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Transmission Index Research of Parallel Manipulators Based on Matrix Orthogonal Degree 被引量:3
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作者 Zhu-Feng Shao Jiao Mo +1 位作者 Xiao-Qiang Tang Li-Ping Wang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2017年第6期1396-1405,共10页
Performance index mance evaluation, and is the is the standard of perfor- foundation of both perfor- mance analysis and optimal design for the parallel manipulator. Seeking the suitable kinematic indices is always an ... Performance index mance evaluation, and is the is the standard of perfor- foundation of both perfor- mance analysis and optimal design for the parallel manipulator. Seeking the suitable kinematic indices is always an important and challenging issue for the parallel manipulator. So far, there are extensive studies in this field, but few existing indices can meet all the requirements, such as simple, intuitive, and universal. To solve this problem, the matrix orthogonal degree is adopted, and generalized transmission indices that can evaluate motion/force trans- missibility of fully parallel manipulators are proposed. Transmission performance analysis of typical branches, end effectors, and parallel manipulators is given to illus- trate proposed indices and analysis methodology. Simula- tion and analysis results reveal that proposed transmission indices possess significant advantages, such as normalized finite (ranging from 0 to l), dimensionally homogeneous, frame-free, intuitive and easy to calculate. Besides, pro- posed indices well indicate the good transmission region and relativity to the singularity with better resolution than the traditional local conditioning index, and provide a novel tool for kinematic analysis and optimal design of fully parallel manipulators. 展开更多
关键词 Transmission index Parallel mechanism Kinematic performance matrix orthogonal degree
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REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS
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作者 Xiaohui LI Meiqi LIU Chunyuan DENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1229-1243,共15页
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq... In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value. 展开更多
关键词 NORM orthogonal projection positive operator SPECTRAL block operator valued matrix
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ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS 被引量:5
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作者 L.Jódar E.Defez E.Ponsoda 《Analysis in Theory and Applications》 1996年第1期96-115,共20页
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro... In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given. 展开更多
关键词 orthogonal matrix POLYNOMIALS WITH RESPECT TO LINEAR matrix MOMENT FUNCTION ALS 艺人 APPI
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A SEMI-CONJUGATE MATRIX BOUNDARY VALUE PROBLEM FOR GENERAL ORTHOGONAL POLYNOMIALS ON AN ARBITRARY SMOOTH JORDAN CURVE 被引量:1
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作者 杜志华 《Acta Mathematica Scientia》 SCIE CSCD 2008年第2期401-407,共7页
In this article, the author characterizes orthogonal polynomials on an arbitrary smooth Jordan curve by a semi-conjugate matrix boundary value problem, which is different from the Riemann-Hilbert problems that appear ... In this article, the author characterizes orthogonal polynomials on an arbitrary smooth Jordan curve by a semi-conjugate matrix boundary value problem, which is different from the Riemann-Hilbert problems that appear in the theory of Riemann -Hilbert approach to asymptotic analysis for orthogonal polynomials on a real interval introduced by Fokas, Its, and Kitaev and on the unit circle introduced by Baik, Deift, and Johansson. The author hopes that their characterization may be applied to asymptotic analysis for general orthogonal polynomials by combining with a new extension of steepest descent method which we are looking for. 展开更多
关键词 Semi-conjugate matrix boundary value problem orthogonal polynomials smooth Jordan curve
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The Construction of a Class of Compactly Supported Orthogonal Matrix-valued 被引量:1
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作者 CHEN Qing-jiang CHENG Chuan-rui CHENG Zheng-xing 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期608-616,共9页
In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of ... In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory. 展开更多
关键词 orthogonal matrix-valued multiresolution analysis matrix-valued scal-ing fun-nctions matrix-valued wavelets Hermitian matrix
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ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A CONJUGATE BILINEAR MATRIX MOMENT FUNCTIONAL: BASIC THEORY 被引量:1
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作者 Lucas Jodar and Emilio Defez (Polytechnical University of Valencia, Spain) 《Analysis in Theory and Applications》 1997年第1期66-79,共14页
In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th... In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined. 展开更多
关键词 orthogonal matrix POLYNOMIALS WITH RESPECT TO A CONJUGATE BILINEAR matrix MOMENT FUNCTIONAL
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A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS
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作者 Zhihui Zhu Zhongkai Li 《Analysis in Theory and Applications》 2007年第1期26-34,共9页
Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×... Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) 〉 -1 for every z E or(a). In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln^(A,λ)(x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case. 展开更多
关键词 Laguerre matrix polynomial Sobolev orthogonality matrix moment functional
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Matrix Expression of the Orthogonal Wavelet (Packets) Transform
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作者 杜红彬 滕虎 姚平经 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2002年第6期701-705,共5页
Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provi... Matrix expression of finite orthogonal wavelet transform of finite impulse response signal is more valuable for theoretical analysis and understanding. However, clear deduction for matrix expression has not been provided yet. In this paper, the formulation to generate the re-lated matrix is put forward and the theorem on the orthogonality of this matrix proved. This effort deploys a basis for more deeper and wider applications in chemical processes. * 展开更多
关键词 finite orthogonal wavelet (packets) transform matrix expression finite impulse response signal
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RELATIVE ASYMPTOTICS FOR ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO A PERTURBED MATRIX MEASURE ON THE UNIT CIRCLE
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作者 Hossain O. Yakhlef Francisco Marcellán 《Approximation Theory and Its Applications》 2002年第4期1-19,共19页
Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w... Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I. 展开更多
关键词 RELATIVE ASYMPTOTICS FOR orthogonal matrix POLYNOMIALS WITH RESPECT TO A PERTURBED matrix MEASURE ON THE UNIT CIRCLE
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Orthogonalization of unified and extended Bézier basis and its transformation matrix
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作者 FANG Meie JI Zhongping WANG Guozhao 《Computer Aided Drafting,Design and Manufacturing》 2013年第1期41-46,共6页
UE-Brzier (unified and extended Brzier) basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brz... UE-Brzier (unified and extended Brzier) basis is the unified form of Brzier-like bases, including polynomial Brzier basis, trigonometric polynomial and hyperbolic polynomial Brzier basis. Similar to the original Brzier-like bases, UE-Brzier basis func-tions are not orthogonal. In this paper, a group of orthogonal basis is constructed based on UE-Brzier basis. The transformation matrices between UE-Brzier basis and the proposed orthogonal basis are also solved. 展开更多
关键词 UE-B6zier basis orthogonalIZATION legendre basis transformation matrix
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A REPLACEMENT SCHEME ON THE CONSTRUCTION OF ORTHOGONAL ARRAYS 被引量:1
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作者 PangShanqi ZhangYingshan LiuSanyang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第1期93-98,共6页
A method of constructing orthogonal arrays is presented by Zhang, Lu and Pang in 1999.In this paper,the method is developed by introducing a replacement scheme on the construction of orthogonal arrays ,and some new mi... A method of constructing orthogonal arrays is presented by Zhang, Lu and Pang in 1999.In this paper,the method is developed by introducing a replacement scheme on the construction of orthogonal arrays ,and some new mixed-level orthogonal arrays of run size 36 are constructed. 展开更多
关键词 mixed-level orthogonal array projection matrix Hadamard product.
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Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets 被引量:1
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作者 CHEN Qing-jiang LIU Hong-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期360-367,共8页
The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec... The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2(R, C^n) from these wavelet packets. 展开更多
关键词 orthogonal Hermitian matrix vector-valued multiresolution analysis vector-valued scaling functions vector-valued wavelets vector-valued wavelet packets
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On a Grouping Method for Constructing Mixed Orthogonal Arrays 被引量:1
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作者 Chung-Yi Suen 《Open Journal of Statistics》 2012年第2期188-197,共10页
Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-... Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1, s). If there exists a (t-1)-flat over GF(s) in PG(m-1, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0i(smn-1)(s-1)/( sm-1)( sn-1) New orthogonal arrays of sizes 256, 512, and 1024 are obtained by using PG(7,2), PG(8,2), and PG(9,2) respectively. 展开更多
关键词 FINITE field FINITE PROJECTIVE geometry (t-1)-flat over GF(s) in PG(m-1 sn ) Geometric orthogonal array matrix representation Minimal polynomial orthogonal main-effect plan PRIMITIVE element Tight.
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Expression of strain tensor in orthogonal curvilinear coordinates
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作者 Xuyan Liu Yingfeng Ji Quanqiang Liang 《Geodesy and Geodynamics》 2010年第1期48-56,共9页
Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a func... Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal eurvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates. 展开更多
关键词 orthogonal Curvilinear Coordinates OCC Cartesian coordinates strain tensor transformation matrix universal expression
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Mathematical Description of Acousto-Optic Tunable Filter Orthogonal Polarizing Method
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作者 徐可欣 文慧智 +2 位作者 张浩 范国芳 杨吉生 《Transactions of Tianjin University》 EI CAS 2005年第4期295-298,共4页
The transfer function of the optical splitting system of the acousto-optic tunable filter (AOTF) is deduced to be a reference to optical design. The characteristic matrix ( transfer function) of AOTF is used to de... The transfer function of the optical splitting system of the acousto-optic tunable filter (AOTF) is deduced to be a reference to optical design. The characteristic matrix ( transfer function) of AOTF is used to describe quantitatively the characters of polarization elements in the orthogonal polarizing system. According to the characteristic matrix, the included angle of polarizer's transmission direction and polarization analyzer's transmission direction should be 90°. As a result the signal to noise ratio increased about 20 times though the light intensity was reduced to 54.3%,because both the transmittances of polarizer and polarization analyzer are 0. 74, which is an intrinsic character. The orthogonal polarizing method is an effective method to get rid of the influence of zero order light and improve the spectrum resolution and signal-to-noise ratio. 展开更多
关键词 acousto-optic tunable filter: characteristic matrix optical splitting system orthogonal polarizing method
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Orthogonal matrix of polarization combinations:concept and application to multichannel holographic recording
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作者 Shujun Zheng Jiaren Tan +4 位作者 Hongjie Liu Xiao Lin Yusuke Saita Takanori Nomura Xiaodi Tan 《Opto-Electronic Advances》 SCIE EI CAS 2024年第10期4-13,共10页
Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties.Although orthogonal matrices based on amplitude or phase combinations have been extensivel... Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties.Although orthogonal matrices based on amplitude or phase combinations have been extensively explored,the orthogonal matrix of polarization combinations(OMPC)is a novel,relatively unexplored concept.Herein,we propose a method for constructing OMPCs of any dimension encompassing 4n(where n is 1,2,4,8,…)mutually orthogonal 2ncomponent polarization combinations.In the field of holography,the integration of polarization multiplexing techniques with polarization-sensitive materials is expected to emerge as a groundbreaking approach for multichannel hologram multiplexing,offering considerable enhancements in data storage capacity and security.A multidimensional OMPC enables the realization of multichannel multiplexing and dynamical modulation of information in polarization holographic recording.Despite consolidating all information into a single position within the material,we effectively avoided extraneous crosstalk during the reconstruction process.Our results show that achieving four distinct holographic images individually and simultaneously depends on the polarization combination represented by the incident wave.This discovery opens up a new avenue for achieving highly holographic information storage and dynamically displayed information,harnessing the potential of OMPC to expand the heretofore limited dimensionality of orthogonal polarization. 展开更多
关键词 orthogonal matrix of polarization combinations polarization-modulated multiplexing multichannel recording polarization holography dynamical information modulation
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Matrix orthogonal polynomials,non-abelian Toda lattices,and Bäcklund transformations
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作者 Shi-Hao Li 《Science China Mathematics》 SCIE CSCD 2024年第9期2071-2090,共20页
A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper.The normalization factors of matrix orthogonal polynomials expressed using quasideterminants are sho... A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper.The normalization factors of matrix orthogonal polynomials expressed using quasideterminants are shown to be the solutions to the non-abelian Toda lattice in semi-discrete and full-discrete cases.Moreover,with a moment modification method,we demonstrate that the B¨acklund transformation of the non-abelian Toda lattice given by Popowicz(1983)is equivalent to the non-abelian Volterra lattice,whose solutions can be expressed using quasi-determinants as well. 展开更多
关键词 matrix orthogonal polynomial non-abelian Toda lattice Backlund transformation quasideterminant technique
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Wear Studies on Metal Matrix Composites: a Taguchi Approach 被引量:8
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作者 S.Basavarajappa G.Chandramohan 《Journal of Materials Science & Technology》 SCIE EI CAS CSCD 2005年第6期845-850,共6页
An attempt has been made to study the influence of wear parameters like applied load, sliding speed, sliding distance and percentage of reinforcement on the dry sliding wear of the metal matrix composites. A plan of e... An attempt has been made to study the influence of wear parameters like applied load, sliding speed, sliding distance and percentage of reinforcement on the dry sliding wear of the metal matrix composites. A plan of experiments, based on techniques of Taguchi, was performed to acquire data in controlled way. An orthogonal array and the analysis of variance were employed to investigate the influence of process parameters on the wear of composites. The objective is to establish a correlation between dry sliding wear of composites and wear parameters. These correlations were obtained by multiple regressions. Finally, confirmation tests were conducted to verify the experimental results foreseen from the mentioned correlations. 展开更多
关键词 Metal matrix composites WEAR orthogonal array Analysis of variance Taguchi method
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Tribological Behaviour of Aluminium/Alumina/Graphite Hybrid Metal Matrix Composite Using Taguchi’s Techniques 被引量:2
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作者 N. Radhika R. Subramanian S. Venkat Prasat 《Journal of Minerals and Materials Characterization and Engineering》 2011年第5期427-443,共17页
Tribological behaviour of aluminium alloy (Al-Si10Mg) reinforced with alumina (9%) and graphite (3%) fabricated by stir casting process was investigated. The wear and frictional properties of the hybrid metal matrix c... Tribological behaviour of aluminium alloy (Al-Si10Mg) reinforced with alumina (9%) and graphite (3%) fabricated by stir casting process was investigated. The wear and frictional properties of the hybrid metal matrix composites was studied by performing dry sliding wear test using a pin-on-disc wear tester. Experiments were conducted based on the plan of experiments generated through Taguchi’s technique. A L27 Orthogonal array was selected for analysis of the data. Investigation to find the influence of applied load, sliding speed and sliding distance on wear rate, as well as the coefficient of friction during wearing process was carried out using ANOVA and regression equations for each response were developed. Objective of the model was chosen as ‘smaller the better’ characteristics to analyse the dry sliding wear resistance. Results show that sliding distance has the highest influence followed by load and sliding speed. Finally, confirmation tests were carried out to verify the experimental results and Scanning Electron Microscopic studies were done on the wear surfaces. 展开更多
关键词 Metal matrix Composites STIR CASTING Taguchi’s TECHNIQUES orthogonal array Analysis of variance wear behaviour.
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Optimization of Friction and Wear Behaviour in Hybrid Metal Matrix Composites Using Taguchi Technique 被引量:2
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作者 V. C. Uvaraja N. Natarajan 《Journal of Minerals and Materials Characterization and Engineering》 2012年第8期757-768,共12页
Al-7075 alloy-base matrix, reinforced with mixtures of silicon carbide (SiC) and boron carbide (B4C) particles, know as hybrid composites have been fabricated by stir casting technique (liquid metallurgy route) and op... Al-7075 alloy-base matrix, reinforced with mixtures of silicon carbide (SiC) and boron carbide (B4C) particles, know as hybrid composites have been fabricated by stir casting technique (liquid metallurgy route) and optimized at different parameters like sliding speed, applied load, sliding time, and percentage of reinforcement by Taguchi method. The specimens were examined by Rockwell hardness test machine, Pin on Disc, Scanning Electron Microscope (SEM) and Optical Microscope. A plan of experiment generated through Taguchi’s technique is used to conduct experiments based on L27 orthogonal array. The developed ANOVA and the regression equations were used to find the optimum wear as well as co-efficient of friction under the influence of sliding speed, applied load, sliding time and percentage of reinforcement. The dry sliding wear resistance was analyzed on the basis of “smaller the best”. Finally, confirmation tests were carried out to verify the experimental results. 展开更多
关键词 Hybrid Metal matrix Composites Stir-Cast DRY SLIDING WEAR orthogonal Array Taguchi Technique Analysis of Variance
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