Static Stiffness Research Articles

On the influence of sorbents on the static stiffness of Air Springs

Air Springs are deployed in many technical areas today. In the premium segment of the automotive industry in particular, they are being used more and more frequently. The load-independent spring rate results in a better ride comfort. Since the stiffness of the Air Spring is significantly influenced by the enclosed air volume, this usually leads to a conflict of objectives between the available installation space and the stiffness optimum. To reduce the spring stiffness while maintaining the same design space, Coackley and Elliot describe in their patent the use of adsorbents such as activated carbon in the enclosed air volume of the spring. By binding air molecules to the adsorbent, more air molecules fit into the enclosed Air Spring volume, while the size and pressure of the Air Spring remain the same.This paper describes how the so-called “virtual volume” is created by adsorption and how it can be determined by simplified measurements using a gas pycnometer. Furthermore, it is shown how these measurements are related to the static stiffness of an Air Spring, so that a prediction of the static stiffness of an Air Spring filled with sorbent, in this case activated carbon, is possible by simple pycnometric measurements.

Vibration isolation performance of silica aerogel blankets and boards, fumed silica, polymer aerogel and nanofoams

Buildings are often constructed on a continuous layer of vibration isolation to reduce vibrations and structure-borne noise. There are many vibration isolation products (rubber mats, textiles, polymer foams), but none fulfils all requirements in terms of load-bearing capacity, performance, and cost. In previous work, we have shown that silica aerogel particle beds display a low resonance frequency and correspondingly high vibration isolation performance. Loose silica aerogel granules are not a practical vibration isolation solution. In order to guide the future development of dedicated vibration isolation products based on aerogels, we determine the vibro-acoustic properties of a variety of existing commercial and R&D stage mesoporous composites, that have been developed for thermal insulation applications. The sample set includes monolithic aerogels (polyurethane), silica aerogel composites (aerogel – fibers, aerogel impregnated foams, aerogel bound with polymer foam), glued fumed silica-fiber boards, and nanoporous polymer foam composite boards. The silica aerogel and fumed silica composites display low resonance frequencies (down to 8 Hz for 40 mm, strongly dependent on composite type) and a low dynamic stiffness and loss factor over a wide range of static loads. The polymer aerogel, nanoporous foam and polymer-bound silica aerogel granule board all display higher resonance frequencies, consistent with their higher static stiffness. Although optimized for thermal insulation rather than vibration isolation, many of the tested silica aerogel and fumed silica composites are competitive with the best vibration isolation products on the market in terms of vibration isolation performance. The diversity of materials tested informs on which approaches, materials, and materials combinations are most promising to target vibration isolation.

Topology optimization of programable quasi-zero-stiffness metastructures for low-frequency vibration isolation

Quasi-zero-stiffness (QZS) isolators have been demonstrated to realize low-frequency vibration isolation without loss of static stiffness. However, most previous designs are based on spring-driven links, cam-roller structures, or two-phased network structures resorting to complex assembling components, other than compact and integrative single-phased solid structures. In this paper, we propose a topology optimization scheme to inversely design QZS metastructures with smooth boundaries for customized nonlinear force-displacement curves. The optimization model is established based on the distinguishing features of the QZS force-displacement curve. The boundary smoothing procedure is introduced in the genetic algorithm to improve the convergence and stability of topology optimization. The designed metastructures are verified to have robust QZS feature. A linear relationship between the platform force and the initial modulus of the base material is obtained. We numerically show the high-static-low-dynamic performance, the load bearing, and even full band vibration isolation capabilities of the designed QZS metastructures. In addition, experiments are performed to verify the QZS feature of the designed metastructure. The inverse design scheme developed in this paper can efficiently design QZS isolators suitable for different scenarios with great flexibility. The metastructures with smooth boundaries are obtained so that postprocessing is not required before manufacture. The proposed inverse-design methodology paves the way for low-frequency vibration isolation using compact solid structures without any positive or negative stiffness units.

A ring metastructure vibration isolator with thin beams

Conventional linear vibration isolators are difficult to have the function of high load-bearing capacity and low-frequency isolation, however nonlinear metastructure vibration isolators can effectively achieve this function. In this study, a new ring metastructure vibration isolator with thin beams was designed to have high static and low dynamic stiffnesses. We have accurately derived the static expression of these thin beams, obtained the stiffness characteristic and innovatively analyzed the vibration transmission characteristics of the ring isolator by deriving its dispersion equation. The influences of damping, frequency ratio, mass ratio, stiffness ratio, linear stiffness and nonlinear stiffness on the wave vector were obtained using the dispersion equation. Finally, a ring metastructure isolator sample with the high load-bearing capacity was designed and fabricated, and a vibration experiment was conducted to verify that the isolator has a lower vibration transmissibility in the target frequency band. This study not only demonstrates the feasibility of applying thin beams to nonlinear metastructure isolator design from mathematics, but also reveals profoundly its physical connotation from structural dynamics.

Simulation Analysis and Key Performance Index for Experimental Verification of a New Type of Press Transmission Mechanism

In this paper, the characteristics of special stamping process requirements and the shortcomings of existing application technology are studied. Through repeated motion simulation analysis and size optimization calculation, a kind of inertia-controlled molding press is proposed to make up for this technical vacancy. This paper first describes the working principle and structure scheme of the main transmission mechanism of the inertia-controlled molding press. With the help of Adams-View x64 2013, the main transmission mechanism is simulated and analyzed from the aspects of kinematics and dynamics, and a physical prototype is made to test the key reliability indexes of the main transmission mechanism. According to the test data, the static strength, stiffness, vibration characteristics, and dynamic characteristics of the 200 t inertia-controlled molding press are evaluated, which provides a reference for the design of this kind of machine tool.

Dynamics of Liver Stiffness Measurement and Clinical Course of Primary Biliary Cholangitis

Background & aimsIn primary biliary cholangitis (PBC), static liver stiffness measurement (LSM) has proven prognostic value. However, the added prognostic value of LSM time course in this disease remains uncertain. MethodsWe conducted an international retrospective cohort study among PBC patients treated with ursodeoxycholic acid (UDCA) and followed by vibration-controlled transient elastography (VCTE) between 2003 and 2022. Using joint modeling, the association of LSM trajectory and the incidence of serious clinical events (SCE), defined as cirrhosis complications, liver transplantation (LT) or death, was quantified using the hazard ratio (HR) and its confidence interval (CI). ResultsA total of 6,362 LSMs were performed in 3,078 patients (2,007 on UDCA alone; 13% with cirrhosis), in whom 316 SCE occurred over 14,445 person-years (median follow-up, 4.2 years; incidence rate, 21.9 per 1,000 person-years). LSM progressed in 59% of patients (mean 0.39 kPa/year). After adjusting for prognostic factors at baseline, including LSM, any relative change in LSM was associated with a significant variation in SCE risk (p<0.001). For example, the adjusted HRs (95% CI) associated with a 20% annual variation in LSM were 2.13 (1.89 – 2.45) for the increase and 0.40 (0.33 – 0.46) for the decrease. The association between LSM trajectory and SCE risk persisted regardless of treatment response or duration, when patients with cirrhosis were excluded, and when only death or LT was considered. ConclusionsTracking longitudinal changes in LSM using VCTE provides valuable insights into PBC prognosis, offering a robust predictive measure for the risk of SCE. LSM could be used as a clinically relevant surrogate endpoint in PBC clinical trials.

Dual characteristics of static stiffness and adjustable bandgap of innovative re-entrant hybrid chiral metamaterials

In this paper, an improved re-entrant metamaterial based on 3D printing was proposed, which exhibits enhanced stiffness and vibration suppression ability compared to the original metamaterial. The proposed metamaterial allows for intentional adjustment of the bandgap by incorporating metal pins of varying sizes or weight into the ring structures. Furthermore, the addition of particle damping inside the rings enhances the design flexibility of the bandgap, enabling customization of the middle and low frequency ranges. Experimental and simulation comparisons are conducted to evaluate the static properties and vibration suppression ability of the metamaterial. The results demonstrate a 172.4 % increase in load-bearing capacity and a significant improvement in vibration suppression of the proposed metamaterial relative to the original configuration. The vibration suppression of the proposed metamaterial can be further enhanced by introducing particle damping into the metal tube, and the vibration suppression frequency can be intentionally adjusted by changing the dosage of particle damping. This research presents a novel approach for the design and optimization of metamaterials.

Theoretical and experimental research on static stiffness, performance, and lift-off characteristics of multi-layer gas foil thrust bearings

In this study, a new comprehensive fully coupled elastic-hydrodynamic model is developed for a multi-layer gas foil thrust bearing (GFTB). The interaction effects among the top foil, back board, middle foil, and bottom foil, as well as the Coulomb friction effect, are considered. The stiffness and static characteristics obtained by the experimental and theoretical approaches are in good agreement, which verifies the accuracy of the model. The contribution of each foil layer to the overall stiffness and the load-carrying mechanism are analyzed. Interaction effects of the load, preload, and rotational speed on the static performance are investigated comprehensively. Furthermore, start-stop tests are performed to achieve the lift-off speed, start-up torque, and shut-down torque under various operating conditions.

The low-frequency bandgap characteristics of phononic crystal isolators with multi-hole

A vibration isolator for a floating slab track, based on a locally resonant phononic crystal, has been designed to suppress vibrations caused by the wheel-rail interaction. In this isolator, a circular vibrator is connected to a connector through a rubber layer uniformly embedded in holes. The finite element method is utilized to compute the energy band structure and transmission loss of the vibration isolator, while the mechanism of bandgap is elucidated through the analysis of modes. The static stiffness and dynamic stiffness of the vibration isolator are calculated, which proves that the vibration isolator meets the requirements of engineering applications. The influence of the number of circular holes and the geometric parameters of the vibration isolator on the bandgap is examined. It is discovered that augmenting the number of holes and the hole diameter in the rubber layer leads to a decreased bandgap. A low-frequency locally resonant bandgap of 38.2–97.1 Hz and a relative bandgap bandwidth of 86.9 % are obtained by optimizing the vibration isolator. The vibration isolation performance of a floating slab track equipped with vibration isolators is analyzed and more robust vibration attenuation performance is obtained in the bandgap. The multi-hole phononic crystal vibration isolator is employed in floating slab tracks for rail transportation, effectively mitigating vibrations transmitted to tunnels, thus further minimizing the effects on the surrounding environment.

Numerical Investigation of the Seismic-Induced Rocking Behavior of Unbonded Post-Tensioned Bridge Piers

It is essential and convenient to use accurate and validated numerical models to simulate the seismic performance of post-tensioned (PT) rocking bridge piers, with a particular emphasis on accurately capturing rocking behavior. The primary contribution of this study is a comparison of the effectiveness of four commonly used numerical base rocking models (namely, the lumped plasticity (LP) model and the multi-contact spring (MCS) models with linear elastic (MCS-LE), bilinear elastic–plastic (MCS-EP) and nonlinear plastic (MCS-NP) material behavior, respectively) in modeling both the cyclic and seismic responses of PT rocking bridge piers. Also, this study validates the 3D contact stiffness equation for numerical models and assesses the differences between the dynamic and static stiffness values of the contact springs. Both quasi-static and shaking table tests of typical PT rocking piers are adopted to calibrate/validate these numerical models. These models describing the PT rocking piers’ seismic performance are formulated and calibrated, showing good agreement with test results for test specimens. Additionally, the suggested values of model spring stiffness for dynamic and quasi-static analyses are identified by parametric analysis. All base rocking models can predict the pier’s cyclic and seismic behavior after the calibration of contact spring stiffness values. The recommended contact stiffness for the dynamic analysis of PT rocking piers is smaller than that used for the quasi-static analysis. The results and findings provide a valuable reference and solution for the numerical simulation of PT rocking piers.

Full-scale laboratory investigation on laminated rubber bearings for metro-induced vibration mitigation

The vibration response generated by the operation of a metro system has a profound impact on the physical and mental well-being of urban residents. Vibration control is essential to effectively isolate the multi-band vibration response and structure-borne noise of buildings. Laminated rubber bearings between the foundation and the superstructures serve as a common, cost-effective solution for the seismic isolation of structures and have great potential to be used for metro-induced vibration mitigation. In this study, two types of full-scale laminated rubber bearings (i.e., linear natural rubber bearing and lead rubber bearing) were tested under various compressive stresses, ranging from 5 MPa to 15 MPa, to examine the static and dynamic characteristics of the bearings, including vertical hysteresis curves, vertical static stiffness, time history response, and frequency spectrum. Then, the numerical simulation of a base-isolated building structure equipped with laminated rubber bearings was conducted to evaluate the vertical vibration isolation performance and structure-borne noise isolation capability. It was demonstrated that the laminated rubber bearings have stable vertical bearing capacities and performance in isolating vertical vibrations.

On the static performance of aerostatic elements

Porous aerostatic bearings and seals offer several advantages in precision engineering applications. The static performance of aerostatic elements, i.e., bearings and seals, is investigated both experimentally and numerically. This study presents a method, a test setup, and a measurement of the air gap pressure distribution with high spatial and temporal resolution. This study presents experimental and numerical results of the load capacity, air gap height, static stiffness, air consumption, and air gap pressure distribution. The experimental results are compared to a numerical model based on the modified Reynolds equation. Furthermore, boundaries for the operating parameter space of the investigated seal are determined by stiffness and leakage. The experimental results and the numerical model showed good correlation, providing corroborative evidence for the accuracy of the measurement setup and the feasibility of the pressure measurement method.

Stiffness calibration of qPlus sensors at low temperature through thermal noise measurements.

Non-contact atomic force microscopy (nc-AFM) offers a unique experimental framework for topographical imaging of surfaces with atomic and/or sub-molecular resolution. The technique also permits to perform frequency shift spectroscopy to quantitatively evaluate the tip-sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with little precision. An accurate stiffness calibration is therefore mandatory if accurate force measurements are targeted. In nc-AFM, the probe may either be a silicon cantilever, a quartz tuning fork (QTF), or a length extensional resonator (LER). When used in ultrahigh vacuum (UHV) and at low temperature, the technique mostly employs QTFs, based on the so-called qPlus design, which actually covers different types of sensors in terms of size and design of the electrodes. They all have in common a QTF featuring a metallic tip glued at the free end of one of its prongs. In this study, we report the stiffness calibration of a particular type of qPlus sensor in UHV and at 9.8 K by means of thermal noise measurements. The stiffness calibration of such high-k sensors, featuring high quality factors (Q) as well, requires to master both the acquisition parameters and the data post-processing. Our approach relies both on numerical simulations and experimental results. A thorough analysis of the thermal noise power spectral density of the qPlus fluctuations leads to an estimated stiffness of the first flexural eigenmode of ≃2000 N/m, with a maximum uncertainty of 10%, whereas the static stiffness of the sensor without tip is expected to be ≃3300 N/m. The former value must not be considered as being representative of a generic value for any qPlus, as our study stresses the influence of the tip on the estimated stiffness and points towards the need for the individual calibration of these probes. Although the framework focuses on a particular kind of sensor, it may be adapted to any high-k, high-Q nc-AFM probe used under similar conditions, such as silicon cantilevers and LERs.

RETRACTED: Screening of hindered phenol antioxidants by quantum chemical method for improving the aging properties of polyurethane railpad in railway

Polyurethane material has excellent performance and is widely used as railpad in railway, but it is prone to aging and fatigue during long-term service, resulting in a decrease in its performance. In order to improve the aging and fatigue resistance of polyurethane railpad, as well as the efficiency of screening antioxidant, this paper first used quantum chemical method to calculate three types of grafted hindered phenolic antioxidants. Then, polyurethane elastomer railpads with grafted preferred hindered phenolic antioxidants were prepared, and thermal oxidative aging experiments and thermo-oxygen-fatigue coupling aging experiments were conducted. The research results indicate that 3,5-di-tert-butyl-4-hydroxyphenylpropionic acid molecules have better antioxidant properties. When the degradation rate is less than 20%, the activation energy of polyurethane railpads with grafted hindered phenolic antioxidants is about 20% higher than that of ungrafted materials. After 200 days of thermal oxidative aging, polyurethane railpads with grafted hindered phenolic antioxidants maintain high tensile strength and elongation at break, while maintaining stable static stiffness. Their carbonyl index and loss tangent increase only by 10% and 14.8%, respectively, while unmodified samples increase by 29.4% and 26.4%. Scanning electron microscopy also shows a significant reduction in surface cracks on polyurethane railpads grafted with hindered phenolic antioxidants.

Research on the stability prediction for multi-posture robotic side milling based on FRF measurements

In robotic side milling, frequent chatter extremely restricts the acquisition of high surface quality due to weak stiffness, and cutting parameters optimization guided by stability boundary is regarded as an effective solution to solve the chatter problem. In this research, the influence mechanisms of stability were analyzed by evaluating the structural static stiffness and dynamic parameters, and the main factor was characterized as regenerative chatter by means of stability measurements and the theoretical prediction model. The distance-driven multi-posture frequency response function (FRF) prediction model was improved in terms of the dominant modal. Grey correlation analysis was carried out to investigate the influence law of robotic joints to modal parameters, and the difference between far-distance posture and near-distance posture was re-characterized by cross-validation of FRF measurements. Finally, the third-order Hermite–Newton approximation was employed to solve the dynamic model by considering process damping effect, and the results showed the prediction accuracy of the constructed stability boundary was over 85%.

Static and dynamic stiffness optimization on the body structure of an electric quadricycle

Reducing vehicle vibrations is of particular importance due to the adverse effect of vibrations on the ride comfort of passengers. Electric quadricycles are growing rapidly because they are quieter and less polluting than fossil-fuelled vehicles, and these reasons make them a green alternative to personal transportation, and their popularity increases day by day. In this article, the optimization of the body structure of EQ10, an electric quadricycle under development, is discussed to reduce the weight and vibrations transmitted to the passengers with the constraints of bending stiffness and torsional stiffness and yield stress of the elements. The vibrations transmitted to the occupants are measured beneath the driver’s seat by reading the acceleration resulting from the EQ10 excitation sources vibrations. First, a finite element model of the body structure was designed. Then, for optimization, the EQ10 body structure is divided into 29 modules, and in the optimization process, the thickness of these 29 modules is considered as a design variable. The BIGOPT gradient-based method was chosen to solve the optimization problem due to its superior performance to other numerical solution algorithms. To calculate static and dynamic stiffness, modal analyses, and frequency transfer function are conducted to evaluate its general behavior under various functional conditions. Following optimization, results show that the bending and torsional stiffness increased by 45% and 31%, respectively; such fascinating results could not have been obtained without the methods employed in this investigation.

Topology optimization of the wheel frame of the tracked robot with multiple working conditions and multiple objectives

Based on ensuring the static stiffness and dynamic vibration frequency of the caterpillar robot wheel frame under various working conditions, the lightweight design of the caterpillar robot wheel frame is realized. The compromise programming approach is used to establish the multi-objective optimization function and three typical target conditions are simulated and analyzed. An analytic hierarchy process is used to determine the weight coefficient of each target working condition, and the topology optimization of the wheel frame of the tracked robot is carried out comprehensively, considering multi-working conditions and multi-target. The secondary design of the optimized rear wheel frame was carried out, as a result of which, the mass was reduced by 8.4% after optimization, and the first-order frequency was increased by 20 Hz after optimization. The optimized rear wheel frame strength and stiffness met the requirements.

Dynamic performance enhancement of machining center with epoxy granite base: Experiments and finite element simulations

Epoxy granite (EG) is used for machine building applications owing to excellent dynamic properties compared to cast iron (CI). Steel is preferred to reinforce with EG to improve the static stiffness of structures. The effects of addition of steel content on stiffness and damping properties of EG composite were assessed through a specimen level study. Subsequently, the base, which is a primary structure that affects the dynamics of the vertical machining center (VMC) was taken up for investigation. The novelty of the present work is the development of scaled down model of EG base with optimum reinforcement ratio to improve the dynamic response of VMC without compromising the static rigidity of the existing CI base. An experimental study was carried out to validate the assumption made in numerical analysis that EG is isotropic and homogeneous. The results of similitude relations revealed that the EG base exhibited sixteen times higher damping compared to CI base. The influence of EG base on the overall dynamics of VMC was assessed by performing pre-stressed finite element modal analysis and harmonic analysis. Upto seven-fold improvements in directional stiffnesses of VMC with the EG base were observed compared to VMC with CI base. The results of stability lobe diagram revealed a three-fold improvement in material removal rate for VMC with EG base compared to VMC with CI base. Thus, the proposed steel reinforced configuration of EG base has demonstrated a better dynamic performance of VMC without compromising static rigidity.

Wide quasi-zero stiffness region isolator with decoupled high static and low dynamic stiffness

Quasi-zero stiffness (QZS) isolators can achieve the two goals of relatively high static and low dynamic stiffness (HSLDS). However, the static and dynamic stiffness of most QZS isolators remains coupled, causing conflicts in optimizing these dual objectives, especially in the case of large displacement excitations and heavy loads, leading to limited performance. To overcome these limitations, this paper presents an isolator with an extended QZS region that allows for the independent design of HSLDS. The positive stiffness provided by the cantilever beam with curve fixture (CBCF) precisely counteracts the negative stiffness offered by a pair of inclined springs, thereby achieving continuous and extensive QZS characteristics from a point to a region. Dynamic equations are established based on the Lagrangian principle and swiftly solved utilizing the Runge-Kutta-4 method. The proposed isolator exhibits a low resonance frequency, and superior performance when exposed to large displacement excitations compared to alternative isolators. Both static and dynamic experiments confirm a QZS region of 0.023 m and resonance frequencies of below 1 Hz. The proposed isolator facilitates effective vibration isolation for ultra-low-frequency and large displacement excitations.

Pressure and stiffness of a new air-inflated compression wrap.

To report pressure and stiffness, in healthy volunteers, of a new compression device with an air bladder inflated by a pump to regulate pressure. The device was applied to 60 legs of 30 volunteers and set to exert different pressures of 20-50mmHg. The exerted pressure was measured in supine and standing positions and during simple physical exercises; static stiffness index, dynamic stiffness index, and walking pressure amplitudes were calculated. The exerted pressure showed a good correlation with the expected pressure at each pressure range. The stiffness indices were >10mmHg in the range of inelastic materials. The device was considered very easy to apply and use by the testing researchers. The device stiffness is in the same range as the inelastic bandages. Consequently, similar hemodynamic effectiveness could be expected but must be proved. Unlike inelastic bandages, this device was easy to apply and use.