Investigation of the Effect of the Force Arm on the Bending Capability of Prestressed Glulam Beam

Prestress enables the Glulam beam could make full use of the compression strength,and then increase the span,but it still could not reduce all drawbacks,such as cross-section weakening and small force arm.To avoid slotting and ensure suitable tension and compression couple,one kind of novel anchor has been proposed,which could meet the bearing capacity requirement.And then the bending test of prestressed Glulam beams with a geometric scale ratio of 1:2 was simulated,to investigate the effect of the force arm on bending capacities,failure modes,and deformation performance.Results show that increasing the force arm could improve the ultimate bending per-formance of the beam significantly,and the anchor arm length has a certain effect on the performance,but it is not obvious.Finally,based on Finite element method analysis,the practice design suggestions have been offered.

Seismic stability of reinforced soil walls under bearing capacity failure by pseudo-dynamic method

In order to evaluate the seismic stability of reinforced soil walls against bearing capacity failure,the seismic safety factor of reinforced soil walls was determined by using pseudo-dynamic method,and calculated by considering different parameters,such as horizontal and vertical seismic acceleration coefficients,ratio of reinforcement length to wall height,back fill friction angle,foundation soil friction angle,soil reinforcement interface friction angle and surcharge.The parametric study shows that the seismic safety factor increases by 24-fold when the foundation soil friction angle varies from 25°to 45°,and increases by 2-fold when the soil reinforcement interface friction angle varies from 0 to 30°.That is to say,the bigger values the foundation soil and/or soil reinforcement interface friction angles have,the safer the reinforced soil walls become in the seismic design.The results were also compared with those obtained from pseudo-static method.It is found that there is a higher value of the safety factor by the present work.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

3D FE Analysis of Effect of Ground Subsidence and Piled Spacing on Ultimate Bearing Capacity of Piled Raft and Axial Force of Piles in Piled Raft

The effects of ground subsidence and piled spacing on axial force of piles in squared piled rafts were investigated using numerical analysis. Two cases of piled rafts in soft clay including case 1 (s = 2d) and case 2 (s = 4d) with s and d were piled spacing and piled diameter respectively were considered in this study. Undrained (without ground water pumping) and drained (with ground water pumping) conditions were applied in each case in order to evaluate variations of ultimate bearing capacity of piled raft and axial force of the piles in piled raft. The results showed that ultimate bearing capacity increased about 25% for undrained condition and about 32% for drained condition when piled spacing increased from 2d to 4d. In the same piled spacing, axial force of the piles increased about 9% for piled spacing of 2d and 7% for piled spacing of 4d when drained condition was applied. When piled spacing increased 2 times (2d to 4d), the axial force of piles increased about 7% for undrained condition and about 5% for drained condition.

NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

Characteristics of the Main Journal Bearings of an Engine Based on Non-linear Dynamics

Many simple nonlinear main journal bearing models have been studied theoretically, but the connection to existing engineering system has not been equally investigated. The consideration of the characteristics of engine main journal bearings may provide a prediction of the bearing load and lubrication. Due to the strong non-linear features in bearing lubrication procedure, it is difficult to predict those characteristics. A non-linear dynamic model is described for analyzing the characteristics of engine main journal bearings. Components such as crankshaft, main journals and con rods are found by applying the finite element method. Non-linear spring/dampers are introduced to imitate the constraint and supporting functions provided by the main bearing and oil film. The engine gas pressure is imposed as excitation on the model via the engine piston, con rod, etc. The bearing reaction force is calculated over one engine cycle, and meanwhile, the oil film thickness and pressure distribution are obtained based on Reynolds differential equation. It can be found that the maximum bearing reaction force always occurs when the maximum cylinder pressure arises in the cylinder adjacent to that bearing. The simulated minimum oil film thickness, which is 3 μm, demonstrates the reliability of the main journal bearings. This non-linear dynamic analysis may save computing efforts of engine main bearing design and also is of good precision and close connection to actual engine main journal bearing conditions.

POSTBUCKLING RESPONSE OF CANTILEVER BEAMS OF NON-LINEAR ELASTIC MATERIAL SUBJECTED TO SUBTANGENTIAL FOLLOWER FORCES

This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvature relation, the proposed problem is reduced to a specialeigenvalue problem of non-linear differential equation. An approximate solution is achieved byusing a simple and very effective technique, which leads to reliable results even in the case of verylarge deflections. The initial postbuckling path depending on the subtangential follower forces inequilibrium is then obtained. Moreover, the individual and coupling effect of the subtangential fol-lower force, the material non-linearity and the beam slenderness ratio on the initial postbucklingpath are also discussed in detail.

Non-Linear Forces and Irreversibility Problem in Classical Mechanics

Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Three-dimensional seismic isolation bearing and its application in long span hangars

Based on the seismic response characteristics of space frame structures,a new type of seismic isolation bearing defined as a three-dimensional seismic isolation bearing（3DSIB） is developed in this paper.The bearing offers excellent properties such as multi-dimensional seismic isolation,reasonable rotation capability,good ability to resist lifting load,uncoupled stiffness in horizontal and vertical directions,etc.In the 3DSIB,the horizontal dimension is designed by combining the Teflon sliding device and helical spring,while the vertical dimension is developed by introducing disk springs or helical springs.The mathematical model of the 3DSIB was established and its performance with the critical parameters was tested on a shaking table.Furthermore,the 3DSIB was applied in a 120 m span hangar structure and simulated using SAP2000 software to evaluate its performance in practical structures.The performance of the structures with and without 3DSIB was compared.It is shown that the hangar structure with 3D bearings achieves a better performance.The axial force and acceleration response of the structures with 3DSIB are effectively reduced,while the displacement response of the bearing is within the predetermined range.

UNBALANCE RESPONSE AND TOUCH-RUBBING THRESHOLD SPEED OF ROTOR SUBJECTED TO NONLINEAR MAGNETIC FORCES

Because of the effect of unbalance excitation and nonlinear magnetic force, the large vibration of the rotor supported by active magnetic bearing（AMB） will go beyond the radial gap of the bearing, even causing mechanical touch-rubbing when the system works at an operational speed closer to the critical speed. In order to investigate this problem, the linear model and nonlinear model of the single mass symmetric rigid rotor system supported by AMB are established respectively and the corresponding transfer functions of close-loop system are given. To pass through the numerical calculation by using MATLAB/Simulink, the effect of both the unbalance response and threshold speed of touch-rubbing of the system subjected to nonlinear magnetic forces and nonlinear output current of power amplifier are studied. Furthermore, threshold speed of touch-rubbing of the rotor-bearing system is defined and the results of numerical simulation are presented. Finally, based on above studies, two methods of increasing the touch-rubbing threshold speed are discussed.

Application of the Non-Stationary Oil Film Force Database

The technique of non stationary oil film force database for hydrodynamic bearing is introduced and its potential applications in nonlinear rotor dynamics are demonstrated. Through simulations of the locus of the shaft center aided by the database technique, nonlinear stability analysis can be performed and the natural frequency can be obtained as well. The easiness of 'assembling' the individual bush forces from the database to form the bearing force, makes it very convenient to evaluate the stability of various types of journal bearings. Examples are demonstrated to show how the database technique makes it possible to get technically abundant simulation results at the expense of very short calculation time.

Analysis of axial force of double circular arc helical gear hydraulic pump and design of its balancing device

In view of the axial force produced in the working process of double arc helical gear hydraulic pump,the theory of differential equation of curve and curved surface was utilized so that the calculation formula of axial force was obtained and the relationship between the axial force and structure parameters of gears was clarified.In order to balance the axial force,the pressure oil in the high pressure area was introduced into the end face of the plunger to press the plunger against the gear shaft,and the hydrostatic bearing whose type is plunger at the end of the shaft was designed.In order to verify the balance effect of axial force,the leakage owing to end clearance and volume efficiency of gear hydraulic pump before and after the balancing process was analyzed.This paper provides a new analysis idea and balance scheme for the axial force produced in the working process of the double arc helical gear hydraulic pump,which can reduce the leakage owing to end clearance caused by the axial force and improve the volume efficiency of the gear hydraulic pump.

Nonlinear dynamic behaviors of ball bearing rotor system

Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.

GA-BASED PID NEURAL NETWORK CONTROL FOR MAGNETIC BEARING SYSTEMS

In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA（genetic algnrithm）-based PID neural network controller is designed and trained tO emulate the operation of a complete system （magnetic bearing, controller, and power amplifiers）. The feasibility of using a neural network to control nonlinear magnetic bearing systems with unknown dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions （chromosomes）, increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.

Analysis of bearing capacity of pile foundation in discontinued permafrost regions

Piles are the main building foundation in permafrost regions. Thawing the permafrost foundation would have a negative effect on a pile, and may cause damage to the building. This paper focuses on the effects of negative friction force due to the melt of permafrost, and presents four calculated methods for bearing capacity of a pile. An engineering station was taken as an example, where the lengths of a pile were compared based on four methods. Finally, quick field load tests were carried out, and some meaningful conclusions are presented. Thus, these analytical results can be used to design a pile for permafrost regions.

A COMPUTATIONAL APPROACH FOR PRESSURE DISTRIBUTION AND ROTORDYNAMIC COEFFICIENTS OF JOURNAL BEARINGS WITH COMBINED RADIAL AND MISALIGNMENT MOTIONS

A computational approach is presented to handle an enlarged linear rotordynamic model whichsimultaneously includes both radial and misalignment motions.The interactive force and momentbetween the rotating and non-rotating members are modeled using an adaptation of the classicalReynolds lubrication equation for incompressible laminar isoviscous films.First,the governingequation is derived and the method of solution is introduced based on a 2-dimension,9-point cen-tral difference.Second,force and moment components are computed by numerical integration ofthe film pressure distribution.Finally,the rotordynamic coefficients are yielded according to thegeneralized force gradients.

THE EDDY LOSSES OF A MAGNETIC THRUST BEARING

Accurate calculations of losses associated with the operation of magnetic bearings are particularly important for high speed applications where the rotor losses are expected to be large and for some particular applications where even low power losses will be critical. Power losses in the magnetic thrust bearing is often neglected, but if there is misaligned in the rotor and bearing, the magnetic field in the thrust bearing is no longer axisymmetric one, or the dynamic control current in the winding is time dependent one, eddy currents are caused to flow inside the conducting material, then the power losses are very important for magnetic bearing design. This paper presents an analytical model of a thrust magnetic bearing, and the magnetic fields, forces and losses of thrust magnetic bearing are calculated. In the calculations the frequency of dynamic control current is up to 1 000 Hz, rotating speed is from 60 rpm to 1 200 rpm, and the non-linearity of material is also taken into consideration. The results shows that if the magnetic field is not saturation, the eddy losses is proportional to dynamic control current frequency and a square function of dynamic control current, and also 5/2 power function of shaft's speed.

A combined experimental and analytical method to determine the EHL friction force distribution between rollers and outer raceway in a cylindrical roller bearing

Friction force is a crucial factor causing power loss and fatigue spalling of rolling element bearings.A combined experimental and analytical method is proposed to quantitatively determine the elastohydrodynamic lubrication(EHL)friction force distribution between rollers and outer raceway in a cylindrical roller bearing(CRB).An experimental system with the instrumented bearing and housing was developed for measuring radial load distribution and friction torque of bearings.A simplified model of friction force expressed by dimensionless speed,load,and material parameters was given.An inequality constrained optimization problem was established and solved by using an experimental data-driven learning algorithm for determining the uncertain parameters in the model.The effect of speed,load,and lubricant property on friction force and friction coefficient was discussed.

An Experimental Investigation on the Quasi-Static Flotation Transport of a Glass Substrate Using Vortex Bearing Elements

In this paper, we build an air conveyor with newly developed vortex bearing elements, and study the flotation precision of the front-end of the substrate in quasi-static flotation transport. We experimentally discuss the three influential factors: air supply pressure, thickness of the substrates and installing direction of the vortex bearing element. We find that during the process of transport the movement of the substrate leads to the variation of flotation height. The amplitude of variation (e.g. flotation precision) is dependent upon the bearing stiffness and the suction force of the vortex bearing elements. Increasing air supply pressure properly can improve the flotation precision, but an excess pressure can cause over-suction due to high negative pressure and result in a poor flotation precision. We also know that the flotation precision of thin and light substrates are easily affected by the suction force of vortex flow because they float with a high flotation height and are more susceptible to deformation. Finally, we investigate four installing directions of the vortex bearing element. Different installing direction can lead to different variation of flotation height.