variable can be achieved through methods based on mathematical models. Mathematical models are usually classified as empirical, mechanistic, and hybrid. To mathematically model photosynthesis, it is essential to know: the input/output variables and their units; the modeling to be used based on its classification (empirical, mechanistic, or hybrid); existing measurement methods and their invasiveness; the validation shapes and the plant species required for experimentation. Until now, a collection of such information in a single reference has not been found in the literature, so the objective of this manuscript is to analyze the most relevant mathematical models for the photosynthesis estimation and discuss their formulation, complexity, validation, number of samples, units of the input/output variables, and invasiveness in the estimation method. According to the state of the art reviewed here, 67% of the photosynthesis measurement models are mechanistic, 13% are empirical and 20% hybrid. These models estimate gross photosynthesis, net photosynthesis, photosynthesis rate, biomass, or carbon assimilation. Therefore, this review provides an update on the state of research and mathematical modeling of photosynthesis.

The electrical discharge machining is a machining method applied when the workpiece material has a high hardness or the shape of the surface to be machined is to complicate to be obtained by a classical machining method. A problem of actual interest is the electrical discharge machining of small diameter external cylindrical surfaces in the case of materials characterized by high hardness. Among the distinct electrical discharge machining processes capable to be used in order to obtain small diameter cylindrical surfaces, a process based on the use of a plate type tool electrode was selected. A full factorial experiment with three independent variables and two experimental levels was designed and materialized to highlight the influence exerted by the pulse on time, pulse off time and peak current intensity on the heights of the cylindrical columns generated by electrical discharge machining. By mathematical processing of the experimental results, power type empirical mathematical models were established. The empirical models confirmed the strong influence exerted by the peak current intensity on the process output parameter.

3D printing is a process that has become widely used in recent years, allowing the production of parts with relatively complicated shapes from metallic and non-metallic materials. In some cases, it is challenging to evaluate the ability of 3D printers to make fine details of parts. For such an assessment, the printing of samples showing intersections of surfaces with low angle values was considered. An experimental plan was designed and materialized to highlight the influence of different factors, such as the thickness of the deposited material layer, the printing speed, the cooling and filling conditions of the 3D-printed part, and the thickness of the sample. Samples using areas in the form of isosceles triangles with constant height or bases with the same length, respectively, were used. The mathematical processing of the experimental results allowed the determination of empirical mathematical models of the power-function type. It allowed the detection of both the direction of actions and the intensity of the influence exerted by the input factors. It is concluded that the strongest influence on the printer’s ability to produce fine detail, from the point of view addressed in the paper, is exerted by the vertex angle, whose reduction leads to a decrease in printing accuracy.

The electrical discharge machining is a machining method applied when the workpiece material has a high hardness or the shape of the surface to be machined is to complicate to be obtained by a classical machining method. A problem of actual interest is the electrical discharge machining of small diameter external cylindrical surfaces in the case of materials characterized by high hardness. Among the distinct electrical discharge machining processes capable to be used in order to obtain small diameter cylindrical surfaces, a process based on the use of a plate type tool electrode was selected. A full factorial experiment with three independent variables and two experimental levels was designed and materialized to highlight the influence exerted by the pulse on time, pulse off time and peak current intensity on the heights of the cylindrical columns generated by electrical discharge machining. By mathematical processing of the experimental results, power type empirical mathematical models were established. The empirical models confirmed the strong influence exerted by the peak current intensity on the process output parameter. [ABSTRACT FROM AUTHOR]

The wire electrical discharge cutting can be used to separate parts from plateshaped workpieces or to make slots with various contours in electroconductive materials generally characterized by low machinability by conventional machining processes. The analysis of the wire electrical discharge machining process showed that there are many groups of factors able to affect the process results. The axiomatic design principles were used to define the conditions in which experimental research aiming to highlight the factors able to affect the sizes of technological interest in the case of wire electrical discharge machining. To evaluate the influence exerted by some input factors of the wire electrical discharge machining process, namely by the pulse on time, pulse off time, and by the average intensity of the discharge current, on some results of technological interest, an experimental research in accordance with the requirements of a full factorial experiment was designed and materialized. By processing the experimental results, it was possible to determine empirical mathematical models of power type function. [ABSTRACT FROM AUTHOR]

External cylindrical surfaces could be obtained in workpieces made of electro conductive materials both by classical machining methods and nonconventional machining methods. One of such nonconventional machining methods is the electrical discharge machining method. If it is necessary to obtain small diameter external cylindrical surfaces, a method based on the use of a plate type tool electrode with holes of adequate diameters could be applied. Practically, as a consequence of the common linear work movement, the workpiece material is gradually removed and only the material corresponding to the hole is not affected by the process of material removal, constituting gradually a cylindrical column. The theoretical analysis of the process developed in such conditions showed that various factors could affect the depth of tool electrode penetration into the test piece material. Experimental researches aiming to highlight the influence exerted by some process input factors (pulse on time, pulse off time, peak current intensity, and process duration) on the height of columns generated by electrical discharge machining were designed and materialized. By mathematical processing of the experimental results, empirical mathematical models were determined. These models showed that the penetration depth increases when the peak current intensity and process duration increase and diminishes when the pulse on time and pulse off time increase. [ABSTRACT FROM AUTHOR]

The electrochemical machining with forced hydrodynamic depassivation allows the material removal from workpiece by electrochemical erosion. The products resulted as a consequence of the electrochemical reactions developed between the workpiece material and electrolyte are removed from the machining zone by forced circulation of the electrolyte. A theoretical analysis led to formulation of several hypothesis concerning the behaviour of some metallic materials when test samples presenting a conical surface are affected by the electrochemical machining process with forced hydrodynamic depassivation. In the paper, the results of some experimental researches developed on test samples from steel, bronze and aluminium are presented. By mathematical processing of the experimental results, some empirical mathematical models were established. The empirical models highlight the influence exerted by the gap size, by the size of angle corresponding to the conical surface and by the voltage applied to the two electrodes on the size of the final gap and on the quantity of material removed from the test piece, for a certain duration of the machining process.

The electrochemical machining with forced hydrodynamic depassivation allows the material removal from workpiece by electrochemical erosion. The products resulted as a consequence of the electrochemical reactions developed between the workpiece material and electrolyte are removed from the machining zone by forced circulation of the electrolyte. A theoretical analysis led to formulation of several hypothesis concerning the behaviour of some metallic materials when test samples presenting a conical surface are affected by the electrochemical machining process with forced hydrodynamic depassivation. In the paper, the results of some experimental researches developed on test samples from steel, bronze and aluminium are presented. By mathematical processing of the experimental results, some empirical mathematical models were established. The empirical models highlight the influence exerted by the gap size, by the size of angle corresponding to the conical surface and by the voltage applied to the two electrodes on the size of the final gap and on the quantity of material removed from the test piece, for a certain duration of the machining process. [ABSTRACT FROM AUTHOR]

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to better fit mouse gastric emptying data including when two peaks are present in the gastric emptying curve. We fitted 175 gastric emptying data sets with two standard models (gamma variate and power exponential), with a gamma variate model that includes stretched exponential and with a proposed two-component model. The appropriateness of the fit was assessed by the Akaike Information Criterion. We found that extension of the gamma variate model to include a stretched exponential improves the fit, which allows for a better estimation of T1/2 and Tlag. When two distinct peaks in gastric emptying are present, a two-component model is required for the most appropriate fit. We conclude that use of a stretched exponential gamma variate model and when appropriate a two-component model will result in a better estimate of physiologically relevant parameters when analyzing mouse gastric emptying data. [ABSTRACT FROM AUTHOR]

The wire electrical discharge machining is a machining method in which the pulse electrical discharges developed between workpiece and travelling wire tool electrode are used in order to detach parts having complex ruled surfaces in plate type workpieces. The problem of evaluation of wire tool electrode wear was considered. A theoretical analysis of phenomena developed in work zone during wire electrical discharge machining process was developed. An experimental research in accordance with the rules valid in the case of a factorial experiment with six independent variables at two levels was designed and materialized. Power type empirical mathematical models were determined by mathematical processing of the experimental results, in order to highlight the influence exerted by workpiece thickness, pulse on time, pulse off time, wire tensioning force and current intensity and travelling speed on the wire tool electrode wear. [ABSTRACT FROM AUTHOR]

3D printing is a process that has become widely used in recent years, allowing the production of parts with relatively complicated shapes from metallic and non-metallic materials. In some cases, it is challenging to evaluate the ability of 3D printers to make fine details of parts. For such an assessment, the printing of samples showing intersections of surfaces with low angle values was considered. An experimental plan was designed and materialized to highlight the influence of different factors, such as the thickness of the deposited material layer, the printing speed, the cooling and filling conditions of the 3D-printed part, and the thickness of the sample. Samples using areas in the form of isosceles triangles with constant height or bases with the same length, respectively, were used. The mathematical processing of the experimental results allowed the determination of empirical mathematical models of the power-function type. It allowed the detection of both the direction of actions and the intensity of the influence exerted by the input factors. It is concluded that the strongest influence on the printer's ability to produce fine detail, from the point of view addressed in the paper, is exerted by the vertex angle, whose reduction leads to a decrease in printing accuracy. [ABSTRACT FROM AUTHOR]