Analysing the hopping conveyor

The most common type of vibrating conveyor consists of a track that oscillates in a straight line inclined with respect to the horizontal, but does not have any net motion. Particles placed on the track advance because of the variation in normal and friction forces during the forward/upward and backward/downward strokes. In the present paper, the performance prediction is extended to the regime of hopping, which occurs when the vertical track acceleration exceeds the gravitational constant. At the onset of hopping, performance is shown to increase considerably above that possible with sliding conveying alone. At larger values of vertical track acceleration, the improvement in performance diminishes, while the impact velocity of the particle on the track increases, increasing also both noise and wear.Great emphasis is given in the paper to the non-dimensional representation of all variables, which reduces the number of design and performance parameters from the usual five dimensional ones to three non-dimensional ones, thus greatly simplifying the presentation of the results.     

Thermo-hydrodynamic analysis of the finite slider pad—Adiabatic conditions

Results are presented of a three-dimensional analysis of the fluid film under a square fixed-geometry inclined slider pad. The analysis is applied to adiabatic conditions as a first step in the investigation of transverse viscosity gradient effects for a wide range of operating conditions. The predicted performance is compared with that obtained on the assumption of viscosity constant through the film thickness. The effect of the transverse viscosity variation is shown to reduce or enhance pressure generation according to the magnitude of two characteristic non-dimensional groups. The results are also compared with performance predicted on the basis of constant viscosity theory using an “effective” viscosity derived from an overall film energy balance.     

Consteel振动输送机的水平运动建模

对于Consteel振动输送机,四轴惯性激振器产生水平激振力,槽体在拉杆作用下可看做一个倒立摆。当激振力为水平激振力且拉杆较长时,槽体在垂直方向的运动很小,可以看做只有水平运动。当不考虑物料与槽体的滑动,把物料看做附加质量时,得到槽体和基座的两自由度模型。当把基座看做固定不动时,得到槽体和物料的两自由度模型。同时考虑基座、槽体和物料得到一个三自由度模型,以便综合分析输送机的水平运动。     

Stress and failure probability analysis for a transversely isotropic, brittle, elastic cylinder subjected to internal pressure and axisymmetric thermal loading

Procedures are developed for the determination of the stresses in and thence the probability of failure of a transversely isotropic cylinder made of a brittle material and loaded by an internal pressure and an axisymmetric radial temperature gradient. As examples of the application of the procedures a cylinder is analysed first with isotropic material properties, then with various degrees of anisotropy including both the “fibrous” and “laminar” types. The treatment is non-dimensional; results are presented graphically in the form of failure probability “contours”. For the dimensions and materials considered it is shown that the probability of failure is affected only slightly by the fibrous form of anisotropy but markedly by the laminar form when the thermal loading predominates.     

Design and characterization of a low-profile micropositioning stage

This paper discusses the design and characterization of a new, single-axis, low-profile, piezo-driven vertical motion micropositioning stage for use in laser welding applications. A low-profile configuration is attained by mounting the piezo actuator horizontally and using a novel lever arrangement to transfer the horizontal motion of the actuator into the desired vertical motion. An analytical model for the static and dynamic behavior of the stage is presented, along with finite element (FE) modeling verification. A 200 μm motion-range stage was built, and tests show that the stage has a vertical stiffness of 6.0 N/μm and a resonance frequency of 364 Hz. The results are in very close agreement to those predicted by the model.     

Analysis of cross and vertical buckling in sheet metal rolling

In sheet metal rolling, shape defects called “cross buckling” or “vertical buckling” sometimes appear, which are wrinkles like washboards. The direction of the crest line of the cross buckling inclines at a certain degree against the rolling direction, while that of the vertical buckling is parallel to the rolling direction. In this study, analysis of the cross and vertical buckling is performed using the elementary theory of buckling. First, we calculate the stress distribution in three-dimensional sheet metal rolling near the exit cross section inside the roll gap. Next, we calculate the residual stress distribution near the exit cross section outside the roll gap. Furthermore, sheet metal buckling is analysed using the residual stress distribution. Type of buckling, distance between neighboring wrinkles, inclination of the crest line of the wrinkles against the width direction and the region where the wrinkles appear are obtained. We compare analytical results with published experimental results, and find that the former agree well with the latter. Hence, we conclude that this method of analysis is valid, and that the cause of the cross and vertical buckling is the residual stress distribution near the exit cross section outside the roll gap.     

Incorporation of Lagrangian Multipliers into an algorithm for finding exact natural frequencies or critical buckling loads

An existing algorithm enables natural frequencies or critical load factors to be found with certainty when “exact” stiffness matrices are used. This algorithm is extended to permit Lagrangian Multipliers to be used to couple the “exact” stiffness matrices of component structures to represent connections between the structures. The new algorithm also permits coupling of the stiffness matrices for different assumed wavelengths of sinusoidal response of a given structure with the stiffness matrices of other structures to satisfy required constraint conditions. The algorithm applies to problems formulated using real or complex arithmetic.     

Analysis of vibratory feeding where the track has directional friction characteristics

This paper treats the influence of directional friction characteristics on the performance of a newly-developed vibratory feeder. It is found that, when a particle is fed without hopping on a vibratory surface, its motion can be classified into seven modes and that these modes can be defined by two dimensionless quantities similar to those obtained in conventional vibratory feeding. These dimensionless quantities are functions of the coefficient of friction, the inclination of the feed track, the frequency of vibration, the amplitude of vibration and gravitational acceleration. It is found that the non-dimensional conveying velocity can be defined as the function of four dimensionless quantities. The relations between conveying velocity and feeding conditions are derived and presented in diagrammatic form. The theoretical results show that the conveying velocity obtained with the newly-developed feeder should be considerably higher than that of a conventional feeder; these finding are supported by experimental results.     

Polynomial solutions for thin plates

A least-squares approach is used to obtain polynomial solutions for the deflected shape of thin plates in flexure. The method corresponds to the finite element method with an energy basis, except that a single “macro” element is used. Satisfactory results are obtained for both triangular and rectangular plates and the method is clearly widely applicable.     

Principally on sheet metal forming defects as described in the eleventh biennial congress of the International Deep Drawing Research Group (IDDRG)

The major defects encountered in sheet metal forming operations are listed and some appropriate references given. The most common defects that arise in press-shop situations as described in the recent congress of the IDDRG are briefly reviewed.Defect—“Want or absence of something necessary for completeness or perfection”.Failure—“Omission to perform or want of success”.From Webster's Dictionary of English.     

激光制导测量机器人系统设计及运动学分析

提出新型“光束运动—光靶跟踪”激光跟踪测量方法,并在此方法基础上研究激光制导测量机器人技术,研制并开发一种能够在水平和垂直被测对象表面上运动的小型轮臂复合式激光制导测量机器人系统。该机器人机构融合轮式机构、爬行臂式结构和真空吸附式机构的优点,具有重量轻、体积小、运动灵活和反应快速等特点,可以根据不同被测对象表面特征变换测量模式,利用轮式结构实现机器人在水平被测表面上高速远距离运动,利用爬行臂式和真空吸附式机构实现机器人在倾斜光滑表面上灵活地爬行和转向。建立机器人的运动学模型并对其运动特性进行分析,利用激光跟踪仪和三坐标测量机对研制激光制导测量机器人进行性能测试,试验结果不仅证明了该机器人能够跟踪激光束自动高效地完成被测对象实体测量,同时也验证了所建模型的有效性和正确性。     

Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure

The dynamic plastic collapse of energy-absorbing structures is more difficult to understand than the corresponding quasi-static collapse, on account of two effects which may be described as the “strain-rate factor” and the “inertia factor” respectively. The first of these is a material property whereby the yield stress is raised, while the second can affect the collapse mode, etc. It has recently been discovered [6,7]that structures whose load-deflection curve falls sharply after an initial “peak” are much more “velocity sensitive” than structures whose load-deflection curve is “flat-topped” (Fig. 1a); that is, when a given amount of energy is delivered by a moving mass, the final deflection depends more strongly on the impact velocity. In this paper we investigate strain-rate and inertia effects in these two types of structure by means of some simple experiments performed in a “drop hammer” testing machine, together with some simple analysis which enables us to give a satisfactory account of the experimental observations. The work is motivated partly by difficulties which occur in small-scale model testing of energy-absorbing structures, on account of the fact that the “strain-rate” and “inertia” factors not only scale differently in general, but also affect the two distinct types of structure differently.     

Conditions of crank existence for a particular case of the RSSR linkage

Necessary and sufficient conditions of motion transfer for a particular case of the RSSR linkage is further derived and simplified. This particular case is considered when the frame is coincided with input and output axes distance, which may also be called as “simply skewed form” of RSSR. The results show that the conditions of crank existence for this particular case can be represented in a way quite resembling the Grashof criterion applicable to planar four bar linkages, and thus are of very simple expression and geometric sense. (The term “simple” normally implies that overhand computation by “rigours” programming may not be needed.)     

Chaos of rub-impact rotor supported by bearings with nonlinear suspension

The nonlinear dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil-film short bearings with nonlinear suspension. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed. Therefore for more precise analysis of rotor-bearing systems, the rub-impact between rotor and stator is also proposed in this paper. The displacements in the horizontal and the vertical directions charactering the theoretical model of the system are considered with non-dimensional speed ratio. Inclusive of the analysis methods of the dynamic trajectory, the power spectrum, the Poincaré maps and the bifurcation diagrams are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent analysis is also used in this study to identify the chaotic motion. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. Especially at s=5.6, the rotor centre is at chaotic motion but the bearing centre is still at quasi-periodic motion. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems and optimizing their operation can be more precise.     

Large deflexion, geometrically non-linear finite element analysis of circular arches

This paper presents the results of an investigation into the geometrically nonlinear behaviour of circular arches. A curved element is used, based on satisfying the condition that the circumferential strain and change in curvature, rather than the displacements, should be simple independent functions of the co-ordinate axes. The analysis was carried out using the linearized incremental method based on the mid-increment stiffness in conjunction with the Newton-Raphson iterative technique. A comparison is first made between the results obtained with this element and those using a simple polynomial shape function. The behaviour of a range of arches is then considered and the results are compared and found to agree well with an analytical method. The results include the behaviour of deeper but still shallow arches which exhibit “looping” of the load-deflexion curve, and bifurcation of the equilibrium path into unsymmetric deflexions of the arch.A computer program was developed to allow any of the generalized degrees of freedom which are designated for incrementation to be expressed as either forces, to avoid failure at the vertical tangent to the load deflexion curves, or as generalized displacements to avoid failure at the horizontal tangent. The program also allows the quantity subjected to incrementation to be changed as necessary to follow complex load-deflexion equilibrium paths.     

Investigation of influence of constraints with radius links on locomotive axle load distribution and wheelset steering ability

The problem of improving the tractive and dynamic performance of locomotives by means of using axle boxes with inclined radius links was investigated. The kinematics of axle boxes with different variants (different angles) and designs of inclined radius links, based on the vector contour method for link mechanisms, was studied. The results of a bogie design with vertically inclined radius links were used for the improvement of vertical load distribution for locomotives. The behavior of a locomotive running in a curve is more complicated because the lateral forces appear between a flange of the wheel and the head of the rail in the contact zone, and the values of wheel slip are higher than for straight sections of track. These two factors are the main reasons for wheel wear. Theoretical and experimental investigations to reduce wear and to improve vehicle dynamics were made, and the results obtained show that an effective solution can be reached by the use of inclined links to the longitudinal axis of a bogie in the horizontal plane. Questions about the development of a bogie with a radial installation and active steering are discussed.     

The lubrication of lightly loaded cylinders in combined rolling, sliding and normal motion with couple stress fluid

The lubrication of lightly loaded cylinders with combined rolling, sliding and normal motion is investigated with a couple stress fluid as lubricant under cavitation boundary conditions. It is shown that the major bearing performance characteristics can be accounted for by means of a dimensionless parameter, q, involving the “normal” and “entraining” velocities, the minimum film thickness and the radius of the geometrically equivalent cylinder near a plane. The load capacity and frictional drag increase as the squeeze velocity increases. This increase is enhanced by decreasing the couple stress parameter, τ. However, when the two surfaces move apart these results are reversed. It is convenient to adopt the least-squares procedure for the accurate representation of the line of cavitation and the line of maximum pressure. The effect of couple stresses on the point of cavitation is quite significant compared with viscous fluid of the same viscosity.     

Hydrodynamic effects of tailored inlet roughnesses: extended theory

In a recent paper (STLE/ASME, Tribology Conference, 1999), the author introduced the idea of generating hydrodynamic pressure in bearings and other devices by means of an inlet zone having tailored roughness. The latter implies removal of material and therefore eases the ingress of fluid into the device. The inlet microstructure thus replaces the macrostructure—steps, inclined surfaces, etc.—of standard devices, and can operate with a nominally parallel film.In a few subsequent papers (JSME ITC, 2000, 1549; Tribology International, 34, 2002, 847; NORDTRIB’02, Intnl Tribology Conference), this concept was developed, resulting in the prediction of very desirable properties. Compared to values of standard devices, film stiffness and damping may be strongly enhanced.Only one family of surface structure has been investigated, namely that of parallel striations running along the direction of motion or at right angles to it. In the present paper two more structure patterns have been studied, i.e. checkerboard and sinusoidal dimples.The most typical hydrodynamic parameters of sliders have been calculated for a wide variety of cases and the results are compared with step profile sliders of similar dimensions.The tailored surfaces show a consistent improvement in performance compared to the smooth ones. The effects are, however, less marked than those of the best combinations of striations and macro-geometries.Finally, a thorough discussion of various aspects of the new devices is given.     

Analytical dynamics of mechanisms—a computer oriented overview

General-purpose computer programs such as IMP, DRAM, MEDUSA and DYMAC, for the solution of inertia-variant (linkage-type) mechanisms are beginning to emerge. These programs, which automatically generate, and numerically integrate, the equations of motions, are based upon different but related analytical and numerical principles. There has also been much recent discussion of “influence coefficient” methods, energy methods and related matters. This paper reviews the various principles and techniques available for formulating the equations of motion, for integrating them numerically, and for solving the associated kinetostatic problem for the determination of bearing reactions. The relative advantages of vector methods, d'Alembert's Principle, Lagrange's Equations with and without multipliers, Hamilton's Equations, Virtual work, and energy methods are discussed. Particular emphasis is placed on how well-suited the various methods are to the automatic generation of the equations of motion, and to the form and order of the systems of differential equations they lead to. It is shown how velocity ratios, influence coefficients, centripetal coefficients, generalized inertia coefficients, and Christoffel symbols interrelate the various methods, and tie them to classical results of Analytical Dynamics such as the “explicit” equations of motion and the power-balance principle. Methods for solving both the general dynamics problem, and the kinetostatic problem, are reviewed, and the particular methods of implementation used in the recently developed general-purpose computer programs, and in other recent literature, are described.     

Analytical solution for interface stresses due to concentrated surface force

The two-dimensional analytical solution for interface stresses due to concentrated surface force has been deduced, by introducing infinite mirror points which are the images of the load point reflected by the interface and the free surface, and adopting the interchange law of differentiation. The analytical solution can be represented in terms of the summation of the “partial” Goursat's complex stress functions defined in the local coordinate systems with their origins placed at each of the mirror points. It is found that the “partial” stress functions corresponding to a higher order mirror point can be determined from those to the lower one. It is also found that the contribution of the “partial” stress functions to the stress field decreases with the increase of the corresponding mirror point order, therefore, only considering the stress functions corresponding to the first several order mirror points can give the accurate enough solution. Numerical examination by the use of boundary element method has also been carried out to verify the theoretical development.