High Static Stiffness Research Articles

A novel bio-inspired multi-joint anti-vibration structure and its nonlinear HSLDS properties

A unique bio-inspired multi-joint leg-like or limb-like vibration isolation structure is studied by mimicking the skeleton and joint structures of animal legs, and its advantage in passive vibration isolation is systematically investigated. This bio-inspired structure uses several small quadrilateral structures composed by short adjustable rods and a transverse spring to simulate the multi-articulation of animal legs and adopts long rods to simulate the skeleton. The equivalent static stiffness property, loading capacity and dynamic vibration isolation performance of the structure are systematically studied. It is shown that the nonlinear stiffness characteristics of the structure can lead to very excellent vibration isolation capability in the low-frequency band. Different from many existing quasi-zero-stiffness (QZS) isolators in the literature, this novel anti-vibration structure can demonstrate superior high static but low dynamic stiffness (HSLDS) property and thus excellent vibration isolation performance, subject to large vibration amplitude. Through adjusting proper structural parameters including the rod-length, assembly angle, spring stiffness and layer number according to the influence of the structural parameters on the nonlinear stiffness property, the new structure can have the optimal vibration isolation performance without sacrificing its loading capacity to meet actual requirements. Especially, the length of long rods which is used to simulate the skeleton can be adjusted to obtain better vibration isolation performance than adjusting other parameters, followed by the adjustment of the parameters of small quadrilateral structures. The analysis of the influence of structural parameters on the vibration isolation performance shows that the symmetry between different layers has an important role in maintaining the characteristic of the HSLDS. The comparison with other existing vibration isolation structures of the QZS property also indicates that, the new vibration isolation structure can have a better vibration isolation performance with relatively a smaller size of the overall structure. Experiments are successfully conducted and validated the beneficial nonlinear properties of the structure. This novelbio-inspired anti-vibration structure would have great advantages in practical engineering applications.

Design and analysis of epoxy granite vertical machining centre base for improved static and dynamic characteristics

The structural vibration in conventional machine tools which are generally made of cast iron may lead to poor surface finish of the machined components. This has led to the investigations on alternative materials for machine tool structures such as concrete, polymer concrete and epoxy granite which have higher damping properties but lesser Young's modulus. However, higher static stiffness with higher damping is essential for improving the static and dynamic characteristics of machine tool structures. Hence, this work focuses on replacing the vertical machining centre base made of cast iron with steel reinforced epoxy granite to improve the structural static stiffness. A finite element model of the above base is developed and validated against the experimental data obtained using modal analysis. The validated numerical approach is applied for investigating the seven progressive design configurations of base reinforced with steel. It is found that the epoxy granite base of Design configuration-7 with L-channels has significantly reduced the deformation by 56 and 36% considering milling and drilling operations, respectively, in comparison to cast iron base. Further, the natural frequencies of the above configuration are higher in all the modes (by more than 50%) under consideration than those of the existing cast iron structure. Therefore, the proposed configuration of base is a viable alternative for the existing base in order to achieve higher structural damping. The novelty of the present work is the design of epoxy granite vertical machining centre base using steel reinforcements to improve structural rigidity with ease of manufacturing.

Hobbing of Cylindrical Wheels without Coolants

This article studies dry hobbing of external cylindrical wheels by worm wheel hobs and reasons why some gear manufactures use hobbing without cutting fluids. Cutting fluids reduce frictional wear, provides temperature cooling of the tool or workpiece and helps flush away the chips from the cutting zone. But uneven cooling and different cutting conditions on the engaging and disengaging sides of a gear mesh provoke intensive wear of the teeth of the worm wheel hob, thus decreasing the life of worm hobs and increasing both the consumption of cutting tools and expenses for them. In this context, it becomes rather difficult to achieve efficiency and stability for the hobbing process. In the recent times, the cost of coolant disposal has been raised; in some cases, it accounts for 15-20% in terms of shop costs. Research was carried out under the following experimental conditions: a hobbing machine equipped with an automation system of high efficiency and with basic units of high static and dynamic stiffness; a high-accuracy worm hob from powdered metal wear-resistant high-speed steel of grade Р6М5К5; a workholding device with an elastic bush, and various cutting modes. Recommendations are given on using the multi-cycle hob-shifting strategy rather than the strategy of single-cycle shifting; and advantages gained by this technique are observed. Best cutting conditions and precision attained by dry gear-hobbing are described.

Measurement and analysis of sound absorption by a metallic composite foam

A composite foam consisting of polyurethane foam embedded in metallic foam is fabricated and evaluated for sound absorbing properties. The normal incidence sound absorption coefficient is measured in an impedance tube for three different types of foams including the composite foam, a rigid framed metallic foam, and an elastic framed polyurethane foam. A lumped element model is used to predict the energy dissipation mechanisms, which include viscous and thermal losses, structural losses, and coupling losses at the metal and polyurethane interface. The best performing composite foam increased sound absorption by a factor of 6 (from 0.1 to 0.6) in the low frequency test range (around 600 Hz) and by a factor of 2 (from 0.2 to 0.4) over the entire test frequency range (250–4500 Hz). The composite foam maintains the high static stiffness of the metal foam and exhibits acoustic compliance characteristic of the polyurethane foam. Composites such as those presented in this work are advantageous for engineering applications where combined high stiffness and energy absorption are required.

Stability and dynamics of an orifice based aerostatic bearing with a compliant back plate

Abstract Aerostatic bearings are extensively used in precision machines. The dynamic performance of aerostatic bearings is limited by the inherent compromise between stiffness and damping. To enhance their performance, the bearing surface is made compliant to the pressure distribution, leading to high static stiffness. To investigate the damping characteristics of bearings with structural compliance, this work presents a dynamic model encapsulating the fluid-structure interaction. Experimental analysis validated the model and a sensitivity analysis established a design guideline ensuring high stiffness and positive damping. The findings reported an increase by a factor of three in stiffness compared to conventional bearing while ensuring a positive damping.

An interpolating element-free Galerkin scaled boundary method applied to structural dynamic analysis

• An efficient semi-analytical method, namely the IEFG-SBM is developed for structural dynamic analysis. • The proposed method unifies the advantages of the SBM and the IEFG method. • The IIMLS method is superior to the MLS approximation because its shape function has the delta function property . • The IIMLS method is also superior to the IMLS method because the weight function involved is nonsingular. • The improved continued fraction solution can represent the inertial effect at high frequencies with no internal mesh. An efficient semi-analytical method, namely the interpolating element-free Galerkin scaled boundary method (IEFG-SBM) is developed for structural dynamic analysis in this paper, which is based on boundary scattered nodes with no need of element connectivity. Since the shape functions of the improved interpolating moving least-squares (IIMLS) method satisfy the delta function property, the essential boundary conditions, as a result, can be enforced accurately without any additional efforts. Based on the improved continued fraction, the dynamic properties of a bounded domain are expressed by the high order static stiffness and mass matrices. This continued fraction solution is computationally more robust and the transient response can be obtained directly in the time domain using standard procedures in structural dynamics. It is testified from the computational results that the present method for structural dynamic analysis is quite easy to be implemented with high accuracy.

Structural investigation of steel-reinforced epoxy granite machine tool column by finite element analysis

Higher damping with higher static stiffness is essential for improving the static and dynamic characteristics of machine tool structures. The structural vibration in conventional machine tools, which are generally made up of cast iron and cast steel, may lead to poor surface finish and the dimensional inaccuracy in the machined products. It leads to the investigation of alternative machine tool structural materials such as concrete, polymer concrete, and epoxy granite. Although epoxy granite has a better damping capacity, its structural stiffness (Young's modulus) is one-third as compared to cast iron. Therefore, the present work represents optimization of the structural design of the vertical machining center column by introducing various designs of steel reinforcement in the epoxy granite structure to improve its static and dynamic characteristics using experimental and numerical approaches. A finite element model of the existing cast iron vertical machining center column has been developed and validated against the experimental data obtained using modal analysis. Furthermore, finite element models for various epoxy granite column designs have been developed and compared with the static and dynamic characteristics of cast iron column. A total of nine design configurations for epoxy granite column with steel reinforcement are evolved and numerical investigations are carried out by finite element analysis. The proposed final configuration with standard steel sections has been modeled using finite element analysis for an equivalent static stiffness and natural frequencies of about 12–20% higher than cast iron structure. Therefore, the proposed finite element model of epoxy-granite-made vertical machining center column can be used as a viable alternative for the existing column in order to achieve higher structural damping, equivalent or higher static stiffness and, easy and environmental-friendly manufacturing process.

A novel eight-legged vibration isolation platform with dual-pyramid-shape struts

An eight-legged vibration isolation platform (ELVIP) with dual-pyramid-shape (DPS) struts is proposed in this paper to achieve six-degree-of-freedom vibration isolation. The DPS strut has higher static stiffness and lower dynamic stiffness than the equivalent linear strut due to geometric nonlinearity, and therefore the ELVIP with DPS struts possesses high-static–low-dynamic-stiffness characteristic which is desirable for widening the frequency range of isolation. The layout of the ELVIP legs is conducive to vibration decoupling and has higher reliability than six-legged platforms. Firstly, the stiffness characteristics of the DPS strut are derived; then the dynamic model of the ELVIP with DPS struts is established and the steady-state responses are obtained analytically; finally, the isolation performance is studied and the effects of damping and excitation amplitudes are investigated. It is shown that the ELVIP with DPS struts, as a passive approach, can achieve good isolation performance in all six directions with a small static deflection.

Active-passive hybrid vibration isolation with magnetic negative stiffness isolator based on Maxwell normal stress

Abstract A new magnetic negative stiffness isolator based on Maxwell normal stress is proposed to improve the low-frequency vibration isolation performance of a system with high static support stiffness. The isolator can provide high negative stiffness maintaining compact size and light weight. The negative stiffness characteristic of the isolator was first modeled through magnetic circuit analysis. Then, the passive vibration isolation performance of the isolator was validated experimentally. Active control was then introduced into the isolation system to improve its ability to adapt to external disturbances and suppress the system’s resonance response. The governing equation of the active-passive hybrid vibration isolation system was established. The simulated and experimental results showed that the magnetic negative stiffness isolator with active-passive hybrid control can greatly reduce the isolation initial frequency and significantly suppress the system resonance response in comparison with passive methods. The present work provides a promising way to realize low-frequency broad-band vibration isolation for systems with high static support stiffness.

Vibration control of high-speed trains self-excitation under-chassis equipment by HSLDS vibration isolators

To minimize the self-excitation effects of the equipment on the carbody, a high static and low dynamic stiffness (HSLDS) vibration isolator is proposed by connecting a negative stiffness unit and a positive linear stiffness spring in parallel. The nonlinear stiffness of the HSLDS isolator can be designed according to the needs of any target stiffness curve. A vibration test is applied to obtain the vibration acceleration of the under-chassis equipment. A rigid-flexible coupling multi-body dynamic model of a high-speed train is established which considers the elastic vibration of the carbody and the self-excitation of the under-chassis equipment based on the tested result. Different connection methods of the under-chassis equipment including rigid hanging, vibration isolation theory (VIT) hanging, dynamic vibration absorber (DVA) hanging and HSLDS hanging are applied and their effects on the carbody vibration and ride quality are investigated. The simulation results reveal that the proposed HSLDS vibration isolator can effectively isolate the self-excitation of the under-chassis equipment from the carbody and enhance the ride quality of the high-speed train.

Design of the Hydrostatic Thrust Spherical Bearing with Restrictors (Fitted Type)

The hydrostatic bearings are broadly observed in industrial applications owing to their potential characteristics of low running friction, high load-carrying capacity, high stiffness and small viscous dissipation. Spherical bearings have advantages over other configurations of bearings because of their self-aligning property and also their capacity to accept both radial and thrust loads. Operation of the spherical bearings is unaffected by angular miss-alignment. They are mainly used in machine tools, precision measuring instruments, hydraulic piston pumps and motors, gyroscope gimbals, telescopes, radar tracking units, air craft engines and rotary drum of centrifugal separator for enriched uranium. The main objective of this part of study is to handle the fitted bearing design taking into consideration the combined effects of rotational inertia, surface roughness and the fluid film viscosity variability. The mathematical expressions derived in part 2 for this type of bearings with its different configurations (with and without recess; hemispherical and partial hemispherical seats) have been used in the detailed bearing design. Improving the previous design through developing some mathematical expressions, a new conception is adopted to reveal the bearing consistency showing how the fluid flow rate pulsation or intermittent could be prevented. The detailed design procedures show the advantages of this method to get the central pressure ratio mathematically through maximizing the flow rate with minimizing the supply pressure which means minimum pump power to get maximum discharge. This design showed very high mean static stiffness of all the bearing configurations and an acceptable temperature rise for a heavy duty bearing without the need to a use a cooling system.

A Simulation Study for the Design of Membrane Restrictor in an Opposed-Pad Hydrostatic Bearing to Achieve High Static Stiffness

The effects of a membrane restrictor’s design parameters on the performance of a hydrostatic opposed-pad bearing are presented in this article. Compared to the single-pad bearing, the opposed-pad bearing can perform much better in terms of static stiffness over a wider load range. It is also found that, for small bearing eccentricity, the optimal design restriction ratio of 0.25 still results in high bearing stiffness even if the dimensionless stiffness of membrane is not the optimal value of 1.33. Furthermore, decreasing the ratio of the upper effective area to the lower effective area generally increases the applicable working range of the bearing. Additionally, for high loading demands, the chance for further improvement of bearing performance by employing different design parameter for each pad is examined. Finally, a design procedure for designing the membrane restrictor for an opposed-pad bearing to achieve high static stiffness is given.

A six degree of freedom passive vibration isolator with quasi-zero-stiffness-based supporting

A six degree of freedom nonlinear passive vibration isolator is proposed based on Stewart platform configuration with the quasi-zero-stiffness structure as its legs. Due to the high static stiffness and low dynamic stiffness of each leg, the proposed six degree of freedom system can realize very good vibration isolation performance in all six directions while keeping high static load-bearing capacity in a pure passive manner. The mechanic model of the proposed six degree of freedom isolator and the dynamic equation of the isolator are established successively. Theoretical analysis on cross coupling stiffness reveals that the system can demonstrate quasi-zero-stiffness property in all six degree of freedom. Moreover, an analysis on stability shows that the condition of structural parameters for the isolator to realize quasi-zero-stiffness is also the stability boundary of the system. A series of numerical simulations on displacement transmissibilities in coupled degree of freedoms, the coupling effects of transmissibility, and a dynamic response in random excitation are carried out to show the effectiveness of the proposed six degree of freedom isolator, as well as the influence of structural parameters on vibration attenuation performance. Considering its high performance in a simple passive manner, it can be foreseen that the proposed six degree of freedom isolator will be applied in various engineering practices with multi-degree of freedom vibration isolation.

A 6-DOF passive vibration isolator based on Stewart structure with X-shaped legs

By employing the nonlinear stiffness and damping characteristics of a bio-inspired X-shaped structure (XSS) with passive springs and the Stewart platform with six degrees of freedom, a passive 6-DOF vibration isolation platform is designed and experimentally studied for its vibration isolation performance. A three-layer asymmetrical XSS is adopted as legs to construct a passive Stewart platform. Because of the specially designed XSS, the stiffness and damping properties of the system can be adjusted by changing structural parameters and thus it is designable to achieve an excellent performance including excellent stability and high-static-low-dynamic-stiffness isolation effect in all six directions with satisfactory loading capacity in the vertical direction, without any active control. Analytical and extensive experimental analysis of static stiffness and vibration response of the system revealed that (a) the aXSS Stewart platform has very beneficial high static nonlinear stiffness which can provide sufficient loading capacity; (b) the platform can achieve very low dynamic stiffness in each direction without losing loading capacity; (c) both static and dynamic stiffness is adjustable and designable with structure parameters and very easy to implement in a pure passive manner.

Band gaps in grid structure with periodic local resonator subsystems

The grid structure is widely used in architectural and mechanical field for its high strength and saving material. This paper will present a study on an acoustic metamaterial beam (AMB) based on the normal square grid structure with local resonators owning both flexible band gaps and high static stiffness, which have high application potential in vibration control. Firstly, the AMB with variable cross-section frame is analytically modeled by the beam–spring–mass model that is provided by using the extended Hamilton’s principle and Bloch’s theorem. The above model is used for computing the dispersion relation of the designed AMB in terms of the design parameters, and the influences of relevant parameters on band gaps are discussed. Then a two-dimensional finite element model of the AMB is built and analyzed in COMSOL Multiphysics, both the dispersion properties of unit cell and the wave attenuation in a finite AMB have fine agreement with the derived model. The effects of design parameters of the two-dimensional model in band gaps are further examined, and the obtained results can well verify the analytical model. Finally, the wave attenuation performances in three-dimensional AMBs with equal and unequal thickness are presented and discussed.

Analysis Method of Stiffness and Load Capacity of Euler Spring with High Static Stiffness and Low Dynamic Stiffness

A large number of studies have shown that nonlinear passive control devices have good vibration attenuation and isolation effect. And vibration isolation systems with nonlinear stiffness have more advantages than linear systems. The paper addresses the stiffness and load capacity design problem of Euler springs with varying cross-sections. Firstly, in order to analyze nonlinear behavior of curved beams due to large geometric deformations, a set of first-order differential equations are established, which can be easily solved by numerical integration. Secondly, a curved beam is taken for example to compare analytical results calculated by using the first-order differential equations and ANSYS simulation results. Then the influence of geometric parameters of curved beams with varying cross-sections on structural stiffness and load capacity is investigated by using ANSYS. Finally, a design strategy for stiffness and load capacity of curved beams is summed up.

Static characteristics of a water-lubricated hydrostatic thrust bearing with a porous land region and a capillary restrictor

In this paper, a water-lubricated hydrostatic thrust bearing with a porous land region and capillary restrictor is proposed, and the results of theoretical and experimental investigations of its static characteristics are presented. The results showed that the water-lubricated hydrostatic thrust bearing with a porous land region had good operating characteristics; in particular, it had a high load capacity and static stiffness close to that of a porous bearing when operating with a clearance of less than 15μm, and a high load capacity and static stiffness equivalent to that of a pocket bearing when running with a clearance larger than 15μm.

Comparison of the dynamic performance of nonlinear one and two degree-of-freedom vibration isolators with quasi-zero stiffness

Nonlinear stiffness isolation mounts, which offer a high static stiffness alongside a low dynamic stiffness or even quasi-zero stiffness (QZS) over a displacement range, have been proposed. These vibration isolators offer a higher isolation frequency band of low transmissibility than conventional linear devices. Here, three kinds of nonlinear two degree-of-freedom (DOF) vibration isolators with QZS characteristic are analyzed in order to further improve the isolation performance. The dynamic response is obtained using the harmonic balance method, and the peak dynamic displacement is obtained using backbone curve analysis and energy balancing method. The optimum isolation performance of the nonlinear 2DOF vibration isolators is evaluated for four performance indexes and compared with three baseline vibration isolators. These are a linear and a QZS 1DOF vibration isolator as well as a linear 2DOF vibration isolator. To ensure a fair comparison, the static displacement of each vibration isolator is kept constant. The comparison demonstrates that a nonlinear 2DOF vibration isolator can be tuned to achieve a better isolation performance in the higher isolation frequency band than the baseline vibration isolators, while retaining a moderate peak dynamic displacement and peak transmissibility. In addition, the best vibration isolator is identified for each of the four performance indexes.

Parameters design of a membrane-type restrictor with single-pad hydrostatic bearing to achieve high static stiffness

The analysis described in this article shows that a high static stiffness of the bearing is attainable as two design parameters of membrane-type restrictor are properly chosen. The first one is the dimensionless stiffness of the membrane and the other one is the design restriction ratio of the bearing system. When the deformation-load relationship of the restrictor is compliance with the ideal trend, the stiffness of the bearing should theoretically approach infinite in most application range. It was derived that a dimensionless membrane stiffness of 1.33 and a design restriction ratio of 0.25 is the solution for such condition. The film thickness for the bearing will be maintained at designed levels over a loading range.

Mechanical design of buckled beams for low-stiffness elastic suspensions: Theory and application

Axially compressed buckled beams have been used for several decades as elastic suspensions characterized by high static stiffness and low dynamic stiffness. The most comprehensive mathematical modelling of buckled beams is based on the elastica theory, a rational framework that seeks the equilibrium configuration for arbitrarily large deflections and rotations. The use of the elastica model is straightforward for analysis purposes but is rather awkward for design tasks because it requires handling of elliptic functions. This paper presents approximate equations developed from the elastica solution to facilitate the structural synthesis of buckled-beam suspensions starting from high-level engineering specifications. The step-by-step design procedure is illustrated by means of a case study and the theoretical predictions are validated against test data and finite element results.