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Semi-analytical Stiffness Model of Bolted Joints in Machine Tools Considering the Coupling Effect

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Nanomanufacturing and Metrology 2023年第2期6卷 66-78页

作者： Yiwei Ma Yutao Fu Yanling Tian Xianping Liu School of Engineering The University of WarwickCoventry CV47ALUK School of Mechanical Engineering Tianjin UniversityTianjin 300072China

This study proposes an improved semi-analytical approach for contact stiffness modeling of bolted joints in a machine tool ***,nonlinear contact stress distribution within a single-bolted joint is obtained from the simulation results of finite element analysis ***,employing the Hertz contact theory and fractal theory,the contact stiffness model of a single asperity is formulated,affording analytical expressions for normal and tangential contact stiffnesses of a single-bolted joint by integrating multi-asperities in the contact ***,considering two test specimens as illustrations,the mode shapes and natural frequencies of the proposed model and modal analysis tests are compared,and the influence of coupling effects between two adjacent bolts is *** maximum error in the natural frequencies of the proposed approach is<2.73%relative to the experimental ***,the measurements of frequency response functions on a box-in-box precision horizontal machine tool are conducted to demonstrate the accuracy and efficiency of the proposed *** proposed model is highly efficient in revealing the influence of microcontact factors on the contact stiffness of bolted joints and in guiding the optimal functional design of bolt arrangements under the framework of virtual machine tools.

关键词： Stiffness modeling Bolted joint Microcontact mechanics fractal theory Rough surface

fractal analysis of thermal conduction of loose coal

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Mining Science and Technology 2010年第6期20卷 831-834,838页

作者： WANG Yijiang ZHOU Guoqing WEI Yazhi ZHOU Yang School of Mechanics & Civil Engineering China University of Mining & Technology Xuzhou 221116 China State Key Laboratory of Geomechanics & Deep Underground Engineering China University of Mining & Technology Xuzhou 221008 China

For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.

关键词： loose coal thermal conductivity fractal theory box-counting dimension

The Application of fractal to Design Knitted Sweaters

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Journal of Donghua University(English Edition) 2011年第2期28卷 187-189页

作者：陈莉张蕊谢月凤 School of Textiles Tianjin Polytechnic University Key Laboratory of Advanced Textile Composite Ministry of Education Department of Automotive Engineering Tianjin Transportation Vocational College

Pattern design is very important for knitting industry. fractal theory is adopted to create image automatically, which is applied to design knitted sweaters. Based on Mandelbrot set(M-set), image could be generated automatically by visual basic (VB) program. Plenty of wonderful patterns are created by the following methods: selecting any parts of the image and magnifying, extending generalized M-set, editing the selected images with photoshop. The edited pattern is used to set on any parts of clothes to show fashion effect. Actual knitted structure is simulated by knitting CAD software. The results show that the fractal theory has greater potential applications in knitted pattern design, and it deserves further research.

关键词： fractal theory Mandelbrot set image created automatically application on knitted sweater design

Numerical Modeling of Dendrite Growth in Al Alloys

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Tsinghua Science and Technology 2004年第5期9卷 546-549页

作者：许庆彦柳百成 Department of Mechanical Engineering Tsinghua University Beijing 100084 China

Dendritic grains are the most often observed microstructure in metals and alloys. In the past decade, more and more attention has been paid to the modeling and simulation of dendritic microstructures. This paper describes a modified diffusion-limited aggregation model to simulate the complex shape of the dendrite grains during metal solidification. The fractal model was used to simulate equiaxed dendrite growth. The fractal dimensions of simulated Al alloy structures range from 1.63-1.88 which compares well with the experimentally-measured fractal dimension of 1.85; therefore, the model accurately predicts not only the dendritic structure morphology, but also the fractal dimension of the dendrite structure formed during solidification.

关键词： fractal theory diffusion-limited aggregation model dendrite growth metal solidification

The theory of Biomedical Knowledge Integration (Ⅶ)──The Non-Euclid Macro-Micro Transform Law

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医学信息（西安上半月） 2007年第2期20卷 175-182页

作者： Hanfei Bao Lab of Informationization and Standardization of TCM Shanghai Univ. of Traditional Chinese Medicine Shanghai China

This article continued to do the scholastic pursuits on some profound mechanisms in the life systems, which are believed to be related to the further development of Medical Informatics. It discussed at first the structural nature of things, then probed a principle which is a basis for both of the fractal theory and the wavelet analysis, being called the shape-constancy law of the basic constructors at the different scale levels. And the paper also ventured the equivalency between the shape of wave and matrix, thus presented a new concept "shaped-number", being expected to work in the operations of some bio-medical functions or shapes.

关键词： BioMedical Informatics Artificial Intelligence the theory BioMedical Knowledge Integration fractal theory Wavelet Analysis

Two Network Structure Indicators for Conventional Public Transit

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Journal of Harbin Institute of Technology(New Series) 2016年第5期23卷 90-96页

作者： Min Fu Hao Wang Wei Wang Sida Luo De Zhao School of Transportation Southeast University Nanjing 210096 China Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies Nanjing 210096 China

The significance of network structure indicators for the planning and management of conventional public transit is widely *** order to improve and enrich the conventional public transit assessment system,two network structure indicators are ***,according to the obvious defects lying in the traditional no-linear coefficient,the realistic no-linear coefficient γRNL,a modified no-linear coefficient indicator,is put forward,which takes into account the effects of barriers in a ***,to cover the gap of an indicator which can reflect the coverage homogeneity of a transit network,the length dimension LDis proposed on the basis of fractal ***,a case study is applied to verify the validity and practicability of the two indicators in problem diagnosis using regression *** results validate that γRNLcan evaluate the detour of bus lines more reasonably than the previous no-linear coefficient because it reflects the layout of bus lines,and LDcan represent the rate of change of the network density,adding a new member to the scheme of network structure indicators for public transit.

关键词： conventional public transit network structure indicator realistic no-linear coefficient length dimension fractal theory

Sensor Fault Diagnosis Method Based on fractal Dimension

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Sensor Fault Diagnosis Method Based on Fractal Dimension

fractal evolution mechanism of rock fracture in undersea metal mining

第25届中国控制与决策会议

作者： Qian Pengpeng Liu Jinguo Zhang Wei Li Yangmin Shenyang Institute of Automation Chinese Academy of Sciences Department of Electromechanical Engineering University of Macau

ISBN: (纸本)9781467355339

The development of automation technology has opened a new field - sensor fault diagnosis. Sensor is the source and foundation of information, once the sensor faults occur, which will lead to the degradation of automation system’s performance, even disastrous consequences. There are various sensor fault diagnosis methods, while each method has its imperfection, so this paper has proposed to use fractal dimension for sensor fault diagnosis. fractal theory is a powerful tool to deal with nature fragmented or complex phenomenon, which can describe the non-linear behaviour of the signal quantitatively. Firstly, this paper indicates the necessity and practical utility of sensor fault diagnosis and the development status of fractal theory. Then it describes the correlation dimension in detail which is the most suitable one to analyze sequenced dynamic signal, thereafter analyzing the type of the sensor fault. Finally, in order to verify the effectiveness of the method proposed, we set up an experimental platform. Five kinds of signals （no-fault signal and four kinds of fault signals） are gathered, whose correlation dimensions are calculated. The experimental results show that: various sensor faults can be diagnosed effectively by correlation dimension. At last, in order to verify the correctness of the correlation dimensions’ results, the paper also gives the box counting dimension results, which further verifies the correctness of the results.

关键词： Sensor Fault Diagnosis fractal Dimension fractal theory Correlation Dimension Box Counting Dimension

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Journal of Central South University 2020年第4期27卷 1320-1333页

作者： LIU Zhi-xiang HAN Ke-wen YANG Shan LIU Yu-xi School of Resources and Safety Engineering Central South UniversityChangsha 410083China Engineering Faculty Monash UniversityMelbourne 3800Australia

Through rock mechanics test, similar simulation experiment, borehole photographic observation of rock fissure, numerical simulation calculation of plastic zone distribution and deformation monitoring of rock mass during undersea mining, the fractal evolution mechanisms of rock fracture in undersea metallic deposits of Sanshandao Gold Mine were studied by fractal theory. The experimental researches on granite mechanics test in undersea deposit indicate that with the increase of load, the granite deformation energy and the fractal dimension of acoustic emission(FDAE) increase gradually. However, after reaching the peak stress of specimen, the fractal dimensions of acoustic emission(FDAEs) decrease and the granite specimen fails. Therefore, the fractal dimension evolution of rock failure can be divided into four stages, which are fissure inoculation stage, fissure growth stage, fissure expansion stage and fracture instability stage, respectively. By calculating and analyzing the damage photographs of rock specimens in Sanshandao Gold Mine, the fractal dimension of rock fissure is 1.4514, which is close to the average value of FDAE during granite destruction, i.e., 1.4693. Similar simulation experiments of undersea mining show that with the excavation proceeding, the FDAE in rock stratum increases gradually, and when the thickness of the isolation roof is less than 40 m, the FDAE begins to decrease, and meanwhile the sign of water inrush emerges. The numerical simulation researches on the plastic zone distribution of undersea mining in Sanshandao Gold Mine indicate that the fractal dimension of plastic zone(FDPZ) where the failure characteristics occur is 1.4598, close to the result of similar simulation experiment of 1.4364, which shows the sign of water inrush. Meanwhile, the thickness of the isolation roof for undersea mining should be more than 40 m, which is consistent with the results of similar simulation experiment. In Sanshandao Gold Mine, the rock fissures in

关键词： undersea mining of metal deposit evolution of rock fracture fractal theory energy of rock failure

Modeling and application of thermal contact resistance of ball screws

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Journal of Central South University 2019年第1期26卷 168-183页

作者： GAO Xiang-sheng WANG Min LIU Xue-bin Beijing Key Laboratory of Advanced Manufacturing Technology College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology Beijing Key Laboratory of Electrical Discharge Machining Technology

Aiming at determining the thermal contact resistance of ball screws,a new analytical method combining the minimum excess principle with the MB fractal theory is proposed to estimate thermal contact resistance of ball screws considering microscopic fractal characteristics of contact *** minimum excess principle is employed for normal stress ***,the MB fractal theory is adopted for thermal contact *** effectiveness of the proposed method is validated by self-designed *** comparison between theoretical and experimental results demonstrates that thermal contact resistance of ball screws can be obtained by the proposed *** this basis,effects of fractal parameters on thermal contact resistance of ball screws are ***,effects of the axial load on thermal contact resistance of ball screws are also *** conclusion can be drawn that the thermal contact resistance decreases along with the fractal dimension D increase and it increases along with the scale parameter G increase,and thermal contact resistance of ball screws is retained almost constant along with axial load increase before the preload of the right nut turns into zero in *** application of the proposed method is also conducted and validated by the temperature measurement on a self-designed test bed.

关键词： ball screw fractal theory thermal contact resistance contact stress preload