Theoretical Stiffness Research Articles

Nano-scanner for scanning probe microscopes

A two-axes nano-scanner for a scanning probe microscope (SPMs) was developed. The flexure-guided nano-scanner can move SPM samples or the probe itself along the x and y axes. The theoretical stiffness and resonant frequency of the flexure guide were obtained by using Castigliano’s theorem. An optimal nano-scanner that maximize the scanning speed under appropriate constraints was designed. The optimal results were compared with the results of a finite element analysis. The scanner performance was evaluated by using various experiments and was compared with the optimal design results. Finally, atomic force microscope images obtained by using the proposed nano-scanner are presented.

Variations in nanomechanical properties and tissue composition within trabeculae from an ovine model of osteoporosis and treatment

Osteoporosis and treatment may affect both composition and nanomechanical properties and their spatial distributions within the individual trabeculae of cancellous bone at length scales that cannot be captured by bulk measurements. This study utilized 25 mature adult ewes divided into 5 treatment groups. Four treatment groups were given a dietary model for human high-turnover osteoporosis, and two of these were treated with antiresorptive drugs, either zoledronate (ZOL) or raloxifene (RAL), to examine their effects on bulk tissue properties and nanoscale tissue composition and mechanical properties within trabeculae. Treatment effects were most pronounced at the nanoscale, where RAL increased indentation modulus and hardness throughout trabeculae by 10% relative to the osteoporosis model. In comparison, ZOL increased these properties exclusively at the surfaces of trabeculae (indentation modulus +12%, hardness +16%). Nanomechanical alterations correlated with changes in tissue mineralization, carbonate substitution, crystallinity, and aligned collagen. Despite only minimal changes in bulk tissue tBMD, the nanomechanical improvements within trabeculae with both treatments greatly improved the predicted theoretical bending stiffness of individual trabeculae when idealized as cylindrical struts. Hence, small tissue-level alterations in critical locations for resisting trabecular failure could account for some of the discrepancy between the large reductions in fracture risk and the only modest changes in BMD with antiresorptive treatments.

Theoretical and Experimental Contact Stiffness Characterisation of Nominally Flat Surfaces

In this study the tangential contact stiffness between two elastic bodies having nominally flat surfaces with different material combinations is investigated. The tangential contact stiffness between these two elastic bodies is first calculated based on the Greenwood-Williamson-McCool contact theory. Then, the tangential contact stiffness is determined by experimental investigation on a tribometer under the effect of different values of normal load and tangential displacement amplitude. The tangential contact stiffnesses obtained from the experimental data show a good agreement with the theoretical results, where the trends are similar and they are in the same order of magnitude.

Experimental and theoretical rotordynamic stiffness coefficients for a three-stage brush seal

Experimental and theoretical results are presented for a multistage brush seal. Experimental stiffness is obtained from integrating circumferential pressure distribution measured in seal cavities. A CFD analysis is used to predict seal performance. Bristle packs are modeled by the porous medium approach. Leakage is predicted well by the CFD method. Theoretical stiffness coefficients are in reasonable agreement with the measurements. Experimental results are also compared with a three-teeth-on-stator labyrinth seal. The multistage brush seal gives about 60% leakage reduction over the labyrinth seal. Rotordynamic stiffness coefficients are also improved: the brush seal has positive direct stiffness and smaller cross-coupled stiffness.

Study on Dynamical Modeling of the Rolling Mill Vertical System

Vertical vibration is universal in the vertical system of rolling mill. It has a seriously bad effect on the quality of strip. Dynamic model of the vertical system plays an important role in the analysis of vertical vibration in rolling mill. On the basis of 1420mm six roller cold rolling mill, ADAMS rigid model and flexibility model are established in this paper. Contact stiffness of rollers is calculated through ansys simulation. Contact stiffness between the work-roll and strip is calculated by using theoretical methods and stiffness of mill stand is calculated by simplifying mill stand structure. Natural frequency and some amplitude-frequency response of vertical vibration are analyzed. The test results prove that the modeling method is feasible. Vibration derived from the deformation of rolls can be observed directly in the flexible model, which can’t be realized in the rigid body model. At the same time, the new method of calculating vertical system stiffness is also proved to be reasonable.

Stiffness Calculation and Predetermined Preload Optimal Design of Cable Control System

The stiffness of cable flight control systems is one of the most important design parameter for aviation aircraft, because it can change the characteristic of control stick and influence the maneuverability and stability of the flight control system. Flexible cable control system is the main type of mechanical flight control system, in which movement can only be transmitted by cable in tension, the stiffness of cable control system is affected mainly by predetermined preload(PP), however the excessive PP would increase friction between cable and pulley which leads pilot an unfavorable maneuver. In this paper, the theoretical stiffness calculation of cable control system with the complex cable braided construction has been calculated and discussed, in addition the effects of cable deflection and linkage pulley are taken into account to obtain a precise stiffness calculation, and also the predetermined preload related to friction is studied through numerical example, as well as the numerical results have been compared with the experimental results.

Damage Monitoring and Field Analysis of Dynamic Responses of Ha Shuang Prestressed Concrete Box Girder Oblique Bridge before Strengthening

Ha Shuang Bridge is located in Harbin city within Heilongjiang province in the east north of China. The purposes of this study are to monitor the damage in structural members of Ha Shuang prestressed concrete box girder oblique bridge before strengthening and to evaluate the dynamic performance of the bridge structure by adopting dynamic load test. Monitoring process of damage of the bridge structure shows that the web of box girder in the quarter of the second span (about 10.5m from the pier) suffers from serious shear cracks. These cracks extend from the top to lower flange of box girder. The width of cracks rang from 0.5mm to 2mm and the angle is 45 degree. There are 6 bending cracks. The spacing between these cracks rang from 20cm to 30cm and the width is 035mm. In the span No. 3 near the pier, the web of box girder appears 12 diagonal cracks have width rang from 0.1mm to 0.12 mm. The results of dynamic load test analysis show that the values of measured vertical natural frequency is w1 = 3.616Hz and horizontal natural frequency w2 = 4.492Hz less than the values of theoretical natural frequency which is 3.863Hz and 4.848Hz, indicating that the actual stiffness of the bridge structure is less than the theoretical stiffness. Therefore the dynamic working state of bridge structure is not good. Therefore the working state of bridge is not good and it need to repair and strengthening.

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.

Failure Behaviour of Sandwich Beam Subjected to Projectile Impact

Aerodynamic gun impact test is carried out to investigate sandwich beam with metallic skin and Nomex honeycomb core damage mechanism and failure behaviour. Details of the deformation and damage progression within the sandwich beam are observed in particular. The comparisons between the two kinds of specimen with different thickness skins clearly show that the difference in the impact energy consumed in global bending deformation and the localized indentation. Theoretical elastic bending stiffness of the sandwich beam with thicker skins is approximately 2.26 times greater than that of sandwich beam with thinner skins.

Shape Optimization Study of Mild Steel Slit Dampers

This paper presented a new mild steel slit damper(SSD). The new shape was parabolic according to all the cross section having the same maximal stress, and the elastic stiffness and yield displacement formula were derived. Finite element analysis showed that the parabolic shaped damper had a more reasonable load - displacement curve compared with the previously proposed shape. The theoretical stiffness and yield displacement were consistent with the results by finite element method (FEM), and that indicated the presented design method was simple and feasible.

Stiffness Analysis for Large-Travel Rotational Butterfly Pivot

Butterfly pivot is a large-travel rotational flexure pivot, which can provide elastic support for the rotational shaft in several ten degrees. Because of the complex structure, stiffness calculation of butterfly pivot is always completed by the method of Finite Element Analysis (FEA), which is not suitable for parameter design and optimization. The serial structure of four-blade isosceles-trapezoid (FBIT)is proposed to simplified the complex structure of the butterfly pivot. The FBIT is analyzed and the theoretical formula of stiffness calculation for rotation stiffness is derived in detail based on the essential theory of Mechanics of Materials. Design and optimization of rotation stiffness for each element can be achieved easily with the obtained the theoretical formula of rotation stiffness. The total rotation stiffness of the whole butterfly pivot is calculated and the rotation stiffness comparison between using the theoretical method and by the method of FEA is performed. The error between the theoretical rotation stiffness and the result of the FEA is less than 10%. It is acceptable and without any influence on the validity of the work and concept presented in this paper.

A Compact Vertical Scanner for Atomic Force Microscopes

A compact vertical scanner for an atomic force microscope (AFM) is developed. The vertical scanner is designed to have no interference with the optical microscope for viewing the cantilever. The theoretical stiffness and resonance of the scanner are derived and verified via finite element analysis. An optimal design process that maximizes the resonance frequency is performed. To evaluate the scanner’s performance, experiments are performed to evaluate the travel range, resonance frequency, and feedback noise level. In addition, an AFM image using the proposed vertical scanner is generated.

Theoretical elastic stiffness, structural stability and thermal conductivity of La 2T2O 7 ( T = Ge, Ti, Sn, Zr, Hf) pyrochlore

In order to achieve better understanding of the structural/property relationships of La 2 T 2O 7 ( T = Ge, Ti, Sn, Zr, Hf) pyrochlore, first-principles calculations were conducted to investigate the bonding characteristics, elastic stiffness, structural stability and minimum thermal conductivity. The results show that the relatively weak La–O bonds play a predominant role in determining the structural stability, mechanical and thermal properties of these compounds. In addition, the elastic and thermal properties are influenced when the T atom changes from Ge to Hf. When the bonding strength is enhanced by applying hydrostatic pressure, apart from c 11, c 12, and B, which normally increase at high pressures, it is found that the shear elastic moduli, c 44 and G, which relate to the shear deformation resistance, abnormally remain almost constant. The underlying mechanism may help to explain the damage tolerance of pyrochlore compounds. After comprehensive consideration of the elastic anisotropy, a modified David Clarke-type equation is used to calculate the minimum thermal conductivity of the studied pyrochlore materials, which display an extraordinary low thermal conductivity.

Calibration of the Stiffness and Damping Characteristics of a Magnetorheological Fluid Long Squeeze Film Damper in Terms of Reynolds Number

Magnetorheological (MR) fluids are suspensions of fine micron-sized magnetizable particles in a suitable carrier liquid. The rheological properties of the fluid can be controlled by application of a suitable magnetic field and can be used in a variety of applications where variable damping and stiffness characteristics are required, based on the requirements of the rotor dynamic system. In this work, the stiffness and damping characteristics of MR fluid long squeeze film damper operating at low eccentricity ratios are calibrated in terms of Reynolds number of the squeeze film for different clearance and L/D ratios. A theoretical constant magnetic field viscosity model is developed, based on the literature, and is subsequently used to evaluate the theoretical stiffness and damping coefficients, at a particular excitation frequency. The results indicate that the stiffness and damping coefficients decrease with increasing Reynolds number of the squeeze film and is found to be abysmally low, indicating that the flow has ceased and the film has solidified. This is in accordance with the literature that predicts the formation of chain-like semi-solid structures, restricting the flow, and consequently increasing the viscosity, under the influence of the magnetic field. This change in viscosity, in turn, influences the stiffness and damping coefficients and the Reynolds number of the squeeze film. The stiffness and damping coefficients are found to increase with decreasing clearance, increasing L/D ratio, and eccentricity ratio. The results of the investigation assist the designer in obtaining the stiffness and damping characteristics of the squeeze film damper based on the Reynolds number of the squeeze film. Conversely, the stiffness and damping characteristics of the squeeze film damper are calibrated in terms of the Reynolds number of the squeeze film for different damper configurations.

A Contact Stiffness Model of Machined Plane Joint Based on Fractal Theory

A general contact stiffness model is proposed in this paper to study the contacts between rough surfaces of machined plane joints. The proposed model uses fractal geometry for surface topography description, elastic-plastic deformation of contacting asperities, and size-dependent contact stiffness of microcontacts, where the contact stiffness is derived from Hertz contact theory. Three cast iron specimens are produced from different machining methods (milling, grinding, and scraping), and their rough surface profiles are extracted. The structure function method was used to calculate each profile’s fractal dimension and scale coefficient. Both theoretical analysis and experimental results of contact stiffness are obtained for these specimens under different contact loads. The comparison between the theoretical contact stiffness and the experimental results at the interface indicates that the present fractal model for the contact stiffness is appropriate and the theoretical contact stiffness is consistent with the experimental data.

Force Characterization and Rigidity Analysis of a Monolithic Cochlear Prosthesis Actuator

Cochlear implants continue to be used in the treatment of profound deafness. Because of the tonotopic nature of the cochlea, more controlled insertion is perhaps the most important factor affecting device performance. The implant stiffness, and therefore the scala tympani (ST) wall contact force, contributes to insertion difficulties. Attempts to correlate the implant carrier structural properties and the intracochlear contact forces during insertion are limited. Researchers in the Michigan Center for Wireless Integrated Microsystems are developing perimodiolar-shaped silicon and parylene-based thin film cochlear electrode arrays and backing devices for a more controllable implantation. We report a method developed for measuring the thin film actuated electrode array rigidity to quantify the ST and modiolus wall contact forces during and after insertion. The method used a pneumatically actuated polyethylene terephthalate (PET) monolithic electrode actuator using pressurized air (0–200 kPa) for actuation. The prototype actuators consisted of PET tubes with an ID of 365 μm and a wall thickness of 58 μm. Force calculations using cantilever beam bending theory were performed to estimate the tube bending forces as a function of internal pressure and therefore variable structural stiffness. Based on estimations, a method was developed to measure such small forces avoiding the use of commercially available, relatively insensitive load cells. A fixture was fabricated incorporating two brass microcantilevers (reference and deflection arms) sensitive to sub-mN forces applied by the actuator on the deflection arm of the cantilevers. Microcantilver deflection data, captured by an interferometric microscope, was used to calculate the actuator force and eventually the reaction force acting on the actuator. The implant actuation forces ranged from 0–0.76 mN over an actuation pressure range of 0–140 kPa, from nearly straight to the relaxed perimodiolar post-implantation shape. For estimating the implant rigidity (EI), the actuator stiffness and the actuation pressure was correlated. The actuator stiffness at different actuation pressures was obtained both theoretically (using beam bending theory and PET tube structural properties) and experimentally (using the derived unconstrained actuator deflections at measured actuator forces). The theoretical and experimental stiffness values ranged from 3.6E-08 to 5.34E-07 N/μm and 2.5E-08 to 7.8E-06 N/μm respectively over the working pressure range. The calculated rigidity constant (EI) of the best prototype insertion tool from the experimental stiffness measurement was 6.71E06 Nμm2. The insertion tool-ST wall contact forces were calculated, using the estimated rigidity, in a hypothetical insertion situation. Force calculations assumed that the implant is equipped with actuator deflection feedback sensors and the actuator's stiffness remains constant over its entire length for a given operating pressure. A contact force of 1.19 mN was found acting on the cochlear ST wall when the insertion tool hits the wall and deflects by 200 μm at an actuation pressure of 140 kPa.

Development of Novel XY Micropositioning Stage

Along with the rapid development of semiconductor, photonics and ultra-precision engineering, ultra-precision positioning stages are becoming more necessary than ever. In this study, one novel XY micropositioning stage is proposed, in which bi-axis circular notch flexure and cantilever hinge mechanism are optimal designed as bearing to provide smooth and guided motion. The theoretical stiffness of stage is provided and verified by FEM analysis. Finally, the micro-positioning stage is built and its resolution is experimentally validated to be less than 4nm.

A New Model for Maximizing the Bending Stiffness of a Symmetric Three-Ply Paper or Board

Based on the theoretical bending stiffness model for a symmetrical three-ply structure, researchers developed a model that could predict the maximum bending stiffness of a three-ply symmetric structure as a function of density and elastic modulus. The model was tested with experimental data either generated in the authors’ laboratory or reported in the literature. The model accurately predicted the maximum bending stiffness based on the middle-layer share of basis weight. Model results indicate that it is possible to increase the middle-layer share without loss of bending stiffness, leading to reduced costs and lower virgin fiber requirements. Results show that the model is a useful and rapid tool for papermakers to predict the maximum bending stiffness of either coated papers or three-ply boards for a given furnish. Furthermore, the model has potential to be developed further to predict maximum bending stiffness for boards with more than three plies.

Theoretical elastic stiffness of quaternary crystalY3Si5N9Oby first-principles investigation

The theoretical elastic stiffness of Y(3)Si(5)N(9)O, the only Y-Si-O-N quaternary crystal that contains a framework of corner-sharing SiN(4) and/or SiON(3) tetrahedron in three dimensions, was investigated using the first-principles total energy calculations. The full set of second order elastic coefficients, polycrystalline bulk and shear moduli, and anisotropic elastic moduli were reported and further compared with those of Y(2)O(3) and beta-Si(3)N(4). The equation of state and compressibility of Y(3)Si(5)N(9)O were investigated at pressures up to 50 GPa. The crystal structure is stable up to 50 GPa and exhibits anisotropic compressibility under hydrostatic pressure. The relatively softer YN(6) and/or YN(5)O polyhedra are more prone to distort or deform than the SiN(4) and/or SiON(3) tetrahedra. Therefore, although the crystal structure of Y(3)Si(5)N(9)O contains a Si-N-O framework similar to that in beta-Si(3)N(4), it displays elastic stiffness between those of Y(2)O(3) and beta-Si(3)N(4).

Stiffness Analysis of Crossed Roller Bearings

This paper introduces an analytical method to calculate the stiffness of crossed roller bearings. Load distribution analysis of rollers considering combined radial, axial and moment load makes it possible to apply to three dimensional elastic deformation problems. From equilibrium conditions on forces and Hertz contact theory, relational equations are derived. Solving these non-linear equations numerically with Newton-Raphson method, load distribution and inner ring displacement with fixed outer ring are obtained. Also experiment has been conducted to estimate a discrepancy between the analytical and experimental results. Experimental displacement of inner ring is confirmed to be almost coincident with theoretical one under radial load but smaller than theoretical one by about 20% in the case of axial and moment load. On the other hand the difference between the theoretical and experimental stiffness at higher load is found to be almost the same.