Calculation of contact temperatures generated by the rotation of a shaft in a bearing

The problem of the distribution of contact stresses resulting from the interaction between a journal and its bearing was considered in [1]. This paper deals with the problem of temperature distribution in the area of contact of a rotating cylindrical shaft and a bearing. The process is assumed to be stabilized.The problem reduces to an integral equation with respect to the contact temperature at the shaft surface.An approximate method is proposed for solving the integral equation which had permitted the derivation of a simple approximate formula for the contact temperature within any range of variation of the parameters of this problem.     

A shrink-fit shaft subject to torsion

The problem studied is an elastic, circular shaft, fitted into a cavity normal to the free surface of a half-space. The cavity is smaller than the shaft, so that there is a residual radial stress. A torque is applied to the shaft, giving rise to a region of slip between the shaft and the socket. Its extent is determined by forming an integral equation whose kernel is given by a circular ring dislocation, which has a Burgers vector whose magnitude is constant, oriented in the tangential direction. The problem has direct application to the study of shrink fitted shafts in wheels, whose diameter is large compared with the shaft.     

Properties of a half space including a twisted shaft of revolution

The properties of an elastic half space including a partly embedded twisting shaft of revolution are studied. Without knowing the exact solution of the torsion problem of a given embedded shaft, these properties can indicate some features of the displacement or stress field of the half space and can sometimes be used for checking a numerical solution. An example for checking the correct stress distribution on surfaces of twisted rigid cylindrical shaft embedded in a half space is given. This Work was Supported by the National Science Foundation of China.     

Active Stabilization of a Rotating Shaft Transmitting Static Torque

The paper is concerned with the problem of stability of a power transmitting thin-walled shaft made of the active laminate PFC (piezoelectric fiber composite). The shaft rotates with a given operational angular velocity, and is loaded by a static torque. Such a system is known to exhibit divergence or oscillating type of instability. On the one hand presence of internal friction in the material of the shaft leads to loss of stability at a certain critical rotation speed. The static torque can be responsible for spatial deformation of the shaft axis on the other. A method preventing the system from such behavior is discussed in the paper. The method is based on application of a composite material, which contains active piezoelectric fibers. The fibers produce bending moments, and this way affect the dynamics of the entire system. Two control strategies are investigated. Results of numerical simulations are presented graphically.     

Stochastic stability of a rotating shaft

The stochastic stability problem of an elastic, balanced rotating shaft subjected to action of axial forces at the ends is studied. The shaft is of circular cross-section, it rotates at a constant rate about its longitudinal axis of symmetry. The effect of rotatory inertia of the shaft cross-section is included in the present formulation. Each force consists of a constant part and a time-dependent stochastic function. Closed form analytical solutions are obtained for simply supported boundary conditions. By using the direct Liapunov method almost sure asymptotic stability conditions are obtained as the function of stochastic process variance, damping coefficient, damping ratio, angular velocity, mode number and geometric and physical parameters of the shaft. Numerical calculations are performed for the Gaussian process with a zero mean and as well as an harmonic process with random phase.     

人工神经网络在实验断裂力学中的应用

提出一种基于人工神经网络的多裂纹柱体扭转问题的数据处理新方法，运用MATLAB中的神经网络工具箱，对柱体的抗扭刚度实验值进行快速拟合，从而得到了裂纹尖端的应力强度因子，实例应用证明该方法是简便、有效的。     

Evaluation of three-dimensional stresses in shrink-fit problems by scattered-light photoelasticity

Stresses caused by shrink fits are commonly evaluated by using Lame's solution or by other analytical methods in which it is assumed that the radial stresses on the surface of contact are distributed uniformly, or in some stepwise manner, and that friction forces between the bodies are zero. These assumptions were not necessary in the experimental problem solved. Heretofore, no experimental techniques have been available to check the existing theories on a three-dimensional basis. The stresses which result when a short, hollow, thick-walled cylinder is shrunk over a shaft which is a solid shaft or a thick-walled, hollow shaft were determined. Equipment and techniques using scattered-light three-dimensional photoelasticity with a laser light source were developed and applied.     

Inverse problem of fracture mechanics for a disk fitted onto a rotating shaft

A plane problem of fracture mechanics for a circular disk fitted onto a rotating shaft is considered. The disk is assumed to be fitted tightly onto the shaft, and there are N randomly located straight-line cracks of length 2l_k (k = 1, 2, ..., N) near the inner surface of the disk. The interference between the disk and the rotating shaft, providing minimization of fracture parameters (stress intensity factor) of the disk, is theoretically studied on the basis of the minimax criterion. A closed system of algebraic equations is constructed, which allows the problem of optimal design to be solved. A simplified method of minimization of disk fracture parameters is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 201–209, July–August, 2009.     

Modeling of a Dynamic Magneto-Fluid Seal in the Presence of a Pressure Drop

The ferrohydrodynamic problem, with a disconnected free surface, of the stability of an annular magneto-fluid seal under the action of centrifugal forces and a pressure drop is solved numerically. The effect of the shaft speed on the critical pressure drop is investigated in relation to the volume of the magneto-fluid plug, the magnetic field strength, the magnetic properties of the fluid, the gap width, and the shaft radius. The flow pattern and the thermal power released in the sealing layer are studied.     

Normalization of the stress concentrations at the rounded edges of an interference fit between a solid shaft subjected to bending and a hub

The elastic stress concentrations are addressed that are developed from the keyless frictionless press fit of a shaft subjected to bending into a hub with rounded bore edges. Derived from a formal modeling of the title problem in terms of an integral equation, a set of normalized parameters is proposed that accounts for the combined effects on the hub stress concentration of the fillet radius, the shaft radius, the hub outer radius, the hub axial length, the interference, the Young's modulus, and the bending couple. A numerical validation of the normalized parameters is presented. With the aid of Finite Elements, various design charts are compiled that (a) forecast the bending couple initiating the detachment between the shaft and the hub, and (b) report the elastic stress concentrations within the hub versus the proposed normalized parameters in the absence of shaft–hub detachment. Such charts assist the designer in dimensioning an interference fit in the presence of a bending couple.     

A new efficient procedure to solve the nonlinear dynamics of a cracked rotor

The dynamic analysis of a cracked rotor with a breathing crack leads to the formulation of a nonlinear time-dependent problem. For the simple Jeffcott rotor model, this problem has been addressed using numerical integration methods that are very time consuming. A first simplification can be done assuming that the stiffness is a time-dependent function obtained with the quasi-static displacements of the shaft. In this study, we propose a new procedure to analyze the nonlinear dynamic of such a kind of cracked rotors using an iterative technique that transforms the full nonlinear problem in a succession of time-dependent linear ones. We show with different examples that this technique virtually gives the same results as the classical integration methods, but being much more efficient and achieving a significant saving of computation time. The calculations using the proposed method are over a 100 times faster than the corresponding to integrate the full nonlinear problem, being very helpful in on-line crack identification procedures. Also, this analysis shows that, in cases for which the vertical whirl amplitude is greater than the shaft weight static deflection, the use of simplified methods based on the quasi-static stiffness matrix could not be adequate.     

Simulation of gas-condensate well blowout under permafront conditions

The blowout problem for a gas-conjugate condensate well is considered in a new formulation. The effect of the fluid flow in the well shaft on the temperature of the surrounding rock and the reaction of the surrounding permanently frozen rock on the flow regime in the shaft during the thawing process are simulated and studied under ordinary operating and blowout conditions.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 101–108, May–June, 1994.     

Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method

Meccanica - Parametric instability problem of a rotating shaft subjected to a periodically varying axial force has been studied by using a numerical simulation method—discrete singular...     

Torsion of rigid circular shaft of varying diameter embedded in an elastic half space

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples of torsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented. Project Supported by the National Science Foundation of China.     

弹性体非线性振动多重共振的能量法

本论文以非线性振动理论的平均法为基础和力学的能量概念结合起来,找到了求解弹性体系非线性振动多重共振的能量法。应用本方法研究了电机轴系的双重共振等问题,证明了它是一个简易适用的方法。揭示了双重共振的一些新现象,理论得到了实验验证。     

An analytical approach to optimally design of electrorheological fluid damper for vehicle suspension system

This work develops an analytical approach to optimally design electrorheological (ER) dampers, especially for vehicle suspension system. The optimal design considers both stability and ride comfort of vehicle application. After describing the schematic configuration and operating principle of the ER damper, a quasi-static model is derived on the basis of Bingham rheological laws of ER fluid. Based on the quasi-static model, the optimization problem for the ER damper is built. The optimization problem is to find optimal value of significant geometric dimensions of the ER damper, such as the ER duct length, ER duct radius, ER duct gap and the piston shaft radius, that maximize damping force of the ER damper. The two constrained conditions for the optimization problem are: the damping ratio of the damper in the absence of the electric field is small enough for ride comfort and the buckling condition of the piston shaft is satisfied. From the proposed optimal design, the optimal solution of the ER damper constrained in a specific volume is obtained. In order to evaluate performance of the optimized ER damper, simulation result of a quarter-car suspension system installed with the optimized ER damper is presented and compared with that of the non-optimized ER damper suspension system. Finally, the optimal results of the ER damper constrained in different volumes are obtained and presented in order to figure out the effect of constrained volume on the optimal design of ER damper.     

Resonant Capture and Separatrix Crossing in Dual-Spin Spacecraft

We consider the rotational motion of a spacecraft composed of two bodies which are free to rotate relative to one another about a common shaft S. A motor on one of the bodies provides a small constant internal torque which influences the relative motion of the two bodies, and which may influence the orientation of their common shaft S. Resonant capture refers to the phenomenon that the spacecraft may end up in one of several possible orientations, including a nearly flat spin (transverse to S), in addition to the expected simple rotation about S.The method of averaging is used to treat the original equations of motion, and it is shown that the essential mathematical problem involves separatrix crossing in a problem with slowly moving separatrices. Energy changes represented by Melnikov integrals are used to supplement the averaged equations in the neighborhood of the heteroclinic motions. The method is used to predict which initial conditions lead to capture into each of three distinct capture regions. The asymptotic results are compared to those obtained by direct numerical integration of the equations of motion.     

Photoelastic analysis for gravity stresses with stress-frozen gelatin

Gravity stresses in a vertical shaft and a sphere are investigated photoelastically using stress-frozen gelatin to demonstrate the potential of this approach for three-dimensional analysis, particularly with body-force loading. Properties of gelatin mixtures at varying temperatures from 20°C to 2°C are outlined in detail sufficient to show variables affecting the basic stress-freezing phenomenon and allow design of experiments. Even using relatively unrefined techniques, the close agreement of analytic to experimental results for the vertical shaft indicates the good accuracy obtainable from this simple and inexpensive method. Using improved techniques, results for the heavy sphere for which no analytic solution is available are then found allowing interpretation of other experimental results for this problem.     

Polymeric liquid sealing of a rotating shaft and rheological effects accompanying its functioning

A new type of contactless sealing of a rotating shaft based on use of normal stress effect developed on shearing in elastic polymeric liquids is reported. Physical phenomena accompanying sealing function, such as self-heating of a liquid, separation of polymer under strain from the walls by a water film, foaming of the polymer have been studied. The problem of polymer flow and of its self-heating between two coaxial disks has been considered; the problem serves as a basis for sealing calculations.     

Numerical simulation of contact problems in vane machinery by a parametric quadratic programming method

Interference fits are widely used for connecting impeller and shaft assembly that are forced together slowly by pressing. The interference fit design ensures stable balance behavior and allows for positive contact between the impeller and shaft assembly throughout the range of operating speeds. In addition to maintaining radial contact, sufficient net radial interface pressure must remain in order to transmit torque when the rotational speed is very high. Therefore, the interference fit between the impeller and the shaft assembly is one of the most important factors influencing the performance of the turbo unit in the design of turbocharger compressor. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference fit loading is used for the analysis. The finite-element (FE) parametric quadratic programming (PQP) method developed based on the parametric variational principle (PVP) is used for the analysis of the stress distribution in the three-dimensional (3D) contact problem of impeller. The advantages of the parametric programming method compared with conventional approaches are that the penalty factors can be canceled and that solutions can be obtained directly without tedious iterative procedures such as the general incremental iterative method. To save time in the computation, a~multi-substructure technique is adopted for structural modeling. This not only simplifies the calculation, but also provides a convenient service for process computer-aided design (CAD) by means of FE simulation. The effects of the fit tolerance, coefficient of friction and rotational speed (centrifugal force), wall thickness of the shaft sleeve and the contact stress on the interference-fitting surfaces are studied in detail in the numerical computation. It is found that a nonuniform initial amount of interference in the structural design avoids the relative displacement generated and ensures uniformity of the contact stress. To assure quality of press-fitting, the amount of interference between the shaft sleeve and shaft should be strictly controlled to avoid the rapid increase of the contact stress. The numerical results demonstrate the high accuracy and good convergence of the algorithm presented here, which provides an effective approach that achieves more-reliable interference-fitted connections and more-precise assembly accuracy with lower manufacturing cost in the structural design.