Influence Of Fractal Parameters Research Articles

Dynamic Modeling and Experimental Modal Analysis for the Central Rod-Fastened Rotor With Hirth Couplings Based on Fractal Contact Theory

Abstract The central rod-fastened rotor of gas turbine exhibits pronounced noncontinuous characteristics due to the large number of contact interfaces between the compressor and turbine disks. It is necessary to establish an accurate dynamic modeling method for the central rod-fastened rotor that fully considers the contact surface effect. In this work, the contact behavior of the rough surface is characterized by the fractal theory. The normal and tangential contact stiffness models are developed, and the influence of fractal parameters is discussed. Besides, the finite element model for the central rod-fastened rotor is established by developing an improved contact element considering the equivalent stiffness segment of Hirth couplings. Finally, the proposed model is verified by conducting the modal testing and measuring the first four modes of natural frequencies and modal shapes of the central rod-fastened rotor. The results show that the numerical results are in good agreement with the experimental ones, and the fractal contact model can effectively predict the connection stiffness of Hirth couplings, which in turn improves the simulation accuracy for the modal characteristics of the central rod-fastened rotor and provides a dynamic modeling approach with high efficiency and less computational complexity.

Study on nonlinear dynamic characteristics of gear system with 3D anisotropic rough tooth surface based on fractal theory

Different from the mainstream research, this study fully considers the anisotropic micro-topography of the tooth surface when studying the dynamic characteristics of gears. An anisotropic 3D fractal rough tooth surface model is proposed based on fractal geometry theory. The major advantage of the novel model is that it contains more surface micro details, especially on the tooth width, which are ignored in general studies. The backlash and time-varying meshing stiffness (TVMS) are then revised on the basis of this model. Finally, a 6-degree-of-freedom nonlinear dynamic model considering surface topography is established and the influence of fractal parameters on gear dynamics is investigated. The results show that the fractal parameters change the backlash and TVMS and have an obvious impact on the dynamics and vibration responses of the transmission system. The rough gear system enters chaos earlier and has better stability at high speeds in comparison with the smooth system. As the fractal dimension increases, the dynamic transmission error amplitude gradually decreases and the system tends to stable periodic motion. The characteristic scale coefficient yields a more moderate but opposite effect on the dynamic response of the system compared with the fractal dimension. The finding of this study can provide theoretical guidance for tooth surface machining from the perspective of tooth surface morphology.

Research on thermal resistance network modeling of motorized spindle based on the influence of various fractal parameters

A mathematical model of the motorized spindle taking into account the influence of various fractal parameters is established. Weierstrass–Mandelbrot function (W–M function) shows that the fractal parameters are important that affect the contact characteristics. According to fractal theory, the thermal contact resistance (TCR) between contact surfaces is proposed, and the thermal contact conductance (TCC) verification experiment verifies its accuracy. The key nodes of the motorized spindle are divided and the heat-balance equations are solved. The accuracy of the thermal resistance network model is verified by the temperature–rise experiment. The results show that: the fractal dimension D and the fractal–amplitude coefficient G affect the complexity and contour height of the contact surface; the temperature of each component rises quickly and then remains stable; An increase in the D causes a decrease in the temperature of the nodes and an increase in the G causes an increase in the temperature of the nodes. The influence of fractal parameters on the thermal characteristics of the motorized spindle can not be neglected.

Elastic-plastic Sliding Asperity Interaction of Machined Multiscale Metal Surface

Sliding process between asperities of machined metal surface is important to analyse wear mechanisms. Elastic-plastic sliding asperity model based on fractal geometry is proposed in this paper to extend the sliding process of single micro-asperity to a macro-asperity. The contact force, the critical interference and residual interference are calculated with fractal dimension D and fractal roughness G in the multiscale views. The influence of fractal parameters on normal and tangential contact force are studied. The results of the simulation show that the plastic deformation and residual interference are the main factors affecting the contacting force and asperity radius. For smaller G and bigger D surfaces, the sliding interaction of asperities is less remarkable and the plastic force accounts for less in the contact force.

Correction to: High Pressure Mercury Intrusion Porosimetry Analysis of the Influence of Fractal Dimensions on the Permeability of Tight Sandstone Oil Reservoirs

In this paper, fractal characteristics of sandstone in the Chang 7 section of the Triassic Yanchang Formation of the Dingbian oilfield, Ordos Basin, China were analyzed by high pressure mercury intrusion porosimetry and the fractal model. The influence offractal parameters on rock permeability is discussed. Results show that fractal dimensions (Df) of sandstone samples range within 2.759-2.987, with an average of 2.890, and the mean capillary tortuosity fractal dimension (DT) ranges within 1.194-1.553, with an average of 1.391; Df is larger than Dr There is a strong negative correlation between rock permeability and Df or Dr Both Df and DT decrease with decreasing porosity of sandstone samples, indicating that connectivity between rock sample pores becomes poor and capillary tortuosity increases. The seepage path in low-permeability (tight) sandstone is much longer than in moderate-permeability sandstone, which is an important reason for the low permeability of the tight sandstone oil reservoir Meanwhile, the fractal model is an effective predictor of the permeability of tight sandstone oil reservoirs.

Three-dimensional fractal model of normal contact damping of dry-friction rough surface

According to the influence of the normal contact damping of joint surfaces on the dynamic characteristics of high-precision machinery (machine tool, robot, etc.), in this article, a three-dimensional fractal model of normal contact damping of dry-friction rough joint surfaces based on Hertz theory and fractal theory is established. The three-dimensional surface topography is constructed, according to the modified double variable Weierstrass–Mandelbrot function. The fractal model of strain energy [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal contact damping [Formula: see text] are deduced in detail, and the influence of fractal parameters and dynamic friction coefficient [Formula: see text] on them are simulated. The simulation curves show that strain energy [Formula: see text], dissipated energy [Formula: see text], damping loss factor [Formula: see text], and normal damping [Formula: see text] increase with the increase in the fractal roughness G; the influence of fractal dimension D on [Formula: see text] is more changeable, first [Formula: see text] decreases with the increase in D and then increases. [Formula: see text], [Formula: see text], and [Formula: see text] increase with the increase in D and [Formula: see text], respectively; the effect of [Formula: see text] on [Formula: see text] is not obvious, so simple change in [Formula: see text] has no significant change in [Formula: see text]; a comparative analysis of the theoretical calculation of normal damping and experimental results show that their general trend is consistent, and they increase with the increase in total normal contact load P, the relative error is 5%–25%. The theoretical model can provide reference for the design of normal contact damping of the joint surfaces.

Fractal surface synthesis based on two dimensional discrete Fourier transform

The discrete Fourier transform(DFT) is used for fractional Brownian motion(FBM) surface synthesis in tribology(i.e., contact, sliding, and sealing, etc). However, the relationship between fractal parameters(fractal dimension and scale factor) and traditional parameters, the influence of fractal parameters on surface appearance, have not been deeply discussed yet. These lead to some kind of difficulty to ensure the synthesized surfaces with ideal fractal characteristic, required traditional parameters and geometric appearance. A quantitative relationship between fractal parameters and the root mean square deviation of surface (Sq) is derived based on the energy conservation property between the space and frequency domain of DFT. Under the stability assumption, the power spectrum of a FBM surface is composed of concentric circles strictly, a series of FBM surfaces with prescribed Sq could be synthesized with given fractal dimension, scale factor, and sampling numbers, but the ten-point height(Sz), the skewness(Ssk) and the kurtosis(Sku) are still in random, where the probability distributions of Sz and Ssk are approximately normal distribution. Furthermore, by iterative searching, a surface with desired Abbott-Firestone curve could be obtained among those surfaces. An intuitive explanation for the influence of fractal dimension and scale factor on surface appearance is obtained by discussing the effects on the ratio of energy between high and low frequency components. Based on the relationship between Sq and surface energy, a filtering method of surface with controllable Sq is proposed. The proposed research ensures the synthesized surfaces possess ideal FBM properties with prescribed Sq, offers a method for selecting desired Abbott-Firestone curve of synthesized fractal surfaces, and makes it possible to control the Sq of surfaces after filtering.

Dynamic conductivity of composites of fractal structure

We have studied the dynamic conductivity of a composite consisting of well- and weak-conducting components with random fractal structure. In order to calculate effective properties of composite medium, we used hierarchic structure model and innovative iterative averaging method based on renormalization group transformations idea. Our results show, that the behavior of a composite over a magnetic field become even more complicated.Unusual peaks and oscillations appear in frequency dependencies of effective conductivity, permittivity and other properties. We discuss the influence of fractal parameters of the composite structure on such unusual behavior of effective properties.

An adhesion model for elastic-plastic fractal surfaces

The strong adherence (stiction) of adjacent surfaces is a major design concern in microelectromechanical system. The present research concerns the elastic-plastic adhesion of a rough surface contacting with a rigid flat. Rough surface is characterized by fractal geometry using a two-variable Weierstrass-Mandelbrot function [The Fractal Geometry of Nature (Freeman, New York, 1982)]. The microcontact model of single asperity is established in terms of fractal parameters, and the plastic adhesion model is also developed with the Dugdale approximation to consider the adhesive interaction within and outside the contact area. Then according to the plastic flow criterion, the Maguis-Dugdale transition theory [Adhesion of Adhesion and Rapture of Elastic Solids (Springer-Verlag, New York, 2005)] and the plastic adhesion model are used to solve the elastic-plastic adhesive interaction for the two approaching surfaces by incorporating the fractal surface model. Simulations of the adherence force versus the approaching distance of surfaces are performed. The necessity of considering the plastic deformation in microsized interface adhesion is also validated by comparing the result of the presented model with that of the Morrow model [J. Tribol 127, 206 (2005)]. The influence of fractal parameters on adherence force shows that controlling the surface topography is a readily means to control the adherence force for the elastic-plastic adhesion of rough surfaces, which is due to the intermolecular adhesive interactions.