Evaluation for Chaos in EDM Generated Surface Topography

2018 ◽  
Vol 765 ◽  
pp. 227-231
Author(s):  
Ushasta Aich ◽  
Simul Banerjee
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Surface Topography ◽  
Correlation Dimension ◽  
Development Process ◽  
Machining Process ◽  
Embedding Dimension ◽  
Self Similarity ◽  
Machined Surface ◽  
Surface Development

Machined surface carries the inherent features of machining process. Investigation of surface topography generated by machining process is helpful to extract the features of surface development process. In the present study, roughness profiles measured on machined surface generated by EDM are considered as time series and used for extraction of inherent features of surface topography through phase space reconstruction. Presence of self-similarity in surface topography is assessed by estimating a second order fractal dimension, called as correlation dimension. Saturation of correlation exponents with the increase of embedding dimension indicates the presence of chaos in surface topography.

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

Evaluation of WEDM Surface Quality

2010 ◽  
Vol 97-101 ◽  
pp. 4080-4083 ◽  
Author(s):  
Lei Geng ◽  
Hua Yan Zhong
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Spectral Density ◽  
Surface Topography ◽  
Surface Quality ◽  
Power Spectral Density ◽  
Evaluation Method ◽  
Fractal Theory ◽  
Machined Surface ◽  
Power Spectral

The formation of WEDM surface is a complicated process. There are many factors which make machined surface topography have the characteristics of complex and irregular, and impact using performance of parts. The work investigated microscopic features of the WEDM surface topography based on power spectral density and fractal theory, and proposed power spectral density evaluation method of the WEDM surface. The fractal dimension of the WEDM surface was calculated by structure function method. The physical meaning of the fractal dimension of the WEDM surface was described. The result shows that topography of the WEDM surface exhibits strong fractal characteristics within a certain scale. The processing parameters and pulse power performance will affect the fractal dimension D. The fractal dimension D has a certain relationship with the surface roughness Ra. It is more reasonable to use the fractal dimension D as well as the surface roughness Ra together to evaluate WEDM surface quality.

scholarly journals Mathematical Modelling of Power Skiving for General Profile based on Numerical Enveloping

2021 ◽  
Author(s):  
Kang Jia ◽  
Junkang Guo ◽  
Tao Ma ◽  
Shaoke Wan
Keyword(s):  
Surface Topography ◽  
Cutting Tools ◽  
Mathematic Model ◽  
Machining Process ◽  
Machined Surface ◽  
High Productivity ◽  
Power Skiving ◽  
Involute Gear ◽  
Motion Speed ◽  
General Profile

Abstract Power skiving is an effective generating machining method for internal parts like gears with respect its high productivity. The general mathematic modelling for power skiving is the basis for cutting tools design, machining precision evaluation, and machining process optimization. Currently, mainly studies are focus on the involute gear machining with adopting the analytical enveloping equation. However, these analytical methods have failed to deal with overcutting for general profile skiving tasks. Moreover, little attention has been devoted to investigate the power skiving process with taking variable configuration parameters, which is significant to control the machined surface topography. Herein, we introduce a mathematic modelling method for power skiving with general profile based on the numerical discrete enveloping. Firstly, the basic mathematic model of power skiving is established, in which the center distance is formulated as polynomial of time. With transforming the power skiving into a forming machining of the swept volume of cutting edge, a numerical algorithm is designed to distinguish the machined transverse profile via the discrete enveloping ideology. Especially, the precise instant contact curve is extracted according to the feed motion speed inversely. Finally, simulations for involute gear and cycloid wheel are carried out to verify the effectiveness of this method and investigate the influence of variable radial motions on the machined slot surface topography. The results show this method is capable to simulate the dynamic power skiving process with general profiles and to evaluate the machined results.

Fractal Analysis of Laser Cutting Heavy Plate Surface Topography

2013 ◽  
Vol 395-396 ◽  
pp. 1049-1052 ◽  
Author(s):  
Lin Zhao ◽  
Yang Zhang ◽  
Da Guo Ma ◽  
Wei Li
Keyword(s):  
Fractal Dimension ◽  
Surface Topography ◽  
Laser Cutting ◽  
Low Carbon Steel ◽  
Processing Parameters ◽  
Plate Surface ◽  
Low Carbon ◽  
Machined Surface ◽  
Heavy Plate ◽  
Cutting Surface

The estimation and characterization of laser cutting heavy plate surface topography is very significant to the study on the formation mechanism of laser cutting surface and the relationship between machined surface formation and the processing parameters. The article characterizes the surface topography of the laser cutting heavy plate based on the fractal geometry theory, use box-counting method to calculate the fractal dimension of the laser cutting heavy plate surface. The results show the laser cutting heavy plate surface of low carbon steel has a obvious fractal feature, the fractal dimension of laser cutting surface range from 1.283 to 1.395 in a certain scale, the laser cutting surface topography is relatively complex, the relation between Fractal dimension D and surface roughness Ra are not linear correspondence, and then the surface topography of laser cutting heavy plate can be comprehensively estimated in accordance with D and Ra.

Analysis and Identification of Chaotic Dynamics in a Flying Vibratory System

2004 ◽  
Author(s):  
Jin-Wei Liang ◽  
Shy-Leh Chen ◽  
Ching-Ming Yen
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Random Noise ◽  
Maximum Lyapunov Exponent ◽  
Embedding Dimension ◽  
Vibratory System ◽  
Experimental Time Series ◽  
Acceleration Signals

This paper aims at determining whether chaotic dynamics exist in a flying vibratory system. It is important to identify chaotic behavior in a flying system since it may jeopardize the structure of the flying object and cause instability subsequently. It can also cause uncomfortable experience for passengers in a passenger airplane or inaccurate targeting for a missile. Identification of chaotic dynamics from experimental time series is a nontrivial task, since the data is likely to be contaminated with random noise that possesses similar properties to chaos. In this work, acceleration signals were measured at nine different locations or orientations of the flying object during a test fly. Steady-state acceleration signals were extracted and analyzed. The analysis is based on the pseudo phase-space trajectories reconstructed from the experimental time series using the method of delays. Two indices, the correlation dimension and the maximum Lyapunov exponent, are employed to identify the chaotic behavior and to distinguish it from random noise. In general, the correlation dimension calculated from the pseudo trajectory depends on the embedding dimension. It is found in three of the nine-channel signals that the correlation dimension saturates when the embedding dimension is larger than a critical value. The critical embedding dimension is the minimum dimension required for fully un-stretching the phase-space trajectories. This phenomenon indicates a possible existence of chaotic dynamics. It is also found that the maximum Lyapunov exponents calculated from the same acceleration signals are all positive, which further verifies the possibility of the existence of chaotic motion. In addition, some computational issues regarding the embedding dimension, correlation dimension, and maximum Lyapunov exponent are discussed in this paper.

Controlling Topography of Machined Surface for Adhesive-Sealing

2017 ◽  
Author(s):  
Shun Liu ◽  
Sun Jin ◽  
Xueping Zhang ◽  
Lixin Wang ◽  
Benfu Mei ◽  
...  
Keyword(s):  
Surface Topography ◽  
Adhesive Bonding ◽  
Bonding Process ◽  
Machining Process ◽  
Machining Parameters ◽  
Machined Surface ◽  
Sealing Performance ◽  
Joint Surfaces ◽  
Machining Productivity ◽  
Adhesive Performance

Adhesive is widely used in engine, airplane and other industry parts to bond and seal machined joint surfaces. Adhesive performance is important and mechanically complex, closely related to the adhesive material property, bonding process and topography of machined surfaces. The effects of material properties, bonding process, and the geometry and dimensions of adhesive layer on adhesive performance have been well studied in adhesive research field. However, the effect of the topography of machined surface on sealing performance was somehow neglected in literature. On the other hand, the texture of machined surface, especially at micro-level of surface roughness, usually used as the objective to determine process parameters in machining and also regarded as indicators of machining productivity, has been systemically and sufficiently studied. However sealing performance has not been widely investigated to relate to topography of machined surface generated from machining operation. Actually, the surface topography plays an important role in the both fields as an index for machining process and also a factor for functional performance. Desired surface should be determined firstly and then machining parameters are designed properly to achieve the desired surface, in order to improve the functional behavior such as the applied adhesive sealing performance of machined components. This research has objectives: 1) the desired surface topography is determined based on the relationship between machining operation and surface texture; 2) The effects of machined surface topography on the reliability of adhesive joint surfaces are analytically investigated. Thus, the research provides a systematic thinking for the selection of surface topography and parameters of face milling operation to improve the performance of adhesive bonding and sealing for its industry implementation.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

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