Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

Simulations and Experimental Investigation on Motion Stability of a Flexible Rotor-bearing System with a Transverse Crack

In the classical process for stability studies on the rotor-bearing system with crack faults, the simple discrete model is adopted for research on such problems, which neglect some needful dynamical influence factor, such as the material damping, shearing effect and gyroscopic effects, etc. Therefore, it is necessary to find a precise calculation model for simulation of the rotor-bearing system with cracks faults. In this paper, instead of the traditional simple discrete model, finite element （FE） model is adopted to investigate the motion stability of a nonlinear rotor system with crack fault. According to finite element theory, the FE model of the cracked rotor system is established firstly. It should be pointed out that the element where the crack occurs is modeled by a particular crack element and the supports at both ends are simulated by two nonlinear loads. Then, based on dimensionless and dimensionality reduction, the Newmark-[3 method and the shooting method are employed to study the effect of eccentricity and the depth of crack on instability speed and bifurcation feature. Furthermore, the simulation results are verified by some corresponding experiments. The simulation and experimental results show that instability speed does not change monotonically, but decreases firstly and then increases when the amount of eccentricity increases. Moreover, as the type of instability changes, the instability speed jumps concomitantly. Additionally, the presence of crack fault can disturb the oil whirl, as a result, instability speed tends to increase slightly, but it does not affect the type of instability and jumping phenomenon. This research presents an effective and convenient method which uses the finite element method （FEM） to research the motion stability of the nonlinear rotor-bearing system with cracked faults and other nonlinear force, and the proposed method can provide a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system.

Modeling and solving for transverse vibration of gear with variational thickness

有车轮中心，网和边界的齿轮的一个分析模型从 Mindlin 中等的板理论被导出。齿轮沿着步骤变化的地点被划分成三个环形的片断。穿越排水量，旋转角度，砍力量和曲折时刻是相等的沿着车轮中心，网和边界片断的接口保证连续性。管理为环形的片断的泛音颤动的微分方程被导出解决齿轮颤动问题。到直径比率的洞的影响，片断厚度比率，片断地点比率，走的圆形的 Mindlin 磁盘的颤动行为上的泊松比率被计算， tabletted 并且阴谋。比较被做，频率从介绍方法，有限元素方法，和结构产生形式的实验。在这三个方法之中的结果关联很好。为所有频率的最大的错误为大多数频率是 5.46% ，和不到 5% 。

Gait Analysis of Quadruped Robot Using the Equivalent Mechanism Concept Based on Metamorphosis

The previous research regarding the gait planning of quadruped robot focuses on the sequence for lifting o and placing the feet, but neglects the influence of body height. However, body height a ects gait performance significantly, such as in terms of the stride length and stability margin. We herein study the performance of a quadruped robot using the equivalent mechanism concept based on metamorphosis. Assuming the constraints between standing feet and the ground with hinges, the ground, standing legs and robot body are considered as a parallel mechanism, and each swing leg is regarded as a typical serial manipulator. The equivalent mechanism varies while the robot moves on the ground. One gait cycle is divided into several periods, including step forward stages and switching stages. There exists a specific equivalent mechanism corresponding to each gait period. The robot's locomotion can be regarded as the motion of these series of equivalent mechanisms. The kinematics model and simplified model of the equivalent mechanism is established. A new definition of the multilegged robot stability margin, based on friction coe cient, is presented to evaluate the robot stability. The stable workspaces of the equivalent mechanism in the step forward stage of trotting gait under di erent friction coe cients are analyzed. The stride length of the robots is presented by analyzing the relationship between the stable workspaces of the equivalent mechanisms of two adjacent step forward stages in one gait cycle. The simulation results show that the stride length is larger with increasing friction coe cient. We herein propose a new method based on metamorphosis, and an equivalent mechanism to analyze the stability margin and stable workspace of the multilegged robot.

Finite element analysis of rolling process for variable cross-section blade

Due to the variation of the blade cross-section, the deformation stress and strain of the workpiece keep changing during the rolling process and the conventional rolling theory is no longer valid. The complexity and diversity of the blade cross-section determine it impossible to establish an universal theoretical model for the rolling process. Finite element analysis(FEA) provides a perspective solution to the prediction. The FEA software DEFORM was applied to discovering the deformation, stress, strain and velocity field of the variable cross-section workpiece, and the effects of friction coefficient and rolling speed during the rolling process. which indicates that the average rolling force at friction coefficient of 0.4 is 6.5% higher than that at 0.12, and the rolling velocity has less effect on the equivalent stress and strain distribution, which would confer instructive significance on the theoretical study as well as the engineering practice.

Comprehensive Reliability Allocation Method for CNC Lathes Based on Cubic Transformed Functions of Failure Mode and Effects Analysis

Reliability allocation of computerized numerical controlled（CNC）lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis（FMEA）is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.

Load Sharing Behavior of Star Gearing Reducer for Geared Turbofan Engine

Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.

Constraint Force Analysis of Metamorphic Joints Based on the Augmented Assur Groups

In order to obtain a simple way for the force analysis of metamorphic mechanisms, the systematic method to unify the force analysis approach of metamorphic mechanisms as that of conventional planar mechanisms is proposed. A force analysis method of metamorphic mechanisms is developed by transforming the augmented Assur groups into Assur groups, so that the force analysis problem of metamorphic mechanisms is converted into the force analysis problems of conventional planar mechanisms. The constraint force change rules and values of metamorphic joints are obtained by the proposed method, and the constraint force analysis equations of revolute metamorphic joints in augmented Assur group RRRR and prismatic metamorphic joints in augmented Assur group RRPR are deduced. The constraint force analysis is illustrated by the constrained spring force design of paper folding metamorphic mechanism, and its metamorphic working process is controlled by the spring force and geometric constraints of metamorphic joints. The results of spring force show that developped design method and approach are feasible and practical. By transforming augmented Assur groups into Assur groups, a new method for the constraint force analysis of metamorphic joints is proposed firstly to provide the basis for dynamic analysis of metamorphic mechanism.

Natural Characteristic of Thin-Wall Pipe under Uniformly Distributed Pressure

Natural characteristics of thin?wall pipe of the compressor under uniformly distributed pressure were presented in this paper based on a cylindrical shell model. In the traditional method, the beam model was usually used to analyze the pipe system. In actual fact, the pipe segment of the compressor was always broken in the form of a long crack or a partial hole and the phenomenon was hardly explained by beam model. According to the structure characteristic of compressor pipe segment, whose radius is large and thickness is little, shell model shows the advantage in this kind of pipe problem. Based on Sanders’ shell theory, the vibration di erential equation of pipe was established by apply?ing the energy method. The influences of length to radius ratio(L/R), thickness to radius ratio(h/R), circumferential wave number(n) and pressure(q) on the natural frequencies of pipe were analyzed. The study shows: Pressure and structural parameters have a great e ect on the natural characteristics of the pipe. Natural frequency increases as the pressure increases, especially for the higher mode. The sensitivity of natural frequency on pressure becomes stronger with h/R ratio increases; when L/R ratio is greater than a certain critical value, the influence of the pressure on natural frequency will no longer be obvious. The value of n corresponding to the minimum natural frequency also depends on the value of pressure. In the end, analysis of the forced vibration of a specific pipeline model was given and the modal shapes were illustrated to understand the break of the pipe. The research here will provide the theory support for the dynamic design of related pressure pipe and further experiment study should be employed.

Effect of Carbon Nanotube on the Oscillating Wear Behaviour of Metal-PTFE Multilayer Composites

Two kinds of metal-PTFE multilayer composites, which were composed of a steel backing, a middle layer of sintered porous bronze and a surface layer of polytetrafluoroethylene（PTFE） filled by carbon nanotubes（CNTs） or not, were prepared. The wear properties of metal-PTFE multilayer composites oscillating against 45 carbon steel under dry condition were evaluated on an oscillating wear tester, and the effect of CNTs on wear behaviour of metal-PTFE multilayer composites was studied. The results showed that the worn surface of metal-PTFE multilayer composites was characterized by adhesive wear, abrasive wear and fatigue wear. The CNTs greatly increased the adhesion strength of PTFE in the metal-PTFE composites and thereby greatly reduced puck, ploughing, and fatigue failure of PTFE during wearing. The PTFE filled with CNTs prevented direct contact between the mating surfaces and served as fine self-lubricating film, in which the oscillating wear mechanism of the composites was changed to a slightly adhesive wear. Therefore, the CNTs significantly decreased the weight loss and obviously increased the wear resistance of metal-PTFE multilayer composites.

Frictional and Optical Properties of Diamond-Like-Carbon Coatings on Polycarbonate

In this work, diamond-like-carbon （DLC） films were deposited onto polycarbonate （PC） substrates by radio-frequency plasma-enhanced cheraical vapor deposition （RF PECVD）, and silicon films were prepared between DLC and PC substrates by magnetron sputtering deposition so as to improve the adhesion of the DLC films. The deposited films were investigated by means of field-emission scanning electron microscopy （FE-SEM）, X-ray photoelectron spectroscopy （XPS） and Raman spectroscopy. Subsequently, the following frictional and optical properties of the films were measured： the friction coefficient by using a ball-on-disk tribometer, the scratch hardness by using a nano-indenter, the optical transmittance by using a UV/visible spectrometer. The effects of incident power upon the frictional and optical properties of the films were investigated. Films deposited at low incident powers showed large optical gaps, which decreased with increasing incident power. The optical properties of DLC films correlated to the sp^2 content of the coatings. High anti-scratch properties were obtained at higher values of incident power. The anti-scratch properties of DLC films correlated to the sp^3 content of the coatings.

Diagnosis of the Argon Plasma in a PECVD Coating Machine

A Langmuir probe plasma diagnostic system was developed to measure the plasma parameters in a PECVD vacuum coating machine. The plasma was a capacitively coupled plasma （CCP） driven by a radio-frequency （RF） power supply. To avoid the disturbance of radio-frequency field on the Langmuir probe measurement, a passive compensation method was applied. This method allowed the ＇dc＇ component to be passed and measured in the probe circuit. It was found that the electron temperature in the range from 2.7 eV to 6.4 eV decreased with the increase in RF power. The measured plasma density ranged from 8×10^16 m^-3 to 0.85×10^15 m^-3 and increased with the increase in RF power.

Control of vacuum arc source cathode spots contraction motion by changing electromagnetic field

This paper investigates the magnetic field component impact on cathode spots motion trajectory and the mechanism of periodic contraction.Electromagnetic coils and permanent magnets were installed at the different sides of cathode surface,the photographs of cathode spots motion trajectory were captured by a camera.Increasing the number of magnets and decreasing the distance between magnets and cathode both lead to enhancing cathode spots motion velocity.Radii of cathode spots trajectory decrease gradually with the increasing of electromagnetic coil＇s current,from 40 mm at 0 A to 10 mm at 2.7 A.Parallel magnetic field component intensity influence the speed of cathode spots rotate motion,and perpendicular magnetic field component drives spots drift in the radial direction.Cathode spot＇s radial drift is controlled by changing the location of the ‘zero line＇ where perpendicular magnetic component shifts direction and the radius of cathode spots trajectory almost equal to ‘zero line＇.

The Effect of Ion Current Density on Target Etching in Radio Frequency-Magnetron Sputtering Process

The effect of ion current density of argon plasma on target sputtering in magnetron sputtering process was investigated. Using home-made ion probe with computer-based data acquisition system, the ion current density as functions of discharge power, gas pressure and positions was measured. A double-hump shape was found in ion current density curve after the analysis of the effects of power and pressure. The data demonstrate that ion current density increases with the increase in gas pressure in spite of slightly at the double-hump site, sharply at wave-trough and side positions. Simultaneously, the ion current density increases upon increase in power. Es- pecially, the ion current density steeply increases at the double-hump site. The highest energy of the secondary electrons arising from Larmor precession was found at the double-hump position, which results in high ion density. The target was etched seriously at the double-hump position due to the high ion density there. The data indicates that the increase in power can lead to a high sputtering speed rate.

Low Temperature Nitriding of 304 Austenitic Stainless Steel Using RF-ICP Method: the Role of Ion Beam Flux Density

The significant role of ion beam flux during nitriding 304 austenitic stainless steel has been investigated by using a radio frequency inductively-coupled plasma reactor into which a sample with negative bias voltage was inserted. A milliammeter is used to detect tile current of ions which collide with the sample and optical emission spectroscopy is used to discern the reactive species included in the nitrogen plasma. The nitriding efficiency is indicated by X-ray diffraction and the microhardness test. The reported data reveal that the ion beam flux density as well as the deposition pressure, bias voltage and time can strongly affect the nitriding of stainless steel via tile expanded multiphase microstructure inside the nitrided layer. The increase in the density of ion flux results in an ascent in the intensity of the expanded peak and a simultaneous decline in the intensity of the 3＇ austenite peak. The evolution trend of ion beam flux density is described as a function of tile operating pressure and the bias voltage. The maxinmm ion flux density has been achieved at 10 Pa pressure and 500 V bias voltage. A reasonable nitriding region has been, consequently, suggested after comparing this work with previously reported results.

Influence of Hysteretic Behaviour in Reactive Magnetron Sputtering on the Crystal Structure and Characteristics of Aluminium Oxide Films

The influence of the hysteretic behaviour in reactive sputtering with a pure aluminium target in the presence of argon and oxygen plasma on transmittance and surface free energy of aluminium oxide films was investigated by plasma optical emission spectroscopy technology. The evolutions of aluminium, and aluminium oxide emission lines as functions of oxygen flow rate at constant power and pressure were studied. A steep transition from the metallic sputtering to the compound sputtering was observed upon increasing the oxygen flow rate from 0.0 SCCM to above 2.0 SCCM. Then an optimal deposition zone was obtained through analyzing the hysteretic curves of aluminium and aluminium oxide emission lines. The evolution of crystal structures of samples was discerned by X-ray diffraction spectra data. Energy dispersive X-ray spectroscopy data also demonstrate the relationship between the chemical compositions of aluminium oxide films and the hysteretic behaviour. The film deposited between 1.5 SCCM and 2.0 SCCM oxygen flow rate displays an optimal and stoichiometic atomic ratio of O to Al and mass ratio of O to Al. The changes in the transmittance of samples were discovered to depend on the oxygen flow rate by UV-VIS transmittance spectra, and the changes in surface free energy were studied by contact angle measurement.

Geometrical structures, vibrational frequencies, force constants and dissociation energies of isotopic water molecules (H_2O, HDO, D_2O, HTO, DTO, and T_2O) under dipole electric field

The dissociation limits of isotopic water molecules are derived for the ground state. The equilibrium geometries, the vibrational frequencies, the force constants and the dissociation energies for the ground states of all isotopic water molecules under the dipole electric fields from -0.05 a.u. to 0.05 a.u. are calculated using B3P86/6-311＋＋G（3df,3pf）. The results show that when the dipole electric fields change from -0.05 a.u. to 0.05 a.u., the bond length of H-O increases whereas the bond angle of H-O H decreases because of the charge transfer induced by the applied dipole electric field. The vibrational frequencies and the force constants of isotopic water molecules change under the influence of the strong external torque. The dissociation energies increase when the dipole electric fields change from -0.05 a.u. to 0.05 a.u. and the increased dissociation energies are in the order of H2O, HDO, HTO, D2O, DTO, and T2O under the same external electric fields.

Helium Plasma Damage of Low-k Carbon Doped Silica Film:the Effect of Si Dangling Bonds on the Dielectric Constant

The low-k carbon doped silica film has been modified by radio frequency helium plasma at 5 Pa pressure and 80 W power with subsequent XPS, FTIR and optical emission spec- troscopy analysis. XPS data indicate that helium ions have broken Si-C bonds, leading to Si-C scission with C（1s） lost seriously. The Si（2p）, O（ls）, peak obviously shifted to higher binding en- ergies, indicating an increasingly oxidized Si（2p）. FTIR data also show that the silanol formation increased with longer exposure time up to a week. Contrarily, the CHa stretch, Si-C stretching bond and the ratio of the Si-O-Si cage and Si-O-Si network peak sharply decreased upon exposure to helium plasma. The OES result indicates that monovalent helium ions in plasma play a key role in damaging carbon doped silica film. So it can be concluded that the monovalent helium ions besides VUV photons can break the weak Si-C bonds to create Si dangling bonds and free methyl radicals, and the latter easily reacts with O_2 from the atmosphere to generate CO_2 and H_2O. The bonds change is due to the Si dangling bonds combining with H_2O, thereby, increasing the dielectric constant k value.

Experimental and Numerical Research on Deformation Behavior of Thin-Walled and Large Expansion Ratio Guide Vane Liner in Hydroforming Process

Some tube hydroforming process tests and further research work were conducted to manufacture hollow guide vane liners( made of super alloy GH3030).The relative thickness( t0/ OD) of the tubular blank is approximately 0. 01,and the maximum expansion ratio( Dmax/ OD) of the needed part is more than 40%,and the length to diameter ratio of the expansion regionis more than 3. 0. It is very hard to manufacture this kind of ultra-thin-wall,curved axis and large expansion ratio tubular part without fracture and wrinkles. The success of the process is highly dependent on useful wrinkles with appropriate internal pressure and axial feeding. A simplified finite element model and a theoretical model are used for detecting the deformation behavior and forming laws. Further study results demonstrate that the useful wrinkles do not appear at the same time and middle-wrinkles need bigger axial force than tube-end-wrinkles and feeding-wrinkles. The wrinkles can transfer bigger axial force after its wave peak has come into contact with the die inner surface. The thickness thinning rate of the element at the peak is bigger than that at the trough. With the increase of the axial and hoop stress ratio,the critical buckling stress also increases. Microstructure examination results show that the grain size in the maximum thinning zone has been stretched and refined after the large deformation and annealing treatment.The process is feasible and the finished part is qualified.

A Calibration Method of Robot Base Frame with Procrustes Analysis

In order to realize high precision industrial operations,based on the POE formula,an effective approach to calibrate the robot's actual base frame(ABF) is proposed. Due to the existence of manufacturing errors,the ABF deviates slightly from nominal base frame( NBF). Using external precision measurement,the ABF can be established only through the three dimension(3D) position of the robot's end-effector.To ensure the orthonormal constraints of rotation matrix as well as the precise solutions,Procrustes Analysis is introduced,where an optimal orthogonal matrix is solved out by the Lagrange Multiplier method and Singular Value Decomposition(SVD). Furthermore,calibration experiment on a serial 6-DOF robot is performed,where a FARO laser tracker is utilized to measure the 3D position. Finally, calibration result indicates that the positioning accuracy has been significantly improved after calibration. The calibration method is also applicable to other similar problems,such as multi-robot coordination and robot hand-eye system calibration.