Dynamic stiffness characteristics of aero-engine elastic support structure and its effects on rotor systems:mechanism and numerical and experimental studies

The support structure of a rotor system is subject to vibration excitation,which results in the stiffness of the support structure varying with the excitation frequency(i.e.,the dynamic stiffness).However,the dynamic stiffness and its effect mechanism have been rarely incorporated in open studies of the rotor system.Therefore,this study theoretically reveals the effect mechanism of dynamic stiffness on the rotor system.Then,the numerical study and experimental verification are conducted on the dynamic stiffness characteristics of a squirrel cage,which is a common support structure for aero-engine.Moreover,the static stiffness experiment is also performed for comparison.Finally,a rotor system model considering the dynamic stiffness of the support structure is presented.The presented rotor model is used to validate the results of the theoretical analysis.The results illustrate that the dynamic stiffness reduces the critical speed of the rotor system and may lead to a new resonance.

Nonlinear Static and Dynamic Stiffness Characteristics of Support Hydraulic System of TBM

Full-face hard rock tunnel boring machines(TBM)are essential equipment in highway and railway tunnel engineering construction.During the tunneling process,TBM have serious vibrations,which can damage some of its key components.The support system,an important part of TBM,is one path through which vibrational energy from the cutter head is transmitted.To reduce the vibration of support systems of TBM during the excavation process,based on the structural features of the support hydraulic system,a nonlinear dynamical model of support hydraulic systems of TBM is established.The influences of the component structure parameters and operating conditions parameters on the stiffness characteristics of the support hydraulic system are analyzed.The analysis results indicate that the static stiffness of the support hydraulic system consists of an increase stage,stable stage and decrease stage.The static stiffness value increases with an increase in the clearances.The pre-compression length of the spring in the relief valve a ects the range of the stable stage of the static stiffness,and it does not a ect the static stiffness value.The dynamic stiffness of the support hydraulic system consists of a U-shape and reverse U-shape.The bottom value of the U-shape increases with the amplitude and frequency of the external force acting on the cylinder body,however,the top value of the reverse U-shape remains constant.This study instructs how to design the support hydraulic system of TBM.

Dynamic characteristics of the planetary gear train excited by time-varying meshing stiffness in the wind turbine

Wind power has attracted increasing attention as a renewable and clean energy. Gear fault frequently occurs under extreme environment and complex loads. The time-varying meshing stiffness is one of the main excitations. This study proposes a 5 degree-of-freedom torsional vibration model for the planetary gear system. The influence of some parameters(e.g., contact ratio and phase difference) is discussed under different conditions of a single teeth pair and double pairs of teeth. The impact load caused by the teeth face fault, ramped load induced by the complex wind conditions, and the harmonic excitation are investigated. The analysis of the time-varying meshing stiffness and the dynamic meshing force shows that the dynamic design under different loads can be made to avoid resonance, can provide the basis for the gear fault location of a wind turbine, and distinguish the fault characteristics from the vibration signals.

Analysis of the Relationship Between the Meshing Stiffness and the Inherent Characteristics of Planetary Gear Transmission Mechanism

According to the relationship between the meshing stiffness and the inherent characteristics of a seven-speed three-row coupled planetary transmission mechanism,a equivalent concentrated mass dynamics model of the planetary transmission mechanism is established.The natural frequency of the planetary gear train at a specific gear is calculated and extracted.The relationship between the meshing stiffness of each row and the natural frequency of the system is analyzed,thereby avoiding possible resonance behavior by changing the meshing stiffness.These results show that the meshing stiffness,in its range of possible values,has nearly no effect on the low order natural frequency(<4.000.Hz),and that the time-varying meshing stiffness mainly affects the natural frequencies of the higher-and middle-order parts of the system.Changes of the natural frequencies lead to the change of the system's corresponding vibration mode,which will change the vibration situation of the system.

Assessment of Existing Bridge’s Beam Bending Stiffness Using Crack Characteristics

At present, the bearing capacity evaluation is mainly based on load detection, which requires closed traffic and has certain risks. With the increase of service time, the cracks of reinforced concrete beam bridge will gradually develop and the stiffness will reduce, resulting in the decrease of bearing capacity. Therefore, in this paper, the calculation of stiffness reduction coefficient by using crack characteristic parameters, which provides basic data for bearing capacity evaluation, has been studied. In this paper, using regression analysis through fracture characteristics of four model beam observation and test load-displacement curve characteristic parameters, crack flexural rigidity of the beam bridge relationship has been set up. The qualitative assessment based appearance of cracks in the structure of checks has been converted to quantitative assessment. And compared with the test results of a real bridge, comparative results show that the assessment is objective and reliable. It makes the assessment more objective and scientific. A new way of Quantitative assessment of the structural performance has been provided for a large number of existing reinforced concrete beam bridge.

Analysis of dynamic characteristics of self-aligning ball bearing

A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method （JHM）, and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric analysis of the centrifugal force and the gyroscopic moment, the contact loads, the contact angles, the radial deformation and the radial stiffness is carried out. The analytical results show that the applied loads and the rotational speed are two main factors that can influence the distributions of the contact loads and values of the contact angles. The centrifugal force and the gyroscopic moment increase with the increase in the rotational speed, resulting in the decrease of the inner raceway contact load and the increase of the outer raceway contact load. The outer raceway contact angle increases under the centrifugal force; on the contrary, the inner raceway contact angle decreases. Furthermore, the differences between the inner and the outer contact angles increase with the increase in the rotational speed. The higher rotational speed results in the decrease in radial stiffness for the self-aligning ball bearing, and the raceway curvature coefficient, to some extent, also influences the radial stiffness.

Dynamic characteristics of a novel damped outrigger system

This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method(DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and effi ciency are verifi ed in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the infl uences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coeffi cient. Results show that the modal damping ratio is signifi cantly infl uenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.

Influence Analysis of Machining and Installation Errors on the Radial Stiffness of a Non-Pneumatic Mechanical Elastic Wheel

Machining and installation errors are unavoidable in mechanical structures. However, the effect of errors on radial stiffness of the mechanical elastic wheel(ME-Wheel) is not considered in previous studies. To this end, the interval mathematical model and interval finite element model of the ME-Wheel were both established and compared with bench test results. The intercomparison of the influence of the machining and installation errors on the ME-Wheel radial stiffness revealed good consistency among the interval mathematical analysis, interval finite element simulation,and bench test results. Within the interval range of the ME-Wheel machining and installation errors, parametric analysis of the combined elastic rings was performed at different initial radial rigidity values. The results showed that the initial radial stiffness of the flexible tire body significantly influenced the ME-Wheel radial stiffness, and the inverse relationship between the hinge unit length or suspension hub and the radial stiffness was nonlinear. The radial stiffness of the ME-Wheel is predicted by using the interval algorithm for the first time, and the regularity of the radial stiffness between the error and the load on the ME-Wheel is studied, which will lay the foundation for the exact study of the ME-Wheel dynamic characteristics in the future.

Numerical Simulation and Experimental Verification of the Stiffness and Stability of Thrust Pad Aerostatic Bearings

Many researchers concentrate on improving the stiffness and stability of aerostatic bearings, however the contradiction between stiffness and stability is still existed. Therefore, orifice, multiple, and porous restrictors are designed to illustrate the influence of restrictor characteristics on the stability and stiffness of the aerostatic circular pad bearings. Because both the stiffness and stability of aerostatic bearings are determined by the internal pressure distribution, the full Navier?Stokes(N?S) equations are applied to solve internal pressure distribution in bearing film by using computational fluid dynamics(CFD) method. Simulation results present that the stiffness and stability of aerostatic circular pad bearings are influenced significantly by geometrical and material parameters, such as film thickness, orifice diameters, and viscous resistance coe cient. Verified by the experimental data, the micro vibration of orifice restrictor is almost the same as multiple restrictors with amplitude of 0.02 m/s~2, but it is much stronger than the porous restrictors with acceleration of 0.006 m/s~2. The optimal stiffness of multiple restrictors increased by 46%, compared to only 30.2 N/μm of orifice restrictor, and the porous restrictors had obvious advantage in the small film thickness less than 6 μm where the optimal stiffness increased to 38.3 N/μm. The numerical and experimental results provide guidance for improving the stiffness and stability of aerostatic bearings.

Research on the Structural Rigidity Characteristics of a Reconfigurable TBM Thrust Mechanism

To improve the adaptability of TBMs in diverse geological environments,this paper proposes a reconfigurable Type-V thrust mechanism(V-TM)with rearrangeable working states,in which structural stiffness can be automatically altered during operation.Therefore,millions of configurations can be obtained,and thousands of instances of working status per configuration can be set respectively.Nonetheless,the complexity of configurations and diversity of working states contributes to further complications for the structural stiffness algorithm.This results in challenges such as difficulty calculating the payload compliance index and the environment adaptability index.To solve this problem,we use the configuration matrix to describe the relationship between propelling jacks under reconfiguration and adopt pattern vectors to describe the working state of each hydraulic cylinder.Then,both the dynamic compatible equation between propeller forces of the hydraulic cylinders and driving forces,and the kinematic harmonizing equation between the hydraulic cylinder displacements and their deformations are established.Next,we derive the stiffness analytical equation using Hooke’s law and the Jacobian Matrix.The proposed approach provides an effective algorithm to support structural rigidity analysis,and lays a solid theoretical foundation for calculating the performance indexes of the V-TM.We then analyze the rigidity characteristics of typical configurations under different working states,and obtain the main factors affecting structural stiffness of the V-TM.The results show the deviation degree of structural parameters in hydraulic cylinders within the same group,and the working status of propelling jacks.Finally,our constructive conclusions contribute valuable information for matching and optimization by drawing on the factors that affect the structural rigidity of the V-TM.

A Study on the Dynamic Characteristics of the Damping Capillary Type Spherical Hydrostatic Bearing

The dynamic mathematical model of the damping capillary type spherical hydrostatic bearing is established firstly,then the dynamic characteristics of the hydrostatic bearing are analysized in detail.By means of theoretical reasoning,a design guide that relates to J0,the static stiffness of the hydrostatic bearing,is put forward to guarantee that the hydrostatic bearing possesses the excellent dynamic characteristics.At last,the effect of the structural parameters on J0 is studied.

Laboratory investigation into effect of bolt profiles on shear behaviors of bolt-grout interface under constant normal stiffness (CNS) conditions

Rock bolts have been widely used for stabilizing rock mass in geotechnical engineering.It is acknowledged that the bolt profiles have a sound influence on the support effect of the rock bolting system.Previous studies have proposed some optimal rib parameters(e.g.rib spacing);unfortunately,the interface shear behaviors are generally ignored.Therefore,determination of radial stress and radial displacement on the bolt-grout interface using traditional pull-out tests is not possible.The load-bearing capacity and deformation capacity vary as bolt profiles differ,suggesting that the support effect of the bolting system can be enhanced by optimizing bolt profiles.The aim of this study is to investigate the effects of bolt profiles(with/without ribs,rib spacing,and rib height)on the shear behaviors between the rock bolt and grout material using direct shear tests.Thereby,systematic interfacial shear tests with different bolt profiles were performed under both constant normal load(CNL)and constant normal stiffness(CNS)boundary conditions.The results suggested that rib spacing has a more marked influence on the interface shear behavior than rib height does,in particular at the post-yield stage.The results could facilitate our understanding of bolt-grout interface shear behavior under CNS conditions,and optimize selection of rock bolts under in situ rock conditions.

Analysis of the hull girder vibration by dynamic stiffness matrix method

Dynamic stiffness matrix method is applied to compute vibration of hull girder in this paper. This method can not only simplify the computational model, but also get much higher frequencies and responses accurately. The analytical expressions of dynamic stiffness matrix of a Timoshenko beam for transverse vibration are presented in this paper. All effects of rotatory inertia and shear deformation are taken into account in the formulation. The resulting dynamic stiffness matrix combined with the Wittrick-Williams algorithm is used to compute natural frequencies and mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solved by the mode superposition method. The computational results are compared with those obtained from other approximate methods and experiment, and it indicates that the method is accurate and efficient.

Numerical characteristics of the full operator hybrid simulation method

The full operator method （FOM） has been proposed to overcome some of the shortcomings of the commonly used operator splitting method （OSM）. In particular, the FOM is improved by increasing the accuracy of both the predictor and corrector using the estimated tangent stiffness of the tested structure. The numerical characteristics of the FOM, including stability and accuracy, are investigated in this study. It is shown that FOM is conditionally stable. The stability and accuracy characteristics are dependent on the accuracy of the estimated tangent stiffness and the parameters associated with the acceleration variation in the time-stepping integration method. Mass-spring systems with different types of nonlinearity, including hardening, stiffening, and softening behavior, are used to evaluate the performance of the FOM. It is found that the FOM can capture these types of nonlinearity with satisfactory accuracy. Using a prototype 12-story composite coupled wall system, the influences of the strong nonlinearity of the system as well as the displacement control errors from hydraulic actuators on the performance of the FOM are explored. The results show that the FOM is capable of generating reasonably accurate results despite the presence of strong structural nonlinearity and displacement control errors.

Mechanical Characteristics of Radial Magnetic Bearing

This paper is based on the example of a radial magnetic bearing possessed of eight-pole, and derives the calculation formulas of static and dynamic mechanical characteristics of the bearing, in which the shape and curvature of surface, eccentricity and tilt of the journal are taken into account. Variations of the static and dynamic characteristics of the radial magnetic bearing versus static tilt parameters of journal are discussed. The outcomes show that the static tilt of the journal has influence on the mechanical characteristics of radial magnetic bearing, and change the static load capacity between two radial magnetic bearings and exert coupling effect between them. To study the dynamics of a practical rotor-magnetic bearing system, at least six stiffness coefficients in each radial magnetic bearing must be considered in ideal case, and twelve stiffness coefficients must be considered in general case of tilting journal. Such a find can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

The Analysis of Stiffness for Rubbery Metallic Material Based on Mesoscopic Features

In this article, deformation and mechanical response of a rubbery metallic material were investigated. First, the mesoscopic structural properties of the material and its evolution during part producing were analyzed and described in detail. Then the inherence relationship between the macroscopic mechanical properties and mesoscopic structural characteristics were studied, in which the related mesoscopic structural characteristics were limited in the basic unit (mm) scale such as the radius of metal wire and unit coil, etc. Furthermore, according to the mesoscopic properties of the material, a curved beam unit based on the mesoscopic scale and shape factor was introduced to bridge the mechanical response and the mesoscopic parameters such as the beam orientation and spatial distribution. In the end, a mesoscopic stiffness model was proposed, from which the macroscopic mechanical properties of material could be deduced from the mesoscopic characteristic size, shape and the mechanical properties of base metallic material.

Vibration transmissibility characteristics of smart spring vibration isolation system

The objective of this work was to study the vibration transmissibility characteristics of the undamped and damped smart spring systems. The frequency response characteristics of them were analyzed by using the equivalent linearization technique, and the possible types of the system motion were distinguished by using the starting and ending frequencies. The influences of system parameters on the vibration transmissibility characteristics were discussed. The following conclusions may be drawn from the analysis results. The undamped smart spring system may simultaneously have one starting frequency and one ending frequency or only have one starting frequency, and the damped system may simultaneously have two starting frequencies and one ending frequency. There is an optimal control parameter to make the peak value of the vibration transmissibility curve of the system be minimum. When the mass ratio is far away from the stiffness ratio, the vibration transmissibility is small. The effect of the damping ratio on the system vibration transmissibility is significant while the control parameter is less than its optimal value. But the influence of the relative damping ratio on the vibration transmissibility is small.

Simulation and Experimental Study on Load-bearing Deformation Characteristics of 11R22.5 Vehicle Retreaded Tire

The finite element bearing deformation simulation was implemented on 11.00R22.5 retreaded tires by ANSYS software in the paper in order to further clarify the bearing deformation characteristics of retreaded tires and improve the performance of retreaded tires effectively.The characteristic laws of bearing radial deformation and bearing lateral deformation of retreaded tire and new tires of the same model under different working conditions were obtained through load deformation tests.The radial deformation calculation results,simulation results and measured results of retreaded tires were comparatively analyzed.The calculation formula of bearing radial deformation of retreaded tires was proposed based on the linear regression principle.The difference of bearing deformation characteristics and ground area characteristics of retreaded tires and new tires were comparatively analyzed.The results showed that the radial and lateral deformation of retreaded tires and new tires is increased with the increase of radial load when the tire pressure was constant,and the increase trend is approximately linear.The radial stiffness of retreaded tires is similar to that of new tires under certain tire pressure and low load.The radial stiffness of retreaded tires is larger than that of new tires,and the stiffness difference is increased with the increasing of load under constant tire pressure and high load.Rubber aging phenomenon in retreaded tire carcass have an impact on the bearing deformation characteristics of retreaded tires,thereby producing great impact on the remaining service life of retreaded tires.

开挖顺序及内支撑早期刚度对软土基坑稳定性影响规律

深基坑开挖变形控制是软土基坑工程的难题,工程中常采用密集的混凝土内支撑来提高支撑刚度,然而实际工程中未能合理考虑软土深基坑的开挖顺序和混凝土内支撑早期刚度影响,往往导致基坑实际变形远大于设计值。结合珠三角水资源配置工程的软土深基坑,利用验证后的数值模拟方法研究了不同开挖顺序及混凝土内支撑早期刚度对基坑受力和变形特性的影响规律,得出了分层分区非对称开挖和对称开挖对地连墙水平位移和地表沉降的影响规律。结果表明:尽管非对称开挖会造成基坑两侧的地连墙位移和地表沉降差异,但是密集内支撑条件下非对称开挖比对称开挖对于基坑周围地表沉降和地连墙水平位移影响更小并能够大量节约工期;受混凝土内支撑早期刚度影响,施作内支撑后越早进入下一步开挖,地连墙水平位移和周围地表沉降越大;考虑内支撑早期刚度影响时基坑上部的内支撑轴力会增大,而下部的内支撑轴力会减小,早期刚度越小,这种趋势越明显;现场施工时难以实时动态监测混凝土的弹性模量,极易造成内支撑轴力的早期监测数据失真,甚至给工程带来错误决策。