Mathematical Model Of Mechanism Research Articles

STUDY OF THE STRESS-STRAIN STATE OF THE MAXILLA DURING ORTHODONTIC TREATMENT OF DENTOGNATHIC DEFORMATIONS IN CHILDREN WITH CONGENITAL CLEFT LIP AND PALATE.

The aim: To create a three-dimensional simulation mechanical-mathematical model of the biomechanical system "Orthodontic appliance-maxilla", to study peculiarities of the stress-strained state of the maxilla. Materials and methods: A simulation model of the biomechanical system "Orthodontic appliance-maxilla" was created using computed tomography (CBCT) data. Mathematical modeling was used to determine the stress-strain state of the simulation model. Results: The patterns of changes in the stress state were determined and the values of deformation displacements in the structural elements of the biome-chanical system "Orthodontic appliance-maxilla" were determined under a force stress of the orthodontic device with an amplitude of 50 N. Conclusions: Simulation computer modeling of the stress-strain state of the "Orthodontic appliance-maxilla" system showed that activation of the kinematic mechanism of the appliance with a force of 50 N causes the emergence of a complex stress-strain state of bones. When the orthodontic appliance is activated, there is an asymmetry in the distribution of stresses by Mises between the right and left sides both for the appliance itself and for the maxillary bone tissue.

Numerical modeling of crack formation and propagation using contact elements

The work is devoted to modeling the process of formation, development and propagation of cracks. Currently, there is a large number of physical and mechanical-mathematical models describing the process of destruction of various materials. In addition to the fracture criteria, it is also important to correctly take into account changes in the rheology of the fractured material, including the contact interaction between the surfaces of cracks and fragments. This paper proposes a numerical approach to solving the problems of contact interaction and brittle fracture of elastically deformable bodies. Crack bank interactions, including frictional forces and contact pressures, is modeled by the means of frame-type contact finite elements (CFE) using a stepwise analysis method. Various contact conditions – separation, clutch, friction-sliding, as well as rheological properties of crack surfaces and fragments – contact layer pliability, adhesion strength, etc. are modeled with the help of CFE. The proposed approach was used in the numerical modeling of bone damage under the penetrating action of a rigid indenter. The conducted numerical studies have shown a good correspondence of the calculated and experimental results, despite the substantial approximation of the used calculation schemes.

Parameter Optimization of Large-Size High-Speed Cam-Linkage Mechanism for Kinematic Performance

The cam-linkage mechanism is a typical transmission mechanism in mechanical science and is widely used in various automated production equipment. However, conventional modeling methods mainly focus on the design and dimensional synthesis of the cam-linkage mechanism in the slow-speed scenario. The influence of component dimensions is not taken into consideration. As a result, the model accuracy dramatically falls when analyzing large-size cam-linkage mechanisms, especially in high-speed environments. The kinematic aspects of cam design have been investigated, but there are few studies discussing the motion characteristic and accuracy analysis models of the large-size cam-linkage mechanism under high-speed scenarios. To handle such issues, this paper proposes a parameter optimization methodology for the design analysis of the large-size high-speed cam-linkage mechanism considering kinematic performance. Firstly, the mathematical model of the cam five-bar mechanism is presented. The cam curve and motion parameters are solved forward with linkage length and output speed. Then, a particle swarm-based multi-objective optimization method is developed to find the optimal structure parameters and output speed curve to minimize cam pressure angle and roller acceleration and maximize linkage mechanism drive angle. A Monte Carlo-based framework is put forward for the reliability and sensitivity analysis of kinematic accuracy. Finally, a transverse device of a sanitary product production line is provided to demonstrate the applicability of the proposed method. With the parameter optimization, the productivity of the transverse device is doubled, from 600 pieces per minute (PPM) to 1200 PPM.

Design and Verification of Crab Steering System for High Clearance Self-Propelled Sprayer

A crab steering system aiming at improving the steering flexibility and operation efficiency of the high clearance sprayer was designed. First, a steering transmission mechanism of the high clearance sprayer was designed according to the operational and structural characteristics of the sprayer. Meanwhile, a crab steering hydraulic system based on load sensing was designed, and a mathematical model of the steering transmission mechanism and hydraulic system was established to describe the working characteristics of the crab steering system. On the basis of analyzing the operating environment of the sprayer and the operating characteristics of crab steering mode, a control strategy and algorithm of the crab steering system were proposed. The simulation model of the crab steering control system was built according to the established mathematical model, and the simulation analysis of the crab steering system was carried out. The simulation results showed that under the excitation of step signal, the average deviation of the two front wheels is 0.063°, and the absolute value of the maximum deviation is 2.75°, which is within the allowable range of deviation and meets the crab steering demand of the sprayer. Additionally, in order to verify the effectiveness of the designed system, an actual vehicle test platform of the crab steering system was built based on the 3WPG-3000 high clearance self-propelled sprayer independently developed by the research group, and the field test results revealed that the average deviation of the four wheels was 0.285°, the maximum absolute deviation was 2.587°, the rotation deviation was small, within the allowable and reasonable range. Altogether, the results of the simulation and field test verify the accuracy, stability and practicability of the crab steering system, which effectively improved the maneuverability of the sprayer.

Active reconfiguration of cytoplasmic lipid droplets governs migration of nutrient-limited phytoplankton.

Nutrient availability, along with light and temperature, drives marine primary production. The ability to migrate vertically, a critical trait of motile phytoplankton, allows species to optimize nutrient uptake, storage, and growth. However, this traditional view discounts the possibility that migration in nutrient-limited waters may be actively modulated by the emergence of energy-storing organelles. Here, we report that bloom-forming raphidophytes harness energy-storing cytoplasmic lipid droplets (LDs) to biomechanically regulate vertical migration in nutrient-limited settings. LDs grow and translocate directionally within the cytoplasm, steering strain-specific shifts in the speed, trajectory, and stability of swimming cells. Nutrient reincorporation restores their swimming traits, mediated by an active reconfiguration of LD size and coordinates. A mathematical model of cell mechanics establishes the mechanistic coupling between intracellular changes and emergent migratory behavior. Amenable to the associated photophysiology, LD-governed behavioral shift highlights an exquisite microbial strategy toward niche expansion and resource optimization in nutrient-limited oceans.

Structural optimization of a pipe-climbing robot based on ANSYS

Abstract. In order to improve the structural performance of the out-of-pipe pipe-climbing robot, the out-of-pipe pipe-climbing robot is optimized. First, MATLAB software was used to optimize the structure and size of the robot according to the mathematical model of robot mechanics and size constraints. Then, SolidWorks software was used to establish a three-dimensional model of the robot which was then imported into ANSYS Workbench software. Static and modal analyses were then performed on key robot components under different working conditions and the topology optimization module in ANSYS Workbench was used to perform the topology optimization of the key components. Finally, the optimized components were statically analysed. By comparing the performance of the components before and after optimization, it was found the weights of the optimized frame and clamping arm were respectively reduced by 24 % and 20 %, and the maximum stress was respectively reduced by 46 % and 20 %. Ultimately, it was found that the stiffness and strength of the robot were improved and a lighter weight was achieved via optimization; thus, this work provides a reference for future research on pipe-climbing robots.

Quantitative mapping of force-pCa curves to whole-heart contraction and relaxation.

The force–pCa (F–pCa) curve is used to characterize steady‐state contractile properties of cardiac muscle cells in different physiological, pathological and pharmacological conditions. This provides a reduced preparation in which to isolate sarcomere mechanisms. However, it is unclear how changes in the F–pCa curve impact emergent whole‐heart mechanics quantitatively. We study the link between sarcomere and whole‐heart function using a multiscale mathematical model of rat biventricular mechanics that describes sarcomere, tissue, anatomy, preload and afterload properties quantitatively. We first map individual cell‐level changes in sarcomere‐regulating parameters to organ‐level changes in the left ventricular function described by pressure–volume loop characteristics (e.g. end‐diastolic and end‐systolic volumes, ejection fraction and isovolumetric relaxation time). We next map changes in the sarcomere‐regulating parameters to changes in the F–pCa curve. We demonstrate that a change in the F–pCa curve can be caused by multiple different changes in sarcomere properties. We demonstrate that changes in sarcomere properties cause non‐linear and, importantly, non‐monotonic changes in left ventricular function. As a result, a change in sarcomere properties yielding changes in the F–pCa curve that improve contractility does not guarantee an improvement in whole‐heart function. Likewise, a desired change in whole‐heart function (i.e. ejection fraction or relaxation time) is not caused by a unique shift in the F–pCa curve. Changes in the F–pCa curve alone cannot be used to predict the impact of a compound on whole‐heart function. Key points The force–pCa (F–pCa) curve is used to assess myofilament calcium sensitivity after pharmacological modulation and to infer pharmacological effects on whole‐heart function.We demonstrate that there is a non‐unique mapping from changes in F–pCa curves to changes in left ventricular (LV) function.The effect of changes in F–pCa on LV function depend on the state of the heart and could be different for different pathological conditions.Screening of compounds to impact whole‐heart function by F–pCa should be combined with active tension and calcium transient measurements to predict better how changes in muscle function will impact whole‐heart physiology.

Optimization design method of upper limb exoskeleton cam mechanism’s motion trajectory model

In order to solve the problem caused by the coupling clearance of the upper-limb cam mechanism, based on cam entity structure’s data and motion trajectory characteristics, with the cam axle acceleration αc and the output torque accuracy σT as the optimization targets, a mathematical model of cam mechanism is established in the study. Cam mechanisms was established with the radial basis function (RBF) method to restore the physical model of upper-limb exoskeleton’s motion trajectory model accurately. Then, global optimization was performed with adaptive non-dominated sorting genetic algorithm-II (NSGA-II) to get αc and σT s’ Pareto solution sets and form a data mapping cam mechanism with the dynamic feedback between the motion trajectory model and the entity model. In the verification experiments, the motion trajectory model established with only 37 response points only required a low amount of computation, and the response point verification error was within 3%, indicating the high restoration accuracy. After physical parameters were optimized with NSGA-II, the optimal pareto solution sets of dynamic characteristic parameters of the cam mechanism were obtained. αc and σT were respectively decreased by 52% and 81%. The deviation of αc between the entity model test data and simulation data was 3.84°/s2 and σT was 30.23 N·mm, indicating that cam motion deviation could be adjusted by dynamic data feedback. This study verifies that the dynamic characteristics of the cam mechanism can be optimized by optimizing the material parameters of the rollers, thereby improving the performance of the upper limb exoskeleton.

Efficient Model of the Interaction of Elastomeric Filler with an Open Shell and a Chrome-Plated Shaft in a Dry Friction Damper.

The results of a study of the contact interaction of an open shell and a chrome-plated shaft with elastomeric filler installed coaxially are presented. The considered contact system is a model of the original design of the shell damper of dry friction. The design feature is the following: the bearing link of the damper is a thin-walled cylindrical shell with a cut along the generatrix; the working body of the damper is elastomeric filler; a hollow chrome-plated shaft centers the damper elements and allows it to be used in technological processes with the presence of aggressive and abrasive-containing media. The mechanical-mathematical modeling of the behavior of the presented damper under the conditions of operational loads has been carried out. The idea of identifying the properties of a cut isotropic shell, which bends under the conditions of a nonaxisymmetric contact load, and a strongly orthotropic continuous shell is applied. As a result, dependences were obtained to determine the rigidity and the maximum allowable load of the damper. The effect of the coefficient of friction of the contact pairs elastomer-shell and elastomer-shaft on the damper performance properties has been studied. A technique for the quasi-static analysis of structural damping in non-mobile, non-conservative shell systems with deforming filler has been developed. The hysteresis loops of the damper under a nonmonotonic load are constructed, the dependence of the amount of dissipated energy on the cycle asymmetry coefficient is found. An analysis of the results obtained showed that the use of open shells in friction shock absorbers can significantly reduce their rigidity compared to solid shells and thereby reduce the resonant frequencies of the dynamic system. This circumstance makes such vibration isolators particularly attractive for use in superresonance vibrators as working modules of drilling shock absorbers and elastic hangers of sucker rods in oil and gas production.

Mathematical modeling and simulation of system operation: Power hacksaw

The primary objective of this article is to develop a mathematical model of a power hacksaw operation mechanism. A MATLAB code was developed and implemented to run the simulation of the mechanism. The paper presents a MATLAB code implementation of the system using rotary to reciprocating motion to develop a mathematical model of the power hacksaw in a MATLAB software. The theory of rotary to reciprocating motion has been effectively used as an efficient approach to analyze the power hacksaw system and acceleration of the blade for two to three revolutions of the power hacksaw machine.

Ultrahigh‐Resolution Optical Fiber Thermometer Based on Microcavity Opto‐Mechanical Oscillation

High‐resolution temperature measurement is nerve‐wracking obstruction for precise characterization of many physical, chemical, and biological processes. To solve this problem, a novel microcavity–optomechanical–oscillation‐based thermometer is proposed. The microcavity serving as a link parametrically couples the mechanical resonator and optical resonator in the same structure and provides a natural and highly sensitive temperature transduction mechanism and ultrahigh‐resolution optical demodulation. The mathematical model of geometrical parameters, mechanics, and material properties for temperature response mechanism is established and verified experimentally. The proposed thermometer has a thermal sensitivity of 11 300 Hz °C−1 and an ultrahigh‐temperature resolution of 1 × 10−4 °C, to the best of one's knowledge, which is the highest temperature resolution with a silica cavity.

A Closed-Loop Modeling Framework for Cardiac-to-Coronary Coupling.

The mechanisms by which cardiac mechanics effect coronary perfusion (cardiac-to-coronary coupling) remain incompletely understood. Several coronary models have been proposed to deepen our understanding of coronary hemodynamics, but possibilities for in-depth studies on cardiac-to-coronary coupling are limited as mechanical properties like myocardial stress and strain are most often neglected. To overcome this limitation, a mathematical model of coronary mechanics and hemodynamics was implemented in the previously published multi-scale CircAdapt model of the closed-loop cardiovascular system. The coronary model consisted of a relatively simple one-dimensional network of the major conduit arteries and veins as well as a lumped parameter model with three transmural layers for the microcirculation. Intramyocardial pressure was assumed to arise from transmission of ventricular cavity pressure into the myocardial wall as well as myocardial stiffness, based on global pump mechanics and local myofiber mechanics. Model-predicted waveforms of global epicardial flow velocity, as well as of intramyocardial flow and diameter were qualitatively and quantitatively compared with reported data. Versatility of the model was demonstrated in a case study of aortic valve stenosis. The reference simulation correctly described the phasic pattern of coronary flow velocity, arterial flow impediment, and intramyocardial differences in coronary flow and diameter. Predicted retrograde flow during early systole in aortic valve stenosis was in agreement with measurements obtained in patients. In conclusion, we presented a powerful multi-scale modeling framework that enables realistic simulation of coronary mechanics and hemodynamics. This modeling framework can be used as a research platform for in-depth studies of cardiac-to-coronary coupling, enabling study of the effect of abnormal myocardial tissue properties on coronary hemodynamics.

Discovering potential interactions between rare diseases and COVID-19 by combining mechanistic models of viral infection with statistical modeling.

Recent studies have demonstrated a relevant role of the host genetics in the coronavirus disease 2019 (COVID-19) prognosis. Most of the 7000 rare diseases described to date have a genetic component, typically highly penetrant. However, this vast spectrum of genetic variability remains yet unexplored with respect to possible interactions with COVID-19. Here, a mathematical mechanistic model of the COVID-19 molecular disease mechanism has been used to detect potential interactions between rare disease genes and the COVID-19 infection process and downstream consequences. Out of the 2518 disease genes analyzed, causative of 3854 rare diseases, a total of 254 genes have a direct effect on the COVID-19 molecular disease mechanism and 207 have an indirect effect revealed by a significant strong correlation. This remarkable potential of interaction occurs for >300 rare diseases. Mechanistic modeling of COVID-19 disease map has allowed a holistic systematic analysis of the potential interactions between the loss of function in known rare disease genes and the pathological consequences of COVID-19 infection. The results identify links between disease genes and COVID-19 hallmarks and demonstrate the usefulness of the proposed approach for future preventive measures in some rare diseases.

Mathematical Model of the Nuclear Fuel Refueling Mechanism of the BN-800 Reactor and Optimization of its operation

In connection with the burning of nuclear fuel in the reactors of nuclear power plants, the nuclear fuel refueling procedure is periodically carried out. Part of the spent fuel assemblies is removed to the spent fuel pool. Some of them are rearranged inside the reactor to other places, and instead of the unloaded fuel assemblies, fresh fuel assemblies are loaded into the vacated places. The problem under consideration can be considered as a route problem with specific restrictions Beltyukov (2013); Korobkin (2012). The goal of the optimization route problem is to minimize the time spent on reloading fuel assemblies. This is motivated by the fact that the reactor stops during the refueling period and the nuclear power plant incurs material losses. Due to the fact that the optimality criterion is the total operating time of the mechanism, it is necessary to learn how to find the time spent on an elementary operation - moving the grip from one position to another. Knowing the time spent on elementary operations, we can calculate the time spent on the rearrangement of fuel assemblies for a given order of fuel assemblies movement. This work is devoted to the time-optimal algorithm for performing an elementary operation - transferring a grip from one position to another. Knowledge of such an algorithm will make it possible to construct an objective function for the route problem of permutation of fuel assemblies.

Mathematical model of inflammation and neurodegeneration cellular mechanisms linking

Mathematical model of inflammation and neurodegeneration cellular mechanisms linking

Динамический расчет тандемного ротора гребных электродвигателей

The article presents the results of modeling the dynamic response of the tandem rotors of ice-class vessel electric propulsion motors under extreme operating conditions. The loading of rotors by torques in combination with vibration transmitted through the supports to the electric motors is considered as an external non-stationary action. A method for constructing a three-dimensional finite element model of the structure under study by fragmentary assembly has been developed on the basis of the ANSYS Mechanical software package. A scheme of elastic-compliant 3D-links allowing simulating the reciprocating-rotational vibrations of a tandem of rotors is presented. A test example is used to verify the proposed mechanical-mathematical model of the torsion system. Based on the calculated data, the analysis of the dynamic parameters of the tandem rotors is performed for the most unfavorable operating scenarios.

Distinct time courses and mechanics of right ventricular hypertrophy and diastolic stiffening in a male rat model of pulmonary arterial hypertension.

Although pulmonary arterial hypertension (PAH) leads to right ventricle (RV) hypertrophy and structural remodeling, the relative contributions of changes in myocardial geometric and mechanical properties to systolic and diastolic chamber dysfunction and their time courses remain unknown. Using measurements of RV hemodynamic and morphological changes over 10 wk in a male rat model of PAH and a mathematical model of RV mechanics, we discriminated the contributions of RV geometric remodeling and alterations of myocardial material properties to changes in systolic and diastolic chamber function. Significant and rapid RV hypertrophic wall thickening was sufficient to stabilize ejection fraction in response to increased pulmonary arterial pressure by week 4 without significant changes in systolic myofilament activation. After week 4, RV end-diastolic pressure increased significantly with no corresponding changes in end-diastolic volume. Significant RV diastolic chamber stiffening by week 5 was not explained by RV hypertrophy. Instead, model analysis showed that the increases in RV end-diastolic chamber stiffness were entirely attributable to increased resting myocardial material stiffness that was not associated with significant myocardial fibrosis or changes in myocardial collagen content or type. These findings suggest that whereas systolic volume in this model of RV pressure overload is stabilized by early RV hypertrophy, diastolic dilation is prevented by subsequent resting myocardial stiffening.NEW & NOTEWORTHY Using a novel combination of hemodynamic and morphological measurements over 10 wk in a male rat model of PAH and a mathematical model of RV mechanics, we found that compensated systolic function was almost entirely explained by RV hypertrophy, but subsequently altered RV end-diastolic mechanics were primarily explained by passive myocardial stiffening that was not associated with significant collagen extracellular matrix accumulation.

A Mathematical Model of COVID-19 with Vaccination and Treatment.

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures—vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R0(v) is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R0(v) > 1, even if vaccine coverage is high. Pontryagin's maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R0(v) > 1, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b, the vaccine efficacy ε, the vaccination rate v, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.

Kinetic Study on the Preparation of Aluminum Fluoride Based on Fluosilicic Acid

Abstract Reasonable mathematical derivation and mechanism model in the process of producing aluminum fluoride by fluosilicic acid is the key to the industrial treatment of fluorine resources in the tail gas of phosphate ore. In this work, aluminum fluoride was generated directly by fluosilicic acid to extract fluorine from the tail gas of phosphate rock. The uncreated-core model dominated by interfacial reaction and the uncreated-core model dominated by internal diffusion-reaction were then respectively utilized to describe the reaction kinetics of the generation of aluminum fluoride. The result showed that the uncreated-core model was dominated by interface reaction and internal diffusion, the apparent reaction order n = 1, and the activation energy Ea = 30.8632 kJ · mol–1. Product characterization and kinetic analysis were employed to deduce the reaction mechanism of preparing aluminum fluoride. The theoretical basis for the low-cost recycling of fluorine resources in the tail gas of industrial phosphate ore was provided in this work.

Improving the mechanical-mathematical model of pneumatic vibration centrifugal fractionation of grain materials based on their density

This paper has substantiated the mechanical-mathematical modeling of the process of fractionation of grain material into fractions. It has been established that this could optimize the process parameters and would make it possible to design new or improve existing working surfaces of centrifugal separators. A mechanical-mathematical model of the pneumatic vibratory centrifugal separation of grain material by density has been improved. This research is based on the method of hydrodynamics of multiphase media. The improved mechanical-mathematical model takes into consideration the interaction between the discrete and continuous phases of grain material by introducing conditions of interaction at the interface of these phases. In the hydrodynamic modeling of the movement of the circular layer of seeds, the coefficient of dynamic viscosity of discrete and continuous phases was taken into consideration. It was established that the pneumatic vibratory centrifugal separation process parameters are critically affected by the circular frequency of rotation of the cylindrical working surface, the frequency and amplitude of its oscillations. As well as such process characteristics as the airflow rate, dynamic viscosity coefficient, the average thickness of a grain material layer, and the mean density of its particles. Rational values for the technical parameters of the grain material pneumatic vibratory centrifugal fractionation process in terms of density have been determined by using the improved mechanical-mathematical model. The amplitude and oscillation frequency of the working surface are in the ranges A=(35…50)·10–5 m, ω=15.0...15.6 rad/s. The circular rotation frequency of the working surface, ω=24...25 rad/s. The airflow rate, V=2 m/s. It was established that using the improved mechanical-mathematical model of fractionation makes it possible to improve the performance of a pneumatic vibratory centrifugal separator by 9 %. At the same time, the effectiveness of grain material separation could reach 100 %.