Simple Spring Research Articles

A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots

Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is critical for CDPR’s operation in which highly accurate motion is required. However, most of the current methods related to vibration analysis of CDPRs rely on simple spring models which have limitations in their performance and complexity that are not general to analyze the vibration of various CDPRs. Hence, accurate, simple and general approaches for vibration analysis in CDPRs are need. To solve this problem, this paper presents the finite element method (FEM) and the modified analytical method to analyze the vibration of CDPRs. To validate these methods, free vibration analysis was conducted using the proposed methods for the planar and spatial cable-driven parallel robots. The natural frequencies of these two CDPRs were computed by the proposed two methods and compared with those of the commercial software, SAP2000. The solutions obtained by the FEM and the modified analytical models turned out to be close to SAP2000’s results, thereby verifying the validity of the proposed methods.

Stiffness of a Nonlinear Adiabatic Polytropic Air Spring Model: Quantitative and Conductive Investigation

The conservation of mass and energy formulas along with the Newton’s second law of motion are used to derive a simple nonlinear adiabatic air spring model. The purpose of this paper is to evaluate air spring stiffness and identify the characteristic behavior of this model. The model consists of six coupled nonlinear differential equations. The assessment of this model is based on solving these governing equations numerically using the Runge Kutta routine Matlab based platform. It has been found out that the air spring stiffness increases exponentially with the increase in the air spring piston diameter. Due to its sensitivity and its nonlinearity, the model shows signs of chaos, which have been observed in the vertical motion or in the control volume, pressure for the chosen range of parameters.

A Novel Simple Approach to Material Parameters from Commonly Accessible Rheometer Data.

When characterizing the viscoelastic properties of polymers, shear rheological measurements are commonly the method of choice. These properties are known to affect extrusion and nozzle-based processes such as fiber melt spinning, cast film extrusion and 3D-printing. However, an adequate characterization of shear thinning polymers can be challenging and still insufficient to not only describe but predict process relevant influences. Furthermore, the evaluation of rheological model systems in literature is mostly based on stress–relaxation experiments, which are rarely available for various polymeric materials. Therefore, a simple approach is presented, that can be used to evaluate and benchmark a wide range of rheological model systems based on commonly accessible frequency sweep data. The approach is validated by analyzing alginate PH176 solutions of various concentrations, a thermoplastic poly-urethane (TPU) Elastollan 1180A melt, the liquid silicon rubber Elastosil 7670 and a polycaprolactone (PCL) fiber-alginate composite system. The used rheological model systems, consisting of simple springs and dashpots, are suitable for the description of complex, viscoelastic material properties that can be observed for polymer solutions and gel-like systems. After revealing a suitable model system for describing those material properties, the determination and evaluation of relevant model parameters can take place. We present a detailed guideline for the systematic parameter revelation using alginate solutions of different concentrations as example. Furthermore, a starting point for future correlations of strut spreading in 3D-bioprinting and model parameters is revealed. This work establishes the basis for a better understanding and potential predictability of key parameters for various fabrication techniques.

Output decoupling modeling of a XY flexure-based compliant manipulator

This paper presents the coupling stiffness modeling of an XY flexure-based manipulator. Stiffness/compliance equations for compliant mechanisms are first obtained. According to a simplified spring model, the input stiffness and coupling stiffness of the proposed manipulator consisting of outer and inner kinematic chains are then derived. This simplified spring model is composed of four parallel chains, such as the left, lower, upper and right parallel chain. Subsequently, the external force/moment and the output displacement of the manipulator are analyzed by using finite element analysis (FEA). Finally, a prototype of the manipulator is fabricated. Its motion range and the corresponding cross-coupling displacements are measured, and thus the cross-coupling ratios can be derived. It demonstrates that the manipulator possesses good decoupling characteristic, and the proposed theoretical model is reasonable and accurate.

Simplified spring models for concrete segmental lining longitudinal joints with gaskets

To investigate the full mechanical behavior of concrete segmental lining longitudinal joints with gaskets, a numerical bending test is performed by a detailed three dimensional (3D) continuum numerical model for the segment joint of the Yellow River Crossing Tunnel lining. Simplified spring models including a simplified plate-spring analytical model and a simplified solid-spring numerical model are proposed to analyze the rotational stiffness of the longitudinal joint. The bending test reveals that the mechanical behavior of the longitudinal joint with gaskets can be divided into four stages. The proposed simplified plate-spring analytical model and simplified solid-spring numerical model allow the effect of the properties of bolts and various gaskets, the concrete contact force, the geometry of the joint section and the subjected loads to be taken into consideration. The results of the simplified spring models are well consistent with these of the detailed 3D continuum numerical model, and the proposed models can be adopted for the simulation of the segment longitudinal joints with various gaskets.

Damage mechanism and dynamic constitutive model of frozen soil under uniaxial impact loading

The dynamic mechanical properties of frozen soil at different temperatures and high strain rates were tested using a split Hopkinson pressure bar (SHPB), and the variation of the wave impedance of the frozen soil was analyzed. Viscoelastic theory confirmed that an increase in the wave impedance in frozen soil over short times is the result of unfrozen water relaxation. Unfrozen water is an important factor that increases the peak stress of frozen soil under impact loading. Based on the compression failure mechanism of frozen soil, the internal microcracks were classified as random or vertical microcracks. The mesoscopic parameter (microcrack density) and the macroscopic physical quantity (wave velocity) were connected by the effective medium theory, and the longitudinal wave velocity was selected as the damage variable. The effects of the low-frequency parameters in the ZWT (Zhu–Wang–Tang) model (Wang, 2003) when applied to frozen soil were evaluated. Under impact-loading conditions, with the initiation and expansion of the internal microcracks in the frozen soil, the Maxwell element represented by the low-frequency parameters lost its function rather than degenerating into a simple spring, and thus, it continued to contribute to the macroscopic mechanical properties of the frozen soil. Finally, damage was introduced into the improved ZWT model to establish a dynamic constitutive model of the frozen soil. The predicted and experimental results agreed well, which verified the applicability of the model.

Influence of soil-structure interaction on seismic demands in shear wall building gravity load frames

This paper presents a complete and simple linear method, with a suitable force modification factor, to compute seismic demands in the gravity load resisting system (GLRS) of shear wall buildings including foundation movement. Based on the method first proposed by Beauchamp, Paultre and Léger in 2017, this paper compares two approaches to consider foundation movement on linear soil media such as (a) a simple rotational spring under each core and (b) a complete set of springs and dashpots. A fixed-base model using code foundation factors is also used for comparison. Springs and dashpots are assessed by modelling soil-structure interaction (SSI) with solid finite elements. Then, these approaches are evaluated for a typical 12-storey concrete shear wall building considering several nonlinear time history analyses (NLTHAs). SSI is modelled with a set of springs and dashpots, and ground motions are selected from the conditional spectrum method. NLTHAs are performed for soil classes ranging from stiff to soft, and the effect of the underground structure cracking is analysed. Analysis results show that the proposed methods are accurate in computing seismic demands in the GLRS compared to NLTHA. Foundation movements should be explicitly modelled for soil class D or softer, and underground structure cracking should be considered. For the very soft soil class E, the behaviour of the building is poorly captured in linear analysis methods; thus, nonlinear analyses are required.

A Simple Spring Mechanics for Molar Intrusion

Loss of the mandibular molar can lead to extrusion of maxillary molar, which may result in occlusal interference and inadequate space to restore the mandibular edentulous space with prosthesis. This molar extrusion also leads to functional disturbance. Thus, the present article will showcase the fabrication of simplified spring to intrude the maxillary first molar within 9 weeks.

Stability and dynamic analysis of partially cracked thin orthotropic microplates under thermal environment: an analytical approach

An analytical model is proposed to analyze the vibration and buckling problem of partially cracked thin orthotropic microplate in the presence of thermal environment. The differential governing equation for the cracked plate is derived using the classical plate theory in conjunction with the strain gradient theory of elasticity. The crack is modeled using appropriate crack compliance coefficients based on the simplified line spring model. The influence of thermal environment is incorporated in governing equation in form thermal moments and in-plane compressive forces. The governing equation for cracked plate has been solved analytically to get fundamental frequency and central deflection of plate. To demonstrate the accuracy of the present model, few comparison studies are carried out with the published literature. The stability and dynamic characteristics of the cracked plate are studied considering various parameters such as crack length, plate thickness, change in temperature, and internal length scale of microstructure. It has been concluded that the frequency and deflection are affected by crack length, temperature, and internal length scale of microstructure. Furthermore, to study the buckling behavior of cracked plate, the classical relations for critical buckling load and critical buckling temperature is also proposed considering the effect of crack length, temperature, and internal length scale of microstructure.

A nonlinear rubber spring model for the dynamics simulation of a high-speed train

ABSTRACT A simple and more-accurate nonlinear rubber spring model is proposed for railway vehicle dynamics analysis. The characteristics of dynamic stiffness and damping are investigated through both simulations and lab tests with various displacement amplitude and frequency. Similar to the existing rubber models, the proposed model contains three components, an elastic force, damper force and the Maxwell element, which are used to present the frequency- and amplitude-dependence. The model has four nonlinear inputs, which are determined by test results. In order to utilise all the test results under various excitations, five extra constants are introduced during the model parameter identification to minimise the error between the computing results and tests. Comparative analysis shows that the computing results of the proposed model has an overall good agreement with measurements under various excitations at either low or high frequency under environment temperature −40°C to 50°C, and requires a lower computational cost than the existing rubber spring model with either friction or fractional calculus. Thus it is more suitable for the vehicle dynamics analysis of a high-speed train.

Bond strength of deformed bar embedded in steel-polypropylene hybrid fiber reinforced concrete

This paper deals with the bond strength of deformed bar embedded in steel-polypropylene hybrid fiber reinforced concrete (HFRC) matrix. The benefits of hybrid fibers were evaluated through a series of monotonic/cyclic pull-out testing on 72 specimens. The influences of fiber characteristics, i.e. the volume fraction and aspect ratio, on the failure mode and the complete bond-slip responses were analyzed. Upon a simplified spring model, the effects of fiber reinforcement at different loading stages were further discussed. The results showed that for a well-confined HFRC specimen, the cyclic bond response at the pre-peak stage almost approached its monotonic response with slight reduction in the ultimate bond strength. Compared to the specimen made with plain concrete, the introduction of hybrid fibers could exert obvious positive influences on the bond strength, due to the synergetic effects in inhibiting the propagation of cracks at multi-scale and multi-stages. Finally, an analytical model was proposed to estimate the ultimate bond strength, in which the effects of fiber reinforcement, stirrup confinement and geometrical shape of deformed bar were taken into consideration. The model was subsequently well validated by various independent experimental results.

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.

Response of a linear viscoelastic splitter plate attached to a cylinder in laminar flow

The flow-induced deformation of a viscoelastic thin plate attached to the lee side of a circular cylinder subjected to laminar flow is numerically investigated. An in-house fluid–structure interaction solver couples the sharp-interface immersed boundary method for fluid dynamics with a finite-element method for structural dynamics. Extending published results on elastic materials, the Standard Linear Solid (SLS) model is used to represent viscoelasticity of the plate, governed by the following two parameters: (a) the ratio of the non-equilibrium to equilibrium Young’s modulus (R), and (b) the ratio of dimensionless material damping to the dimensionless non-equilibrium Young’s modulus (τ). The focus of the present study is to examine the dynamic response of the viscoelastic plate at Reynolds number of Re=100. The amplitude and the time to achieve a dynamic steady state of a plate with 0.1<R<5 and 0.1<τ<10 have been investigated. The plate attains a self-sustained time-periodic oscillation with a plateau amplitude for the range of R=[0.1–5] for all values of τ. The dimensionless tip displacement amplitude (AY,tip) is found to be a non-monotonic function of τ. When the forcing frequency (vortex shedding frequency) is lesser (greater) than the natural frequency (considering the equilibrium Young modulus) of the plate, AY,tip decreases (increases) asymptotically. The theoretical analysis of a simple spring–mass–dashpot model of SLS is undertaken to understand the effect of sinusoidal forcing on the plate dynamics. Analytical predictions show general agreement with the non-monotonic behaviour of the numerically computed AY,tip. The results suggest that careful tuning of the damping may be effectively employed to enhance power output for energy extraction applications or to suppress flow-induced vibration when it is detrimental to the structure.

Flexural Behavior of Hybrid Composite Beam (HCB) Bridges

A new hybrid composite beam (HCB) has recently been used in the construction of three bridges in Missouri, USA. HCB consists of self-consolidating concrete (SCC) that is poured into classical arch shape and tied at the ends by steel tendons. Both the concrete and the steel are tucked inside a durable fiberglass shell, and the voids are filled with polyiso foam. This paper aims to examine the flexural behavior of an in-service HCB, evaluate the current methodology and assumptions, and propose modifications to that methodology. To achieve these goals, the strains induced in HCB elements due to different loading stages were experimentally measured. Numerical predictions of the strains were performed via the existing methodology, the modified procedure, and a finite element model (FEM) that was constructed using ANSYS V14. The linear FEM predicted the strains with acceptable accuracy. The model clarified that the foam achieves partial composite action between the HCB elements, resulting in a strain incompatibility between them. The current methodology was found to be unable to predict the maximum compressive strain in the concrete arch. The modified procedure is based on the strain compatibility assumption. However, it models the HCBs as curved beam rather than a straight one, using a simplified spring model to represent the beam supports. These modifications achieved significant enhancements in estimating the strains under service loads.

A model study of 3-dimensional localization of breast tumors using piezoelectric fingers of different probe sizes.

Mammography is the only Food and Drug Administration approved breast cancer screening method. The drawback of the tumor image in a mammogram is the lack of tumor depth information as it is only a 2-dimensional projection of a 3-dimensional (3D) tumor. In this work, we investigated 3D tumor imaging by assessing tumor depth information using a set of piezoelectric fingers (PEFs) with different probe sizes which were known to be capable of eliciting tissue elastic responses to different depths and tested it on model tumor tissues consisted of gelatin with suspended clay inclusions. The locations of the top and bottom surfaces of an inclusion were resolved by solving a simple spring model using the elastic measurements of the PEFs of different probe sizes as the input. The lateral sizes of an inclusion were determined as the full width at half maximum of the Gaussian fit to the measured lateral tumor elastic modulus profile. The obtained lateral inclusion sizes were in close agreement with the actual values, and the deduced depth profiles of an inclusion also agreed with the actual depth profiles so long as the bottom surface of the inclusion was within the depth sensitivity of the PEF with the largest probe size. This work offers a simple non-invasive method to predict the extent of a tumor in all 3 dimensions. The method is also non-radioactive.

Connecting the legs with a spring improves human running economy.

Human running is inefficient. For every 10 calories burned, less than 1 is needed to maintain a constant forward velocity - the remaining energy is, in a sense, wasted. The majority of this wasted energy is expended to support the bodyweight and redirect the center of mass during the stance phase of gait. An order of magnitude less energy is expended to brake and accelerate the swinging leg. Accordingly, most devices designed to increase running efficiency have targeted the costlier stance phase of gait. An alternative approach is seen in nature: spring-like tissues in some animals and humans are believed to assist leg swing. While it has been assumed that such a spring simply offloads the muscles that swing the legs, thus saving energy, this mechanism has not been experimentally investigated. Here, we show that a spring, or 'exotendon', connecting the legs of a human reduces the energy required for running by 6.4±2.8%, and does so through a complex mechanism that produces savings beyond those associated with leg swing. The exotendon applies assistive forces to the swinging legs, increasing the energy optimal stride frequency. Runners then adopt this frequency, taking faster and shorter strides, and reduce the joint mechanical work to redirect their center of mass. Our study shows how a simple spring improves running economy through a complex interaction between the changing dynamics of the body and the adaptive strategies of the runner, highlighting the importance of considering each when designing systems that couple human and machine.

Computing arbitrary Lagrangian Eulerian maps for evolving surfaces

The good mesh quality of a discretized closed evolving surface is often compromised during time evolution. In recent years this phenomenon has been theoretically addressed in a few ways, one of them uses arbitrary Lagrangian Eulerian (ALE) maps. However, the numerical computation of such maps still remained an unsolved problem in the literature. An approach, using differential algebraic problems, is proposed here to numerically compute an arbitrary Lagrangian Eulerian map, which preserves the mesh properties over time. The ALE velocity is obtained by finding an equilibrium of a simple spring system, based on the connectivity of the nodes in the mesh. We also consider the algorithmic question of constructing acute surface meshes. We present various numerical experiments illustrating the good properties of the obtained meshes and the low computational cost of the proposed approach.

Modeling collisions of arbitrary-shaped particles in simulations of particulate flows

Simulations of dense suspensions containing arbitrary-shaped particles must deal with particle collision models. This paper deals with the wet collisional interactions between particles in a carrier fluid, in the context of immersed boundary treatment of fully resolved particles. When collisions of non-spherical particles occur, several parameters that govern collisional mechanics are challenging to obtain: these include collision point, normal and tangential forces, degree of overlapping between particles, the local relative velocity and the local curvatures at the collision point. These challenges are overcome in this paper by defining a field variable, i.e. a distance function that describes the particle on a regular Cartesian grid. A Simplified Spring Collision Method (SSCM) is proposed to model wet collision forces. The Stokes number at the collision point is computed from the particle's relative velocities and local curvatures and is used to calculate the restitution coefficient; damping is incorporated into the model by modifying the restitution coefficient when the rebound phase starts. The methods are validated against experiments and other benchmarks and shown to provide good results over a wide range of Stokes numbers. The capability of the method is also tested successfully for non-circular particle shapes.

A novel design for an adaptive aeroelastic energy harvesting system: flutter and power analysis

Extracting energy from waste sources could be a new prospect toward energy crisis, specially from wind energy. A simple mechanical system, including mass and spring, if combined with a wing, could extract more energy. A novel design for a cantilever beam with an airfoil is presented in this paper for harvesting more energy. This design allows the harvester to operate in a wider range of airspeeds. Electrical energy will be extracted from a piezoelectric patch on the beam. This novel design moves a point mass along the beam regarding the airspeed because this movement might compromise between flutter occurrence and more energy extraction. In order to understand this compromise, the effect of the position of the point mass on the onset of flutter instability and output power of the system is investigated. Mathematical models include both linear and nonlinear aeroelastic models. For flutter analysis, a linear model called finite state model is used. The nonlinear part of the problem is modeled by ONERA dynamic stall model. A parametric study is conducted in order to have a better understanding of design criteria. Both flutter onset airspeed and output power are achieved for ten different places of the point mass on the beam. According to the results, a passive mass-positioning system could be able to set the position of the point mass for any given airspeed. Based on these results, a proper passive mechanism is designed including a set of springs, strings, guiding rails, pulleys, and a parachute. The aeroelastic model used in this paper is validated by experiments of the state of the art. The novel mechanism in this design-oriented paper continues the concepts and experiments, presented in the literature.

A piezoelectric spring pendulum oscillator used for multi-directional and ultra-low frequency vibration energy harvesting

Low frequency vibration is a ubiquitous energy existing in our environment, but a large efficient harvesting of which remains challenging. This paper presents a simple piezoelectric spring architecture based on a common binder clip structure. The harvester with pendulum spring allows the energy of the dynamic mass to be converted into electrical energy in the piezoelectric transducer. Due to the basic characteristics of spring pendulums, the proposed harvester can efficiently scavenge not only ultra-low frequency but also multi-directional vibrational energies. Modeling and design are conducted and a normalized expression of the harvester behavior is given. Chirp and human motion excitations are used to evaluate the proposed harvester’s performances. Simulation and experimental results are in good agreement. The proposed device could generate a high output power (13.29 mW) at a low operating frequency (2.03 Hz), which shows great application prospects in the power supply of wearable products, ocean buoys, etc.