The effect of interface plate compliance on dynamometers incorporating octagonal strain rings

This paper reports on the design, calibration, and accuracy check of a six-load component dynamometer incorporating octagonal strain rings. The dynamometer was designed using the computer-aided design procedure described in an earlier article by Kroencke and Hull¹. The accuracy check revealed inaccuracy which was traced to non-linearity in cross-sensitive load-strain relations. Interface plate compliance was determined as the cause of the nonlinearity by means of finite-element analysis. From this analysis two methods for avoiding the nonlinearity were identified. One is to insure that the interface plates are much stiffer than the octagonal strain rings and the other is to connect the interface plates to the environment so that the boundary conditions are identical for both plates.     

Optimal design of an uncoupled six degree of freedom dynamometer

A design analysis of a class of six degree of freedom strain-gage dynamometers which are virtually uncoupled in each force and moment component is presented. The method of design is detailed and an optimal design algorithm is implemented. The dynamometer is made of six or more T-sections with thin webs and flanges called shear panel elements (SPE). Complete stress and buckling analyses are carried out for the SPE, and experiments confirm the predictions of the analyses. The optimal design method is illustrated with several case studies. A dynamometer has been built and used in laboratory and field experiments.     

The Fascination of Vortex Rings

We present inviscid and viscous models for the formation and propagation of single, and co-axial pairs of, vortex rings. Inviscid flows are based on both thin rings, and thick rings treated by a contour dynamics approach, whilst viscous flows are determined from numerical solutions of the Navier–Stokes equations. A kaleidoscope of different flow behaviours for these axisymmetric flows is presented.     

Dynamics of medium thickness plates interacting with a periodic Winkler’s foundation: non-asymptotic tolerance modelling

Medium thickness plates resting on a periodic Winkler’s foundation are investigated. New averaged non-asymptotic models for those plates are proposed. These models are based on the tolerance averaging technique. The main feature of these models is that they describe the effect of period lengths on the overall behaviour of the plate. It is also shown that from governing equations of these models, equations of simplified averaged models (called asymptotic models) can be obtained. An additional interesting feature of the proposed models is that the equations describe also the effect of normal stress in the thickness direction.     

Internal ring buckle arrestors for pipe-in-pipe systems

A new buckle arrestor concept for pipe-in-pipe systems is introduced and the results of a systematic study of its performance is presented. The concept involves either one single ring or a number of closely packed narrow rings placed in the annulus between the two pipes. Its effectiveness has been studied through a combination of experiments and analyses. The experiments involved two inch carrier tubes of three different D/t values and internal rings of various dimensions. A number of experiments were first conducted using pipe-in-pipe systems. It was found that the inner tube had only a small effect on the crossover pressure of this arrestor and, as a result, in many of the following experiments inner tubes were not included.The crossover pressure of the ring arrestors was studied by varying their length, wall thickness and yield stress. Other parameters varied were the dimensions and properties of the two tubes and the gap between the arrestor and the carrier tube. The process resulted in an empirical design formula for the arresting efficiency expressed as a function of the key nondimensional variables of the problem. Large-scale finite element models which simulate the buckle crossover process have also been developed. They have been shown capable of reproducing experiments accurately. Such models can be used to prove an arrestor design developed through the empirical process described in the report.     

An analytical design method of thin,isotropic press-fit retention sleeve for surface-mounted permanent magnet drives

Electric drives with surface-mounted permanent magnets feature magnet retention sleeves found in the air gap between the rotor and the stator. The design of these components, whose thickness affects the size of the magnetic air gap, has thus significant implications for the overall drive performance. The present work proposes a systematic analytical method for the mechanical design of press-fit retention sleeves for surface-mounted permanent magnet drives. The model relies on the premise that the sleeve is thin and mounted on a much stiffer rotor-magnet assembly. This leads to the assumption of constant thickness before and after the interference fit, as well as the only significant deformation being the hoop extension of the sleeve induced by the press fit. The proposed design method allows for rapid estimations of such sleeve parameters as the thickness and effective overlap, providing critical design points to be verified by subsequent high fidelity approaches. Accordingly, finite-element analysis results are provided as verification of the analytical approach, demonstrating very good agreement between the two approaches.     

Simulation of impacts in geartrains using different approaches

Gear hammering in diesel engines is a well-known phenomenon in geared drives, exhibiting not only noise but also influencing the performance and durability of diesel engines. Gear hammering is characterised by flanks in contact that lift off and cause impacts when the contact reestablishes, which induces high, sharp dynamic loads. The knowledge of these contact forces is very important for the design of gears. Since contact forces in meshing gears are extremely difficult and expensive to measure, the simulation of these forces plays an important role. Nowadays, these contact simulations are usually carried out within overall models of entire engines using commercial multibody programs that provide submodels for gear contacts, usually based on rigid-body models. However, to reduce inertia effects, gears in geartrains are often designed with very thin bodies, whose elastic compliance influences the contact behaviour to a large extent. For a closer insight into the dynamic behaviour, and especially the influence of thin gear bodies during impact, a typical gear pairing is selected and impacts between one tooth pair are investigated for different boundary and initial conditions with three different models. Besides a multibody model, similar to those used in commercial multibody programs, a fully nonlinear finite-element model and a modally reduced model in combination with a local force law is used. The results of the different approaches are benchmarked in terms of accuracy and numerical effort.     

Bending of thin circular rings

The basic equations for the bending of circular rings are deduced from a set of accurate equations for circular cylindrical shells. The advantages in using these differential equations as compared with the customary energy method are shown through examples. It turns out that solutions of these equations can be as easily obtained as solutions of the well-known differential equation for straight beams. It is also shown that the center line of the ring is essentially inextensible, which is assumed ab initio in the classical ring theory.     

Qualitative analysis of forced response of blisks with friction ring dampers

A damping strategy for blisks (integrally bladed disks) of turbomachinery involving a friction ring is investigated. These rings, located in grooves underside the wheel of the blisks, are held in contact by centrifugal loads and the energy is dissipated when relative motions between the ring and the disk occur. A representative lumped parameter model of the system is introduced and the steady-state nonlinear response is derived using a multi-harmonic balance method combined with an AFT procedure where the friction force is calculated in the time domain. Numerical simulations are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given.     

Two-dimensional equations for electromagnetic waves in multi-layered thin dielectric films

Two-dimensional equations for electromagnetic fields in a multi-layered thin dielectric film are derived from the three-dimensional equations of electrodynamics by expanding the vector potential of the electromagnetic fields into trigonometric series expansions of the film thickness coordinate. The lower order equations are examined. It is shown that they can describe certain long waves in the film. The equations are useful for modeling thin film devices.     

Nonlinear oscillations of a floating elastic plate

The multi-scales method is used to derive third-order equations of gravitational bending oscillations of a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of finite depth. The equations incorporate the compressive force and nonlinear acceleration of vertical displacements of the plate. Based on these equations, the deflection of the plate and the velocity potential of the fluid induced by a traveling periodic wave of finite amplitude are expanded into asymptotic series to terms of the third order of smallness. The dependence of the oscillation characteristics on the elastic modulus and thickness of the plate, compressive force, the initial length and steepness of the wave is analyzed     

Experimental techniques employed for photoelastic analysis of cellular shells

The search for a shell construction superior to the usual ring-stiffened shells in strength and stability under external pressure with minimum weight has led to consideration of several other shell wall constructions.¹ The cellular-shell structure is one of the most promising designs of shells because of its ability to withstand high-pressure loading while maintaining a high degree of material efficiency. The analytical treatment of cellular shells has been undertaken only recently² and limited experimental study of these shells has been conducted. Thus, for obtaining reliable design formulas for the cellular-shell construction, these studies were undertaken. The cellular-shell construction may be visualized as two concentric thin cylinders spaced radially by a series of thin rings along their common longitudinal axis. The optimum wall thickness, rib thickness and rib spacing for a cellular shell of a given diameter and material which will result in the most efficient utilization of the material when the shell is placed under external pressure is the information required for shell design. The experimental techniques described in this paper have been employed to assist in the determination of the necessary design parameters.     

The Ring-Pull Assay for Mechanical Properties of Fibrous Soft Tissues – an Analysis of the Uniaxial Approximation and a Correction for Nonlinear Thick-Walled Tissues

Background: The ring-pull test, where a ring of tissue is hooked via two pins and stretched, is a popular biomechanical test, especially for small arteries. Although convenient and reliable, the ring test produces inhomogeneous strain, making determination of material parameters non-trivial. Objective: To determine correction factors between ring-pull-estimated and true tissue properties. Methods: A finite-element model of ring pulling was constructed for a sample with nonlinear, anisotropic mechanical behavior typical of arteries. The pin force and sample cross-section were used to compute an apparent modulus at small and large strain, which were compared to the specified properties. The resulting corrections were validated with experiments on porcine and ovine arteries. The correction was further applied to experiments on mouse aortic rings to determine material and failure properties. Results: Calculating strain based on centerline stretch rather than inner-wall or outer-wall stretch afforded better estimation of tissue properties. Additional correction factors were developed based on ring wall thickness H, centerline ring radius R_c, and pin radius a. The corrected estimates for tissue properties were in good agreement with uniaxial stretch experiments. Conclusions: The computed corrections improved estimation of tissue material properties for both the small-strain (toe) modulus and the large-strain (lockout) modulus. When measuring tensile strength, one should minimize H/a to ensure that peak stress occurs at the sample midplane rather than near the pin. In this scenario, tensile strength can be estimated accurately by using inner-wall stretch at the midplane and the corrected properties.

     

The stability of elastically strained nanorings and the formation of quantum dot molecules

Self-assembled nanorings have recently been identified in a number of heteroepitaxially strained material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the elastic strain energy of non-axisymmetric epitaxially strained nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In_0.5Ga_0.5P system investigated by Jevasuwan et al. (2013), the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The strained In_0.4Ga_0.6As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules.     

A real-space phase field model for the domain evolution of ferromagnetic materials

A real-space phase field model based on the time-dependent Ginzburg–Landau (TDGL) equation is developed to predict the domain evolution of ferromagnetic materials. The phase field model stems from a thermodynamic theory of ferromagnetic materials which employs the strain and magnetization as independent variables. The phase field equations are shown to reduce to the common micromagnetic model when the magnetostriction is absent and the magnitude of magnetization is constant. The strain and magnetization in the equilibrium state are obtained simultaneously by solving the phase field equations via a nonlinear finite element method. The finite-element based phase field model is applicable for the domain evolution of ferromagnetic materials with arbitrary geometries and boundary conditions. The evolution of magnetization domains in ferromagnetic thin film subjected to external stresses and magnetic fields are simulated and the magnetoelastic coupling behavior is investigated. Phase field simulations show that the magnetization vectors form a single magnetic vortex in ferromagnetic disks and rings. The configuration and size of the simulated magnetization vortex are in agreement with the experimental observation, suggesting that the phase field model is a powerful tool for the domain evolution of ferromagnetic materials.     

Nonlinear deformation and buckling of elastic inhomogeneous shells under thermomechanical loads

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads     

Acoustic waves emitted by a vortex ring passing near a wedge-like plate

Acoustic waves emitted by a vortex ring moving near a thin wedge-like plate of finite width have been studied. The experiments are performed for three configurations: the plate (A) is held edgeways to the direction of the vortex motion, (B) is held sideways to the direction, and (C) is held edgeways at an angle of 45° against the vortex motion. The observed sound wave is of dipole radiation type, and the magnitude of the pressure is large in the direction of the normal to the plate plane and small in parallel. The observed pressure is proportional to the third power of the vortex speed. The instantaneous force exerted on the plate by the vortex motion has also been examined. The force vector is mainly normal to the plate plane. The observed profiles agree within a reasonable degree of accuracy with the theoretical ones calculated for the vortex ring interacting with the flat plate of thickness zero.     

An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates

A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.     

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

内燃机活塞环－缸套摩擦功耗的设计计算方法之研究

以往在计算内燃机活塞环－缸套摩擦副的摩擦功耗时，只是计算活塞环与缸套之间流体润滑剂的粘性剪应力，这显然不能客观地反映出该摩擦副的润滑状态。实际上，活塞环－缸套间的摩擦力产生于两个方面，一是粘性流体的剪应力，二是摩擦界面相互接触峰元的剪切作用。然而截至目前，针对这两方面进行全面分析研究的报道却还很少，因此，为了给低摩擦功耗环组的设计提供科学依据，基于对活塞环在运动过程中润滑状态的分析，提出了一种适用于不同类型内燃机设计计算的活塞环－缸套摩擦功耗的计算方法，并以其对现有结构的Ｓ１９５柴油机活塞环－缸套摩擦副的摩擦功耗进行了计算，同时还对影响摩擦功耗的因素作了考察与讨论，利用台架试验测量油膜厚度的方法对这种算法进行试验验证的研究结果表明，理论值与实测值吻合得很好。