Search

The research and development of flexible forming technology have a crucial role in the personalized production and manufacturing of three-dimensional (3D) surface sheet metal parts. Three-dimensional surface rolling with rigid arc-shaped rollers (TSRRAR), a new flexible forming technology, was investigated to effortlessly produce 3D surface parts. Numerical simulation and experimental analysis mainly include data at four values of the difference in axial radius of roller (−2, 2, 6 and 10 mm) to explore this technology’s forming ability. It was demonstrated that various shapes could be obtained only based on one group of rollers. The maximum resultant force decreased from 3.07 to 2.21 KN, and the required maximum compression rate from 4.22 to 2.48 % with the same longitudinal curvature radius (179 mm) to be obtained. Therefore, the forming difficulty can be reduced by selecting the difference in axial radius of roller.

One-in-five people suffer from chronic low back pain (LBP). The incidence of this disease has doubled since 1950s and affects not only the elderly, but also the young population. However, the mechanism of LBP is still unknown. A possible location where the LBP may develop is the facet joint and it has been revealed that the intervertebral disc (IVD) nucleotomy may be a trigger for LBP. The aim of the present study was to investigate the influence of IVD nucleotomy on the load sharing in the spinal facet joint under the loading scenarios of different postures. Finite element (FE) models of the intact and nucleotomised L4 – L5 spinal segments were generated from the clinical CT images. Seven human postures, including upright, 5° extension, 5° flexion, ± 6° lateral bending and ± 2° axial rotation, were simulated. The resultant forces in the fact joint were compared between the intact and the nucleotomised cases. It was revealed that the IVD nucleotomy significantly increased the forces in the facet joints under the loading scenarios of upright, 5° extension and 5° flexion. The IVD nucleotomy increased the force in the ipsilateral facet joint but decreased the force on the contralateral side under the loading scenarios of ± 2° axial rotation. However, the IVD nucleotomy made little influence on the resultant forces in both facet joints in the postures of ± 6° lateral bending. In conclusion, the IVD nucleotomy can cause an increase in the overall force in the facet joint, and thus may serve as a possible explanation for the LBP and a main contributing factor for the pain complaints.

In this paper, an improved bidirectional RRT ∗ vehicle path planning method for smart vehicle is proposed. In this method, the resultant force of the artificial potential field is used to determine the search direction to improve the search efficiency. Different kinds of constraints are considered in the method, including the vehicle constraints and the vehicle driving environment constraints. The collision detection based on separating axis theorem is used to detect the collision between the vehicle and the obstacles to improve the planning efficiency. The cubic B-spline curve is used to optimize the path to make the path’s curvature continuous. Both simulation and experiment are implemented to verify the proposed improved bidirectional RRT ∗ method. In the simulation analysis, this paper’s method can generate the smoothest path and takes the shortest time compared with the other two methods and it can be adaptive to the complicated environment. In the real vehicle experiment, we can see from the test results that this paper’s method can be applied in practice on the smart electric vehicle platform; compared with others’ algorithm, this paper’s algorithm can generate shortest and smoothest path.

PURPOSE Glenohumeral instability accounts for 23% of all shoulder injuries among collegiate athletes. The apprehension position-combined shoulder abduction and external rotation-commonly reproduces symptoms in athletes with instability. Rehabilitation aims to increase glenohumeral stability by strengthening functional positions. However, it is unclear how much glenohumeral stability increases with muscle contraction in the apprehension position. The purpose of this study was to determine whether the ability to increase translational glenohumeral stiffness, a quantitative measure of glenohumeral stability, with muscle contraction is reduced in the apprehension position. METHODS Seventeen asymptomatic adults participated. A precision-instrumented robotic system applied pseudorandom, anterior-posterior displacements to translate the humeral head within the glenoid fossa and measured the resultant forces as participants produced isometric shoulder torques. Measurements were made in neutral abduction (90° abduction/0° external rotation) and apprehension (90° abduction/90° external rotation) positions. Glenohumeral stiffness was estimated from the relationship between applied displacements and resultant forces. The ability to increase glenohumeral stiffness with increasing torque magnitude was compared between positions. RESULTS On average, participants increased glenohumeral stiffness from passive levels by 91% in the neutral abduction position and only 64% in the apprehension position while producing 10% of maximum torque production. The biggest decrease in the ability to modulate glenohumeral stiffness in the apprehension position was observed for torques generated in abduction (49% lower, P < 0.001) and horizontal abduction (25% lower, P < 0.001). CONCLUSION Our results demonstrate that individuals are less able to increase glenohumeral stiffness with muscle contraction in the apprehension position compared with a neutral shoulder position. These results may help explain why individuals with shoulder instability more frequently experience symptoms in the apprehension position compared with neutral shoulder positions.

In order to analyze the influence position of prestressed reinforcement on the cracking load of composite girders, scale test and finite element analysis is used to study the cracking behavior of prestressed composite beam at the negative moment zone. The load–deflection curve and the cracking law of the scaled beam are obtained from the experimental results. The influence law of the resultant point and the spacing change through the symmetrical axis of the prestressed beam on the cracking load is obtained through the finite element parametric analysis. Furthermore, the prototype beam's mechanical performance in terms of the scaled test data is verified by both similarity theory and the prototype beam's numerical model. The results show that: Under different prestress levels, the cracking load is larger when the resultant force point of prestressed reinforcement on one side of the concrete slab's symmetric axis is within 0.15 ~ 0.50 times of slab half-width. In addition, the cracking moment of the specimen can be increased up to 11% by optimizing the prestress arrangement.

In the past few years, pit-in-pit excavations have become common to maximize urban underground space. Estimating passive earth pressure is a critical prerequisite to using them. However, Rankine an...

To reveal the internal unsteady flow state of the guide vane centrifugal pump, in this paper, the standard SST k‐ω turbulent flow model is used for unsteady numerical simulation of the centrifugal pump. The characteristics of the flow field inside the centrifugal pump are analyzed, the resultant force and vector distribution of the radial force of the guide vane and impeller of the centrifugal pump under different flow rates are obtained, which were verified by experiments. The results show that the main reason of radial force of the impeller is the pressure asymmetry in each flow passage. The radial force will show periodic fluctuations due to the rotor-stator interference between the impeller and the guide vanes under different flow rates. The radial force on the impeller decreases gradually with the increase of the flow, the distribution is hexagonal or hexagonal shape, and the number of impeller blades is the same. The results can provide reference for the design of impeller and guide vane of centrifugal pump.

Owing to their inferior hot hardness in comparison with alumina-based ceramics and polycrystalline cubic boron nitride, the performance of coated carbide tools when turning hardened steels strongly relies on proper chemical composition and carbide grain size, together with adequate cutting edge preparation. This work investigates the effect of geometric parameters on the performance of cutting tools applied to turning of AISI 4140 steel hardened to 40 and 50 HRC, in terms of the components of the turning force and temperature. Additionally to well-established geometric parameters, such as the projection of the hone radius on the rake face (Sγ), the projection of the hone radius on the clearance face (Sα), and the form factor K (ratio of Sγ to Sα), a novel parameter is proposed, namely perimeter ratio (P), which represents the ratio of the perimeter of the modified cutting edge to the circumference of the standard honed edge. Moreover, the experimental results were compared with analytical and numerical findings in order to assess their effectiveness in predicting the components of the turning force and chip temperature. The results indicated that analytical modeling was capable to satisfactorily predict the variation of the force components with edge preparation, using as input the value of the corresponding experimental forces for the standard honed cutting edge. On the other hand, the numerical modeling was successfully applied to predict the components of the resultant force at the expense of higher computational effort. The cutting force was not drastically affected by edge preparation, whereas the feed and passive forces increased with P and Sα and the form factor K was not capable to provide a consistent relationship with both the feed and passive forces. Both the experimental and numerical temperatures of the chip and the numerical temperature at the tool-chip interface did not present a straightforward trend with regard to edge preparation.

Simulation models are increasingly used lately to analyze machining conditions during process design. The knowledge of resultant cutting forces along the tool trajectory provides essential information in order to optimize the tool path layout. An analytical cutting force model implemented in a process simulation environment allows to predict resultant forces along a complete NC tool path without the need for extensive testing and parameter identification beforehand. Instead, tool geometry, cutting parameters, material data and friction parameters are the only input parameters needed. The model is presented and simulation and experimental results for different tool trajectories are compared against each other.

This work presents and discusses a method for evaluating a dynamic eddy-current damping (ECD) force that is automatically generated in response to eddy currents induced within a conductive plate while moving across a magnetic field in relative motion to a nearby stationary magnet. In the experiment, a Doppler shift frequency signal between the optical interference fringe frequencies was used to calculate the velocity of the moving conductive plate. The other relevant mechanical quantities acting on the plate, such as the displacement, acceleration, and resultant force, were then evaluated by performing numerical calculations of the velocity. Finally, the evaluation of the ECD force could be achieved by performing a calculation to remove the frictional force component from the resultant force. Furthermore, an approximation analysis used to calculate the value of the ECD force was proposed and compared with the measured value as well. From the experimental results, the combined standard uncertainty for evaluating the ECD force was approximately 3.57 mN, corresponding to 3.13% of the maximum eddy-current force of approximately 114.0 mN.

Objective: The objective of this systematic review was to assess the available evidence to evaluate the effectiveness of en-masse retraction design with mini-screw with respect to the retraction hook and mini-implant position and height. Methods: The following electronic databases were searched till July 31, 2020: Pro-Quest Dissertation Abstracts and Thesis database Cochrane Central Register of Controlled Trials (CENTRAL), PubMed, Google Scholar, US National Library of Medicine, and National Research Register. En-masse retractions with anterior retraction hooks assisted by mini-implant three-dimensional finite element method (3D FEM) models were included in the study. The selected studies were assessed for the risk of bias using the Cochrane Collaboration risk of bias tool. The “traffic plot” and “weighted plot” risk of bias distribution were designed using the ROBVIS tool. The authors extracted and analyzed the data. Results: Twelve studies fulfilled the inclusion criteria. The risks of biases were low for 9 studies and high for 3 studies. Data on mini-implant, retraction hook, and the center of resistance/force vectors were extracted. The outcomes of the included studies were heterogeneous. Conclusions: According to the currently available literature review for successful bodily en-masse tooth movement, the force vector should pass through the center of resistance, which can be achieved by the clinical judgment of placing a mini-screw and an anterior retraction hook. The force from an implant placed at a higher level from the anterior retraction hook will cause intrusion; an implant placed at the medium level shows bodily movement; and an implant placed at a lower level shows tipping forces in consolidated arches.

Tool wear is an important criterion for economic machining. It does not only determine the tool life, but also affects the surface layer properties of metallic components and thus their performance. In addition to the machining parameters, there are numerous other influencing factors like batch variations, workpiece inhomogeneities, process vibrations, or the formation of built-up edges that can impact the wear progression. Consequently, it is difficult to predict the tool wear analytically. Therefore, the determination of the tool condition during machining is of great importance. The tool-workpiece thermocouple enables the in-process measurement of a thermoelectric voltage and current during machining generated by the Seebeck effect at the interface between two electrically conductive materials. Thus, the thermoelectric signals are sensitive for the changing contact interface between the tool and the specimen. To allow for an in-process characterization of the tool wear, finding an empirical relationship between the flank wear land width of cemented carbide indexable inserts and the thermoelectric signals in turning is aspired. To vary the flank wear land width in a reproducible manner, tools with a flank face chamfer resulting in a clearance angle of 0° and five different flank face land widths (80 µm – 280 µm) are used. These geometrical properties are measured with a 3D laser scanning microscope. Afterwards, cylindrical specimens of the aluminum alloy EN AW-2017 are machined by turning applying the modified tools and cutting speeds in the range of 300 m/min to 550 m/min. The depth of cut (0.4 mm) and the feed (0.04 mm) are kept constant. Besides the tool-workpiece thermocouple, the components of the resultant force are measured by a dynamometer. The geometrical properties of the machined surfaces are characterized using a stylus measurement instrument. The experimental investigations show an increase of the temperature and the components of the resultant forces with increasing flank wear land width, which impacts the geometrical properties of the surface. An empirical regression model derived from the in-process measurement results depicts the relationship between the thermoelectric signals, the force components, and the changing area of the tool which is in contact with the specimen. Consequently, the combined in-process measurement of the process forces and thermoelectric signals allows for an in-process determination of the tool wear progression and therefore enables the prevention of a strong impairment of the surface-layer properties by a timely tool change or a controlled adjustment of the machining parameters.

A linear actuator controlled by the reversed-phase connection of two piezoelectric bimorphs is proposed in this study to solve the problem of drawback in the existing piezoelectric linear actuators. The actuator is driven by one excitation signal, the two piezoelectric bimorphs will always bend in opposite directions by the reversed-phase connection, so the directions of the force output by the two piezoelectric bimorphs are opposite. Because of the length difference of the clamping blocks, the two forces outputted by each bending is different in magnitude, and always have a resultant force in the same direction to make the actuator move forward two steps in one cycle without drawback. A series of experiments were conducted to evaluate the performance of the actuator provided. The starting voltage is 40 $\text{V}_{\mathrm {p-p}}$ , resolution can reach $1.16~\mu \text{m}$ without load. The load capacity of the actuator is 450 g with a 100 $\text{V}_{\mathrm {p-p}}$ voltage, a 2-Hz frequency, and the average step displacement in this case is $0.725~\mu \text{m}$ . The prototype has high linearity and good repeatability. Experiments have proved that the actuator controlled by reversed-phase connection can eliminate drawback in principle, and can move forward two steps in one cycle. The resolution of the prototype by the reversed-phase connection is much higher than the in-phase connection, and it is a new method to improve the driving performance of piezoelectric actuators.

The article deals with the effectiveness of Head-to-tail method for addition vectors. The empirical investigations were carried out at a specialized school. In the research, the number of respondents was 24. As a part of the experiments, it was conducted questionnaires among them and they were given pre-test and post-test, which consists of 12 questions. Statistical analysis was performed using SPSS software. A paired t-test was carried out on pre-test and post-test to determine the possible difference between them. According to the statistically analysed data, it was established that by using Head-to-tail method, students could understand and solve more complicated test task regarding the motion of an object under the many forces. It was concluded that this method could be the best way of solving the most challenging issues related to one or two-dimensional motion and it makes a significant contribution to the more in-depth adoption of the students' understanding of finding the direction of resultant force for numerous forces vectors.

A three wedge failure mechanism is proposed to determine active earth pressure exerted by narrow backfills on gravity retaining walls and its point of application. Gravity retaining wall proportions are optimized against external failure modes using proposed active earth pressure and its line of action of resultant thrust. Overturning failure, eccentricity failure of the resultant force, sliding failure on its base, and bearing capacity failure are given due consideration for the determination of optimum proportions of gravity wall. Optimum dimensions of the gravity wall are evaluated such that factors of safety against overturning, eccentricity, sliding, and bearing capacity should be greater than 2.0, 1.0, 1.5, and 2.5 respectively. Significant reduction in active earth pressure in narrow backfill width gravity retaining walls is noticed due to the inadequate development of shear bands because of the constraint of rock face boundary. The study recommends employing an appropriate failure mechanism for the development of shear bands behind retaining wall based on depth and width of narrow backfill. The proposed study indicates that significant savings in the cross sectional area may be accomplished as compared to a classical design by Coulomb’s theory.

The various mode of stresses for the interaction between two inclined cracks in the upper part of bonded two half planes which are normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress was studied. For this problem, the modified complex potentials (MCPs) method was used to develop the new system of hypersingular integral equations (HSIEs) by applying the conditions for continuity of resultant force and displacement functions with the unknown variable of crack opening displacement (COD) function and the right hand terms are the tractions along the crack. The curve length coordinate method and Gauss quadrature rules were used to solve numerically the obtained HSIEs to compute the stress intensity factors (SIFs) in order to determine the strength of the materials containing cracks. Numerical solutions presented the characteristic of nondimensional SIFs at the cracks tips. It is obtained that the various stresses and the elastic constants ratio are influences to the value of nondimensional SIFs at the crack tips.

Bone-anchored attachment of amputation limb prostheses is increasingly becoming a clinically accepted alternative to conventional socket suspension. The direct transfer of loads demands that the percutaneous implant system and the residual bone withstand all forces and moments transferred from the prosthesis. This study presents load measurements recorded at the bone-anchored attachment in 20 individuals with unilateral transfemoral amputation performing the everyday ambulatory activities: level ground walking, stairs ascent/descent and slope ascent/descent. Mean peak values for the sample populations across activities ranged from 498–684 N for the resultant force, 26.5–39.8 Nm for the bending moment, and 3.1–5.5 Nm for the longitudinal moment. Significant differences with respect to level walking were found for the resultant force during stairs ascent, (higher, p = 0.002), and stairs descent, (lower, p = 0.005). Using a crutch reduced the peak resultant forces and the peak bending moments with averages ranging from 5.5–12.6 % and 13.2–15.6 %, respectively. Large inter-participant variations were observed and no single activity resulted in consistently higher loading of the bone-anchored attachment across the participants. Results from this study can guide future development of percutaneous osseointegrated implant systems for limb prostheses and their rehabilitation protocols.

The thermally insulated inclined or circular arc cracks problems subjected to axial stress in the upper part of bonded two half planes are considered. The modified complex potential function method with the continuity conditions of the resultant force, displacement, and heat conduction functions is used to develop the new system of hypersingular integral equations (HSIEs) for the problems. The new system of HSIEs is solved numerically for the unknown crack opening displacement function and the known traction along the crack as the right-hand term using the appropriate quadrature formulas. Numerical results for the nondimensional stress intensity factors (SIFs) at all cracks tips are presented. A comparison between the nondimensional SIFs for cracks with and without thermal influence is also given

In light of the limit equilibrium conditions of soil mass retained by rigid retaining walls with distanced strip surcharge on its top surface, a variational calculus method is provided to calculate the passive earth pressure on the wall. By establishing the functional relationship between the earth pressure and potential slip surface as well as normal stress on it under a specified action point of the resultant force of the earth pressure, a unified closed-form solution to the passive earth pressure is derived and preformed easily by an implicit solution tactic via Matlab. It can quantitatively exhibit the influences of fundamental parameters on the force and corresponding critical slip surface including the soil properties, soil-wall interface friction angle, dip angle of the wall back, dip angle of the top surface of the retained soil, strip surcharge, net distance from the wall back to the surcharge, distribution width of the surcharge, and so on. These parameters except for unit weight, cohesion of soil and strip surcharge have nonlinear influence on the value of the passive earth pressure. Analysis results of some examples indicate the passive earth pressure by the proposed method is usually less than that by traditional limit equilibrium methods, and equal to the Coulomb's solution under certain conditions.

Further analysis of limit rolling conditions in a stable mode with clarification of the mechanism of longitudinal stability of the strip in the rolls and development of recommendations on this issue. Estimation of longitudinal stability of the strip based on the determination of the average resulting internal longitudinal forces. The use of a new limit condition for a stable rolling process, based on the determination of the average resultant force of plastically deformed metal, is developed and substantiated. For the first time, the criterion for optimization of the tension regimes for the construction of energy-saving rolling technology was proposed to use the values of the average resultant longitudinal forces of plastically deformable of the strip, which allowed proving the feasibility of conducting the process at close to zero values of this force. Using the proposed criteria can more accurately determine the limit conditions of rolling, which in turn allows further improve compression and tension modes for continuous production of strips and sheets on the conditions under which the deformation process will proceed in optimum conditions in terms of energy and longitudinal stability strips and sheets in rolls.

The paper presents results of numerical simulations of the stress distribution and deformations within of foundations of huge monument of Christ The King erected in Świebodzin (Poland) in 2010. It is 3 meters taller than the better known statue of Christ the Redeemer in Rio de Janeiro, standing at 30.1 meters tall without its pedestal. Foundations were built as a system of reinforced concrete columns and slabs which can be classified as a spatial column-slab system. Actual mechanical parameters of the substrate and of the artificial mound made of field stones, sand, gravel and clay were adopted in calculations. The numerical simulations of structural members of foundation and determination of the stress distribution are presented in the article. Monument itself was not included into the model. Instead of it the rigid cantilever was introduced to which resultant forces were applied. Three different stages were distinguished: the initial state after foundation and mound accomplishment, the initial state plus the dead load and the initial state plus the dead load and the wind load. It was assumed that the wind load was taken into account in a quasi-static formulation by applying the equivalent horizontal force and the torque. Stresses and displacements for these three stages were determined by Finite Element Method using Simulia ABAQUS system. It was disclosed what was a contribution of particular parts of foundations in sustaining loads in considered load cases. The state of exertion of structural members of foundations and the soil itself was assessed. It was showed that the column-slab foundations and soils of the mound play important role in taking loads of the statue, spreading them and safe transferring to the undisturbed level of natural soils. According to the numerical simulations results the columns of foundation take as much as 64% of the vertical load (in the most unfavourable load conditions). At the same time soils of the mound take through the side surface of piles about 20 % of the vertical load.

Background The differences in anatomical structure between men and women are widely known. Unfortunately, the influence of gender on the biomechanics of a healthy knee joint during gait is still poorly understood. Research question The aim of the presented study was to determine loads acting in the knee joint during gait, based on the observation of a large group of healthy young adults, in particular to determine the influence of gender on values of forces and moments and their time characteristics during gait cycle. Methods Time-spatial gait parameters and ground reaction force were registered for 86 persons (43 females and 43 males) using a motion capture system and force plates. The numerical simulation with the AnyBody system was used to estimate loadings acting in the knee joint. Differences between women and men were tested using the unpaired Student's t-test with a Bonferroni correction. Results The maximum values of loadings acting in the knee joint were: 411.1 %BW (body weight) for resultant force, 390.6 %BW for proximo-distal force, 110.8 %BW for antero-posterior force, 77.0 %BW for medio-lateral force, 2.63 %BWh (body weight times height) for flexion/extension moment, 0.97 %BWh for internal/external rotation moment and 5.7 %BWh for abduction/adduction moment. In general, the normalised forces were greater in the male group, while the normalised external moments acting on the knee were greater in the female group. Local extrema of forces during the stance phase were observed earlier for women. Significance Knowledge about gender differences in loadings acting in the knee joint can be of great importance in the case of detecting the early stages of gait abnormalities and treatment planning.

Philosophers have disagreed on the composition of force for decades. The main divergence concerns the fundamental question: given a certain motion that is observable, which force or forces are present in it, component or resultant forces? The present paper focuses on the conditions for dealing with this problem. I will argue that we are not able to infer force from the observation of a motion, as required by the problem. I will further argue that the validity of the Newtonian algorithm is not a sufficient condition for that inference because the Gaussian algorithm, which is equally valid, differs from the former with regard to the forces present in motions. Under these circumstances, I will make recourse to an experiment available in physics in which the force present in a motion is measured. Thus, we obtain a numerical value for this force. This result, playing the role of a counterexample, clarifies the composition of force issue significantly.

The traditional Hertz contact theory has been widely used in solving contact problems. However, it is only applicable to the elastic contact, and cannot truly reflect the contact stress distribution and contact radius in the elasto-plastic contact. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elasto-plastic contact between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, and the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elasto-plastic contact can be solved. Finally, an elasto-plastic contact example of two spheres is given based on the power-law hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between the numerical results by finite element method and the predicted ones by the proposed method. It is shown that the proposed method can accurately calculate the maximum contact stress and contact radius in the elasto-plastic contact, and the relative errors of both maximum contact stress and contact radius are within $$\pm \,5{\%}$$ . To sum up, the proposed fast solving method can be applied to perform the elasto-plastic contact analysis in engineering practice.

Knowledge of the nature and behavior of forces acting on an arc is important when designing furnaces, controlling and automating their work. The effect of electromagnetic arc blowing has a negative effect on technical and economic indicators of the furnace, since the arc is removed from dimples in metal and slag. Radiation of the arc on walls and arch increases. And the effective power absorbed by the metal decreases. For this and a number of other tasks, it is necessary to know the dynamic behavior of the arc, which is largely determined by the instantaneous values and directions of the individual forces and the resultant force. The paper discusses the behavior of an electromagnetic force acting on an arc column from currents flowing through a liquid metal and currents flowing through other parallel arcs and graphitized electrodes in a three-phase AC arc furnace. It was assumed that the arcs burn perpendicular to the surface of the metal bath (their axes coincide with the axes of the electrodes) and effective value of the linear currents in different phases is the same. A mathematical model is proposed for calculating the instantaneous values and directions of the main electromagnetic forces acting on arcs in a three-phase arc furnace, allowing to reveal the nature of arcs dynamic behavior. A computer program has been created that makes it possible to visualize the behavior of a hodograph of forces acting on an arc. Hodographs of forces acting on the arc from the currents flowing through the melt are shown; they are ellipses lying in a horizontal plane. The resulting force deflecting an arc is also an even harmonic function with a frequency twice as high as the industrial frequency of the current. Its hodograph is an ellipse lying in a horizontal plane, the big semi-axis of which makes an angle of 20 – 80° with a line connecting the center of decay of the electrodes and the electrode axis.

Research on cutting force revealed that the cutting force decreases as cutting speed increases, which is in line with Salomon’s Theory. However, the fundamental behaviour was never clearly explained because most studies had focused on increasing the cutting speed by increasing spindle speed without retaining the rate of chip load. On that note, the effect of increasing spindle speed while chip load is constant on the cutting force of Hastelloy X is presented in this paper. Third Wave AdvantEdge software was applied and half-immersion up-milling simulations were conducted in dry condition. Result showed that the resultant force was primarily affected by the axial force, followed by normal force and feed force. Trend-lines indicated that the behaviour of cutting force components and resultant force was quadratic. Desirability Function Analysis (DFA) results revealed that the optimum combination of chip load and spindle speed led to lowest cutting force components and resultant force was at 0.013 mm/tooth and 24,100 RPM. Furthermore, the optimum cutting conditions that led to the lowest cutting force components and resultant force at chip loads of 0.016 mm/tooth and 0.019 mm/tooth was 24,100 RPM also. Therefore, increasing Material Removal Rate (MRR) while minimizing cutting force components and resultant force can be achieved by increasing the amount of chip load at spindle speed of 24,100 RPM.

The deceleration of a viscoelastic cylinder rolling with slipping on a viscoelastic half-space of the same material without driving forces and torques is studied. The interaction of the cylinder and the half-space is described from the solution of the 2D quasistatic contact problem of viscoelasticity (Goryacheva in J Appl Math Mech 37(5):877–885, 1973, Contact mechanics in tribology, Kluwer, Dordrecht, 1998). This solution states that the contact region consists of the slip and stick zones, and it is shifted forward in the direction of motion. Contact normal and shear stresses and, therefore, the resultant force and torque depend on the values of the linear velocity of the cylinder and creep ratio, as well as the mechanical properties of contacting bodies and sliding friction coefficient. The Cauchy problem for dynamical equations of the cylinder’s deceleration was solved numerically. The analysis of the deceleration process and changes in the contact normal and shear stress distributions in time for various initial conditions is presented.

At present, the most common tools for drilling operations are those rock-destroying ones that are equipped with cutting elements made from polycrystalline diamonds (PDC) and diamond carbide inserts (DCI). Given this, it is a relevant task to study the influence of the degree of wear of cutting elements on the strength and energy parameters of the process of rock destruction. In order to determine this influence, we have experimentally investigated the cutting process involving a single cutter under laboratory conditions. The mean values of the cutting force components (circular ((Рz) and normal (Рy)) have been established at the cutting depth 0.5; 1.0; 1.5; and 2.0mm, at a varying degree of the cutting element wear (a flat of 0; 5.0; and 8.0mm). We have determined the magnitude of cutting work and the specific energy of rock destruction. At a cutting depth of 0.5mm, with an increase in the cutting element wear rate from 0 to 8mm, the magnitude of work grows from 0.06376 to 0.121 N∙m. At a cutting depth of 2.0mm, the magnitude of work increases from 0.624 to 3.603 N∙m. The energy intensity of the rock destruction process increases, with an increase in the cutting depth from 0.5 to 2.0mm, from 3.88kJ/m2to 11.66kJ/m2for a sharp cutter. Based on the study results, we have built dependence charts of the average values of the cutting force components and its normal component (Рy) on cutting depth and the cutting element wear degree. The results obtained have shown a significant influence of the size of the wear flat on the increase in the process strength parameters, which is the basis for regulating a wear degree of cutting elements during drilling. We have established the tendency towards a growth in the resultant force and specific work of rock cutting by a cutting element with an increase in wear degree. This makes it possible to determine, based on the indicators of fluctuations in the instantaneous strength values during drilling of wells, or based on a change in power, the wear degree of the cutting elements, and to predict the probability of their destruction