Mechanical Efficiency of Planetary Gear Trains: An Estimate
|
|
- Arnold Willis
- 6 years ago
- Views:
Transcription
1 Mechaical Efficiecy of Plaetary Gear Trais: A Estimate Dr. A. Sriath Professor, Dept. of Mechaical Egieerig K L Uiversity, A.P, Idia sriath_me@klce.ac.i G. Yedukodalu Assistat Professor, Dept. of Mechaical Egieerig K L Uiversity, A.P, Idia yedukodalu@kluiversity.i Dr. A. Jagadeesh Group Director, GD Rugta College Kohka Kurud Road, Bhilai, Chhattisgarh, Idia jagadeesh.ae@gmail.com Received: November 20, 2011 Accepted: November 29, 2011 Published: December 31, 2011 doi: /mer.v11p97 URL: Abstract I this paper a easy method is preseted to estimate the mechaical efficiecy of a gear-trai-whe the umber of teeth o gear wheels is specified. Also, the ifluece of the structure is icluded i estimatig the efficiecy. This helps i comparig the gear trais for mechaical efficiecy. Keywords: Gear Trais, Mechaical efficiecy, Graph theory, Trasmissio, Frictio 1. Itroductio Methods for geeratig distict plaetary gear trais with the specified elemets or gear pairs are available (F. Buchsbaum & F. Freudestei, 1970; R. Ravisaker & T. S. Mruthyujaya, 1985; L. W. Tsai, 1989; C. H. Hsu & J. J. Hsu, 1997). Also, some methods are available to estimate umber of the trasmissio efficiecy of gear trais. These methods are mathematically more rigorous ad do ot lead to a quick estimate. I the preset paper a semi-empirical method is proposed to estimate the mechaical efficiecy of a plaetary gear trai. The mechaical efficiecy ot oly depeds upo the size of the gear wheels but also o their relative arragemet i.e., structure. This aspect is also cosidered. This method gives reasoably good results. The structure of a gear trai is best represeted by a graph ad hece the use of graphs is explaied. 2. Method Assumig that there is o power loss at bearigs ad the etire power loss is due to gear pairs oly, the efficiecy of a simple gear trai ca be expressed by the relatio (M.F. Spotts),. f ( N E 1 N N 1 N 2 ) Where, E is the mechaical efficiecy of a gear pair, f is the coefficiet of frictio, N 1 ad N 2 are the umber of teeth o the matig wheels. As per (J. E. Shigley, Miscke, 2003), the eq. (1) is a excellet approximatio. From eq. (1) it is devious that the efficiecy of a gear pair is maximum whe N 1 = N 2, I other words, great variatio i the umber of teeth leads a great reductio i the trasmissio efficiecy. Eq. (1) is useful i estimatig the trasmissio efficiecy of every gear pair i a gear trai. I order to estimate the 1 2 (1) Published by Caadia Ceter of Sciece ad Educatio 97
2 trasmissio efficiecy of a gear trai as a whole, i which the gear pairs are arraged differetly i.e structure of a trai, the followig approach that uses graph theory is proposed. 3. Graph Represetatio of Gear-Trais A graph cosists of vertices ad edges. A vertex is represeted by a small circle while a edge is represeted by a lie joiig the vertices. A elemet of a gear trai such as a gear wheel or a carrier is represeted by a vertex of a graph while the joits betwee various elemets of a gear trai area represeted by edges. I gear trais, we have two types of pairs (i) turig pairs ad (ii) gear pairs. I order to differetiate the turig ad gear pairs, turig pair edges are represeted by a sigle lie edge while a gear pair is represeted by a double lie edge. For example the gear trais show schematically i figure.1 (a) is represeted by the graph, figure. 1(b), N 2 ad N 3, the umber of teeth are show i both the figures 1 (a & b). The efficiecy E ij of each gear pair (i - j) with specified umber of teeth ca be estimated usig eq.(1) ad the same ca be show ear the gear pair, figure 1 example, E 23, 4. Applicatio to Gear Trais The simple gear trai figure.1 has three elemets or three vertices. Next group of gear trais cosist of four vertices or two gear pairs. There are oly two distict gear trais with four elemets. They ad their graphs are show i figures 2 ad 3. Kowig the teeth umbers of gear wheels the efficiecy of each gear pair (2-3) ad (2-4) i case of figure. 2 ad gear pairs (1-3) ad (2-4) i figure. 3 ca be determied usig eq. (1). The resultig efficiecies E 23, E 24 etc. are show o the graphs, figures 2 & 3. Figure 2. Gear Trai cosistig of 4 elemets-first Type Figure 3. Gear Trai cosistig of 4 elemets-secod Type 5. Efficiecy Estimate Efficiecy of a system with compoets havig efficiecy E 1, E 2 etc. will deped upo the structural arragemets i.e. whether the compoets are (i) i series (ii) i parallel or (iii) mixed. The estimate of the system efficiecy is explaied below. (i) Efficiecy of a series system: 98 ISSN E-ISSN
3 Figure 4. Arragemet of Efficiecies i a Series system Figure 4 shows compoets with efficiecies E 1, E 2 etc. arraged i series. It ca easily be derived that the overall efficiecy E or the system is equal to the product of the compoet efficiecies, i.e., E= E 1.E 2 E = (2) i = 1 (ii) Efficiecy of a parallel system: Figure 5 shows -compoets with efficiecies E 1, E 2 etc. arraged parallely. Figure 5. Arragemet of Efficiecies i a Parallel system The compoets i parallel will share the iput power ad let the power i differet compoets be P 1, P 2 etc. The, the output from each compoets will be E 1 P 1, E 2 P 2 etc. so that P 0 the output power ca be expressed as follows, Where P EP. 0 i i i 1 i i P0 i 1 E, the system Efficiecy = (3) Pi Pi Whe greater part of the iput power flows through the compoets of higher efficiecy resultig efficiecy E of the system will be high ad vice-versa. O the other had if the iput power is shared equally amog all the compoets, E P 1 E E i, (4) For the efficiecy values of gear pairs which are high i practice, the system efficiecy is ot very much sesitive to the power sharig amog differet circuits or gear pairs. Hece the system efficiecy ca be take approximately equal to the average of the compoet efficiecies, eq. (4). (iii) Mixed System: I a mixed system, the combied efficiecy of the compoets i series ca be pairs such as (2-3) ad (2-4) i figure i 1 Published by Caadia Ceter of Sciece ad Educatio 99
4 2 should be take i series so that their combied efficiecy is (E 23, E 24 ). Gear pairs (1-3) ad (2-4) i Figure.3 are to be cosidered i parallel. Notig the remarks made i the estimate of efficiecy of a parallel system their combied efficiecy will be 1/2 (E 13 + E 24 ). Now, let us cosider some gear trais with five elemets (vertices) i.e. gear trais with three gear pairs. Simplest amog them is show i figure 6. The compoet efficiecy of the gear trai will be as give below. Figure 6. Gear trais with 5 elemets First Type E =E 23.E 24. E 35 (5) For compariso, aother gear trai with a mixed arragemet i.e., both parallel ad series, of gear wheels is show i figure 7 the schematic diagram is show i figure 7a while the correspodig graph is show i figure 7b. Figure 7 gear trais with five elemets Secod Type As suggested earlier, the gears 2, 3 ad 4 are cosidered i series so that their E 23, E 24. Now, the combied system of gear pairs (4-2-3) should be ½( E 15 + E 23.E 24 )j (6) For a clear uderstadig let us cosider gear trais with 6-elemets or four gear pairs Figure 8 shows the graphs of such gear trais. With the uderstadig we have from the previous examples oe ca see, figure 8(b), that the gear pairs (2-3) ad (2-4) are i series ad so is the case with gear pairs (1-5) ad (5-6). The assembly of the wheels (4-2-3) is the cosidered to be parallel with the assembly of the wheels (1-5-6). Now the efficiecy of the gear trai ca be writte directly. 100 ISSN E-ISSN
5 Figure 8 Gear trais with 6 elemets-first Type E= ½ [(E 23.E 24 ) + (E 15.E 56 )] (7a) For the gear trai, figure 8a, the efficiecy E=1/2 [(E 15 + E 23.E 24.E 36 )] As a last example let us cosider aother gear trai which is slightly complicated, figure 9 (a & b) (7b) Figure 9. Gear trais with 6 elemets-secod Type Cosider the cluster of the gear pairs (2-3), (2-4) ad (2-6). The above arragemet suggests that of the three gear pairs, if pairs (2-3) ad (2-4) are cosidered i series the the pair (2-6) is parallel to the. Similarly, the pair (2-3) ad (2-6) ca be cosidered i series while the third pair (2-4) is i parallel with them. I geeral, ay two pairs ca be take i series while the third pair is i parallel with them. The efficiecies of all the possible combiatios are give below. Case (i) Pairs (2-3) ad (2-4) are i series ad pair (2-6) is i parallel. The Ec = The efficiecy of the cluster of gear wheels 2, 3, 4 ad 6 =1/2 (E 23.E 24 +E 26 ) (8) Case (ii) Gear Pairs (2-3) ad (2-6) are i series ad pair (2-4) is i parallel. The Ec = ½(E 23.E 26 +E 26 ), (9) Case (iii): Pairs (2-4) ad (2-6) are i series ad the pair (2-3) is i parallel. The Ec=1/2(E 24.E 26 +E 23 )j (10) I such a case it is safer to take the lowest value of the above three efficiecies, eq.(8-10) ad let this be E mi. Now, the et efficiecy of the gear trai =E=1/2(E mi +E 15 ) Published by Caadia Ceter of Sciece ad Educatio 101
6 6. Coclusios Assigmet of equal efficiecies to all the gear pairs eables the compariso of distict structures. For example structure figure. 3 is better tha figure. 2. Similarly, the gear trai, figure.7 is superior to figure.6. Specifyig the umber of teeth o the gear wheels eables estimatio of the aticipated efficiecy of the gear trai. I gear trais with equal umber of gear pairs, the gear trais with parallely arraged pairs are more efficiet. Parallely arraged serial pairs, figure.8(b), appear to be iferior to the arragemet i which more pairs arraged i series which i tur are parallel with the remaiig gear pairs (ot i series), figure.8(a). Gear trais with a cluster of wheels figure.9 is better tha the trais figure.8. Refereces C. H. Hsu, & J. J. Hsu. (1997). A efficiet methodology for the structural sythesis of geared kiematic chais. Mech. Mach. Theory, 1997, vol. 32, pp F. Buchsbaum, & F. Freudestei. (1970). Sythesis of kiematic structure of geared kiematic chais ad other mechaisms. J. Mechaisms,vol. 5, pp. ( ). J. E. Shigley, Miscke. (2003). Mechaical Egieerig Desig (SI Uits), Sixth editio, Tata Mc Graw Hill, p L. W. Tsai. (1989). O the Coceptual Desig of a Novel Class of Robot Cofiguratios, Tras ASME J. Mech. Tras. Auto. Desig, vol. 109, pp M. F. Spotts. Mechaical Desig Aalysis, Pretice-Hall, Eagle wood cliffs, NJ, pp R. Ravisaker, & T. S. Mruthyujaya. (1985). Computerized sythesis of the structure of geared kiematic chais. Mech. Mach. Theory, vol. 20, pp ISSN E-ISSN
Modified Ratio Estimators Using Known Median and Co-Efficent of Kurtosis
America Joural of Mathematics ad Statistics 01, (4): 95-100 DOI: 10.593/j.ajms.01004.05 Modified Ratio s Usig Kow Media ad Co-Efficet of Kurtosis J.Subramai *, G.Kumarapadiya Departmet of Statistics, Podicherry
More informationEstimation of Population Mean Using Co-Efficient of Variation and Median of an Auxiliary Variable
Iteratioal Joural of Probability ad Statistics 01, 1(4: 111-118 DOI: 10.593/j.ijps.010104.04 Estimatio of Populatio Mea Usig Co-Efficiet of Variatio ad Media of a Auxiliary Variable J. Subramai *, G. Kumarapadiya
More informationSection 5.1 The Basics of Counting
1 Sectio 5.1 The Basics of Coutig Combiatorics, the study of arragemets of objects, is a importat part of discrete mathematics. I this chapter, we will lear basic techiques of coutig which has a lot of
More informationAlgorithm Analysis. Chapter 3
Data Structures Dr Ahmed Rafat Abas Computer Sciece Dept, Faculty of Computer ad Iformatio, Zagazig Uiversity arabas@zu.edu.eg http://www.arsaliem.faculty.zu.edu.eg/ Algorithm Aalysis Chapter 3 3. Itroductio
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationRecursive Algorithm for Generating Partitions of an Integer. 1 Preliminary
Recursive Algorithm for Geeratig Partitios of a Iteger Sug-Hyuk Cha Computer Sciece Departmet, Pace Uiversity 1 Pace Plaza, New York, NY 10038 USA scha@pace.edu Abstract. This article first reviews the
More informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationTR/46 OCTOBER THE ZEROS OF PARTIAL SUMS OF A MACLAURIN EXPANSION A. TALBOT
TR/46 OCTOBER 974 THE ZEROS OF PARTIAL SUMS OF A MACLAURIN EXPANSION by A. TALBOT .. Itroductio. A problem i approximatio theory o which I have recetly worked [] required for its solutio a proof that the
More informationMultilayer perceptrons
Multilayer perceptros If traiig set is ot liearly separable, a etwork of McCulloch-Pitts uits ca give a solutio If o loop exists i etwork, called a feedforward etwork (else, recurret etwork) A two-layer
More informationSpectral Partitioning in the Planted Partition Model
Spectral Graph Theory Lecture 21 Spectral Partitioig i the Plated Partitio Model Daiel A. Spielma November 11, 2009 21.1 Itroductio I this lecture, we will perform a crude aalysis of the performace of
More informationProperties and Hypothesis Testing
Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.
More informationDr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore
Lecture 0 Coversio Betwee State Space ad Trasfer Fuctio Represetatios i Liear Systems II Dr. Radhakat Padhi Asst. Professor Dept. of Aerospace Egieerig Idia Istitute of Sciece - Bagalore A Alterate First
More informationTHE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS
R775 Philips Res. Repts 26,414-423, 1971' THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS by H. W. HANNEMAN Abstract Usig the law of propagatio of errors, approximated
More informationChapter 7 COMBINATIONS AND PERMUTATIONS. where we have the specific formula for the binomial coefficients:
Chapter 7 COMBINATIONS AND PERMUTATIONS We have see i the previous chapter that (a + b) ca be writte as 0 a % a & b%þ% a & b %þ% b where we have the specific formula for the biomial coefficiets: '!!(&)!
More informationSequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence
Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet
More informationChapter 1 : Combinatorial Analysis
STAT/MATH 394 A - PROBABILITY I UW Autum Quarter 205 Néhémy Lim Chapter : Combiatorial Aalysis A major brach of combiatorial aalysis called eumerative combiatorics cosists of studyig methods for coutig
More informationReliability and Queueing
Copyright 999 Uiversity of Califoria Reliability ad Queueig by David G. Messerschmitt Supplemetary sectio for Uderstadig Networked Applicatios: A First Course, Morga Kaufma, 999. Copyright otice: Permissio
More informationProof of Fermat s Last Theorem by Algebra Identities and Linear Algebra
Proof of Fermat s Last Theorem by Algebra Idetities ad Liear Algebra Javad Babaee Ragai Youg Researchers ad Elite Club, Qaemshahr Brach, Islamic Azad Uiversity, Qaemshahr, Ira Departmet of Civil Egieerig,
More informationA Block Cipher Using Linear Congruences
Joural of Computer Sciece 3 (7): 556-560, 2007 ISSN 1549-3636 2007 Sciece Publicatios A Block Cipher Usig Liear Cogrueces 1 V.U.K. Sastry ad 2 V. Jaaki 1 Academic Affairs, Sreeidhi Istitute of Sciece &
More informationOptimization Methods: Linear Programming Applications Assignment Problem 1. Module 4 Lecture Notes 3. Assignment Problem
Optimizatio Methods: Liear Programmig Applicatios Assigmet Problem Itroductio Module 4 Lecture Notes 3 Assigmet Problem I the previous lecture, we discussed about oe of the bech mark problems called trasportatio
More information6.003 Homework #3 Solutions
6.00 Homework # Solutios Problems. Complex umbers a. Evaluate the real ad imagiary parts of j j. π/ Real part = Imagiary part = 0 e Euler s formula says that j = e jπ/, so jπ/ j π/ j j = e = e. Thus the
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationEE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders
EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig MUXs, Ecoders, Decoders Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Overview of Ecoder ad Decoder MUX Gate
More informationCALCULATING FIBONACCI VECTORS
THE GENERALIZED BINET FORMULA FOR CALCULATING FIBONACCI VECTORS Stuart D Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithacaedu ad Dai Novak Departmet
More informationChapter 13, Part A Analysis of Variance and Experimental Design
Slides Prepared by JOHN S. LOUCKS St. Edward s Uiversity Slide 1 Chapter 13, Part A Aalysis of Variace ad Eperimetal Desig Itroductio to Aalysis of Variace Aalysis of Variace: Testig for the Equality of
More informationPOWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS
Joural of Applied Mathematics ad Computatioal Mechaics 4 3(3) 3-8 POWER SERIES SOLUION OF FIRS ORDER MARIX DIFFERENIAL EQUAIONS Staisław Kukla Izabela Zamorska Istitute of Mathematics Czestochowa Uiversity
More informationAnna Janicka Mathematical Statistics 2018/2019 Lecture 1, Parts 1 & 2
Aa Jaicka Mathematical Statistics 18/19 Lecture 1, Parts 1 & 1. Descriptive Statistics By the term descriptive statistics we will mea the tools used for quatitative descriptio of the properties of a sample
More informationChapter 1. Complex Numbers. Dr. Pulak Sahoo
Chapter 1 Complex Numbers BY Dr. Pulak Sahoo Assistat Professor Departmet of Mathematics Uiversity Of Kalyai West Begal, Idia E-mail : sahoopulak1@gmail.com 1 Module-2: Stereographic Projectio 1 Euler
More informationModule 18 Discrete Time Signals and Z-Transforms Objective: Introduction : Description: Discrete Time Signal representation
Module 8 Discrete Time Sigals ad Z-Trasforms Objective:To uderstad represetig discrete time sigals, apply z trasform for aalyzigdiscrete time sigals ad to uderstad the relatio to Fourier trasform Itroductio
More informationAdjacent vertex distinguishing total coloring of tensor product of graphs
America Iteratioal Joural of Available olie at http://wwwiasiret Research i Sciece Techology Egieerig & Mathematics ISSN Prit): 38-3491 ISSN Olie): 38-3580 ISSN CD-ROM): 38-369 AIJRSTEM is a refereed idexed
More informationInformation-based Feature Selection
Iformatio-based Feature Selectio Farza Faria, Abbas Kazeroui, Afshi Babveyh Email: {faria,abbask,afshib}@staford.edu 1 Itroductio Feature selectio is a topic of great iterest i applicatios dealig with
More information(a) (b) All real numbers. (c) All real numbers. (d) None. to show the. (a) 3. (b) [ 7, 1) (c) ( 7, 1) (d) At x = 7. (a) (b)
Chapter 0 Review 597. E; a ( + )( + ) + + S S + S + + + + + + S lim + l. D; a diverges by the Itegral l k Test sice d lim [(l ) ], so k l ( ) does ot coverge absolutely. But it coverges by the Alteratig
More informationCommutativity in Permutation Groups
Commutativity i Permutatio Groups Richard Wito, PhD Abstract I the group Sym(S) of permutatios o a oempty set S, fixed poits ad trasiet poits are defied Prelimiary results o fixed ad trasiet poits are
More informationP1 Chapter 8 :: Binomial Expansion
P Chapter 8 :: Biomial Expasio jfrost@tiffi.kigsto.sch.uk www.drfrostmaths.com @DrFrostMaths Last modified: 6 th August 7 Use of DrFrostMaths for practice Register for free at: www.drfrostmaths.com/homework
More informationSequence A sequence is a function whose domain of definition is the set of natural numbers.
Chapter Sequeces Course Title: Real Aalysis Course Code: MTH3 Course istructor: Dr Atiq ur Rehma Class: MSc-I Course URL: wwwmathcityorg/atiq/fa8-mth3 Sequeces form a importat compoet of Mathematical Aalysis
More informationAlgorithm of Superposition of Boolean Functions Given with Truth Vectors
IJCSI Iteratioal Joural of Computer Sciece Issues, Vol 9, Issue 4, No, July ISSN (Olie: 694-84 wwwijcsiorg 9 Algorithm of Superpositio of Boolea Fuctios Give with Truth Vectors Aatoly Plotikov, Aleader
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationCOMPARISON OF FPGA IMPLEMENTATION OF THE MOD M REDUCTION
Lati America Applied Research 37:93-97 (2007) COMPARISON OF FPGA IMPLEMENTATION OF THE MOD M REDUCTION J-P. DESCHAMPS ad G. SUTTER Escola Tècica Superior d Egiyeria, Uiversitat Rovira i Virgili, Tarragoa,
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More informationMA131 - Analysis 1. Workbook 2 Sequences I
MA3 - Aalysis Workbook 2 Sequeces I Autum 203 Cotets 2 Sequeces I 2. Itroductio.............................. 2.2 Icreasig ad Decreasig Sequeces................ 2 2.3 Bouded Sequeces..........................
More informationECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations
ECE-S352 Itroductio to Digital Sigal Processig Lecture 3A Direct Solutio of Differece Equatios Discrete Time Systems Described by Differece Equatios Uit impulse (sample) respose h() of a DT system allows
More informationELE B7 Power Systems Engineering. Symmetrical Components
ELE B7 Power Systems Egieerig Symmetrical Compoets Aalysis of Ubalaced Systems Except for the balaced three-phase fault, faults result i a ubalaced system. The most commo types of faults are sigle liegroud
More informationSignal Processing in Mechatronics. Lecture 3, Convolution, Fourier Series and Fourier Transform
Sigal Processig i Mechatroics Summer semester, 1 Lecture 3, Covolutio, Fourier Series ad Fourier rasform Dr. Zhu K.P. AIS, UM 1 1. Covolutio Covolutio Descriptio of LI Systems he mai premise is that the
More informationInvestigating the Significance of a Correlation Coefficient using Jackknife Estimates
Iteratioal Joural of Scieces: Basic ad Applied Research (IJSBAR) ISSN 2307-4531 (Prit & Olie) http://gssrr.org/idex.php?joural=jouralofbasicadapplied ---------------------------------------------------------------------------------------------------------------------------
More informationImproved Class of Ratio -Cum- Product Estimators of Finite Population Mean in two Phase Sampling
Global Joural of Sciece Frotier Research: F Mathematics ad Decisio Scieces Volume 4 Issue 2 Versio.0 Year 204 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic. (USA
More informationChapter 10: Power Series
Chapter : Power Series 57 Chapter Overview: Power Series The reaso series are part of a Calculus course is that there are fuctios which caot be itegrated. All power series, though, ca be itegrated because
More informationAbsolutely Harmonious Labeling of Graphs
Iteratioal J.Math. Combi. Vol. (011), 40-51 Absolutely Harmoious Labelig of Graphs M.Seeivasa (Sri Paramakalyai College, Alwarkurichi-6741, Idia) A.Lourdusamy (St.Xavier s College (Autoomous), Palayamkottai,
More informationDIGITAL FILTER ORDER REDUCTION
DIGITAL FILTER RDER REDUTI VAHID RAISSI DEHKRDI, McGILL UIVERSITY, AADA, vahid@cim.mcgill.ca AMIR G. AGHDAM, RDIA UIVERSITY, AADA, aghdam@ece.cocordia.ca ABSTRAT I this paper, a method is proposed to reduce
More informationPrinciple Of Superposition
ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give
More informationSOME TRIBONACCI IDENTITIES
Mathematics Today Vol.7(Dec-011) 1-9 ISSN 0976-38 Abstract: SOME TRIBONACCI IDENTITIES Shah Devbhadra V. Sir P.T.Sarvajaik College of Sciece, Athwalies, Surat 395001. e-mail : drdvshah@yahoo.com The sequece
More informationChapter Vectors
Chapter 4. Vectors fter readig this chapter you should be able to:. defie a vector. add ad subtract vectors. fid liear combiatios of vectors ad their relatioship to a set of equatios 4. explai what it
More information3.1 Counting Principles
3.1 Coutig Priciples Goal: Cout the umber of objects i a set. Notatio: Whe S is a set, S deotes the umber of objects i the set. This is also called S s cardiality. Additio Priciple: Whe you wat to cout
More informationA Recurrence Formula for Packing Hyper-Spheres
A Recurrece Formula for Packig Hyper-Spheres DokeyFt. Itroductio We cosider packig of -D hyper-spheres of uit diameter aroud a similar sphere. The kissig spheres ad the kerel sphere form cells of equilateral
More informationGLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES
GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES A STUDY ON THE HYPERBOLA x 9 0 S. Vidhyalakshmi, M.A. Gopala & T. Mahalakshmi*, Professor, Departmet of Mathematics, Shrimati Idira Gadhi College, Trichy-60
More informationMTH Assignment 1 : Real Numbers, Sequences
MTH -26 Assigmet : Real Numbers, Sequeces. Fid the supremum of the set { m m+ : N, m Z}. 2. Let A be a o-empty subset of R ad α R. Show that α = supa if ad oly if α is ot a upper boud of A but α + is a
More informationStochastic Matrices in a Finite Field
Stochastic Matrices i a Fiite Field Abstract: I this project we will explore the properties of stochastic matrices i both the real ad the fiite fields. We first explore what properties 2 2 stochastic matrices
More informationc. Explain the basic Newsvendor model. Why is it useful for SC models? e. What additional research do you believe will be helpful in this area?
1. Research Methodology a. What is meat by the supply chai (SC) coordiatio problem ad does it apply to all types of SC s? Does the Bullwhip effect relate to all types of SC s? Also does it relate to SC
More informationPAijpam.eu IRREGULAR SET COLORINGS OF GRAPHS
Iteratioal Joural of Pure ad Applied Mathematics Volume 109 No. 7 016, 143-150 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: 10.173/ijpam.v109i7.18 PAijpam.eu
More informationLargest families without an r-fork
Largest families without a r-for Aalisa De Bois Uiversity of Salero Salero, Italy debois@math.it Gyula O.H. Katoa Réyi Istitute Budapest, Hugary ohatoa@reyi.hu Itroductio Let [] = {,,..., } be a fiite
More informationLecture 2 Clustering Part II
COMS 4995: Usupervised Learig (Summer 8) May 24, 208 Lecture 2 Clusterig Part II Istructor: Nakul Verma Scribes: Jie Li, Yadi Rozov Today, we will be talkig about the hardess results for k-meas. More specifically,
More informationEstimation of the Population Mean in Presence of Non-Response
Commuicatios of the Korea Statistical Society 0, Vol. 8, No. 4, 537 548 DOI: 0.535/CKSS.0.8.4.537 Estimatio of the Populatio Mea i Presece of No-Respose Suil Kumar,a, Sadeep Bhougal b a Departmet of Statistics,
More informationA sequence of numbers is a function whose domain is the positive integers. We can see that the sequence
Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece,, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet as
More informationReliability Measures of a Series System with Weibull Failure Laws
Iteratioal Joural of Statistics ad Systems ISSN 973-2675 Volume, Number 2 (26), pp. 73-86 Research Idia Publicatios http://www.ripublicatio.com Reliability Measures of a Series System with Weibull Failure
More informationDiscrete-Time Systems, LTI Systems, and Discrete-Time Convolution
EEL5: Discrete-Time Sigals ad Systems. Itroductio I this set of otes, we begi our mathematical treatmet of discrete-time s. As show i Figure, a discrete-time operates or trasforms some iput sequece x [
More informationA NEW APPROACH TO SOLVE AN UNBALANCED ASSIGNMENT PROBLEM
A NEW APPROACH TO SOLVE AN UNBALANCED ASSIGNMENT PROBLEM *Kore B. G. Departmet Of Statistics, Balwat College, VITA - 415 311, Dist.: Sagli (M. S.). Idia *Author for Correspodece ABSTRACT I this paper I
More informationRoger Apéry's proof that zeta(3) is irrational
Cliff Bott cliffbott@hotmail.com 11 October 2011 Roger Apéry's proof that zeta(3) is irratioal Roger Apéry developed a method for searchig for cotiued fractio represetatios of umbers that have a form such
More informationMath 778S Spectral Graph Theory Handout #3: Eigenvalues of Adjacency Matrix
Math 778S Spectral Graph Theory Hadout #3: Eigevalues of Adjacecy Matrix The Cartesia product (deoted by G H) of two simple graphs G ad H has the vertex-set V (G) V (H). For ay u, v V (G) ad x, y V (H),
More informationPAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
More informationModule 5 EMBEDDED WAVELET CODING. Version 2 ECE IIT, Kharagpur
Module 5 EMBEDDED WAVELET CODING Versio ECE IIT, Kharagpur Lesso 4 SPIHT algorithm Versio ECE IIT, Kharagpur Istructioal Objectives At the ed of this lesso, the studets should be able to:. State the limitatios
More informationWarped, Chirp Z-Transform: Radar Signal Processing
arped, Chirp Z-Trasform: Radar Sigal Processig by Garimella Ramamurthy Report o: IIIT/TR// Cetre for Commuicatios Iteratioal Istitute of Iformatio Techology Hyderabad - 5 3, IDIA Jauary ARPED, CHIRP Z
More informationThe Mathematical Model and the Simulation Modelling Algoritm of the Multitiered Mechanical System
The Mathematical Model ad the Simulatio Modellig Algoritm of the Multitiered Mechaical System Demi Aatoliy, Kovalev Iva Dept. of Optical Digital Systems ad Techologies, The St. Petersburg Natioal Research
More informationLecture 10: Mathematical Preliminaries
Lecture : Mathematical Prelimiaries Obective: Reviewig mathematical cocepts ad tools that are frequetly used i the aalysis of algorithms. Lecture # Slide # I this
More informationMath 113 Exam 3 Practice
Math Exam Practice Exam will cover.-.9. This sheet has three sectios. The first sectio will remid you about techiques ad formulas that you should kow. The secod gives a umber of practice questios for you
More informationNumerical Simulation of Thermomechanical Problems in Applied Mechanics: Application to Solidification Problem
Leoardo Joural of Scieces ISSN 1583-0233 Issue 9, July-December 2006 p. 25-32 Numerical Simulatio of Thermomechaical Problems i Applied Mechaics: Applicatio to Solidificatio Problem Vicet Obiajulu OGWUAGWU
More informationEDGE AND SECANT IDEALS OF SHARED-VERTEX GRAPHS
EDGE AND SECANT IDEALS OF SHARED-VERTEX GRAPHS ZVI ROSEN Abstract. We examie miimal free resolutios ad Betti diagrams of the edge ad secat ideals of oe family of graphs. We demostrate how splittig the
More informationCS 270 Algorithms. Oliver Kullmann. Growth of Functions. Divide-and- Conquer Min-Max- Problem. Tutorial. Reading from CLRS for week 2
Geeral remarks Week 2 1 Divide ad First we cosider a importat tool for the aalysis of algorithms: Big-Oh. The we itroduce a importat algorithmic paradigm:. We coclude by presetig ad aalysig two examples.
More information~W I F
A FIBONACCI PROPERTY OF WYTHOFF PAIRS ROBERT SILBER North Carolia State Uiversity, Raleigh, North Carolia 27607 I this paper we poit out aother of those fasciatig "coicideces" which are so characteristically
More informationU8L1: Sec Equations of Lines in R 2
MCVU U8L: Sec. 8.9. Equatios of Lies i R Review of Equatios of a Straight Lie (-D) Cosider the lie passig through A (-,) with slope, as show i the diagram below. I poit slope form, the equatio of the lie
More informationAppendix: The Laplace Transform
Appedix: The Laplace Trasform The Laplace trasform is a powerful method that ca be used to solve differetial equatio, ad other mathematical problems. Its stregth lies i the fact that it allows the trasformatio
More informationSOLID MECHANICS TUTORIAL BALANCING OF RECIPROCATING MACHINERY
SOLID MECHANICS TUTORIAL BALANCING OF RECIPROCATING MACHINERY This work covers elemets of the syllabus for the Egieerig Coucil Exam D5 Dyamics of Mechaical Systems. O completio of this tutorial you should
More informationAssignment 1 : Real Numbers, Sequences. for n 1. Show that (x n ) converges. Further, by observing that x n+2 + x n+1
Assigmet : Real Numbers, Sequeces. Let A be a o-empty subset of R ad α R. Show that α = supa if ad oly if α is ot a upper boud of A but α + is a upper boud of A for every N. 2. Let y (, ) ad x (, ). Evaluate
More informationSome New Iterative Methods for Solving Nonlinear Equations
World Applied Scieces Joural 0 (6): 870-874, 01 ISSN 1818-495 IDOSI Publicatios, 01 DOI: 10.589/idosi.wasj.01.0.06.830 Some New Iterative Methods for Solvig Noliear Equatios Muhammad Aslam Noor, Khalida
More informationSYSTEMATIC SAMPLING FOR NON-LINEAR TREND IN MILK YIELD DATA
Joural of Reliability ad Statistical Studies; ISS (Prit): 0974-804, (Olie):9-5666 Vol. 7, Issue (04): 57-68 SYSTEMATIC SAMPLIG FOR O-LIEAR TRED I MILK YIELD DATA Tauj Kumar Padey ad Viod Kumar Departmet
More informationDisjoint Systems. Abstract
Disjoit Systems Noga Alo ad Bey Sudaov Departmet of Mathematics Raymod ad Beverly Sacler Faculty of Exact Scieces Tel Aviv Uiversity, Tel Aviv, Israel Abstract A disjoit system of type (,,, ) is a collectio
More informationThe Random Walk For Dummies
The Radom Walk For Dummies Richard A Mote Abstract We look at the priciples goverig the oe-dimesioal discrete radom walk First we review five basic cocepts of probability theory The we cosider the Beroulli
More informationMAT1026 Calculus II Basic Convergence Tests for Series
MAT026 Calculus II Basic Covergece Tests for Series Egi MERMUT 202.03.08 Dokuz Eylül Uiversity Faculty of Sciece Departmet of Mathematics İzmir/TURKEY Cotets Mootoe Covergece Theorem 2 2 Series of Real
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationBasics of Probability Theory (for Theory of Computation courses)
Basics of Probability Theory (for Theory of Computatio courses) Oded Goldreich Departmet of Computer Sciece Weizma Istitute of Sciece Rehovot, Israel. oded.goldreich@weizma.ac.il November 24, 2008 Preface.
More informationAs stated by Laplace, Probability is common sense reduced to calculation.
Note: Hadouts DO NOT replace the book. I most cases, they oly provide a guidelie o topics ad a ituitive feel. The math details will be covered i class, so it is importat to atted class ad also you MUST
More informationLecture Overview. 2 Permutations and Combinations. n(n 1) (n (k 1)) = n(n 1) (n k + 1) =
COMPSCI 230: Discrete Mathematics for Computer Sciece April 8, 2019 Lecturer: Debmalya Paigrahi Lecture 22 Scribe: Kevi Su 1 Overview I this lecture, we begi studyig the fudametals of coutig discrete objects.
More informationImproved Ratio Estimators of Population Mean In Adaptive Cluster Sampling
J. Stat. Appl. Pro. Lett. 3, o. 1, 1-6 (016) 1 Joural of Statistics Applicatios & Probability Letters A Iteratioal Joural http://dx.doi.org/10.18576/jsapl/030101 Improved Ratio Estimators of Populatio
More information7. Modern Techniques. Data Encryption Standard (DES)
7. Moder Techiques. Data Ecryptio Stadard (DES) The objective of this chapter is to illustrate the priciples of moder covetioal ecryptio. For this purpose, we focus o the most widely used covetioal ecryptio
More informationCALCULATION OF FIBONACCI VECTORS
CALCULATION OF FIBONACCI VECTORS Stuart D. Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithaca.edu ad Dai Novak Departmet of Mathematics, Ithaca College
More informationBest Optimal Stable Matching
Applied Mathematical Scieces, Vol., 0, o. 7, 7-7 Best Optimal Stable Matchig T. Ramachadra Departmet of Mathematics Govermet Arts College(Autoomous) Karur-6900, Tamiladu, Idia yasrams@gmail.com K. Velusamy
More informationUsing An Accelerating Method With The Trapezoidal And Mid-Point Rules To Evaluate The Double Integrals With Continuous Integrands Numerically
ISSN -50 (Paper) ISSN 5-05 (Olie) Vol.7, No., 017 Usig A Acceleratig Method With The Trapezoidal Ad Mid-Poit Rules To Evaluate The Double Itegrals With Cotiuous Itegrads Numerically Azal Taha Abdul Wahab
More informationMath 475, Problem Set #12: Answers
Math 475, Problem Set #12: Aswers A. Chapter 8, problem 12, parts (b) ad (d). (b) S # (, 2) = 2 2, sice, from amog the 2 ways of puttig elemets ito 2 distiguishable boxes, exactly 2 of them result i oe
More informationTo the use of Sellmeier formula
To the use of Sellmeier formula by Volkmar Brücker Seior Experte Service (SES) Bo ad HfT Leipzig, Germay Abstract Based o dispersio of pure silica we proposed a geeral Sellmeier formula for various dopats
More information3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationBACKMIXING IN SCREW EXTRUDERS
BACKMIXING IN SCREW EXTRUDERS Chris Rauwedaal, Rauwedaal Extrusio Egieerig, Ic. Paul Grama, The Madiso Group Abstract Mixig is a critical fuctio i most extrusio operatios. Oe of the most difficult mixig
More information