Equivalent Deformation Research Articles

Structural strength analysis of a rotary drum mower during harvesting

A Rotary Drum Mower (RDM) is a tractor-mounted mechanism used for harvesting green fodder crops. It faces dynamic forces from rough field surfaces and cutting resistance, posing design challenges and potential failures. This study aims to present a well-designed procedure for analysing the structural strength of an RDM during harvesting, employing both experimental and engineering simulation methods. A specific harvesting scenario was created to simulate realistic load conditions. Experimental testing and advanced computer-aided engineering (CAE) simulations were conducted. Tractor Power Take-off (PTO) torque measurements during harvesting revealed values of 231.07 Nm, 264.44 Nm, and 269.39 Nm at speeds of 8.56 km h-1, 12.6 km h-1, and 16.23 km h-1, respectively. Finite element analysis (FEA) was conducted to determine stress levels in the RDM components (RDM165-A-004, RDM165-B-003, and RDM165-B-004). The FEA stress results ranged from 5.070 MPa to 20.600 MPa, 13.800 MPa to 28.600 MPa, and 5.400 MPa to 27.550 MPa, respectively. Experimental testing yielded stress results ranging from 2.127 MPa to 18.600 MPa, 14.618 MPa to 33.229 MPa, and 8.838 MPa to 31.248 MPa, respectively. The comparison between experimental and FEA results showed reasonable correlation. FEA visual outputs provided insights into the maximum equivalent stress and deformation distributions on the RDM, with no indications of failure in the machine's structure observed in either the experimental or numerical analyses. In conclusion, this study demonstrates that the machine analysed operates safely under harvesting conditions. Moreover, the combination of experimental and advanced CAE methodologies presented in this research offers a valuable approach for future investigations into the complex stress and deformation evaluations of rotary drum mowers.

Modelling analysis and optimisation of porous structural scaffolds for human bones

Two different types of unit structure models, ortho tetrahedral and hexahedral, are established, and a series of different porosities are obtained by controlling the parameters such as rod diameter and rod length, and the porous structure can be obtained by stacking the unit structure in an orderly manner in the three-dimensional space, and then finite element simulation and analysis are carried out by simulating compression experiments using Ansys to obtain the equivalent stresses, deformation maps and data, and the elastic modulus, which is close to that of the human hip bone, is calculated to investigate the mechanical properties under different porous structures and different porosities. The modulus of elasticity was calculated to be close to that of the human hip bone, and the mechanical properties were investigated under different porous structures and different porosities. The Fluent module is also used to simulate the fluid field, and the pressure and velocity maps of the fluid inside the two porous structures are obtained for comparative and comprehensive analyses. From the simulation of the created porous model, it is learnt that, for the same structure, with the increase of porosity, the equivalent force and deformation increase and the elastic modulus decreases significantly; for the same porosity, under the same loading environment, the longitudinal deformation of the hexahedron is smaller than that of the tetrahedron, its equivalent force is much lower than that of the tetrahedron, and it has suitable elastic modulus. Its strength is higher than that of the tetrahedron when under pressure. When the fluid flows in the hexahedron, the hexahedral structure is less compressed than the ortho tetrahedral structure, and the flow rate is more suitable for the blood flow rate in the human body.

ЧИСЛОВЕ МОДЕЛЮВАННЯ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ПРИ АДИТИВНОМУ MIG НАПЛАВЛЕННІ КРЕМНІЄВОЮ БРОНЗОЮ CuSi3Mn1

The article analyzes in detail the stress-strain state during additive manufacturing using silicon bronze CuSi3Mn1 (БрКМц3-1), which is widely used in the machine-building industry for the manufacture of bushings, spring parts, and parts of chemical apparatus. The high cost of non-ferrous copper-based alloys makes it important to use Welding Arc Additive Manufacturing (WAAM) technologies. The processes of layer-by-layer surfacing of silicon bronzes lead to residual stresses at the tensile strength of the material, which can eventually provoke the development of critical defects in the form of cracks. Based on the simultaneous solution of the finite element method for the equations of heat balance and mechanics of a solid deformed body, the peculiarities of temperature distribution and parameters of the stress-strain state for the developed model of a triangular equilateral prism, which is additively generated from CuSi3Mn1 bronze, are determined. Verification of the experimental model with the calculated one was carried out by comparing the thermal cycles of surfacing. Based on the anal-ysis of the results of numerical modeling, it was found that the nature of the temperature change and the magnitude of its decrease in the corresponding layer after the deposition of subsequent layers are the same and do not depend on the deposition trajectory, and the largest residual equivalent plastic deformations are formed in the first layer with a gradual decrease inthe value in each subsequent deposited layer, which is associated with a decrease in the degree of volume of the VAT prism from the 1st to the 10th layer. The lower layers are characterized by a volumetric stress state due to the presence of rigid binders in the form of the substrate and the upper welded layers, which increases the probability of cracking in these layers during the cooling stage due to a decrease in the material's strength below σB< 170 MPa in the temperature range of 475-550 °C

SUBSTANTIATION OF THE ROAD CONSTRUCTION UNBOUND MATERIALS CALCULATION MODEL WITH GEOGRIDS STABILIZATION

Summary. Based on the results of experimental studies conducted on different types of flexible pavement structures, the authors of the article examined the behavior of unbound material reinforced with geogrid. A series of static plate load tests were carried out, and the deformation modulus values of traditional and reinforced pavement structures were determined. The impact of the geogrid, installed at the base of the unbound layer of the pavement structure, on its deformation modulus was investigated. It was found that the use of geogrids significantly increases the equivalent deformation modulus of the pavement, depending on the thickness of the inert material layer and the deformation characteristics of the subgrade soil. The effectiveness of the reinforcement depends on the ratio of the deformation characteristics of the pavement and the subgrade soil, as well as the relative depth of the geogrid installation. The greatest effect is achieved on weak soils under large deformations. The results obtained are significant for further research and practical application of pavement reinforcement technology using geosynthetic materials. Keywords: highway, pavement structure, biaxially oriented geogrid, geosynthetic reinforcement, plate load tests, deformation characteristics, loading, reinforcement coefficient, field experiment

A Novel Deformation Analytical Solution and Constitutive Model for Fractured Rock Masses

In order to study the deformation and stability of a fractured rock mass, existing research suggests that fracture deformation, which is usually obtained by evaluating the equivalent deformation modulus, dominates the deformation of a fractured rock mass. However, this parameter is difficult to obtain in theory and practice, which limits the application of rock mass deformation analysis methods. In order to calculate the deformation of fractured rock masses, the mass of the rock is regarded as a sponge-like material, and it is assumed that the deformation of a water-saturated fractured rock mass under external force load is approximately equal to the net flow of fracture water. Based on this assumption, firstly, the relationship between rock mass deformation and fracture flow is studied through a single-fracture rock mass model. The hydraulic properties of the fracture are characterized by the permeability coefficient, and the fracture deformation in the rock mass is equivalent to the fracture flow. The fracture deformation calculation formula is derived from the fracture hydraulics calculation formula, and this is compared with the measured data. The rationality of the calculation formula was verified. On this basis, the calculation formula for rock mass deformation, including multiple groups of fracture surfaces, is proposed, and the stress-strain constitutive relationship of a complex rock mass is established. The correctness of the calculation method was verified by comparing it with other theoretical calculation results.

Pengaruh Variasi Stuktur Rangka Terhadap Kekuatan Pembebanan Pada Stasiun Pengisian Daya Listrik dengan Panel Surya

The use of solar panels in electric power charging stations is becoming increasingly popular as part of efforts to adopt renewable energy sources. In this context, the structural framework supporting the solar panels plays a crucial role in maintaining the stability and reliability of the system. Therefore, this thesis aims to investigate the influence of various structural framework variations on the strength of static loading in solar-powered electric charging stations. The research methodology employed simulation of static loading at three different load levels, namely 40 kg, 50 kg, and 60 kg. The analysis was conducted by comparing the equivalent stresses and total deformations between "Design 1" and "Design 2" at each load level. The research findings reveal significant differences in equivalent stresses and total deformations between the two designs at each load level. Design 1, with a stiffer structural framework, exhibited higher equivalent stresses and greater total deformations compared to Design 2. Consequently, this study provides a deeper understanding of the influence of various structural framework variations on the strength of static loading in solar panel support structures. These findings can serve as a basis for optimizing the structural design of solar-powered electric charging systems.

Numerical analysis method of equivalent deformation parameters for grouted arch dam abutment fractured rock masses considering scale effects and anisotropy

Research on the equivalent deformation parameters of grouted arch dam abutment rock masses has recently emerged as a key in the design, construction and stability assessment of arch dams. With the aim of synthetically considering scale effects and anisotropy of the rock mass equivalent deformation parameters after grouting, in this paper, a practical numerical calculation method is developed. First, the Latin hypercube sampling method is introduced to generate a network of fractures of the arch dam abutment rock mass. Subsequently, the finite element models of the rock masses with different sizes in various directions are constructed. On this basis, equivalent continuum theory and cohesive element model are applied for numerical calculation of grouting fractured rock masses. Then, the scale effect and anisotropy of the deformation modulus of rock mass under different grouting conditions are investigated. Finally, the Jinping super-high arch dam is taken as an example to validate the theoretical significance and application effect of the proposed method. The analysis results indicate that the process of fracture and fragmentation of grouted rock masses is characterized precisely, and the deformation of material units can be described as fully as possible to calculate more realistic equivalent deformation parameters of the fractured rock masses.

FFT-Based Numerical Method for Nonlinear Elastic Contact

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplified to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the finite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efficiency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplified numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

Investigation into the Multistage Mechanical Damage Behavior of Columnar Jointed Basalts with Different Meso-Constitutive Relations and Model Sizes

Abstract The mechanical characteristics of columnar jointed basalts (CJBs) are generally considered to be subject to size effects. They display complex mechanical behaviors under lateral pressure, which may be related to the variation in the rock's mesoproperties. In this study, many nonuniform CJB models with various rock meso-constitutive relations and model sizes were established, and their influences on the strength and deformation properties, multistage mechanical damage behavior, and acoustic emission characteristics of CJBs were investigated. The results show that, as the residual strength coefficient increases, the compressive strength of CJBs rises, and the equivalent deformation modulus of CJBs decreases or increases slightly; with an increase in the model size, the compressive strength slightly decreases at first and then varies moderately, and the equivalent deformation modulus shows a fluctuating trend. Furthermore, the macro stress–strain relationships can be divided into different stages according to the corresponding damage behaviors. The strains and energy accumulations before peak stress was reached were further analyzed. The results greatly improve our understanding of the collapse process of CJBs and the instability precursors of related structures.

The reliability Analysis of Microresistivity Scanning Tool Is Based on System Structure

By controlling the position of the logging tool, the system can ensure that it can accurately descend or rise along the hole, and then measure the required formation properties to obtain higher quality formation data. In order to study the structural reliability of microresistivity scanning logging tool, the statics analysis of the microresistivity scanning logging system is carried out first. It is concluded that the maximum total deformation of the microresistivity scanning logging system is 0.04851m and the maximum equivalent stress is 9.387MPa. Secondly, the load and material parameters of each component of the push-pull system are taken as input variables, and the maximum equivalent stress and maximum total deformation are taken as output variables. Through ANSYS Workbench software, the structural strength and stiffness reliability of the push-pull system are analyzed based on Six Sigma theory. Finally, according to the probability distribution table and probability distribution histogram of the input parameters to the output parameters, when the maximum allowable deformation is 0.048519m, the stiffness reliability of the push-rely system structure is 0.98793, and when the maximum allowable stress is 9.387MPa, the structural strength reliability of the push-rely system is 0.96747.

An approach to stress conversion between different deformation states for incompressible first‐invariant hyperelastic models

AbstractTo characterize generally valid hyperelastic material parameters, tensile tests at different deformation states are essential. This necessity arises from the hyperelasticity theory for incompressible materials, which is based on the first and second invariants of the right Cauchy–Green tensor. These invariants describe the elongation and surface change during a deformation process. By comparing different deformation states using the incompressibility plane of invariants, an equivalent deformation state can be determined for first‐invariant hyperelastic models. This deformation equivalence results in equal strain energy and is used to derive a method for converting stress‐strain relations of different deformation modes. The presented approach is verified and validated with experimental data.

Physical multi-factor driven nonlinear superposition for machining deformation reconstruction

In recent years, the machining deformation of titanium alloy frame parts has become a major research issue in the field of aviation manufacture. Through the generation mechanism, the machining deformation is divided into three parts including bulk residual stresses, cutting forces and other uncertain factors induced deformation. The nonlinearity of physical multi-factor machining deformation is revealed by the comparison between the purely linear addition and coupling superposition. A novel nonlinear superposition model is proposed for machining deformation reconstruction in this work. With the experimental values as simulation inputs, the physical multi-factor driven simulation is developed to solve the nonlinear parameters of machining components in the superposition model. The posterior information embedded in the measurement is utilized to calibrate the nonlinear superposition model in the form of binary polynomials with five orders. The nonlinear superposition model is validated through four series of machining tasks, with the average model accuracy at 91.09%. To quantitively evaluate the proportion share of deformation components, a dimensionless equivalent machining deformation ratio is developed by the integral operation of the established nonlinear model. The results indicate that the bulk residual stresses, cutting forces and other uncertain factors account for percentages of 24.72%, 65.07%, and 13.21% (the ratio among them around 2:5:1). The proposed nonlinear superposition model and dimensionless equivalent ratio in this work display the potential application prospects in the field of machining deformation prediction and control.

Investigation of alloy materials on a sports bike wheel rim designs using finite element analysis

Investigators are dedicating more work to the creation of lightweight vehicles as a result of the rising emphasis placed by the automotive industry on energy efficiency and environmental responsibility. While developing a wheel, it is important to keep both technology and safety considerations in mind simultaneously. Alloy materials are commonly used in the design of sports bike wheel rims due to their lightweight, strength, and durability. The ultimate goal of this study is to lay the groundwork for coming up with new designs for wheels and spokes that can be used on sports bike. In this work, it would be possible to compare how alloys of magnesium and titanium respond to stress and strain compared to structural steel materials. Using an equivalent stress and deformation investigation, two modern designs of wheel spokes for the sports bikes and three materials were compared. This study makes some insightful projections about the reliability of the structural design and provides useful references for the manufacture of alloy wheels. According to the stress analysis, the Ti alloy produces a stress concentration that is about 0.5% lower than on Model A and around 1% lower value for stainless steel on the Model B wheel rim design. Mg alloy has a deflection of about 77% and 53% more than stainless steel and titanium alloy, respectively, in the construction of the model A and B wheel rim.

Influencing Factors on Plasticity and Life of Hydraulic Pipelines for Logging

The bending behavior of the hydraulic pipeline on the roller of the logging winch will cause a certain plastic deformation of the hydraulic pipeline, which has a certain influence on its performance. In view of the above problems, this paper uses finite element analysis software to analyze the plastic deformation law of hydraulic pipelines under different bending radii. It can be found from the analysis results that during the bending process, the plastic deformation of the metal continuous capillary gradually increases with the neutral layer outward. In the range of the bending radius from 75 mm to 150 mm, with the increase of the bending radius, the equivalent plastic deformation decreases from 3.5×10-2 to 1.46×10-2. The changing trend of life also tends to be gentle with the increase of the bending radius, and the number of cycles increases from 25000 to 398107. The analysis of the plastic deformation law and the life of hydraulic pipelines provides a reference for designing winch drums.

Development and validation of a rotating blade-casing rubbing model by considering the blade deformation and abradable coating

Aiming at the phenomenon that blade bending deformation and coating wear are rarely considered in existing rubbing force models, a blade-casing rubbing model based on the Archard wear model was established in this paper. First, the bending deformation of the blade was deduced according to the torque balance relationship, the equivalent deformation of the coated casing was analysed using the equivalent stiffness method, and the clearance between the blade and casing was calculated with the consideration of coating wear based on the Archard model. Second, the influences of the casing stiffness, blade size, and Young's modulus of the coating on the rubbing force were analysed and compared with the existing rubbing force models. Subsequently, a rubbing force characterisation test bench was built considering the AlSi-polyester coating. A strain gauge was used to analyse the blade deformation, the rubbing force was compensated based on the acceleration sensor, and a grating displacement sensor was used to measure the penetration depth, which made the relative error between the experimental and simulation results was less than 15%. Finally, the rubbing force model was applied to the rotor–blade–casing system, and the influence of coating and coating wear on the dynamic characteristics of the rotor system is analyzed. The results show that the model proposed in this paper is more suitable for the rub-impact faults of the elastic blade with an abradable coating on the casing surface. The rubbing force model considering the coating wear is beneficial to accurately predict the rubbing force.

Prediction of distortion in a thin-plate structure with intermittent fillet joints using a local-to-global approach

Fillet welds by intermittent welding are widely used in the welding of centrifugal fans, such as attaching a fan blade to the rear plate. The intermittent welding method transforms the full-length continuous weld into multiple short welds to minimize distortion by reducing the total heat input for a welded joint to control welding distortion. An infinite number of short welds are created during this process. However, depending on the complexity of the model, the computational cost of predicting welding distortion based on full-scale modeling is considerable. These numerous short welds undoubtedly complicate modeling and computations, limiting rapid distortion prediction for large and complex structures. This study develops an equivalent deformation calculation approach based on a local-to-global technique and applies it to predict distortion of a fillet joint welded specimen. The approach consists of two steps. First, the welding-induced structural deformation is calculated for a two-dimensional (2D) weld and a 2D heat-affected zone (local calculation). Second, the 2D structural deformation is applied to the full-scale welded structure using a nearest-point spatial interpolation algorithm to acquire the three-dimensional (3D) equivalent deformation (global calculation). Note that the weld shape was considered in both local and global calculations. In addition, welding tests were performed, and the coordinates of the key points were measured. The geometric parameters of the welds used in the numerical simulations were obtained from experimental observations. Finally, the key point coordinates obtained by the proposed approach were compared with experimental measurements. Furthermore, the distribution of out-of-plane distortion caused by the new approach was compared with the simulation results of the thermo-elastic-plastic method performed on a full-scale welded structure. The proposed approach can be verified by both comparisons.

Technological properties of sheet titanium alloys VT6

This paper presents a comprehensive study of the microstructure, mechanical and technological properties (formability and weldability in solid state) of sheet blanks made of titanium alloy VT6, developed specifically for superplastic forming and diffusion bonding (SPF / DB) in PJSC VSMPO-AVISMA Corporation using various technologies. The conducted studies have made it possible to establish that sheets of titanium alloy VT6 with different microstructure in the temperature range of 850 – 920°C exhibit good superplastic properties. Studies of the technological properties of experimental sheets show their good weldability and high formability under superplasticity conditions. The relative length of the pores in the zone of the solid-phase joints is from 5.3 to 1.8 %, the equivalent deformation during SPF is from 1500 to 2700 %. The technological properties of the VT6 alloy in different states are very similar. The results obtained allow us to recommend this experimental sheet alloy for the manufacture of hollow structures by the SPF / DB process under superplasticity.

Study on the effect of the strengthen grinding process surface coverage on the micro-morphology, micro-hardness, roughness, and residue stress of GCr15 bearing steels

In this study, the surface integrity of GCr15 bearing steels processed by different surface coverage of the strengthen grinding process (SGP) has been theoretical and experimentally investigated. OpenCV-Python-based image processing algorithm was used to extract the evolution of the shot peening coverage. The surface morphology, roughness, equivalent plastic deformation (PEEQ), microhardness, and residual stress were analyzed. Results show that as surface coverage increase from 100 % to 400 %, the PEEQ and microhardness, and theoretical and actual residual stress, behave similarly. The highest microhardness and residual stress reach 851.3 HV and − 1182 MPa, respectively. The variation of surface roughness shows a significant difference, especially at the surface coverage of 300 %, the measured roughness is reduced by approximately 65 % compared to simulation. The possible mechanisms were further discussed. This work demonstrated that the proposed theoretical modeling method could be an efficient approach for controlling the process parameters of multiphase jet flow in practical applications.

Sign problems in elliptic integral solution of planar elastica theory

Elastica theory studies large deformation of slender beams and rods. The elliptic integral solution (EIS) is an accurate and efficient theoretical solution to elastica problem. However, the sign of elliptic integral (SEI) will change with the sign of curvature along an elastica, and also depends on parameters of the coordinate origin, such as elliptical modular angle and curvature. Due to the uncertainty of SEIs, it is quite difficult to obtain an EIS with a uniform final expression.In this study, the sign of elliptic integral (SEI) will be discussed in detail, by classifying the elastica problems into two loading cases: force dominant case (FDC) and bending moment dominant case (MDC). A complete set of EISs and the general solving procedure of EISs, which are applicable to various planar elastica without axial deformation, are presented. The accuracy of current elastica analysis is confirmed by corresponding FE simulations. Employing this EIS method, some metamaterials under large deformation are analyzed efficiently. It is found that the predictions of the equivalent modulus, stress-strain relations, and deformation profiles are both accurate.

Lightweight Design and Structural Analysis of a Wheel Rim Using Finite Element Method and Its Effect on Fuel Economy and Carbon Dioxide Emission

Wheel rims made of metal alloy considerably impact the vehicle’s overall weight. Consequently, employing alloys in the design of wheels results in higher fuel efficiency and lower carbon dioxide emissions. Weight reduction of vehicles also leads to better acceleration. Lightweight automotive design has been increasingly popular in recent years as a means of conserving energy and protecting the environment. The rim is an essential feature of the vehicle since it bears a substantial portion of its overall weight. A vehicle’s weight can be greatly reduced by using a lightweight rim. However, the impact of a lightweight rim on improved fuel economy and reduced carbon dioxide emissions has not been widely explored. In this study, a wheel rim has been designed, and a finite element model has been developed considering radial load, where tire pressure has also been considered. A practical experiment with identical parameters had also been carried out. The values of equivalent stress, strain, and deformation for a metal and an alloy which is steel and cast aluminum alloy (A356.0), respectively, have been compared. In terms of structural stability, steel and cast aluminum alloy have shown fairly similar results based on equivalent stress and deformation. However, the use of cast aluminum alloy has greatly decreased the rim’s weight as a result of its low density and high specific strength. Additionally, the aluminum alloy rim has shown superior fuel efficiency and lower carbon dioxide emissions. According to the findings, cast aluminum alloy rims are more feasible when building a vehicle wheel rim since they minimize the wheel’s and vehicle’s weight while maintaining structural strength. It leads to less fuel consumption, which can save fuel costs and is important for energy conservation.