Three-dimensional Load Research Articles

Three-dimensional loading control of a pneumatic three-universal–prismatic–universal robot

Multidimensional force loading has been widely used in the fields of component and material testing. The pneumatic-driven multidimensional force loading parallel mechanism can meet the requirements of complex force loading. A three-dimensional loading robot based on a pneumatic three-universal–prismatic–universal parallel mechanism is designed to apply time-varying three-dimensional loads on a target. Based on the principle of vector superposition, inverse and forward kinematics are deduced. A second-order mathematical model of a metal seal pneumatic cylinder driven by a flow proportional valve is established. Based on the immersion and invariance technique, the leakage flow in the cylinder is taken as the interference term and estimated. Meanwhile, because of the strong nonlinearity of the actuator, based on suitable disturbance estimation, the control rate of the system is designed through the sliding mode surface, and the stability of the control algorithm is analyzed on the basis of the Lyapunov stability theory. The experimental results show that the immersion and invariance controller exhibits a better control performance than the proportional–integral–differential controller: the steady-state control mean square error is reduced by approximately 21% on average and the dynamic (0.2 Hz) tracking mean square error is approximately 10.35 N.

A Large-Scale Model Test System for Stability Study of Tunnel Under Static-Dynamic Load

In order to study the stability of tunnels under static-dynamic load, a new large-scale static-dynamic model test system was developed. The system was composed of a static loading unit, a dynamic loading unit, a data acquisition unit and a test bench, which were specially designed to overcome the technical problems of large-scale static-dynamic model test, such as dynamic loading and control, high-rate strain measurement and easy operation. The system used a model of 3600 × 3600 × 2500 mm in size to study a larger load disturbance area than static tests. It can accurately apply three-dimensional gradient static stress and dynamic load with adjustable amplitude (or magnitude), frequency and waveform to simulate the true geo-stress field and disturbance field, and accurately and rapidly collect displacement, stress, strain, velocity, acceleration and other important parameters of the model. In addition, it was convenient to adjust the scale of the model, remove and retain the test model. The system was used to carry out a static load model test and a static-dynamic load model test with a tunnel as a prototype. The results of the tests were consistent with the numerical results by FLAC-3D, which proved the reliability and accuracy of the system.

Simulation Design and Analysis of the Three-dimensional Shape Testing Device for Functional Microfilaments

In order to study the micromechanical properties of functional microwires in three-dimensional space morphology, a performance testing device for functional microwires in three-dimensional morphology combined load mode was designed. First, the microwire material is introduced into the three-dimensional weaving process, and the cubic B-spline function curve is used to fit the shape of the three-dimensional microwire, and then the spatial configuration of the microwire is constructed. Secondly, based on the three-dimensional morphology of the microwire, the function and principle of the microwire in the compound loading mode are analyzed, and a three-dimensional testing device for the microwire is designed. Finally, the key components of the designed device were analyzed through simulation, and the key components of the test device were all within their yield limits, which verified the rationality of the test device.

Dynamic load distribution of planetary gear sets subject to both internal and external excitations

Planetary gearsets are widely used in several mechanical systems and have numerous advantages over counter-shaft gears. Despite this, the complex arrangement of components in a planetary gear system makes them susceptible to noise and vibration issues. An exhaustive and rich literature is available on the topic of planetary gear dynamics, but most of these studies consider only the parametric excitation of gear mesh contacts while assuming an ideal power source. But contrary to this popular assumption, realistic power sources (IC Engine, electric motor, wind turbine, etc.) could be subjected to torque fluctuations based on the operating conditions. The current study presents a theoretical investigation on the load distribution and dynamic behavior of planetary gear sets subjected to both internal and external excitations. A three-dimensional dynamic planetary load distribution model that inherently captures the internal excitation due to the elastic gear mesh contacts is employed in this study. The influence of operating conditions on both system-level response and local gear mesh contact stress distribution are explored. Discussed results not only illustrate the potential of the dynamic model but also reinforce the need for such computationally efficient models for design and analysis purposes.

Multiaxial stress-fractional plasticity model for anisotropically overconsolidated clay

Clays in the field can experience various consolidation histories, e.g., isotropic or anisotropic overconsolidation, before subjected to three-dimensional loads exerted by the neighbouring geotechnical infrastructures. Correct representation of the multiaxial strength and deformation behaivour of anisotropically overconsolidated clay is a prerequisite for engineering design. Accordingly, a multiaxial constitutive model is developed in this study, by employing the anisotropic stress-fractional plasticity two surfaces. The consolidation history is represented by using an inclined bounding surface, while the loading behaviour in multiaxial stress space is captured through the stress transformation of an inclined loading surface. The incorporation of such stress transformation method overcomes the difficulty in obtaining the fractional derivative of the Lode's angle. To capture the dilatancy behaviour of anisotropically overconsolidated clay, a multiaxial state-dependant nonassociated plastic flow rule is developed by only using the stress-fractional gradient of the loading surface, which significantly differs from the prior attempts using traditional plasticity. In addition, a multiaxial rotational hardening law for the bounding/loading surface is suggested to characterise the shearing-induced fabric destruction of anisotropically overconsolidated clay. Finally, test results of two different clays under various consolidation histories and stress paths are adopted to validate the developed model. It is found that the predicted strength and deformation behaviour of clay depends the Lode's angle and anisotropic consolidation path, which agrees with the corresponding test results. Specifically speaking, the hardening and softening behaviour of clay induced at seven different overconsolidation ratios ranging from 1 to 10 can be quantified, and the multiaxial strength behaviour of clay loaded from a wide range of Lode's angles ranging from 0° to 60° can be also quantified.

Failure Mechanism and Numerical Simulation of Splitting Failure for Deep High Sidewall Cavern Under High Stress

With the increase of the depth of the underground engineering, the phenomenon of splitting failure of the deep rock will appear, which is very different from the shallow cavern. In order to reveal the formation mechanism of splitting failure, mechanical model test and numerical simulations of splitting failure were carried out respectively. Using the Pubugou Hydropower Station as the engineering background, a three-dimensional (3D) geomechanical model test was conducted relying on a high stress three-dimensional load test system. The splitting failure phenomenon of high sidewall cavern was observed, and the oscillation variations of displacement and stress were measured. Based on strain gradient theory and continuum damage mechanics, an elastic–plastic damage softening model for splitting damage was established. The relationship between rock damage and energy dissipation was analyzed. Based on the strain energy density theory, the splitting failure criterion based on the strain gradient is established. A numerical analysis method for splitting damage was proposed, and a regional disintegration calculation program was developed based on a commercial finite element code. The numerical simulation results are in basic agreement with the 3D geomechanical model test.

Determination of load distribution in a given medium according to the values of the loads at certain points

Taking into account force, temperature and other loads, the stress and strain state calculations methods of spatial structures involve determining the distribution of the loads in the three-dimensional body of the structure [1, 2].
 In many cases the output data for this distribution can be the values of loadings in separate points of the structure. The problem of load distribution in the body of the structure can be solved by three-dimensional discrete interpolation in four-dimensional space based on the method of finite differences, which has been widely used in solving various engineering problems in different fields. A discrete conception of the load distribution at points in the body or in the environment is also required for solving problems by the finite elements method [3-7].
 From a geometrical point of view, the result of three-dimensional interpolation is a multivariate of the four-dimensional space [8], where the three dimensions are the coordinates of a three-dimensional body point, and the fourth is the loading at this point. Such interpolation provides for setting of the three coordinates of the point and determining the load at that point. The simplest three-dimensional grid in the three-dimensional space is the grid based on a single sided hypercube. The coordinates of the nodes of such a grid correspond to the numbering of nodes along the coordinate axes.
 Discrete interpolation of points by the finite difference method is directly related to the numerical solutions of differential equations with given boundary conditions and also requires the setting of boundary conditions.
 If we consider a three-dimensional grid included into a parallelepiped, the boundary conditions are divided into three types: 1) zero-dimensional (loads at points), where the three edges of the grid converge; 2) one-dimensional (loads at points of lines), where the four edges of the grid converge; 3) two-dimensional (loads at the points of faces), where the five edges of the grid converge. The zero-dimensional conditions are boundary conditions for one-dimensional interpolation of the one-dimensional conditions, which, in turn, are boundary conditions for two-dimensional conditions, and the two-dimensional conditions are boundary conditions for determining the load on the inner points of the grid.
 If a load is specified only at certain points of boundary conditions, then the interpolation problem is divided into three stages: one-dimensional load interpolation onto the line nodes, two-dimensional load interpolation onto the surface nodes and three-dimensional load interpolation onto internal grid nodes.
 The proposed method of discrete three-dimensional interpolation allows, according to the specified values of force, temperature or other loads at individual points of the three-dimensional body, to interpolate such loads on all nodes of a given regular three-dimensional grid with cubic cells.
 As a result of interpolation, a discrete point framework of the multivariate is obtained, which is a geometric model of the distribution of physical characteristics in a given medium according to the values of these characteristics at individual points.

Wave-GAN: A deep learning approach for the prediction of nonlinear regular wave loads and run-up on a fixed cylinder

Machine learning techniques have inspired reduced-order solutions in the fluid mechanics field that show benefits of unprecedented capability and efficiency. Targeting ocean-wave problems, this work has developed a novel data-driven computational approach, named Wave-GAN. This new tool is based upon the conditional Generative Adversarial Network (GAN) principle, and it provides the ability to predict three-dimensional nonlinear wave loads and run-up on a fixed structure. The paper presents the principle of Wave-GAN and an application example of regular waves interacting with a vertical fixed cylinder. Computational Fluid Dynamics (CFD) is used to provide training and testing datasets for the Wave-GAN deep learning network. Upon verification, Wave-GAN proved the ability to provide accurate results for predicting wave load and run-up for wave conditions that were not informed during training. Yet the CFD-comparative results were only obtained within seconds by the deep learning tool. The promising results demonstrate Wave-GAN's outstanding potential to act as a pioneering sample of applying machine learning techniques to wave-structural interaction problems. It is envisioned that the new approach could be extended to more complex shapes and wave conditions to facilitate the various design stages of marine and offshore engineering applications such as monopiles. As a result, enhanced reliability is expected to optimise structural performance and prevent environmental disasters.

Experimental Study of Volumetric Fracturing Properties for Shale under Different Stress States

Shale gas can be commercially produced using the stimulated reservoir volume (SRV) with multistage fracturing or multiwell synchronous fracturing. These fracturing technologies can produce additional stress fields that significantly influence the crack initiation pressure and the formation of an effective fracture network. Therefore, this study primarily investigated the evolution of crack initiation and propagation in a hydraulic rock mass under various stress conditions. Combining the in situ stress characteristics of a shale reservoir and fracturing technology, three types of true triaxial volumetric fracturing simulation experiments were designed and performed on shale, including three-dimensional constant loading, one-dimensional pressurization disturbance, and one-dimensional depressurization disturbance. The results indicate that the critical failure strength of the shale rock increases as the three-dimensional constant loads are increased. The rupture surface is always parallel to the maximum principal stress plane in both the simulated vertical and horizontal wells. Under the same in situ stress conditions in the wellbore direction, if the lateral pressure becomes larger, the critical failure strength of shale rock would increase. Additionally, when the lateral in situ stress difference coefficient is smaller, the rock specimen has an evident trend to form more complex cracks. When the shale rock was subjected to lateral disturbance loads, the critical failure strength was approximately 10 MPa less than that in the state of constant loading, indicating that the specimen with disturbance loads is more likely to be fractured. Moreover, shale rock under the depressurization disturbance load is more easily fractured compared with the pressurization disturbance. These findings could provide a theoretical basis and technical support for multistage or multiwell synchronous fracturing in shale gas production.

Characteristics and Mitigation Measures of Floor Heave in Operational High-Speed Railway Tunnels

The rapid development of high-speed railway tunnels has resulted in the increased application of ballastless track slabs. However, floor heave induces ballastless track slab deformation as a result of surrounding rock pressure, imposing serious challenges to the safety of railway systems. In this study, the characteristic of floor heave was analyzed based on field monitoring data. A new tunnel lining structure was then proposed to reduce the effect of floor heave on the slab track. The stress and deformation characteristics of the lining structure under different floor heave loads were analyzed through three-dimensional load structure numerical simulation, and the adaptability of the new tunnel lining structure was numerically studied. The results show that the floor heave typically occurred in the deep-buried sections of tunnel and the maximum floor heave was less than 50 mm during the operation of high-speed railway tunnels. When the new type of tunnel lining was adopted, the influence of the floor heave on the slab track was very small due to the reserved groove of the upper part of the invert and the high rigidity of the steel-reinforced concrete slab, thus effectively reducing the deformation of the tunnel floor heave. This research can be beneficial in the structural design of high-speed railway tunnels and the prevention of tunnel floor heave.

A dynamic load distribution model of planetary gear sets

This study presents, a three-dimensional dynamic load distribution model of planetary gear sets, which can capture the influence of several component and system level design variations. A numerical integration scheme is used in conjunction with an iterative elastic contact algorithm to solve the multibody dynamics problem. This approach inherently captures the mesh stiffness fluctuation, without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The unique dynamic response of the parametrically excited system under various gear mesh phasing conditions is studied using the proposed model. Influence of gear tooth modifications and carrier pin position errors on the dynamics of the gearset is explored, also a brief study to demonstrate the model's capability to capture contact non-linearities in the case of low contact ratio gear sets is included. Discussed results not only illustrate the validity and potential of the proposed dynamic model but also reinforce the need for such computationally efficient models for design purposes.

Establishment and Simulation of 3D Geometric Models of Mini-Pig and Sheep Knee Joints Using Finite Element Analysis.

BackgroundOur objective was to establish and compare three-dimensional models of knee joints of mini-pigs and sheep, the 2 most commonly used animal models of osteoarthritis.Material/MethodsThree-dimensional geometric models of knee joints were used to assess their biomechanical properties by analysis of the three-dimensional finite element stress load for flexion at 30° and 60°.ResultsAnalysis of multiple tissues indicated that the sheep knee had greater stress peaks than the mini-pig knee at 30° flexion (range: 12.5 to 30.4 Mpa for sheep vs. 11.1 to 20.2 Mpa for mini-pig) and at 60° flexion (range: 17.9 to 43.5 Mpa for sheep vs. 15.9 to 28.9 Mpa for mini-pig). In addition, there was uneven distribution of stress loads in the surrounding ligaments during flexion.ConclusionsOur three-dimensional finite element analysis indicated that the mini-pig knee joint had stress values and changes of cartilage, meniscus, and peripheral ligaments that were similar to those of the human knee.

Spatiotemporal Feature Learning Based Hour-Ahead Load Forecasting for Energy Internet

In this paper, we analyze the characteristics of the load forecasting task in the Energy Internet context and the deficiencies of existing methods and then propose a data driven approach for one-hour-ahead load forecasting based on the deep learning paradigm. The proposed scheme involves three aspects. First, we formulate a historical load matrix (HLM) with spatiotemporal correlation combined with the EI scenario and then create a three-dimensional historical load tensor (HLT) that contains the HLMs for multiple consecutive time points before the forecasted hour. Second, we preprocess the HLT leveraging a novel low rank decomposition algorithm and different load gradients, aiming to provide a forecasting model with richer input data. Third, we develop a deep forecasting framework (called the 3D CNN-GRU) featuring a feature learning module followed by a regression module, in which the 3D convolutional neural network (3D CNN) is used to extract the desired feature sequences with time attributes, while the gated recurrent unit (GRU) is responsible for mapping the sequences to the forecast values. By feeding the corresponding load label into the 3D CNN-GRU, our proposed scheme can carry out forecasting tasks for any zone covered by the HLM. The results of self-evaluation and a comparison with several state-of-the-art methods demonstrate the superiority of the proposed scheme.

Spinal loading and lift style in confined vertical space

The objective of this study was to investigate biomechanical loads on the lumbar spine as a function of working in a confined vertical space, consistent with baggage handling inside the baggage compartment of an airplane. Ten male subjects performed baggage handling tasks using confined (kneeling, sitting) and unconfined (stooping) lifting styles. Dependent measures of torso flexion and three-dimensional spinal loads were assessed with an electromyography-driven biomechanical model. Lifting exertions typical to airline baggage handling posed significant risk to the lumbar spine, regardless of lifting style. Statistically significant differences attributable to lift style (stooping, kneeling, sitting) were not observed for peak compressive, lateral shear, or resultant spinal loads, but lifting while kneeling decreased anterior/posterior (A/P) shear spinal loads relative to stooping (p = 0.02). Collectively, kneeling offers the greatest benefit when lifting in confined spaces because of the ability to keep the torso upright, subsequently reducing shear forces on the lumbar spine.

Dynamic mechanical characteristics and failure mode of serpentine under a three-dimensional high static load and frequent dynamic disturbance.

The improved split Hopkinson pressure bar (SHPB) was used to study the dynamic mechanical properties and failure characteristics of surrounding rock in deep rock mass engineering that is under high stress and affected by blasting excavation and other dynamic disturbances. In a three-dimensional high static load and frequent dynamic disturbance test, the preload high axial pressure and confining pressure are used to simulate the high crustal stress of deep rock, and the effect of small disturbances on the rock is simulated by the low impact load. The results show that there are two types of dynamic stress-strain curves of deep rock: an elastic-plastic curve and plastic-elastic-plastic curve. The curves consists of five parts: the compaction stage, micro-crack steady development stage, micro-crack unstable propagation stage, fatigue damage stage, and fatigue failure stage. Reductive phenomena of constringent strain after dynamic peak stress appear because of the different degrees of rock damage. Moreover, these phenomena include two conditions, namely, whether rebound occurs or not. The impact resistance of rock is strongest when the ratio of the confining pressure to axial pressure is optimal, and the dynamic average strength of rock and accumulative impact times decrease with the increase of the preloaded axial compression and increase with the increase of the preloaded confining pressure. Both the dynamic deformation modulus and dynamic peak stress decrease with the increase of the accumulative impact time, while the maximum strain and the dynamic peak strain increase. The corresponding rebound strain as a whole first increases and then decreases with the increasing impact times. For deep rock, tensile failure and single-bevel plane shear failure are the main failure modes, and pull-compression mixed friction failure is the auxiliary failure mode. Additionally, the lumpiness of broken rock decreases with the increase of the preloaded axial compression and increases with the increase of the preloaded confining pressure.

Fully Integrated Voltage Doubler With Dual-Mode Three-Dimensional Load Regulation for On-Chip Photovoltaic-Powered Applications

This paper presents a compact and fully integrated switched-capacitor voltage doubler for voltage boosting in photovoltaic-powered implantable devices. Gate-voltage boosting, nonoverlapping, and interleaving techniques are adopted to enhance the driving capability of the voltage doubler at low supply voltage with high efficiency. A dual-mode three-dimensional (3-D) digital control circuit is proposed to regulate the output voltage under the load current variation. The 3-D control on the number of active converter cells, operation frequency, and on -resistance enable fine output voltage regulation over a wide load current range without extensive device segmentation, thereby reducing the routing complexity and the associated parasitic losses. Other advantages are that the switching loss can be proportionally scaled with the load current for high power efficiency and the periodic charge transfer to the output can keep small for small voltage ripple. Pulse-skipping modulation is employed to allow the converter to operate under ultra-light load. The proposed voltage doubler is designed and implemented using 0.18 μ m-CMOS process. The measurement results demonstrate that the proposed converter can generate a voltage of 0.9 V from an input of 0.6 V, with a power efficiency of more than 60% within the output current range of 30–440 μ A. The peak efficiency is 73% and the active area is 0.33 mm2. These measurement results suggest that the proposed voltage doubler is suitable for voltage boosting at low voltage under the limited availability of power and area.

A New Experimental System for Quantifying the Multidimensional Loads on an on-Site Hydraulic Support in Steeply Dipping Seam Mining

Model supports are widely used for selecting the type of field support and quantifying the working resistance in coal seam mining. These devices may also be employed for reproducing phenomena induced by human activities, such as advancement of the working face, in three-dimensional physical model experiments. This study investigates the relevance of the currently used model supports and finds that the interactions between the model supports and surrounding rocks are unavoidable; the three-dimensional load characteristics of the model support is also immeasurable. Therefore, first, we design a type of hydraulic-powered model support via a real case study. For this, a series of theoretical analyses is performed and the design criteria are proposed. Second, the model support and an integrated measurement system are developed and compared with previous model supports. The newly developed system has the following advantages: i) adopts a hydraulic loading-control system and hydraulic oil for power; ii) equipped with high-precision displacement-measuring elements and pressure-measuring elements for determining the three-dimensional loads of the support (quantitative values for the model support include the working resistance, lateral pushing force transferred from the adjacent supports, and thrust force from the caving-gangue). Subsequently, the performance of the integrated system is tested, following which the integrated system is used in a three-dimensional physical model experiment of working face 3232 of the Lvshuidong coal mine. It is noteworthy that the integrated system can contribute in obtaining the missing load information and increase the quality of the parameters measured in steeply dipping seam mining.

Distributing Three-Dimensional Aerodynamic Load to Fem Nodes

Aiming at the requirement of the load conversion in aeronautics and astronautics static strength analysis, a three-dimensional aerodynamic load equivalent distribution method based on least squares is proposed. Based on the principle of the closest distance, the corresponding relationship between the aerodynamic node and the finite element node is established to ensure that each finite element node has its corresponding aerodynamic node. Under the requirement of minimizing the variance of load obtained by each node allocation, the least squares algorithm is used to obtain the results of the load conversion. Through an engineering example of aerodynamic distribution, it is verified that the method presented in this paper not only has high accuracy but also can ensure the uniformity of load distribution before and after load distribution.

Structure-property relationship for a prepreg platelet molded composite with engineered meso-morphology

The objective of this work was to develop a finite-element based computational model to investigate the complex three-dimensional load transfer from the known meso-structure of a prepreg platelet molded composite (PPMC) system with a layered planar morphology and deterministic orientation state, where platelets are aligned and staggered in each layer. Three-dimensional stress transfer was studied for the prediction of failure under tensile loading. A finite-element model was used for the analysis of the composite structure-property relationship. Variability of meso-structure geometry was shown to control the distributed tensile properties of a PPMC laminate. Platelet length-to-thickness and length-to-width ratios were found to control the composite effective strength. Experimental analysis was used to complement the results of theoretical studies. A PPMC meso-structure with deterministic orientation state of engineered morphology was found to provide enhanced effective tensile properties with reduced variability as compared to stochastic prepreg platelet meso-structure. The mechanisms leading to enhanced structural performance were (i) the improved hierarchical structure of the platelet system and (ii) the ability to define the fiber orientation state of the composite system.

Bifurcation and chaos analysis for a spur gear pair system with friction

Considering time-varying meshing stiffness, gear backlash, static transmission error and tooth face friction, a nonlinear dynamic model for a spur gear pair is proposed to research systematically the dynamic behaviors of system, in which the meshing stiffness of gear pair is deduced and calculated in terms of the extending period method. Meanwhile, the sliding friction force under single-tooth and double-tooth meshing regions is constructed as a function of the meshing principle. Based on the developed model, the bifurcation and chaos characteristics of system under lightly and heavily loaded conditions are studied, respectively, by applied Runge–Kutta numerical method, and the parametric effects of rotational speed, damping ratio and gear backlash on the dynamic behaviors are investigated detailedly. Bifurcation diagram, three-dimensional frequency spectrum, time-domain waveform, frequency plot, phase diagram, Poincare map and dynamic load are used to discuss and determine motion states and dynamic responses of system. The numerical results represent that with the change of control parameters the system undergoes various types of motion states under different loaded conditions. The corresponding meshing contact states of tooth pair are transformed among no impact, single-sided impact and double-sided impact. The research results can provide certain guidance for choosing suitable parameter values to reduce the amplitude of vibration and even avoid the chaotic response in gear system.