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The supercritical design of tail rotor drive shaft has attracted more attention in helicopter design due to its high power–weight ratio and low maintenance cost. However, there exists excessive vibration when the shaft passes through the critical frequency. Dry friction damper is the equipment applied to the drive shaft to suppress the excessive vibration. In order to figure out the damping mechanism of the dry friction damper and improve the damping efficiency, the dynamic model of the shaft/damper system is established based on the Jeffcott rotor model.

The typical frequency response of the system is studied through bifurcation diagrams, amplitude-frequency characteristic curves and waterfall frequency response spectrum. The typical transient responses under frequency sweeps are also obtained.

The results show that the response of the system changes from periodic no-rub motion to quasi-periodic rub-impact motion, and then to synchronous full annular rub-impact, and finally, back to periodic no-rub motion. The slip of the rub-impact ring improves the stability of the system. Besides, the effects of the system parameters including critical dry friction force, rub-impact friction coefficient, initial clearance on the stability and the vibration damping capacity are studied. It is observed that the stability changes significantly varying the three parameters respectively. The vibration damping capacity is mainly affected by the critical dry friction force and the initial clearance.

Presented results provide guidance for the design of the dry friction damper.

The supercritical propulsion shaft equipped with a dry friction damper has been designed for a polish ultra light helicopter named IS‐2. Models of the shaft and the damper and some results of analysis of the shaft flexural vibrations are presented.As it turned out the shaft vibrations strongly depend on parameters of the damper (especially on the damper gap) and can be regular or chaotic. There are two main cases: the damper with a small gap and the damper with a big gap, when compared to shaft eccentricity.

This paper gives a review of the finite element techniques (FE) applied in the analysis and design of machine elements; bolts and screws, belts and chains, springs and dampers, brakes, gears, bearings, gaskets and seals are handled. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of this paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An Appendix included at the end of the paper presents a bibliography on finite element applications in the analysis/design of machine elements for 1977‐1997.

Powered flying‐control systems are a comparatively recent addition to aircraft and, to date, have been devised to modify as little as possible existing piloting technique. At the present time there is a basic similarity in most of the designs being used, and it is the purpose of this paper to consider the reasons for this and to examine the suitability of these systems for such future requirements as can be foreseen. Little has been published about the difficulties encountered in the installation of such systems, particularly of relation to stability and reliability, but some account is given in the paper of experience with one typical system which has been used in a number of aeroplanes of widely differing types. Whilst the scope of this paper is not intended to cover a detailed comparison of the minor features of various designs, some reference is made to those details which have a prime influence on performance. Finally, consideration is given to the extremely important question of pre‐flight rig testing, which is necessary to secure adequate reliability in services so vital to the safety of the whole aeroplane and its occupants.

The purpose of this paper is to provide a static friction coefficient prediction model of rough contact surfaces based on the contact mechanics analysis of elastic-plastic fractal surfaces.

In this paper, the continuous deformation stage of the multi-scale asperity is considered, i.e. asperities on joint surfaces go through three deformation stages in succession, the elastic deformation, the elastic-plastic deformation (the first elastic-plastic region and the second elastic-plastic region) and the plastic deformation, rather than the direct transition from the elastic deformation to the plastic deformation. In addition, the contact between rough metal surfaces should be the contact of three-dimensional topography, which corresponds to the fractal dimension D (2 < D < 3), not two-dimensional curves. So, in consideration of the elastic-plastic deformation mechanism of asperities and the three-dimensional topography, the contact mechanics of the elastic-plastic fractal surface is analyzed, and the static friction coefficient nonlinear prediction model of the surface is further established.

There is a boundary value between the normal load and the fractal dimension. In the range smaller than the boundary value, the normal load decreases with fractal dimension; in the range larger than the boundary value, the normal load increases with fractal dimension. Considering the elastic-plastic deformation of the asperity on the contact surface, the total normal contact load is larger than that of ignoring the elastic-plastic deformation of the asperity. There is a proper fractal dimension, which can make the static friction of the contact surface maximum; there is a negative correlation between the static friction coefficient and the fractal scale coefficient.

In the mechanical structure, the research and prediction of the static friction coefficient characteristics of the interface will lay a foundation for the understanding of the mechanism of friction and wear and the interaction relationship between contact surfaces from the micro asperity-scale level, which has an important engineering application value.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

The purpose of this paper is to investigate the non-linear characteristics and stability of the rolling bearing–axle coupling system under the excitation of the axle/wheel speed of railway freight cars, so as to put forward a rationale for judging the vibration law and running stability of railway freight wagon.

Considering the effects of eccentric force of the railway wagon axle, the non-linear resistance of the wagon and non-linear support forces of axle box rolling bearings, a centralized mass model of rolling bearing-axle coupling system of railway freight wagon is presented on the basis of the theory of rotor dynamics and non-linear dynamics. Then the Runge-Kutta method is adopted to solve the non-linear response of the proposed system, and numerical simulation including bifurcation diagrams, axis trajectory curves, phase plane plots, Poincaré sections and amplitude spectras are analysed when the axle rotating speed is changed. Meantime, the relation curve between Floquet multiplier and axle rotating speed, which affects the stability of coupling system, is plotted by numerical method based on the Floquet theory and method.

The simulation results of the dynamic model reveal the abundant dynamic behaviour of the coupling system when the axle rotating speed changes, including single period, quasi period, multi-period and chaotic motion, as well as the evolution law from multi-period motion to chaotic motion. And especially, the bearing–axle coupling system is in stable state with a single period motion when the axle rotating speed changes from 410 rpm to 510 rpm, in which the running speed of railway freight wagon is changed from 62 km/h to 80 km/h, the vibration displacement of the coupling system in X direction is between 1.2 mm and 1.8 mm, and the vibration displacement of the coupling system in Y direction is between 1.0 mm and 1.45 mm. Meanwhile, the influence law of axle rotating speed on the stability is obtained by comparing the bifurcation diagram and Floquet multiplier graph of the coupling system.

The numerical simulation data obtained in this study can provide a theoretical evidence for designing the running speed of railway freight wagon, utilizing or controlling the non-linear dynamic behaviours of the proposed coupling system, and ensuring the stability of railway freight wagons.

This article presents the 2D computation of the non‐linear dynamics of magnetic domain walls motion in ferromagnetic material such as crystalline, like Fe‐Si, in formulation H, with interactions between walls, and bulk magnetic induction. These terms have important contributions to ferromagnetic losses in high exciting magnetic fields, and are usually neglected. The dynamic trajectories of magnetic domain walls are given as non‐linear coupled ordinary differential time equations. Our simulations use the C^k spline approach, which allows many algebraic facilities in algorithms and in boundary conditions.

The complex cellular structure and chemical nature of fruit and vegetable tissues retard evaporation so that under no conditions of temperature and humidity does the rate of evaporation from them equal that from a free water surface. When conditions are such that surface evaporation from the tissues exceeds the rate of moisture diffusion to the surface, the surface becomes dry and hard and seals in the moisture. This condition, known as case‐hardening, is overcome by reducing the temperature of the air or by increasing the humidity. The maximum rate of drying, then, is attained by using the highest temperature which will not injure the product, the humidity being sufficient to prevent case‐hardening. In general practice the temperature of the air entering the drying chamber should not exceed 160° to 170° F. The humidity at the air‐outlet end of the drier should not greatly exceed 65 per cent. In driers employing recirculation the conditions of temperature and humidity may be largely controlled by varying the recirculation. The velocities of air flow which produce the most efficient results in the drying chamber depend upon several conditions. In general the rate of drying increases with the velocity of air movement. Low air velocities tend to bring about slow and uneven drying. Exceedingly high velocities may not be used profitably because a point is app ched at which the materials will be blown from the trays or at which the increased speed of drying will not offset the cost of operating a larger fan. Velocities of 600 to 800 feet per minute through the drying chamber are satisfactory in tunnel driers; lower velocities are permissible in compartment driers. The most practical means of removing moisture from the air, and at the same time conserving heat, is through the steady discharge of a portion of the air leaving the drying chamber. The rest dries efficiently when mixed with fresh air from the outside and reheated. All forced‐draught driers, therefore, should be provided with recirculation ducts connecting the air‐outlet end of the drying chamber with the heaters and with dampers controlling the air discharged, recirculated, and drawn from the outside. Dehydrated fruits and vegetables should have a uniform moisture content low enough to inhibit undesirable microbic and chemical changes within the food, and they should be free from any part of the life cycle of moths or other insects. The moisture content of dehydrated foods directly controls deterioration within the food, and the protection afforded by sulphuring or blanching will not prevent insufficiently dried products from soon becoming unfit for use. Dehydrated products having a low moisture content are not readily attacked by insects. In the long run the additional protection afforded by a low moisture content will more than make up to the producer the loss resulting from the longer drying time and greater weight shrinkage involved. To assure best keeping qualities the moisture content of fruits containing much sugar should not exceed 15 to 20 per cent., while that of other fruits and vegetables should not exceed 5 to 10 per cent., the preference in both cases being for the lower percentage. The texture, or feel, of products is a guide in determining when the proper stage of dryness has been reached. At a given moisture content products usually feel softer when hot than after they have been cooled, and often they feel softer after standing until the moisture has become evenly distributed throughout the pieces than when first cooled. A rough test for moisture in dried fruits is to take up a double handful, squeeze it tight into a ball, and release the pressure. If the fruit seems soft, mushy, or wet, and sticks together when the pressure is released, the moisture content is probably 25 per cent. or more. If the fruit is springy, and, when the pressure is released, separates in a few seconds to form pieces of approximately the original size and shape, the moisture content is usually about 20 to 25 per cent. If the fruit feels hard or horny and does not press together, falling apart promptly when the pressure is released, the moisture content is probably below 20 per cent. At the proper stage of dryness vegetables look thoroughly dry and are often hard or crisp. The Association of Official Agricultural Chemists has published a method for the determination of moisture in dried fruits. In using methods of this type, care must be taken to select a composite sample from different parts of the lot, so that it will be representative of the lot as a whole, and directions for preparing the sample must be carefully followed in order to obtain dependable results. Products are never uniformly dry when removed from the drier. Large pieces and pieces not as directly exposed to the currents of heated air as most of the material contain more moisture than the rest. Products should be stored in large bins until the moisture becomes evenly distributed. This period of curing will usually take several weeks. An alternative method is to place the dried product in large friction‐top cans for curing, thus insuring complete protection from contamination and insect infestation. Leafy vegetables, like spinach, must remain in the drier until the moisture content of the stems is very low. At this point the product is bulky and the leaves are brittle. For economy in packing and handling it is desirable to reduce the bulk by compression. For this purpose the leaves are exposed to currents of cool damp air until they have reabsorbed just enough moisture to make them slightly flexible. For convenience in handling and to facilitate the application of heat or fumigation, products should be packed in the room where they were cured and stored. Such a room should be strictly clean, dry, cool and well ventilated. The doors should fit tightly, and the windows should be covered with fine‐mesh screen to exclude dust and insects. An abundance of light assists in detecting the presence of insects and in keeping the room clean. The types of containers chosen for packing will depend largely upon the severity of the storage conditions, with particular reference to the humidity and to chances of insect infestation. An ideal container would be one which, while moderate in cost, would keep the product from absorbing moisture when exposed to the most severe conditions of storage and shipment, and would be impervious to insects. Sealed tin cans and glass jars give absolute protection against moisture absorption and insect infestation. Friction‐top cans are nearly as good. Tin containers, necessary for export shipments of dehydrated foods, are more expensive than paper containers. Wooden boxes are generally used for bulk goods. Liners of heavy paper or cardboard, and sometimes additional liners of waxed paper, are used. The use of moisture‐proof cellophane packages is increasing. All types of paper containers with which experiments have been made allow the absorption of moisture when the products are stored in damp places. Also paper containers do not give perfect protection against all insects, some of which can bore holes in paper, while the larval forms of others are so small that they can crawl through the slightest imperfections at the joints where the cartons are sealed. Most products, however, keep satisfactorily in double or triple moisture‐proof cellophane or waxed‐paper bags packed in waxed, moisture‐proof cartons, provided the initial moisture content is low and no live insects in any form enter the package. Packing in insect‐proof and moisture‐proof packages cannot be too greatly stressed.

In this paper, the formulation and analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously mass-spring damper (continuously variable fractional order) systems, have been presented. The authors will demonstrate via two cases where the frictional damping given by fractional derivative, the order of which varies continuously – while the mass moves in a guide. Here, the continuously changing nature of the fractional-order derivative for dynamic systems has been studied for the first time. The solutions of the fractional continuously variable order mass-spring damper systems have been presented here by using a successive recursive method, and the closed form of the solutions has been obtained. By using graphical plots, the nature of the solutions has been discussed for the different cases of continuously variable fractional order of damping force for oscillator. The purpose of the paper is to formulate the continuously variable order mass-spring damper systems and find their analytical solutions by successive recursion method.

The authors have used the viscoelastic and viscous – viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of the fractional derivative varies continuously.

By using the successive recursive method, here, the authors find the solution of the fractional continuously variable order mass-spring damper systems, and then obtain close-form solutions. The authors then present and discuss the solutions obtained in the cases with the continuously variable order of damping for an oscillator through graphical plots.

Formulation of fractional continuously variable order dynamic models has been described. Fractional continuous variable order mass-spring damper systems have been analysed. A new approach to find solutions of the aforementioned dynamic models has been established. Viscoelastic and viscous – viscoelastic dampers are described. The discussed damping nature of the oscillating systems has not been studied yet.