Stiffness Of Parts Research Articles

INVESTIGATION OF THE NONLINEAR DYNAMIC STIFFNESS OF ROLLING-LOBE AIR SPRINGS CONSIDERING RUBBER PAYNE EFFECT

ABSTRACT A nonlinear dynamic stiffness model of rolling-lobe air spring considering the Payne effect of the rubber diaphragm and the thermodynamic equivalent damping is proposed, with an aim to provide a theoretical basis for air spring structure design. A physical explanation and mathematical expression of each decoupled contribution term are given from the two dimensions of amplitude and frequency. An indicator test was designed to identify related parameters of the real and imaginary parts of dynamic stiffness. The results showed that the dynamic stiffness increases under a small excitation amplitude, verifying the correctness of the model considering the Payne effect. The influence of rubber diaphragm and gas terms is decoupled to separately illustrate the amplitude and frequency dependency of the real and imaginary parts of dynamic stiffness. A new evaluation index reflecting the contribution percentage of the rubber diaphragm is given, indicating that the stiffness of the rubber diaphragm at low amplitude cannot be ignored. In the end, the parameter influence and dynamic characteristics are provided so that the dynamic behavior of the rolling-lobe air spring can be predicted at the design stage. The proposed rolling-lobe air spring dynamic model considering the Payne effect of the rubber diaphragm provides guidance for the forward development and theoretical modeling of the air spring.

Semi-analytic shooting methods for Burgers’ equation

We implement new semi-analytic shooting methods for the stationary viscous Burgers’ equation by modifying the classical time differencing methods. When the viscosity is small, a very stiff boundary layer appears and this boundary layer causes significant difficulties to approximate the solution for Burgers’ equation. To overcome this issue and improve the numerical quality of the shooting methods with the classical Integrating Factor (IF) methods and Exponential Time Differencing (ETD) methods, we first employ the singular perturbation analysis for Burgers’ equation, and derived the so-called correctors that approximate the stiff part of the solution. Then, we build our new semi-analytic shooting methods for the stationary viscous Burgers’ equation by embedding these correctors into the IF and ETD methods. By performing numerical simulations, we verify that our new schemes, enriched with the correctors, give much better approximations, compared with the classical schemes.

An all Mach number finite volume method for isentropic two-phase flow

Abstract We present an implicit–explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic thermodynamically compatible models. The key element of the scheme consists of a linearisation of pressure and enthalpy terms at a reference state. The resulting stiff linear parts are integrated implicitly, whereas the non-linear higher order and transport terms are treated explicitly. Due to the flux splitting, the scheme is stable under a CFL condition which is determined by the resolution of the slow material waves and allows large time steps even in the presence of fast acoustic waves. Further the singular Mach number limits of the model are studied and the asymptotic preserving property of the scheme is proven. In numerical simulations the consistency with single phase flow, accuracy and the approximation of material waves in different Mach number regimes are assessed.

Variable stiffness triboelectric nano-generator to harvest high-speed railway bridge’s vibration energy

The integration of vibrating structure and novel energy harvesters is highly desirable for the conversion of vibration energy to electricity. In this paper, a variable stiffness triboelectric nano-generator (VSTENG) composed of a variable stiffness part (VSP) and multiple sets of triboelectric nano-generators (TENGs) is proposed to harvest vibration energy of high-speed railway bridge for meeting the electrical energy requirements of sensor nodes. The working principle of VSTENG is introduced, and the theoretical models of VSP’s force-displacement and TENG’s electrical energy output are derived. The numerical model for the VSTENG is presented and a detailed finite element model for the train-track-bridge system is also established. Then by simulating the running train on the bridge, the vibration responses and corresponding frequency spectrum of the track-bridge structure are analyzed, and the effect of VSTENG’s design parameters is discussed. The results show that the developed energy harvester can enlarge the displacement response and vibrate in a wide-frequency domain inducing partial nonlinearity. Moreover, the shake table tests are conducted, and the effect of design parameters and load resistance are analyzed. The test has shown that the device gets the maximum value of electrical energy output while adopting the track plate response as an input. As the load resistance increases, the electrical energy output would be further increased and then decreases sharply. The TENGs can effectively utilize the amplified displacement and wide-range vibration caused by the VSP and promotes the energy harvesting capacity.

Optimization of mechanical performance of a Bernoulli gripper based on the force characteristic curve synthesis method

PurposeThe Bernoulli gripper fixedly installed on the manipulator is subject to limitations such as a small-working region and poor anti-interference capacity. This paper aims to propose a novel Bernoulli gripper design that involves the connection of a positive stiffness component such as a spring in series, based on the force characteristic curve synthesis method, to optimize the mechanical performance.Design/methodology/approachThe proposed gripper is designed and manufactured. In the suction procedure, the force characteristic curve of the proposed gripper is theoretically and experimentally investigated. In the hovering detection procedure, a dynamic model of the manipulator-gripper-workpiece system is established, and an apparatus is set up to compare the displacements of the workpiece and the manipulator. The proposed gripper is finally applied in the lifting procedure, showing good impact resistance.FindingsThe optimization of mechanical performance of the proposed gripper is realized. The proposed gripper has the effect of increasing the stiffness of the negative stiffness part of the force characteristic curve and reducing the stiffness of the positive stiffness part, increasing the working region. The stability and the anti-interference ability of the workpiece under high-frequency vibration are improved. Meanwhile, the impact resistance in the lifting procedure is enhanced, compared with the original one.Originality/valueThis research proposes a novel design for the Bernoulli grippers to optimize the mechanical performance. The proposed gripper has advantages of a larger working region, better anti-interference ability and better impact resistance. These findings serve as important theoretical and experimental references for the design of the Bernoulli gripper.

In-depth field survey of a rockslide detachment surface to recognise the occurrence of gravity-induced cracking

This work describes field evidence of gravity-induced cracking that has been identified on the failure scar of a small rockslide (volume = 6–7 m3) that occurred in March 2004 in the Rosandra Valley near the town of Trieste (north-eastern Italy). This shallow rock slope failure involved a limestone slope that was re-profiled through blasting about 135 years ago for the construction of an old railway, which has now been reconverted into a cycle path. Field observations ascertained that the slope failure was characterised by a cascading rupture process in which adjacent blocks collapsed in rapid sequence as a result of the progressive breakage of a number of rock bridges (domino-like collapse), thus highlighting a progressive failure mechanism. The rock bridges were localised in eccentric positions on lateral and rear release planes and failed in tension as a result of combined tensile and bending loading conditions (tensile strength of intact rock = 5 ± 2 MPa). The rockslide was triggered by cyclic loading related to freeze-thaw (ice jacking) that occurred over some consecutive days of daily snowmelt and nocturnal frost. The recognition of newly formed fractures also proves the current progressive development of 3D rupture surfaces of some unstable blocks susceptible to failure. This study provides innovative content to detect gravity-induced cracking in the field, which is an important precursory sign relating to the progressive failure of rock slopes. Gravity-induced cracks can be distinguished from pre-existing discontinuities for their more irregular profile (zigzag pattern), rougher surface, lower persistence and potentially different orientation. This study also provides some new insights into the step-path failure process of steep rock slopes. The mechanical process of initiation, growing and coalescence of gravity-induced fractures is strongly time- and stress-dependent. In the absence of external changing factors that profoundly modify the acting stress state (for instance, engineering countermeasures), progressive failure is a dynamic and irreversible process. For excavated slopes, the creation of a new rock face may abruptly provide the kinematic freedom of potentially unstable blocks, thus determining a very quick stress redistribution. If the mechanical system is not able to redistribute the stress on resisting stiff parts without overcoming the intact rock strength, gravity-induced cracking initiates and propagates until reaching slope collapse within times that are much shorter (from hours to 100–200 years) compared to natural rock slopes subjected to long-lasting geological processes (from 1000 to 2000 up to 10,000–20,000 years).

Deep Deterministic Policy Gradient with Reward Function Based on Fuzzy Logic for Robotic Peg-in-Hole Assembly Tasks

Robot automatic assembly of weak stiffness parts is difficult due to potential deformation during assembly. The robot manipulation cannot adapt to the dynamic contact changes during the assembly process. A robot assembly skill learning system is designed by combining the compliance control and deep reinforcement, which could acquire a better robot assembly strategy. In this paper, a robot assembly strategy learning method based on variable impedance control is proposed to solve the robot assembly contact tasks. During the assembly process, the quality evaluation is designed based on fuzzy logic, and the impedance parameters in the assembly process are studied with a deep deterministic policy gradient. Finally, the effectiveness of the method is verified using the KUKA iiwa robot in the weak stiffness peg-in-hole assembly. Experimental results show that the robot obtains the robot assembly strategy with variable compliant in the process of weak stiffness peg-in-hole assembly. Compared with the previous methods, the assembly success rate of the proposed method reaches 100%.

Additive manufacturing with fibre-reinforcement – design guidelines and investigation into the influence of infill patterns

PurposeFibre-reinforced additive manufacturing (FRAM) with short and continuous fibres yields light and stiff parts and thus increasing industry acceptance. High material anisotropy and specific manufacturing constraints shift the focus towards design for AM (DfAM), particularly on toolpath strategies. Assessing the design-property-processing relations of infill patterns is fundamental to establishing design guidelines for FRAM.Design/methodology/approachSubject to the DfAM factors performance, economy and manufacturability, the efficacy of two conventional infill patterns (grid and concentric) was compared with two custom strategies derived from the medial axis transformation (MAT) and guided by the principal stresses (MPS). The recorded stiffness and strength, the required CPU and print time, and the degree of path undulation and effective fibre utilisation (minimum printable fibre length) associated with each pattern, served as assessment indices for different case studies. Moreover, the influence of material anisotropy was examined, and a stiffness-alignment index was introduced to predict a pattern’s performance.FindingsThe highest stiffnesses and strengths were recorded for the MPS infill, emphasising the need for tailoring print paths rather than using fixed patterns. In contrast to the grid infill, the concentric infill offered short print times and reasonable utilisation of continuous fibres. The MAT-based infill yielded an excellent compromise between the three DfAM factors and experimentally resulted in the best performance.Originality/valueThis constitutes the first comprehensive investigation into infill patterns under DfAM consideration for FRAM, facilitating design and processing choices.

Comparison of Biomechanical Gait Parameters and Patient-Reported Outcome in Patients After Total Knee Arthroplasty With the Use of Fixed-Bearing Medial Pivot and Multi-radius Design Implants-Retrospective Matched-Cohort Study.

BackgroundTotal knee arthroplasty (TKA) is considered to be highly successful in treatment of end-stage osteoarthritis. There are multiple implant designs available on the market, and it is difficult to point which one is the best. The aim of this study was to compare the clinical and functional outcomes and gait pattern after TKA with the use of fixed-bearing medial pivot (K-Mod) vs multi-radius design (NexGen) implants and to compare them to norms for healthy patients with no osteoarthritis or arthroplasty procedure in anamnesis.MethodsA group of 30 patients who received the medial pivot (MP) TKA and 33 patients who received the posterior-stabilized (PS) TKA between May and August of 2018 were included. All surgeries were performed in the level III academic hospital by a single surgeon. Every patient was asked to fulfill the The Western Ontario and McMaster Universities Arthritis Index (WOMAC) questionnaire preoperatively and 2 years postoperatively. Standard X-ray, biomechanical gait analysis using a motion capture system, and statistical analysis were performed at 2 years postoperatively.ResultsA total of 28 patients from either MP cohort (93%) or PS (85%) matched-control cohort completed the whole assessment at the final follow-up. There were statistically significant differences in a few gait parameters such as shorter mean step length both in operated and healthy limb, lower mean gait velocity, and lower mean walking cadence than the norm in both MP and PS groups. As to the WOMAC score, there was statistically significant improvement in both groups comparing preoperative and postoperative outcomes. Nevertheless, in the MP group, there was a significantly higher score, indicating worse outcomes, in the stiffness part of the WOMAC score than in the PS group. No significant differences were found between groups during radiological evaluation.ConclusionsThere were satisfying and promising clinical, radiographic, and patient-reported outcomes in both MP and PS groups with very little difference in relation to norm values. However, both implants failed in fully restoring gait patterns similar to the healthy limb of the same patient.

A Stretchable Fiber with Tunable Stiffness for Programmable Shape Change of Soft Robots.

All soft robots require the same functionality, that is, controlling the shape of a structure made from soft materials. However, existing approaches for shape control of soft robots are primarily dominated by modular pneumatic actuators, which require multichambers and complex flow control components. Nature shows exciting examples of manipulation (shape change) in animals, such as worms, using a single-chambered soft body and programmable stiffness changes in the skin; controlling the spatial distribution of changes in stiffness enables achieving complex shape evolutions. However, such stiffness control requires a drastic membrane stiffness contrast between stiffened and nonstiffened states. Generally, this is extremely challenging to accomplish in stretchable materials. Inspired by longitudinal muscle fibers in the skin of worms, we developed a new concept for fabricating a hybrid fiber with tunable stiffness, that is, a fiber comprising both stiff and soft parts connected in a series. A substantial change in membrane stiffness was then observed by the locking/unlocking of the soft part. Our proposed hybrid fiber cyclically produced a membrane stiffness contrast of more than 100 × in less than 6 s using an input power of 3 W. A network of these hybrid fibers with tunable stiffness could manipulate a single-chambered soft body in multiple directions and transform it into a complex shape by selectively varying the stiffness at different locations.

Multi-frequency model reduction for uncertainty quantification in computational vibroacoutics

This work is devoted to the vibroacoustics of complex systems over a broad-frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. On one hand, the global displacements are associated with the main stiff part and on the other hand, the local displacements are associated with the preponderant vibrations of the flexible subparts. Such complex structures induce interweaving of these two types of displacements, which introduce an overlap of the usual three frequency bands (low-, medium- and high-frequency bands (LF, MF, and HF). A reduced-order computational vibroacoustic model is constructed by using a classical modal analysis with the elastic and acoustic modes. Nevertheless, the dimension of such reduced-order model (ROM) is still important when there is an overlap for each one of the three frequency bands. A multi-frequency reduced-order model is then constructed for the structure over the LF, MF, and HF bands. The strategy is based on a multilevel projection consisting in introducing three reduced-order bases that are obtained by using a spatial filtering methodology. To filter out the local displacements in the structure, a set of global shape functions is introduced. In addition, a classical ROM using acoustic modes is carried out for the acoustic cavity. Then, the coupling between the multilevel ROM and the acoustic ROM is presented. A nonparametric probabilistic modeling is then proposed to take into account the model uncertainties induced by modeling errors that increase with the frequency. The proposed approach is applied to a large-scale computational vibroacoustic model of a car.

Delamination evaluation in drilling of composite materials – A review

The persisting challenge for adaptable composite material, to make a remarkable material property along with lighter and stiffer parts. This leads to a wider application of composite materials (CFRPs and GFRPs) due to its better adaptability and predominant properties. Mechanical drilling is inevitable mode of operation and it’s always challenging and difficult for CFRP which leads to various onset damages. Drilling originated delamination at entry and exit of hole is most undesirable and defying damage leads to material rejection. Delamination assessment is always important for correction and improvement of assemble parts to achieve highest performance index. During last few decades, various delamination factors have been derived and suggested as a point of reference for delamination measurement and meanwhile various delamination assessment techniques are being proposed to measure the severity of delaminated zone for evaluation of delamination. This state-of-art review paper summarizes various delamination quantification and measurement techniques for the correction and improvement of drilling approach reported in open literature. It can be referenced not only as an up-to date summary available form past results but also possibilities for future scope to subdue delamination during drilling in CFRP.

Fracture, fatigue, and friction of polymers in which entanglements greatly outnumber cross-links.

In gels and elastomers, the role of entanglements on deformation has been studied, but their effects on fracture, fatigue, and friction are less well understood. In this study, we synthesized polymers in which entanglements greatly outnumber cross-links. The dense entanglements enable transmission of tension in a polymer chain along its length and to many other chains. The sparse cross-links prevent the polymer chains from disentangling. These polymers have high toughness, strength, and fatigue resistance. After submersion in water, the polymers swell to equilibrium, and the resulting hydrogels have low hysteresis, low friction, and high wear resistance.

Toughening hydrogels through force-triggered chemical reactions that lengthen polymer strands.

The utility and lifetime of materials made from polymer networks, including hydrogels, depend on their capacity to stretch and resist tearing. In gels and elastomers, those mechanical properties are often limited by the covalent chemical structure of the polymer strands between cross-links, which is typically fixed during the material synthesis. We report polymer networks in which the constituent strands lengthen through force-coupled reactions that are triggered as the strands reach their nominal breaking point. In comparison with networks made from analogous control strands, reactive strand extensions of up to 40% lead to hydrogels that stretch 40 to 50% further and exhibit tear energies that are twice as large. The enhancements are synergistic with those provided by double-network architectures and complement other existing toughening strategies.

Semi‐analytic time differencing methods for singularly perturbed initial value problems

AbstractWe implement our new semi‐analytic time differencing methods, applied to singularly perturbed non‐linear initial value problems. It is well‐known that, concerning the singularly perturbed initial problem, a very stiff layer, called initial layer, appears when the perturbation parameter is small, and this stiff initial layer causes significant difficulties to approximate the solution. To improve numerical quality of the classical integrating factor (IF) methods and exponential time differencing (ETD) methods for stiff problems, we first derived the so‐called correctors, which are analytic approximations of the stiff part of the solution. Then, by embedding these correctors into the IF and ETD methods, we build our new enriched schemes to improve the IF Runge–Kutta and ETD Runge–Kutta schemes. By performing numerical simulations, we verify that our new enriched schemes give much better approximations of solutions to the stiff problems, compared with the classical schemes without using the correctors.

Tool changing 3D printer for rapid prototyping of advanced soft robotic elements

In the field of soft robotics, pneumatic elements play an important role due to their sensitive and adaptive behavior. Nevertheless, the rapid prototyping of such actuators is still challenging since conventional 3D printers are not designed to fabricate airtight objects or to specify their bending behavior by combining materials of different stiffness. In order to address this challenge, a tool changing multi-material 3D printer has been constructed, which can be equipped with various print-heads fitted to the specific application. By alternately processing filaments with varying mechanical properties, a series of pneumatic elements was produced. The actuators were printed in thermoplastic polyurethane with shore hardness A70 for flexible parts and D65 for stiff parts. A novel procedure for the feature adaptation of the flow rate allowed the fabrication of vertically printed flexible membranes with a thickness of just 500 μm. This way the bending and expanding printed structures can all be actuated with a pressure of 100 kPa or less. Furthermore, a new kind of generic actuator that is customizable to specific tasks and can perform complex motion behavior was designed. All together, these actuators demonstrate the high potential of the developed platform for further research on and production of soft robotic elements and complex pressurized systems.

A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations

Fractional Ginzburg-Landau equations as generalizations of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting matrix differential equation is split into a stiff linear part and a nonstiff (nonlinear) one. For solving these two subproblems, a dynamical low-rank approach is employed. The convergence of our method is proved rigorously. Numerical examples are reported which show that the proposed method is robust and accurate.

A damage model for the frictional shear failure of brittle materials in compression

Damage models have been successfully employed for many decades in the modelling of tensile failure, where the crack surfaces separate as a crack grows. The advantage of this approach is that crack trajectories can be computed simply and efficiently on a fixed finite element mesh without explicit tracking. The development of damage models for shear failure in compression, where the crack faces slide over each other subject to friction, is a non-trivial extension of this approach. A major difference is that part of the material stiffness in the damaged region must be retained to avoid interpenetration of the crack faces. This problem is resolved here by employing an anisotropic modification to the elastic stiffness tensor in the damaged region. This has the benefit of driving frictional cracks into the correct orientation, according to the Mohr–Coulomb failure criteria, but three issues remain. The first is that the shear discontinuity introduces some spurious stress perturbations around crack regions that are narrow (less than 3-4 elements wide). This is ameliorated by Helmholtz smoothing to allow efficient simulation on a coarse mesh. The second is that the complementarity of shear stress means that the shear stiffness is removed normal to the crack interface as well as parallel to it, and the third is that there are two potentially active failure planes at each point. Both these latter two issues are resolved by the introduction of a novel failure plane selection variable, which regulates either single plane or dual plane failure, and prevents the growth of erroneous cracks normal to the crack face. Both local and non-local models are investigated for linear and exponential strain softening responses. Unlike the non-local model, the local model demonstrates some mesh-size dependence, but it still retains some properties of interest, in that it supports narrower cracks and more rapidly forms a preference for the growth of a single crack when there are a number of competing cracks. The model is implemented in commercial finite element package COMSOL Multiphysics v5.5 and validated against two benchmark simulations: biaxial compression and the failure of a 45° slope. The correct crack angles, stipulated by the Mohr–Coulomb friction angle, are correctly reproduced, as is the post-failure residual frictional force in biaxial compression. The effect of the shear fracture energy on the force–displacement response is investigated, demonstrating successful simulation of the range of material behaviour expected in geological samples, from broad ranged gradual collapse to sharp, almost instantaneous failure.

An approach to identify the weak parts of stiffness for the machine tool cantilever structure

Investigating weak parts of the structure is one of the most important issues for improving the stiffness of the machine tool. However, studies show that overcoming the static deformation is a challenging problem in practical structures. In the present study, the dynamic hammer testing approach is applied to analyze the cantilever structure of the machine tool with elastic support. Accordingly, a new weakness index (WI) is proposed to identify weak parts of the cantilever structure with an elastic support. Then the cantilever beam with the elastic support is numerically simulated and weak parts are modeled as stiffness reduction. In this regard, finite element (FE) simulations are carried out to evaluate the effectiveness of the WI method in several scenarios with single and multiple weaknesses, including the noise case. In the combined structure of the tailstock and the bed of the machine tool, sensors are utilized to collect vibration data. Furthermore, the dynamic characteristics are calculated through the modal state-space method to obtain the stiffness data at zero-frequency. Then, weak parts of the structural stiffness are identified based on the weakness index. It is found that the FE simulations are in an excellent agreement with the experiment. Therefore, it is proved that the WI can accurately identify the weak parts of the machine tool cantilever structure.

A review on the topology optimization of the fiber-reinforced composite structures

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.