Torsional Vibration Analysis of an FR Driveline System

Towing tractor drivelines are lightly damped non-linear systems. Interactions between components can cause dynamic behavors such as gear gap impact in gear transmissions, shuffle and clonk phenomena in driveline. The torsional vibration of driveline has an important effect on grand engineering vehicle vibration and noise. Through analyzing torsional vibration equations of driveline, torsional vibration model of driveline is developed by using Matlab/Simulink software, Shuffle and clonk phenomena are observed in torsional vibration. The modeling method of analysizing driveline torsional vibration can be used to research and improve similar engineering vehicle driveline behavors.

New Method for Building Vector of Diagnostic Signs to Classify Technical States of Marine Diesel Engine by Torsional Vibrations on Shaft-Line

Vector of diagnostic signs(VDS)using torsional vibration(TV)signal on the main propulsion plant(MPP)is the vector of z maxima(or minima)values of the TV signal in accordance with the cylinder firing orders.The technical states of the marine diesel engine(MDE)include R=z+1 classes and are presented in z-dimensional space coordinate of VDS.The presentation of Dk,k=1÷R using z diagnostic signs(Vi,i=1÷z)is nonfigurative and quite complicated.This paper aims to develop a new method for converting VDS from z-dimensional to 2-dimensional space(two-axes)based on the firing orders of the diesel cylinders,as an equivalent geometrical sign of the all diagnostic signs.The proposed model is useful for presenting a technical state Dk in two-dimensional space(x,y)for better visualization.The paper verifies the simulation of the classification illustration of the 7–state classes for the MDE 6S46-MCC,installed on the motor vessel(MV)34000DWT,using the new above mentioned method.The seven technical state classes(for 6-cylinder MDE,z=6)are drawn separately and visually in the Descartes.The received results are valuable to improve smart diagnostic system for analyzing normal/misfire states of cylinders in operation regimes.

State Modeling Based Prediction of Torsional Resonances for Horizontal-Axis Drive Train Wind Turbine

This paper focuses on the state space modeling approach and output torques prediction of torsional vibrations for variable speed wind turbines. The multi-body system model under study is mainly comprised of a wind turbine, a three stage planetary gear box and an induction generator. The masses-springs approach of shaft system differential equations is developed from Newton＇s law and Lagrange formulas. For an easy comprehension for electrical engineers and tutorial purpose, an electrical equivalent circuit of the system is proposed by using mechanical and electrical components similarities. Extensive numerical simulations are performed to investigate system mechanical resonances and impacts of damping factors on the system dynamic and stability.

Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Wind-induced vibration control of bridges using liquid column damper

The potential application of tuned liquid column damper (TLCD) for suppressing wind-induced vibration of long span bridges is explored in this paper.By installing the TLCD in the bridge deck,a mathematical model for the bridge-TLCD system is established.The governing equations of the system are developed by considering all three displacement components of the deck in vertical,lateral,and torsional vibrations,in which the interactions between the bridge deck,the TLCD,the aeroelastic forces,and the aerodynamic forces are fully reflected.Both buffeting and flutter analyses are carried out.The buffeting analysis is performed through random vibration approach,and a critical flutter condition is identified from flutter analysis.A numerical example is presented to demonstrate the control effectiveness of the damper and it is shown that the TLCD can be an effective device for suppressing wind-induced vibration of long span bridges,either for reducing the buffeting response or increasing the critical flutter wind velocity of the bridge.

Effects of wheelset vibration on initiation and evolution of rail short-pitch corrugation

The initiation and evolution of short-pitch corrugation in Beijing metro line 4 was studied from the viewpoint of wheelset vibration.A three-dimensional elastic model was set up.Numerical simulations were undertaken with this model to analyze the corrugation by the wheelset vertical vibration and torsional vibration.Based on numerical results,the relation between rail corrugation and wheelset vibration,and the relation between the position of electromotor and wheelset vibration were indicated.It is found that avoiding the wheelset-rail resonance is one method of controlling the rail short-pitch corrugation and solving the vibration and noise problem in metro lines.

APPLICATION OF THE MODIFIED ITERATION METHOD TO NONLINEAR VIBRATION OF CORRUGATED CIRCULAR PLATES

In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.

TORSIONAL RIGIDITY OF SHELLS OF REVOLUTION

In this paper, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of revolutional shells are derived. It is shown that the shearing stress distribution due to torsion is independent of other stress components including those of membrane stress and bending stress. In this paper, the torsional deformation is considered to be represented by membrane action only, and also by the combined action of bending membrane deformation. It is shown that the main contribution of torsional rigidity is that related to membrane action.

DYNAMIC RESPONSE OF SHAPE MEMORY ALLOY SYSTEM AND ITS VIBRATION CONTROL

A hysteric model is represented to describe the dependence of restoring force on deformation of pseudoelastic SMA.The dynamic response of the system is investigated by means of mathematical models.The result shows that this kind of vibration absorbing system can suppress vibration with large amplitude effectively.Furthermore,the vibration absorbing system can work in optimum state by adjusting temperature and using piezoelectric sensors and actuators.

LARGE AMPLITUDE VIBRATION OF THIN ANNULAR PLATES

A pure analytic solution of the axisymmetric large amplitude free vibration of thin annualar plates is presented in this paper: By using the modified iteration method, we derive an analytic relation for the amplitudes vs. frequencies of vibrations. The present paper shows the great potentiality of this method to tackle the large amplitude vibration problems of plates.

NONLINEAR VIBRATION AND THERMAL-BUCKLING OF A HEATED ANNULAR PLATE WITH A RIGID MASS

On the basis of Hamilton's principle and dynamic version of von Karman's equations, the nonlinear vibration and thermal-buckling of a uniformly heated isotropic annular plate with a completely clamped outer edge and a fixed rigid mass along the inner edge are studied. By parametric perturbation and numerical differentiation, the nonlinear response of the plate-mass system and the critical temperature in the mid-plane at which the plate is in buckled state are obtained. Some meaningful characteristic curves and data tables are given.

A New Differential Operator Method to Study the Mechanical Vibration

In this paper, we propose a unified differential operator method to study mechanical vibrations, solving inhomogeneous linear ordinary differential equations with constant coefficients. The main advantage of this new method is that the differential operator D in the numerator of the fraction has no effect on input functions (i.e., the derivative operation is removed) because we take the fraction as a whole part in the partial fraction expansion. The method in various variants is widely implemented in related fields in mechanics and engineering. We also point out that the same mistakes in the differential operator method are found in the related references [1-4].

Improved Twin I-Girder Curved Bridge-Vehicle Interaction Analysis and Human Sensitivity to Vibration

The perceptible vibration of curved twin I-girder bridges under traffic loads is an important design consideration, because this bridge have rather low torsional stiffness that produce excessive vibrations. The objective of this investigation was to study the vibration of curved twin I-girder bridges due to moving vehicles and the effect of vibrations on bridge users. To this end, a comprehensive three-dimensional finite element models for bridge and vehicle are developed by using ANSYS code for studying bridge-vehicle interaction and the resultant sensitivity to vibration. Truck parameters include the body, the suspension and the tires. Gap and actuator elements are incorporated into the tire models to simulate the separation between the tires and road surface, and road surface roughness, respectively. Road roughness profiles are generated from power spectral density and cross spectral functions. To couple the motion of the bridge and vehicle, Lagrange multipliers and constraint equations are utilized through the augmented Lagrangian method. A parametric study is performed to identify the effect of various parameters on the vibration of the bridge. The results have been expressed in the form of human perceptibility curves. This study finds that the bridge response is significantly influenced by the road roughness, bump height at expansion joint and vehicle speeds. The results show that the inclusion of features such as increasing the torsional stiffness by providing additional stiffened bracing has major effects on the reduction of perceptible vibration.

MATHEMATICAL ANALYSIS OF TRANSVERSE VIBRATION OF CONICAL SPIRAL TUBE BUNDLE WITH EXTERNAL FLUID FLOW

The conical spiral tube bundle is a new type of heat transfer elements used to enhance heat transfer through flow-induced vibration. The effect of the external fluid flow on the transverse vibration of the conical spiral tube bundle is investigated with a mathematical method proposed in this article. Firstly, the natural vibration of the tube bundle is obtained by the hammering excitation method and the mode shapes of the transverse vibration are discussed. Then the effect of the external fluid flow on the transverse vibration of tube bundle is analyzed by a combination of experimental data, empirical correlations and FEM. The results show that in the frequency range from 0 Hz to 50 Hz, there exist six transverse vibrations. The external fluid flow has a significant effect on the frequency of the tube＇s transverse vibration, which are decreased by about 18% to 24% when the external fluid flow speed is 0.3 m/s.

TORSION OF ELASTIC SHAFT OF REVOLUTION EMBEDDED IN AN ELASTIC HALF SPACE

The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads 'Point Ring Couple (PRC)' and 'Point Ring Couple in Half Space (PRCHS)' on the axis of symmetry in the interior and external ranges of the shaft occupied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov's regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.

Comparison of rheological analytic model with numerical simulation in powder injection molding filling process

Mathematical model of filling disk-shaped mold cavity in steady state was studied.And the mathematical model under vibration field was developed from the model in steady state.According to the model of filling disk-shaped mold cavity in steady state,the filling time,the distribution of velocity field and the pressure field were obtained.The analysis results from rheological analytic model were compared with the numerical simulation results using Moldflow software in the powder injection molding filling process.Through the comparison,it is found that it is unreasonable to neglect the influence of temperature when calculated the pressure changing with the time at the cavity gate,while it can be neglected in other situations such as calculating the distribution of the velocity fields.This provides a theoretical reference for the establishment of correct model both in steady state and under vibration force field in the future.

APPLICATION OF AN IMPROVED BOUNDARY ELEMENT METHOD ON THE PROBLEM OF ELASTIC TORSION

An improved boundary element method has been used in analyzing and calculating the problems of the torsion of a prismatic bar with elliptical cross-section. In this paper the calculated results correspond with the values of boundary element method. However, the quantity of data required by the improved boundary element method is much less than that required by boundary element method, and the calculating time will be greatly reduced. Therefore, the procedure of this paper is an economical and efficient numerical computational way for solving Poisson equation problem.

Cooling of Granules in Vibrating, Suspended Bed: Engineering Simulation

Here we suggest an algorithm for calculation of the process parameters and design of a vertical cooler with inclined, gas-permeable blades and with a vibrating, suspended layer of granules on them (Vibrating Fluidized Bed—VFB). The algorithm is based on the use of the equations of heat and material balance, taking into account the influx of moisture into the layer with cold air and dust—as a carryover. Mode entrainment of dust particles and moisture from the VFB is described by using empirical formulas and Π-theorem. To calculate the cooling time of granules a model of the dynamics of a variable mass VFB was built, which linked the geometrical and physical process parameters to a single dependency. An example showed that mass flow of granules of 248 kg/h and a volume flow of air of 646 m3/h with temperature of 30℃ to cool the zeolite granules from 110℃ to 42℃ for 49 s required a vertical apparatus of rectangular shape with four chambers and with volume of 0.2 m3. A comparative analysis of technological parameters of the projected cooler with the parameters of typical industrial apparatuses showed that for all indicators: the cooling time of granules, the flow rate of gas (air) and the heat flow, a 4-chambered, vertical apparatus of rectangular shape with VFB was the most effective.

位置扰动影响下的拖拉机底盘横向振动模型研究

为了探明行走速度、地面坡度和地面摩擦因数对拖拉机底盘横向稳定性的影响,建立了拖拉机动力学模型。考虑两种拖拉机失稳类型,即翻车和打滑引起的拖拉机底盘不稳定,为每种情况确定了稳定性指数。选取MITSUBISHI MT-2501D拖拉机进行试验与分析,结果表明:行走速度和地面坡度对所有稳定性指标都有显著的负相关影响(P<0.05),拖拉机的稳定性受拖拉机打滑的影响比翻车的影响更大。因此,为了提高该拖拉机底盘的整体稳定性,应该优先考虑提高由拖拉机打滑动力学得出的拖拉机稳定性指数。研究结果可为提高拖拉机田间运行稳定性提供新的研究思路及技术参考。

纵扭超声振动辅助铣削60%SiC_(p)/Al多目标参数优化研究

针对高体积分数碳化硅颗粒增强型铝基复合材料(SiC_(p)/Al)在铣削过程中加工难度大、表面质量差等问题,提出了纵扭超声振动辅助铣削复合工艺。以超声振幅、切削速度、每齿进给量和切削深度为变量,设计了四因素五水平正交试验。通过响应曲面法和人工神经网络,建立了切削力、切削温度和表面粗糙度的预测模型,分析了4个参数变量中两个指标的交互影响作用,并对预测模型的准确性进行了对比验证。最后,采用遗传算法对切削力、切削温度和表面粗糙度进行了多目标参数优化。结果表明,响应曲面法与人工神经网络建立的模型均有较好的预测能力,但人工神经网络准确性更高。采用遗传算法优选出的最佳参数组合为超声振幅A=1.84μm,切削速度v_(c)=20 m/min,每齿进给量f_(z)=0.015 mm/z,切削深度a_(p)=0.8 mm,经过验证试验后发现,采用优选参数有效降低了切削力、切削温度和表面粗糙度,各值分别为切削力F_(t)=7.23 N,切削温度T=40.18℃,表面粗糙度R_(a)=2.4673μm,预测误差分别为6.91%、6.53%、2.53%,证明了预测模型的准确性与优化参数的有效性。