Variable Stiffness Coefficient Research Articles

Neural network-based variable stiffness impedance control for internal/external forces tracking of dual-arm manipulators under uncertainties

The desired interaction between manipulators, objects, and environments has resulted in the internal/external force control for dual-arm manipulators being in increasing demand. Consequently, this study focused on the internal/external force tracking for dual-arm manipulator systems under external disturbances, geometries, and stiffness uncertainties which continuously lead to unsatisfactory internal force tracking. The proposed scheme is based on a two-level adaptive impedance control scheme, where the stiffness coefficient is adjusted to adapt to uncalibrated objects. An object-level hybrid impedance controller was used to regulate the external disturbance to produce a compliant response. A manipulator-level neural network-based variable stiffness impedance controller (NNVSIC) was proposed to regulate the internal force under various uncertainties. Additionally, an adaptive wavelet neural network was designed to compensate for the geometric estimation errors of the object. The variable stiffness coefficient could automatically adapt to an unknown object during the cooperation process. One advantage of the proposed method is that no prior knowledge was required. The same controller parameters could be adapted to various objects. The asymptotic stability of the proposed NNVSIC was proven via Lyapunov stability analysis. A series of experiments were conducted using two self-developed nine-degrees-of-freedom redundant manipulators. Furthermore, hard and soft objects of various geometries and stiffnesses were used to verify the effectiveness of the algorithm. The experimental results demonstrated the efficiency and superiority of the proposed controller through performance comparison with various algorithms.

Electromagnetic vibration energy harvester using magnetic fluid as lubricant and liquid spring

Using vibration energy harvester (VEH) to achieve self-power supply is an effectively way to ensure long-term use of electronic devices. In this paper, an electromagnetic VEH using magnetic fluid (MF) as lubricant and liquid spring is proposed, the VEH uses a hollow shell with variable internal diameter together with MF to form a liquid spring with variable stiffness coefficient to replace the traditional mechanical or magnetic spring, and planar coils and helical coils are used together to harvest the vibration energy, thereby broadening response frequency, improving energy harvest efficiency, and reducing VEH volume and damping. The influence of MF on the lubrication, liquid spring, and vibration state is studied theoretically, and the induced voltage is simulated. A crank-slider linkage has been built to test the performance of VEH, and the influence of vibration frequency, mass of MF, and coil type on the output performance has been studied during a 7.5 mm reciprocating linear motion of VEH. Results show that an appropriate amount MF can improve the output voltage by 173 % at 3.25 Hz, but too much MF will cause a rapid drop in output voltage. Helical coils generate higher voltage than planar coils, and the output power density of the helical coil is 0.92 mW/cm3 at 8.5 Hz. The energy management module can manage electric energy well, and half wave rectifier with low forward voltage drop may be more suitable for VEH with low output voltage. Besides, the VEH delivers a 1.36 mW/cm3 power density with a 10 Ω load when it is swung by human at 6.4 Hz.

Numerical simulation of the experiment on testing a group of piles using different models of soil base

In the paper, the influence of the selected model of the soil environment on the stress-strain state (SSS) of the pile foundation is studied. The following issue sare considered: 1) analysis of the main models of the soil environment, widely used in modeling the interaction of foundations with soil foundations; 2) Numerical modeling of the stress-strain state of the "base – pile foundation" system was performed using foundation models in the form of: variable stiffness coefficients, volume tricelastic and elastic-plastic elements of the soil mass; 3) a comparison of the SSS of a pile foundation obtained by numerical modelingusing various foundation models and verification of the results by comparing with the data of a field experiment of testing a group of piles is given. This study is based on field experiments on testing full-scale piles, conducted by prof. Bartolomey A.A. and colleagues. In the experiment, a groupof 9 piles with a length of 5 m and a section of 30x30 cm was driven into the ground. The piles were combined with a reinforced concrete grillage. Numerical modeling of the stress-strain state of the system "base - pilefoundation" was carried out using the SP "Lira – SAPR 2019".
 It was revealed that the calculated values of longitud in alforces in piles modeled by rod elements, and the interaction with the base of the base stiffness factors simulated by variables give good convergence with the data of experimental studies. The error for all experimental fields in a wide range of loads is up to 20%. When determining the value of the variable stiffness coefficients, it is necessary to refine the miteratively more than 3 times. The disadvantage of modeling the foundation with variable stiffness factors is the difficulty in obtaining the correct values of bending moments in piles. When using a soil foundation model in the form of volumetric elastic finite elements, the error in determining the longitudinal forces in piles is up to 45%, and the use of elastic-plastic volumetric soil elements increases the accuracy of the calculation. After comparing the calculated and actual values of piles ettlement, we observe an excellent correlation of the results in the variant of the numerical model using volumetric elastic-plastic finite soil elements with the Mohr-Coulomb strength criterion. The error is within 0.8 ... 2%. The use of the model of volumetric elastic elements of the soil massif leads to an under estimation of settlement in piles within the range of up to 8%. The model using variable foundation stiffness factors also under estimates settlement in piles by up to 15%.

Variable actual stiffness of guides in potash mine shafts

The article addresses serviceability of reinforcement in vertical mine shafts. The mathematical framework is presented for the dynamic processes in the capsule–reinforcement system. The main causes of the dynamic loads in the capsule–reinforcement system are discussed. The importance of the processes in the capsule–reinforcement system during movement of hoists in vertical mine shafts is emphasized. It is asserted that solely computational methods are not enough to analyze processes inside the capsule–reinforcement systems in shafts. It is required to examine actual parameters of shaft reinforcement, in particular, the actual stiffness of shaft guides. The actual measurement procedure of guide stiffness in potash mine shafts is presented. The full-scale tests data are set out in connection with the actual step of reinforcement in shafts. The actual and calculated values of stiffness of shaft guides are compared. Based on the obtained results, the variable stiffness coefficient is derived for the shaft guide stiffness for a few alternative of reinforcement step. Considering the described research findings and the many years-long experience gained in operation of mine shafts, the authors have drawn a conclusion on the necessity to take into account the factor of variable stiffness of guides in shaft design and construction in potash mines in the Upper Kama Potash–Magnesium Salt Deposit, especially in case when the shaft reinforcement step exceeds the project design standards.

The effect of contact friction forces on the stress - strain state of an inclined base during the construction of buildings on complex terrain

The paper considers the interaction of contact friction forces in the system “base - inclined foundation - holding structure” and their influence on the stress-strain state of the soil base in the zone of the foundation structure’s adjacency to the holding structure. The main features of the contact friction forces’ distribution, the places of their application and the calculation algorithm are determined. The design scheme of the inclined foundation is developed taking into account the occurrence of a generalized total friction force. Based on the obtained dependences, the additions and refinements to the existing methodology for calculating foundations on an inclined soil base using a variable stiffness coefficient have been made.

Parameter Design of Six-Pole Hybrid Magnetic Bearing Considering Variable Stiffness

Six-pole hybrid magnetic bearing (HMB) which driven by an inverter is a kind of high performance bearing with the advantages of small size and low cost. In order to overcome the disadvantage of the six-pole HMB that the working point of the rotor deviating from the given reference point, which affects the stable operation of the six-pole HMB system, the parameter design of the six-pole HMB is carried out in combination with the steady region determined by variable stiffness coefficient. Firstly, the structure and working principle of the six-pole HMB are described, and mathematical model of the radial suspension force in the x direction which considers static working point offset is derived by equivalent magnetic circuit method. Secondly, variable stiffness of the six-pole HMB which considers the static working point offset is analyzed, and the steady region of the stable operation of the six-pole HMB is obtained. Thirdly, combined with the delineated steady region, the parameter design of six-pole HMB is carried out. Finally, simulation and experimental results show that the six-pole HMB system has well performance of anti-interference, which proved that variable stiffness analysis provides a theoretical basis for the parameter design of the six- pole HMB.

ВЛИЯНИЕ НЕОДНОРОДНОСТИ РАСПРЕДЕЛЕНИЯ КОЭФФИЦИЕНТА ЖЕСТКОСТИ ДЕЙДВУДНЫХ ПОДШИПНИКОВ НА СОБСТВЕННУЮ ЧАСТОТУ ПОПЕРЕЧНЫХ КОЛЕБАНИЙ ВАЛОПРОВОДА СУДНА

One of the most significant factors affecting the natural frequency of transverse vibrations of shaft-slide bearing systems is the stiffness coefficient of the slide bearing. The need to consider the influence of heterogeneity of stiffness coefficient of the bearing on its natural frequency is caused by the fact that when the bearing is worn, the modulus of longitudinal elasticity of the material changes, and since the bearing wears unevenly, the non-uniform distribution of the stiffness coefficient occurs. The problem of determining the natural frequency of transverse vibrations of a ship propeller shaft based on the foundation with a variable stiffness coefficient along the length has been studied. The differential equation of the propeller shaft vibrations written taking into account the stiffness coefficient variable along the shaft length is considered. It has been noted that, in the general case, this equation is a fourth-order partial differential equation and cannot be integrated in quadratures for an arbitrary stiffness distribution function along the shaft length. A numerical-analytical method for determining the natural frequency of a system based on approximation of the stiffness distribution function by a piecewise-linear function is proposed. The method is applied to calculate the natural frequencies of the pipeline section taking into account the functions describing the change in the stiffness coefficient. The proposed method allows to consider the section of the shafting enclosed in the stern bearing, subject to the non-uniform distribution of the stiffness coefficient of the bearing, and is the basis for improving the accuracy of finding the true natural frequency of transverse vibrations of the shafting.

Variable stiffness Fe82Ga13.5Al4.5 spring based on magnetoelastic effect

The elastic modulus of magnetostriction materials can be controlled in real time by changing the magnetic field. Accordingly, spring with variable stiffness coefficients is available. In this work, Fe82Ga13.5Al4.5 wires of 3.5 mm diameter were prepared by heat forging, rolling, and drawing. Holding at 600 °C for 30 min after annealing at 1100 °C significantly improved the magnetostriction and soft magnetic properties of drawn wires. The tensile test shows two types of relative strain at the initial stage of tension: the elastic modulus under the condition of unsaturated magnetized (Ea) and purely mechanical elastic modulus (Es). The modulus defect ((Es−Ea)/Es × 100%) due to the additional magnetoelastic strain is up to 41.6%. Then, Fe82Ga13.5Al4.5 spring and the loading way of the magnetic field were designed and processed. By tuning the magnetic field strength, the stiffness coefficient of the spring is controlled accordingly. An apparent change in the stiffness coefficient of 10.86% is observed by further increasing the magnetic field to 235.5 Oe, which shows good prospect in a range of technical applications, such as force sensors and suspension systems.

Free vibration analysis of homogeneous and FGM skew plates resting on variable Winkler-Pasternak elastic foundation

In this research study, free vibration of homogeneous and functionally graded skew plates resting on Winkler-Pasternak elastic foundation is investigated. The elastic foundation is assumed to be a combination of Winkler and Pasternak elastic support with linearly or parabolically variable stiffness coefficients along the directions. Plate skewness is obtained by using a transformation from Cartesian coordinate to oblique coordinate system. The energy of the functionally graded skew plate and the elastic foundation is derived, and the natural frequency of the plate is calculated by the Rayleigh-Ritz method. The results are compared with available results in the literature, showing an excellent agreement. Furthermore, a parametric study is carried out to thoroughly investigate the effects of different boundary conditions, skew angles, inhomogeneity factors, and variable elastic foundation stiffness on the free vibration of skew plates.

A new tailoring optimization approach for improving structural response and energy absorption capability of laminated and sandwich composites

In this paper a technique for tuning the energy absorption properties of laminated and sandwich composites through a new tailoring concept is presented. The purpose is to minimize the energy absorbed through unwanted modes (ones involving interlaminar strengths) and maximize that absorbed through desired modes (ones involving membrane strengths) by finding a suited in-plane variable distribution of stiffness properties. Herein mode is intended as a strain energy contribution, such as bending energy, in-plane and out-of-plane shear energy, etc., and no vibration mode. This distribution is obtained making extremal certain strain energy contributions of interest (for example, membrane, bending, in-plane, and out-of-plane shear energies) under in-plane variation of the plate stiffness properties. The effect of this technique is to act as an energy absorption tuning, since it minimizes or maximizes the amount of energy absorbed by specific modes. Although the present technique could be applied to laminates or to the face sheets of sandwich composites, in this paper a preliminary application is presented to single plies with variable stiffness coefficients over their plane. Once incorporated into a laminate or a sandwich composite, these layers are shown to have beneficial effects on the strength at the onset of delamination in sample cases where laminated and sandwich composites are subjected to low velocity, low energy impacts

The application of structural nonlinearity in the development of linearly tunable MEMS capacitors

Electrostatically actuated parallel-plate tunable capacitors are the most desired MEMS capacitors because of their smaller sizes and higher Q-factors. However, these capacitors suffer from low tunability and exhibit high sensitivity near the pull-in voltage which counters the concept of tunability. In this paper, a novel design for parallel-plate tunable capacitors with high tunability and linear capacitance–voltage (C–V) response is developed. The design uses nonlinear structural rigidities to relieve intrinsic electrostatic nonlinearity in MEMS capacitors. Based on the force–displacement characteristic of an ideally linear capacitor, a real beam-like nonlinear spring model is developed. The variable stiffness coefficients of such springs improve the linearity of the C–V curve. Moreover, because the structural stiffness increases with deformations, the pull-in is delayed and higher tunability is achieved. Finite element simulations reveal that capacitors with air gaps larger than 4 µm and supporting beams thinner than 1 µm can generate highly linear C–V responses and tunabilities over 120%. Experimental results for capacitors fabricated by PolyMUMPs verify the effect of weak nonlinear geometric stiffness on improving the tunability for designs with a small air gap and relatively thick structural layers.