cm_fasc.2_2010

BULETINUL INSTITUTULUI POLITEHNIC DIN IAI Publicat de UNIVERSITATEA TEHNIC GHEORGHE ASACHI, IAI Tomul LVI (LX) Fasc. 2 Secia

CONSTRUCII DE MAINI 2010

BULETINUL INSTITUTULUI POLITEHNIC DIN IAI PUBLISHED BY

GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IAI Editorial Office: Bd. D. Mangeron 63, 700050, Iai, ROMANIA

Tel. 40-232-278683; Fax: 40-232-237666; e-mail: [email protected]

Editorial Board

President: Prof. dr. eng. Ion Giurm, Member of the Academy of Agricultural Sciences and Forest, Rector of theGheorghe Asachi Technical University of Iai

Editor-in-Chief: Prof. dr. eng. Carmen Teodosiu, Vice-Rector of the Gheorghe Asachi Technical University of Iai

Honorary Editors of the Bulletin: Prof. dr. eng. Alfred Braier,

Prof. dr. eng. Hugo Rosman, Prof. dr. eng. Mihail Voicu, Corresponding Member of the Romanian Academy,

President of the Gheorghe Asachi Technical University of Iai Editors in Chief of the MACHINE CONSTRUCTION Section

Prof. dr. eng. Radu Ibnescu, Assoc. Prof. dr. eng. Aristotel Popescu Honorary Editors: Prof. dr. eng. Gheorghe Nag, Prof. dr. eng. Cezar Oprian

Associated Editor: Prof. dr. eng. Eugen Axinte

Editorial Advisory Board

Prof. dr. eng. Nicuor Amariei, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Noura-Barbu Lupulescu, University Transilvania of Braov, Romania

Assoc.Prof.dr.eng. Aristomenis Antoniadis, Technical University of Crete, Greece

Prof. dr. eng. Francisco Javier Santos Martin, University of Valladolid, Spain

Prof. dr. eng. Virgil Atanasiu, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng.Fabio Miani, University of Udine, Italy

Prof. dr. eng. Manuel San Juan Blanco, University of Valladolid, Spain

Prof. dr. eng.Mircea Mihailide, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Petru Berce, Technical University of Cluj Napoca, Romania

Prof. dr. eng. Sevasti Mitsi, Aristotle University of Thessaloniki Salonic, Greece

Prof. dr. eng. Ion Bostan, Technical University of Chiinu, Repablic of Moldova

Prof. dr. eng. Gheorghe Nag, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Walter Calles, Hochschule fr Technik und Wirtschaft des Saarlandes, Saarbrcken, Germany

Prof. dr. eng.Vasile Neculiasa, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Doru Clrau, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Dumitru Olaru, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Francisco Chinesta, Ecole Centrale de Nantes, France

Prof. dr. eng. Cezar Oprian, Gheorghe Asachi Technical University of Iai, Romania

Assoc.Prof.dr.eng. Conalves Coelho, University Nova of Lisbon, Portugal

Prof. dr. eng. Juan Pablo Contreras Samper, University of Cadiz, Spain

Assoc.Prof.dr.eng. Mircea Cozmnc, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng.Loredana Santo, University Tor Vergata, Rome, Italy

Prof. dr. eng. Spiridon Creu, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng.Cristina Siligardi, University of Modena, Italy

Prof. dr. eng. Gheorghe Dumitracu, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng.Fernando Jos Neto da Silva, University of Aveiro, Portugal

Prof. dr. eng. Ctlin Fetecu, University Dunrea de Jos of Galai, Romania

Prof. dr. eng. Filipe Silva, University of Minho, Portugal

Prof. dr. eng. Mihai Gafitanu, Gheorghe Asachi Technical University of Iai, Romania

Prof. dr. eng. Laureniu Sltineanu, Technical University of Iai, Romania

Prof. dr. eng. Radu Gaiginschi, Gheorghe Asachi Technical University of Iai, Romania

Lecturer dr.eng. Birgit Kjrside Storm, Aalborg Universitet Esbjerg, Denmark

Prof.dr.ir.Dirk Lefeber, Vrije Universiteit Brussels, Belgium Prof. dr. eng. Ezio Spessa, Politecnico di Torino, Italy Prof. dr. eng.Dorel Leon, Gheorghe Asachi Technical

University of Iai, Romania Prof. dr. eng. Alexei Toca, Technical University of

Chiinu, Repablic of Moldova Prof. dr. eng.James A. Liburdy, Oregon State University,

Corvallis, Oregon, SUA Prof. dr. eng.Roberto Teti, University Federico II,

Naples, Italy Prof. dr. eng. dr. H.C. Peter Lorenz, Hochschule fr

Technik und Wirtschaft, Saarbrcken, Germany Prof. dr. eng.Hans-Bernhard Woyand, Bergische

University Wuppertal, Germany

Papers presented at

THE INTERNATIONAL CONFERENCE on DESIGN, TECNOLOGIES & MANAGEMENT

IN MANUFACTURING

Iai, May 14th 16th, 2010

organized by the

FACULTY OF MACHINE MANUFACTURING & INDUSTRIAL MANAGEMENT

Papers published with the support of NATIONAL AUTHORITY for SCIENTIFIC RESEARCHERS

EDITORIAL BOARD

MACHINE CONSTRUCTION Fascicle 2

Conf.univ.dr.ing. Irina Cozmnc Prof.univ.dr.ing. Radu Ibnescu

Conf.univ.dr.ing. Vasile V. Merticaru

BULETINUL INSTITUTULUI POLITEHNIC DIN IAI BULLETIN OF THE POLYTECHNIC INSTITUTE OF IAI

Publicat de UNIVERSITATEA TEHNIC GHEORGHE ASACHI DIN IAI

Tomul LVI(LX), Fasc. 2 2010

Secia

CONSTRUCII DE MAINI

Pag.

ANTNIO M. GONALVES-COELHO, GABRIELA NETIAN i

ANTNIO MOURO, Modelul matricei de proiectare n cazul soluiilor redundante de proiectare (engl., rez. rom.)........................

TAXIARCHIS BELIS i ARISTOMENIS ANTONIADIS, Model pentru evaluarea uzurii dinilor frezelor de danturat pe baza determinrii achiilor 3D (engl., rez. rom.). ..................................................................

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9

NIKOLAOS TAPOGLOU i ARISTOMENIS ANTONIADIS, Determinarea prin simulare CAD a componentelor forei de achiere la frezarea danturilor (engl., rez. rom.)........................................................................

21

EUGEN STRJESCU, CONSTANTIN DOGARIU, OLIMPIA PAVLOV i DUMITRU DUMITRU, Contribuii privind controlul informatizat al cuitelor roat (engl., rez. rom.).................................................................

SILVIU BERBINSCHI, VIRGIL TEODOR, NICOLAE DUMITRACU i NICOLAE OANCEA, Contribuii la elaborarea unei metode grafice pentru profilarea sculelor care genereaz prin nfurare. I. Algoritm. (engl., rez. rom.) .......................................................................................

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S U M A R

SILVIU BERBINSCHI, VIRGIL TEODOR, NICOLAE DUMITRACU i

NICOLAE OANCEA, Contribuii la elaborarea unei metode grafice pentru profilarea sculelor care genereaz prin nfurare. II. Aplicaie pentru profilarea sculei-cremalier (engl., rez. rom.)................................

CTLIN FETECU, DANIEL-VIOREL VLAD i COSTEL MOCANU, Simularea procesului de strunjire folosind analiza cu element finit (engl., rez. rom.)........................................................................................

MIRCEA COZMNC, CRISTIAN CROITORU i CTLIN UNGUREANU, Cercetri experimentale pentru validarea unei noi metode de evaluare a forelor de achiere (engl., rez. rom.) .....................

ANA-MARIA MATEI i MARIUS NICOLAE MILEA, Forele de achiere la frezarea frontal n funcie de forele dezvoltate la nivelul unui dinte (engl., rez. rom.)........................................................................................

MARIUS-IONU RPANU, GHEORGHE NAG, IOLANDA-ELENA MANOLE i ANDREI WEINGOLD, Aspecte comparative privind croirea la operaia de decupare-perforare pe prese clasice i centre de presare prevzute cu comand numeric (engl., rez. rom.).......................

IUSTINA ELENA ROTMAN, PETRU DUA i RADU ADRIAN BACIU LUPACU, Consideraii teoretice i experimentale privind determinarea efectului de divergen (engl., rez. rom.) ...........................

CTLIN UNGUREANU, RADU IBNESCU i IRINA COZMNC, Sistem de msurare computerizat (engl., rez. rom.).................................

BIRGIT KJRSIDE STORM, Lipirea cu adezivi a aluminiului tratat superficial (engl., rez. rom.)......................................................................

IOANA PETRE, DAN PETRE, CRISTINA FILIP i LAVINIA NEAGOE, Aplicaii industriale ale muchilor pneumatici (engl., rez. rom.) .............

MIHI HORODINC, Noi resurse ale cercetrii experimentale asistate de calculator a puterii electrice absorbite n sistemele de fabricaie (engl., rez. rom.)........................................................................................

ION BOSTAN, VALERIU DULGHERU i ANATOL SOCHIREANU, Dezvoltarea integrat CAE a transmisiilor precesionale utiliznd platforma Autodesk Inventor (engl., rez. rom.) .......................................

ILEANA FULGA i EUGEN STRJESCU, Propuneri de optimizare a funcionrii morilor fluidice cu jeturi n spiral (engl., rez. rom.)............

DORU CLRAU, IRINA TIA, DAN SCURTU i BOGDAN CIOBANU, Analiza dinamic a mecanismului mecano-hidraulic de protecie a turbinelor eoliene cu ax orizontal de mic putere prin basculare n plan vertical (engl., rez. rom.)...............................................

CONSTANTIN CHIRI, ADRIAN HANGANU i DANIEL CALFA, Cercetri privind sistemele hidraulice pentru deplasarea maselor mari pe distante mici, cu frecven redus (engl., rez. rom.)............................

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EROL MURAD, CTALIN DUMITRESCU, GEORGETA HARAGA i LILIANA DUMITRESCU, Sistem de msurare pneumatic a masei de ap extras n procesele de uscare convectiv (engl., rez. rom.)...............

MIHAI FLORIN MNESCU i VALERIU PANAITESCU, Tehnologii folosite pentru monitorizarea defeciunilor structurale aprute n funcionarea grupurilor eoliene (engl., rez. rom.)......................................

AURORA ALEXANDRESCU, ADINA SIMONA ALEXANDRESCU i ADRIAN CONSTANTIN ALEXANDRESCU, Reabilitarea staiei de pompare pentru alimentare cu ap (engl., rez. rom.).................................

ILARE BORDEAU, MIRCEA OCTAVIAN POPOVICIU, DRAGO NOVAC, LIVIU MARSAVINA, RADU NEGRU, MIRCEA VOD, VICTOR BLOIU i MARIAN BRAN, Contribuii n evaluarea durabilitii arborilor hidroagregatelor axiale orizontale (engl., rez. rom.) .........................................................................................................

TEODOR MILO, MIRCEA BRGLZAN, EUGEN DOBND, ADRIANA MANEA, RODICA BDRU i DANIEL STROI, Traseul optim al unei conducte de aduciune utiliznd algoritmul Bellman-Kalaba (engl., rez. rom.) ............................................................

DNU ZAHARIEA i MIHAELA TUDORACHE, Analiza structural a cuplajelor fixe de tip manon cu tifturi cilindrice (engl., rez. rom.) .......

DNU ZAHARIEA i MARIUS STACHIE, Analiza structural a arcurilor bimetalice lamelare (engl., rez. rom.) .......................................................

IRNE ALEXANDRESCU, HANS-JOACHIM FRANKE i THOMAS VIETOR, Managementul cunoaterii n configurarea produselor complexe personalizate n fazele incipiente ale dezvoltrii acestora (engl., rez. rom.)........................................................................................

PETRU DUA i IULIANA LAURA TARANOVSCHI, Cercetri cu privire la activitatea de inovare din mediul tehnic (engl., rez. rom.)..........................................................................................................

ANDREI MIHALACHE, GHEORGHE NAG i MARIUS-IONU RPANU, Avantaje i puncte slabe ale diferitelor tehnici de inginerie invers (engl., rez. rom.) ...........................................................................

ROBERTO LOPEZ, MANUEL SAN JUAN, FRANCISCO SANTOS, OSCAR MARTN i FLORIN NEGOESCU, Termografie aplicat n frezarea osoas (engl., rez. rom.)...............................................................

OLGA MARINA MONTES i VASILE V. MERTICARU, Studiu asupra oportunitii unei noi fabrici de reciclare a sticlei, pentru o dezvoltare regional durabil (engl., rez. rom.)..........................................................

CTLIN DUMITRA, CARMEN LOGHIN, SULEYMAN YALDIZ, MEHMET SAHIN i LUMINIA CIOBANU, Modelarea 3D a suprafeelor textile cu destinaia optimizrii curgerii fluidelor (engl., rez. rom.)....................................................................................................

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BULETINUL INSTITUTULUI POLITEHNIC DIN IAI BULLETIN OF THE POLYTECHNIC INSTITUTE OF IAI

Published by the GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IAI

Tomul LVI(LX), Fasc. 2 2010

Section

MACHINE CONSTRUCTION

Pag.

ANTNIO M. GONALVES-COELHO, GABRIELA NETIAN and ANTNIO MOURO, On the Pattern of the Design Matrix in Redundant Design Solutions (English, Romanian summary). .............

TAXIARCHIS BELIS and ARISTOMENIS ANTONIADIS, Hobbing Wear Prediction Model Based on 3D Chips Determination (English, Romanian summary).................................................................................

1

9

NIKOLAOS TAPOGLOU and ARISTOMENIS ANTONIADIS, CAD-Based Calculation of Cutting Force Components in Gear Hobbing (English, Romanian summary)..................................................................

21

EUGEN STRJESCU, CONSTANTIN DOGARIU, OLIMPIA PAVLOV and DUMITRU DUMITRU, Contributions Concerning The Computer Aided Control of the Fellows' Cutter (English, Romanian summary)...................................................................................................

SILVIU BERBINSCHI, VIRGIL TEODOR, NICOLAE DUMITRACU and NICOLAE OANCEA, Contributions to the Elaborations of a Graphical Method for Profiling of Tools which Generate by Enveloping. I. Algorithms (English, Romanian summary).......................

31

41

C O N T E N T S

SILVIU BERBINSCHI, VIRGIL TEODOR, NICOLAE DUMITRACU

and NICOLAE OANCEA, Contributions to the Elaborations of a Graphical Method for Profiling of Tools which Generate by Enveloping. II. Application for Rack-Gear Tools Profiling (English, Romanian summary).................................................................................

CTLIN FETECU, DANIEL-VIOREL VLAD and COSTEL MOCANU, The Numerical Simulation of Turning Process using Finite Element Modeling (English, Romanian summary)...................................

MIRCEA COZMNC, CRISTIAN CROITORU and CTLIN UNGUREANU, Experimental Researches Regarding a New Method for Cutting Forces Evaluation (English, Romanian summary)................

ANA-MARIA MATEI and MARIUS NICOLAE MILEA, Face Milling Forces Depending on the Forces Developed on a Single-Tooth (English, Romanian summary).................................................................................

MARIUS-IONU RPANU, GHEORGHE NAG, IOLANDA-ELENA MANOLE and ANDREI WEINGOLD, Comparative Aspects Regarding the Nesting for Blanking-Punching Operation on Classical Presses and Numerical Commanded Pressing Centers (English, Romanian summary).................................................................................

IUSTINA ELENA ROTMAN, PETRU DUA and RADU ADRIAN BACIU LUPACU, Theoretical and Experimental Considerations on Determining the Effect of Divergence (English, Romanian summary)...................................................................................................

CTLIN UNGUREANU, RADU IBNESCU and IRINA COZMNC, Computerized Measurement System (English, Romanian summary).....

BIRGIT KJRSIDE STORM, Adhesive Bonding of Surface Treated Aluminium (English, Romanian summary)..............................................

IOANA PETRE, DAN PETRE, CRISTINA FILIP, and LAVINIA NEAGOE, Industrial Applications of the Pneumatic Muscles (English, Romanian summary).................................................................................

MIHI HORODINC, Some New Resources on Computer Assisted Experimental Research of the Absorbed Electric Power in Manufacturing Systems (English, Romanian summary)...........................

ION BOSTAN, VALERIU DULGHERU and ANATOL SOCHIREANU, Integrated CAE Development of Precessional Drives using Autodesk Inventor Platform (English, Romanian summary)....................................

ILEANA FULGA and EUGEN STRJESCU, Proposals for the Improvement of the Fluidic Spiral Jetmills' Activity (English, Romanian summary).................................................................................

DORU CLRAU, IRINA TIA, DAN SCURTU and BOGDAN CIOBANU, Dynamic Analysis of Mechanical-Hydraulic Protection Mechanisms of Low Power Horizontal Axis Wind Turbines through Vertical Tilting (English, Romanian summary)........................................

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CONSTANTIN CHIRI, ADRIAN HANGANU and DANIEL CALFA, Research on Hydraulically Systems which Move Heavy Masses on Small Distances with Lower Frequencies (English, Romanian summary)...................................................................................................

EROL MURAD, CTALIN DUMITRESCU, GEORGETA HARAGA and LILIANA DUMITRESCU, Pneumatic Metering System for Amount of Water Extracted in Convective Drying Processes (English, Romanian summary)...................................................................................................

MIHAI FLORIN MNESCU and VALERIU PANAITESCU, Technologies for Monitoring Structural Damages Arising in the Functioning of Wind Turbines (English, Romanian summary)...................................................

AURORA ALEXANDRESCU, ADINA SIMONA ALEXANDRESCU and ADRIAN CONSTANTIN ALEXANDRESCU, Pumping Station Exoneration for Water Supply (English, Romanian summary).................

ILARE BORDEASU, MIRCEA OCTAVIAN POPOVICIU, DRAGOS NOVAC, LIVIU MARSAVINA, RADU NEGRU, MIRCEA VODA, VICTOR BALASOIU and MARIAN BRAN, Contributions regarding Durability Evaluation of Horizontal Axial Hydraulic Turbines Shafts (English, Romanian summary)..................................................................

TEODOR MILO, MIRCEA BRGLZAN, EUGEN DOBND, ADRIANA MANEA, RODICA BDRU and DANIEL STROI, Optimal Routes of Pipeline Supply using the Bellman-Kalaba Algorithm (English, Romanian summary)................................................

DNU ZAHARIEA and MIHAELA TUDORACHE, Structural Analysis of a Sleeve Rigid Coupling with Cylindrical Pins (English, Romanian summary)...................................................................................................

DNU ZAHARIEA and MARIUS STACHIE, Structural Analysis of a Bimetallic Strip Thermostat (English, Romanian summary)....................

IRNE ALEXANDRESCU, HANS-JOACHIM FRANKE and THOMAS VIETOR, Knowledge Management for the Configuration in Early Phases of Complex Custom Products (English, Romanian summary)...

PETRU DUA and IULIANA LAURA TARANOVSCHI, Researches Regarding to Innovative Activity in Technical Environment (English, Romanian summary).................................................................................

ANDREI MIHALACHE, GHEORGHE NAG and MARIUS-IONU RPANU, Advantages and Weak Points of Different Reverse Engineering (RE) Techniques (English, Romanian summary).................

ROBERTO LOPEZ, MANUEL SAN JUAN, FRANCISCO SANTOS, OSCAR MARTN and FLORIN NEGOESCU, Thermography Applied to Bone Drilling (English, Romanian summary).......................................

OLGA MARINA MONTES and VASILE V. MERTICARU, Study on the Opportunity of a New Glass Recycling Factory for Regional Sustainable Development (English, Romanian summary)........................

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CTLIN DUMITRA, CARMEN LOGHIN, SULEYMAN YALDIZ, MEHMET SAHIN i LUMINIA CIOBANU, Modeling 3D Surface of Textile Structures for Fluid Flow Improvement (English, Romanian summary)...................................................................................................

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BULETINUL INSTITUTULUI POLITEHNIC DIN IAI Publicat de

Universitatea Tehnic Gheorghe Asachi din Iai Tomul LVI (LX), Fasc. 2, 2010

Secia CONSTRUCII DE MAINI

ON THE PATTERN OF THE DESIGN MATRIX IN REDUNDANT DESIGN SOLUTIONS

BY

ANTNIO M. GONALVES-COELHO1, GABRIELA NETIAN2,

and ANTNIO MOURO1

Abstract. Axiomatic Design was created with the aim of building a systematic model for engineering education and practice, taking into account the initial hypothesis that there are fundamental principles that govern good design practice. According to this design theory, the design solutions can be classified as uncoupled, decoupled or coupled, depending on the way their design matrices are populated. Uncoupled solutions are the best, decoupled solutions are acceptable, and coupled solutions are poor design and should be avoided. Redundant designs make up a specific class of design solutions, in which the number of functional requirements is lesser than the number of design parameters. This paper discusses how the design matrix could be populated, so that a redundant design could be either uncoupled or decoupled.

Keywords: Axiomatic Design, Design Matrix, Redundant Design, Ideal Design.

1. Introduction

Axiomatic Design (AD) was created in the late 1970s by Nam P. Suh with the aim of building a systematic model for engineering education and practice under the initial hypothesis that there are fundamental principles that govern good design practice [1].

According to AD, any design object being it a product, a process or any other technical system can be described by a vector in each one of four design domains (see Fig. 1). The design process starts at the customer domain with the definition of the customer needs (CNs). Mapping between the customer

2 Antonio M. Gonalves-Coelho et al.

and the functional domains allows finding the functional requirements (FRs). Once this is done, another mapping translates the FRs into design parameters (DPs), i.e. the set of properties that physically describe the design object. Finally, mapping from the physical to the process domain leads to the process variables (PVs), which outline how to make the design object [1].

Fig. 1 The Design Domains [1].

The left-to-right mapping between any two contiguous domains can be

represented by a design equation of the form:

Y = A[ ] X ; Aij ={ } { } Yi(1) X j ; i = 1, ..., m; j = 1,...,n ,

where {Y} is a vector that represents the set of m requirements that should be accomplished, {X} is a vector representing the set of n parameters of the design object that is expected to fulfil the requirements, and [A] is the design matrix. Usually, any prospective design equation is bounded by constraints [1].

Eq. (1) is not unique, and different {X} vectors would represent different design solutions that are characterized by distinct design matrices, which patterns would make the difference between good and poor design. The good or the poor quality of any design solution is ruled by the Independence Axiom, which states that, in good design, the selected parameters {X} should be such that the requirements {Y} are fulfilled independently. As a result, the ideal design solution should have the same number of requirements and parameters (m = n) and the design matrix should be diagonal, case of which the design solution is called uncoupled [1]. A triangular design matrix is acceptable as well and corresponds to a decoupled design [1]. Any other pattern of square design matrix corresponds to a coupled design, which should be recognized as poor and as such should be avoided [1].

For any design solution where m > n, ADs Theorem 1 states that either the design is coupled or some of its FRs can never be fulfilled [1]. An example of such a design can be found elsewhere [2]. In the case of m < n, ADs Theorem 3 states that the design is either redundant or coupled [1]. At last, the specific case of a design with a single requirement (m = 1) is worth to mention. In this case, the design would be either uncoupled (if n = 1), or redundant (if n > 1). In fact,

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 3 the decoupled and the coupled conditions are impossible to attain in any single-requirement design because there is no different FRs to couple.

The present work contains an analysis of the pattern of the design matrix of redundant designs with more than one requirement (m > 1), a matter to which the researchers have not paid sufficient attention so far.

2. The Key Characteristics of Redundant Designs

Fig. 2 depicts the design of a simple clamping device with one only customer need: the clamping action, which can be attained by adjusting one only FR the distance d.

Fig. 2 Example of a simple redundant design.

The adjustment of d can be achieved by suitably setting the values of two

design parameters: the position of the cam in the end of the hand lever (see Fig. 1), which is denoted by angle , and the angular position of the threaded rod, which is represented by angle . Thus, the design equation for this redundant design with one requirement and two parameters is:

(2) d{ }= A11 A12

.

A more general case is the Eq. (3) that represents a design with arbitrary numbers of requirements m and parameters n, with m < n. The equation relates to a redundant design, and its quality depends on the pattern of the design matrix, as per Theorem 3.

To better understand how the pattern of the design matrix of Eq. (3) could characterize a good or a poor design, let us consider the three coexisting designs


represented by Eq. (4), Eq. (5) and Eq. (6), where Akj denotes the possible non-zero elements of the related design matrices.

(3)

(4)

FR1FR2FR3

=

A11 A12 A13 0 0 0 0 0A21 A22 A23 0 0 0 0 0A31 A32 A33 0 0 0 0 0

DP1DP2DP3DP4DP5DP6DP7DP8

,

(5) FR1FR2FR3

=

0 0 0 A14 A15 A16 0 00 0 0 A24 A25 A26 0 00 0 0 A34 A35 A36 0 0


,

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 5

(6)

FR1FR2FR3

=

0 0 0 0 0 0 A17 A180 0 0 0 0 0 A27 A280 0 0 0 0 0 A37 A38


.

One can see that DP1, DP2 and DP3 are the only possible contributing parameters in Eq. (4). As for the design of Eq. (5), just DP4, DP5 and DP6 are significant. At last, in what concerns to Eq. (6), only DP7 and DP8 contribute. In other words, each one of the above-defined coexisting designs can fulfil all the FRs of Eq. (3) using entirely different subsets of the DPs included in the latter equation, in such a manner that all the DPs are taken into account.

Now, one can figure out that the design of Eq. (3) could be achieved by merging the designs of Eq. (4), Eq. (5) and Eq. (6).

The design matrices of Eq. (4) and Eq. (5) could be reduced to block matrices of size m x m by eliminating the zero elements of their design matrices.

Therefore, the surrogate condensed design equations could be obtained from those equations by eliminating the non-relevant DPs, and by using the all the existing FRs and the non-zero block matrices. For example, Eq. (7) is the condensed equation that is obtained from Eq. (5).

The same treatment could be done to Eq. (6), but in this case we would obtain a non-square block matrix of size (n mod m) x m.

(7)

FR1FR2FR3

=

A14 A15 A16A24 A25 A26A34 A35 A36

DP4DP5DP6

.

As a result, the redundant design of Eq. (3) could be considered suitable design if the condensed equations obtained from Eq. (4), Eq. (5) and Eq. (6) are not coupled. The coupled condition is excluded in Eq. (4) and Eq. (5) if the relevant DPs are chosen so that their non-zero block matrices are either triangular or diagonal.

As for Eq. (6), the coupled condition is excluded if its non-zero block matrix is populated in such a manner that the condensed equations correspond to uncoupled or decoupled designs. If this is not the case, one can selectively freeze as many DPs as required, so that the condensed design become uncoupled or decoupled, as exemplified elsewhere [3].


4. Conclusion

The key conclusion of this paper can be summarized as a new theorem: Let

us suppose a design with m requirements and n parameters, with m < n. Its design matrix can be partitioned in (n div m) square block matrices of size m x m, and an extra non-square block matrix of size (n mod m) x m, in such a manner that the block matrices have not common elements. Such a design is acceptable if each block matrix describes either an uncoupled or a decoupled design. Otherwise, the design is of the coupled type. Received: January, 30, 2010 1 UNIDEMI, Universidade Nova de Lisboa,

Faculdade de Cincias e Tecnologia Departamento de Engenharia Mecnica e Industrial

Monte de Caparica, Portugal e-mail: [email protected]

[email protected] 2 Ministerul Comunicaiilor i Societii Informaionale,

Bucureti, Romnia e-mail: [email protected]

R E F E R E N C E S

1. S u h N. P., The Principles of Design, Oxford Univ. Press, N. Y., 1990. 2. G o n a l v e s C o e l h o A. M., M o u r o A. J. F., Axiomatic Design: The

Meaning of the First Axiom. In: A. Toca, O. Pruteanu (Eds.), Tehnologii Moderne, Calitate, Restructurare: Culegere de Lucrri tiinifice, 3, pp. 341-344, Universitatea Tehnic a Moldovei, Chiinu, 2003.

3. F r a d i n h o J., G o n a l v e s C o e l h o A. M., M o u r o A. J. F., An axiomatic design approach for the cost optimisation of industrial coupled designs: A case study. In: Gonalves-Coelho A.M. (Ed.), Proc. 5th International Conference on Axiomatic Design - ICAD 2009, pp. 201-207, Campus de Caparica, 2009.

MODELUL MATRICEI DE PROIECTARE IN CAZUL SOLUTIILOR REDUNDANTE DE PROIECTARE

(Rezumat)

Proiectarea axiomatic a aprut din necesitatea crerii unui model sistematic de

educare i practic inginereasc, pornind de la principiile fundamentale de bune practici ale proiectrii. Conform acestei teorii, n funcie de modul de populare al matricelor de proiectare, soluiile de proiectare pot fi clasificate n soluii necuplate, decuplate sau cuplate. Soluiile de tip necuplat sunt cele mai bune, soluiile de tip decuplat sunt

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 7 acceptabile iar soluiile cuplate nu sunt satisfctoare din punct de vedere tehnic i ar trebui evitate. Matricele diagonale corespund soluiilor necuplate, matricele triunghiulare corespund soluiilor decuplate iar toate celelalte tipuri de matrice ptratice corespund soluiilor cuplate. n cazul n care numrul cerinelor funcionale este mai mare dect numrul parametrilor de proiectare, unele cerine nu pot fi ndeplinite niciodat i soluiile sunt de tip cuplat. Proiectarea redundant creeaz o clas specific de soluii de proiectare n care numrul cerinelor funcionale este mai mic dect numrul de parametri de proiectare.

Aceast lucrare prezint modaliti de populare ale matricei de proiectare, astfel nct un proiect de tip redundant s poat deveni de tip necuplat sau decuplat.

In concluzie putem formula o nou teorem: Presupunnd c avem un produs sau un proces a crui matrice de proiectare are m cerine i n parametri, unde m < n, atunci matricea de proiectare poate fi descompus n (n div m) submatrici ptratice de ordinul m x m i o submatrice neptratic de ordinul (n mod m) x m, astfel nct submatricile s nu aib elemente comune. O astfel de soluie este acceptabil dac fiecare bloc descrie o soluie necuplat sau decuplat, dac nu, atunci soluia este de tip cuplat.




HOBBING WEAR PREDICTION MODEL BASED ON 3D CHIPS DETERMINATION

BY

TAXIARCHIS BELIS and ARISTOMENIS ANTONIADIS

Abstract. Gear hobbing is a machining process widely used in the industry for massive production of external gears. In this process the variant chip formation on each generating position causes uneven wear distribution on the hob teeth. This paper presents a new method for the determination of wear parameters based on 3D chips. The 3D chip characteristics are fed to an existing wear model in order to calculate the hob wear distribution more precisely.

Key words: gear hobbing, tool wear, simulation

1. Introduction

Gear hobbing is one of the most efficient generating processes for cutting external cylindrical gears. Although, hobbing cutters are still quite expensive due to their complex geometry. Thus their extensive exploitation is very important for industry. In gear hobbing the chip formation varies for each cutting tooth due to the fact that every tooth always cuts the same generating position. As a result, different wear laws are developed leading to uneven wear distribution on the hob teeth. Thus, the need to adopt an effective wear prediction model in gear hobbing arises. In this paper 3D chip determination is studied in order to feed more accurate data to an existing wear prediction model. Moreover total wear distribution on the hob teeth can be calculated. This information can be used to optimize tangential shifting conditions in order to maximize tool life and prolong the time interval before hob cutter resharpening.

Figure 1 presents the basic nomenclature of the hob cutter that has been used in the wear simulation program developed in the present work. As it can be seen in the upper part of the figure, three distinct motions are required by this cutting method those being the workpiece revolution, the tool rotation, and the

10 Taxiarchis Belis and Aristomenis Antodiadis tool tangential displacement. Considering the above kinematic, two different hobbing types may be applied according to the direction of the axial feed, the climb and the up-cut hobbing respectively. In the present paper the tooths profile generation complies with DIN 3972 [1].

Fig. 1 Basic kinematics and essential parameters of gear hobbing.

2. State of the Art

As mentioned before, wear prediction in gear hobbing is a challenging task because of the large amount of wear influencing data and the complex kinematics of the process. Many studies have been published, introducing different methods for wear determination. These studies can fall under two categories. The first includes methods based on wear calculation in individual generating positions [2], [3].These methods are based on the simulated chip geometry and cutting conditions. Lately, FEM-based methods for wear determination have been introduced [4]. These methods take into account occurring stresses in the tool-chip contact areas. Nevertheless a FEM-based simulation needs a considerable amount of time before it can be realised. The wear model presented in [2] is used in the present paper,. The contribution of the proposed method is the precise 3D chips determination

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 11 because the chip characteristics can be calculated with the accuracy provided by a CAD system.

3. Hob Wear Simulation Process In order to achieve uniform wear distribution in the majority of the cutting teeth, a hob tangential shifting is required. In the left part of Figure 2, simulated chips and the corresponding gaps formed at the indicated generating positions, are illustrated. These chips are categorized into groups according to their shape and the cutting direction of the process. In the right part of Figure 2 the wear laws of several teeth after tangential shifts can be observed.

Fig. 2 Determination of the flank wear at individual hob teeth

considering the shift data.

12 Taxiarchis Belis and Aristomenis Antodiadis

In the first column the wear laws of teeth number 1, 2, 3 and 4 and the total wear distribution on the hob after a certain number of cuts are presented. The second column shows the wear laws after the first tangential displacement equal to the tool axial pitch . After this sifting the cutting tooth i is placed at the generating position of the tooth i+1. Thus the tooth number 1 that was cutting in the generating position number 1 quits, whereas the tooth number 5 cuts for the first time in the generating position 4. For example, tooth number 4 was cutting initially in the generating position 4. After AS* number of cuts, tooth 4 reaches a certain flank wear depth. In the first tangential shift, tooth 4 cuts in the generating position 3, obeying the wear law that governs that generating position. In this position, flank wear increases with a different rate for another AS* number of cuts. Finally, in the last tangential shift, tooth 4 cuts in generating position number 2, obeying a different wear law. As a result, in the bottom side of figure 2, the normalized flank wear distribution on the hob after two tangential displacements is presented. Consequently the wear distribution becomes uniform and the tool exploitation is enhanced.

Fig. 3 The effect of chip geometry and shape on the tool wear development.


3.1. HOBWEAR Formulation

Figure 3 presents wear laws for different chip groups. There are five chip groups concerning the chip flow obstruction intensity, introduced by [3]. The determination of the chip group involves prior knowledge of the cutting direction and the examined gear flank. As it can be easily noticed, the wear rate in group I is more intense. On the other hand, cutting with chip group 0 causes less flank tooth wear and the achieved number of cuts increases. This can be explained by the fact that in group I there is intense chip flow obstruction. In the region of the tooth head chip flow obstruction phenomena are the most intense due to collision of chip distinct sections. In the bottom side of the figure the included equivalent chip thickness and length are further explained.

Figure 4 presents the general structure of the program developed. The left part of the figure shows the categorized data input. Data such as chip group, equivalent thickness and length are loaded into the program from an external source. The undeformed chip geometries are calculated in various generating and revolving positions with the aid of HOB3D [2], [3].

Fig. 4 HOBWEAR simulation algorithm.

The wear behaviour on the hob teeth is primarily influenced by two sets of parameters. The first set refers to machining data and the geometry of hob and

14 Taxiarchis Belis and Aristomenis Antodiadis gear. The second set refers to the machine tool, the cutting and working material combination and the used cooling lubricant. Every possible combination of the above parameters results in different coefficients in the model. Wear coefficients are experimentally defined for a variety of materials and geometries widely used in gear industry. The middle column of the figure shows the flow chart for wear calculation and optimal tangential displacement determination. The program has the ability to calculate wear progress at all generating positions including transient areas. In order to shift the hob cutter, all the group gears have to be processed. At the bottom of the figure the outputs of the program are presented. The output includes wear progress graphs for all generating positions, and total wear distribution graphs for all tangential displacements. The developed program also calculates the maximum flank wear and the corresponding number of cuts.

3.2. 3D Chips Determination

As illustrated on figure 5, this paper introduces a novel way of calculating equivalent chip dimensions. The equivalent chip thickness calculation is more accurate due to the fact that is measured on the 3D chips cross-sections. Detail A in the upper right part of the figure, shows the chip cross-section in plane 1. The calculation of thickness in tooths head and in arc distance fa

) is hereby determined. The equation predicting the wear progress in the individual generating positions and the equations of equivalent chip dimensions introduced in [2] are presented in the bottom side of the figure.

Fig. 5 Determination of equivalent chip dimensions.

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 15 The wear determination model includes two stages. The first stage involves the employment of hobbing data in order to calculate the chip thickness, length and group for every cutting position of all generating positions. Categorization of chips in groups is determined by the program FRSWEAR [3].

Fig. 6 Calculations of the equivalent chip thickness and length based on 3D chips.

The measurement of the total length of the chip and the length compressed

on the heads corner are quite precise. As shown in the left bottom side of figure 6, the first step for measuring the chips length compressed on the tooths heads corner, is to cut the section of the chip from the left flank to the tool head center H, as the hobs profile is revolving. In this cross-section we can easily

16 Taxiarchis Belis and Aristomenis Antodiadis and precisely measure the chips thickness and length in head hH and lH,TF in CAD environment. This data is fed to the equation illustrated in figure 5 in order to calculate the arc length fa

) . Determination of fa) is very important due

to the fact that maximum wear depth has been observed by researchers in this region [2], [3], [7]-[9]. The calculation method of chip thickness hf is similar to hH. After hs and lH are determined for every generating position, data can be fed to the wear prediction model. All the calculations above can be simplified by the use of parametric design in CAD environment. In the first step the arc fa

) is set as parameter. In the next step the section of the chip from point K to F as the hob profile revolves is cut. In the chip produced hH and lH,TF can be easily measure and the arc fa

) calculated precisely. The parameter is set at the calculated value and the chips regenerated automatically. Thus, chip thickness hf can be easily measured. The final step includes calculation of the equivalent thickness hs. The upper part of figure 6 presents the variation of the chip thickness for all the revolving planes in several generating positions. These diagrams have been generated from the sequence of the chip thickness results hH as mentioned above.

3.3. Development of the Wear Prediction Program

The gear flank wear determination program is implemented in MATLAB high-level matrix array language.

Fig. 7 The Graphical User Interface of the wear simulation program HOBWEAR.

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 17 The user has the ability to select gear and hob material from a variety of the most popular ones in industry. This selection changes the wear coefficients used to determine the flank wear. An automatic report generator has been incorporated for better organization of the program results.

4. Simulation Results

Wear graphs for each individual generating position is the first output of the program developed, as presented in figure 8. As it can be seen, teeth number 10, 11 and 12 have almost reached the wear limit of 0,6 mm. For wear width below 0,2 mm the relation between number of cuts and flank wear is linear.

The normalization progress of total wear distribution on the hob cutter from tangential shifting number 5 to 8 is illustrated in Figure 9. Optimization of tangential shifting in gear hobbing has been studied by [10]. The credibility of the above wear prediction model has been verified with the aid of a wide variety of cutting experiments [2], [3].

Figure 10 presents the wear distribution on the cutting teeth of a hob cutter for two cases. In both cases, 18 gears of the same width have been cut. In the first case, 3 tangential shifts took place with 1 displacement per shift. In the second case, 2 tangential shifts took place with 2 displacement per shift. It is evident that in the second case the maximum wear depth on the hob cutter is less than in the first one.

Fig. 8 Wear progress in individual generating positions.


Fig. 9 Total wear distribution on the hob cutter after shifting.

As it can be seen in the second case, the wear distribution is more uniform due to the fact that more teeth are involved in the cut. Authors in [10] have studied the optimal selection of the shift displacement and number of shifts and introduced a nomogram for various shifting conditions.

Fig. 10 Cutting of 18 gears with different tangential displacement parameters.


5. Conclusion This paper suggests a model which simulates the wear progress on the hobbing cutter. The end-user has the ability to optimize tangential shifting conditions, owing to this model, in order to minimize the total gear manufacturing cost. Acknowledgements. The authors wish to thank the Research Committee of the Technical University of Crete for their financial support (via basic research project 2009). Received:March 10, 2010 Technical University of Crete, Department of Production Engineering & Management

Chania, Crete, Greece e-mail: [email protected]

[email protected]

R E F E R E N C E S

1. D I N 3972, Bezugsprofile von Verzahnwerkzeugen fuer Evolventenverzahnungen Nach DIN 867, 1981.

2. B o u z a k i s K., K o m p o g i a n n i s S., A n t o n i a d i s A., V i d a k i s N., Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models. ASME Journal of Manufacturing Science and Engineering, 124, 1, 42-51 (2002).

3. B o u z a k i s K. D., Konzept und technologishe Grundlagen zur automatisierten Erstellung optimaler Bearbeitungsdaten beim Waelzfraesen, Habilitation, TH Aachen, 1980.

4. F r i d e r i k o s O., Simulation of Chip Formation and Flow in Gear Hobbing Using the Finite Element Method, Ph.D. Thesis, Aristoteles University of Thessaloniki, Greece, 2008.

5. D i m i t r i o u V., V i d a k i s, N., A n t o n i a d i s A., Advanced Computer Aided Design Simulation of Gear Hobbing by Means of 3-Dimensional Kinematics Modeling, ASME Journal of Manufacturing Science and Engineering, 129, 911-918., (2007).

6. D i m i t r i o u V., A n t o n i a d i s A., CAD-based Simulation of the Hobbing Process for the Manufacturing of Spur and Helical Gears, International Journal of Advanced Manufacturing Technology, 41, 3-4, 347-357 (2008).

7. A n t o n i a d i s A., Determination of the Impact Tool Stresses During Gear Hobbing and Determination of Cutting Forces During Hobbing of Hardened Gears, Ph.D. Thesis, Aristoteles University of Thessaloniki, 1989.

8. A n t o n i a d i s A., V i d a k i s N., B i l a l i s, N., Fatique Fracture Investigation of Cemented Carbide Tools in Gear Hobbing. Part 1: FEM Modeling of Fly


Hobbing and Computational Interpretation of Experimental Results. ASME Journal of Manufacturing Science and Engineering, 124, 4, 784-791, (2002).

9. A n t o n i a d i s A., V i d a k i s N., B i l a l i s N., Fatique Fracture Investigation of Cemented Carbide Tools in Gear Hobbing. Part 2: The Effect of Cutting Parameters on the Level of Tool Stresses A Quantitative Parametric Analysis. ASME Journal of Manufacturing Science and Engineering, 124, 4, 792-798, (2002).

10. B o u z a k i s K., A n t o n i a d i s A., Optimizing of Tangential Tool Shift in Gear Hobbing, Annals of the CIRP, 44, 1 (1995).

MODEL PENTRU EVALUAREA UZURII DINILOR FREZELOR DE DANTURAT PE BAZA DETERMINRII ACHIILOR 3D

(Rezumat)

Frezarea danturii este un procedeu de prelucrare larg rspndit n industrie, n

special pentru producia de serie a danturilor exterioare. n acest proces, modul diferit de formare a achiei n fiecare poziie de generare a profilului duce la uzura neuniform a dinilor frezei. Lucrarea prezint o nou metod de determinare a parametrilor uzurii, frezelor pe baza achiilor 3D. Caracteristicile achiilor 3D au fost stabilite pornind de la un model existent de uzur, n vederea determinrii cu mai mult acuratee a distribuiei uzurii la nivelul dinilor frezei.




CAD-BASED CALCULATION OF CUTTING FORCE COMPONENTS IN GEAR HOBBING

BY

NIKOLAOS TAPOGLOU and ARISTOMENIS ANTONIADIS

Abstract. One of the most commonly used gear manufacturing process

especially for external is gear hobbing. The optimisation of the process of gear hobbing is of great importance in the modern industry. This paper presents a novel simulation program called HOB3D that can simulate the cutting process in a commercial CAD environment, thus producing results with the optimal precision. The outputs of the program include the 3D chip and gap geometry as well as the developing cutting forces which were validated using experiments.

Key words: gear hobbing, cutting forces, simulation.

1. Introduction

One of the key components of any torque transmission system is high precision involute gears. Gears can be constructed with a wide variety of methods; Gear hobbing is the one mainly used in the modern industry. Gear hobbing kinematics consists of three relative motions between the cutting tool and the workpiece. This makes it difficult to simulate with analytical models. HOB3D is a novel simulation program based on a commercial CAD environment which can simulate the cutting process and provide results including 3D solid chips and gaps as well as predicting the developing cutting forces.

2. State of the Art

The research conducted in the area of gear hobbing can be divided into two categories: gear hobbing process simulation and wear prediction. In the first field a series of simulation models have been developed using CAD [1],[2], FEA [3] or analytical [4]-[7] based models. Experiment based models [8], [9]

22 Nikolaos Tapoglou and Aristomenis Antoniadis are used in the field of wear prediction order to calculate the wear of the cutting tool and optimize the cutting so as to obtain uniform wear along the cutting tool. Cutting forces prediction is an area of great interest also. Research conducted in this area is based on Kienzle-Victors equations and depend on geometry of chips.

3. Gear Hobbing and HOB3D Simulation Process

Gear hobbing kinematics is based on three relative motions between the cutting tool and the workgear. These motions must be synchronised in order to produce high quality helical and spur gears. As presented in Fig. 1 the work gear rotates round its axis while at the same time the hob rotates round its own axis and moves parallel to the gear axis. The hob is positioned in an angle relative to the gear. The magnitude of this angle is relative to the hob helix angle and the helix angle to the gear produced correspondingly.

Fig. 1 Gear hobbing.

Gear hobbing process is affected by a series of parameters which be divided

in three categories: hob, gear and process parameters. The first include module (m), external diameter (dh), number of origins (z1) and number of columns (ni) of the hob. Gear parameters are number of teeth (z2), helix angle (ha) and gear width. Finally, process parameters include axial feed (fa) and cutting speed (v). A series of parameters can be calculated from those above mentioned, those being distance e, the helix angle of the hob (), gear diameter (dg) and depth of cut (t).

In order to simulate the process of gear hobbing, new software has been developed. The proposed simulation model has been embedded in a commercial CAD program thus taking advantage of its accuracy resulting in more detailed calculations.


The new simulation code called HOB3D uses three coordinate systems in order to calculate the results required. The first (1) is positioned on the examined cutting edge and has the x axis parallel to the hobs axis, the y axis perpendicular to x axis and finally z axis perpendicular to the prior two. Coordinate systems (2) and (3) have axis z running through the workgears axis. In coordinate system (2), x axis is always rotating in order to point to the gap, while the axes of coordinate system (3) are fixed.

Fig. 2 HOB3D flowchart.

24 Nikolaos Tapoglou and Aristomenis Antoniadis

Fig. 2 presents the flowchart of this simulation model. As it is illustrated, after all the input data, shown on the left side of the figure, has been defined, the initial workpiece is developed in the CAD environment and the number of the effective teeth is determined accordingly. The gear hobbing simulation process is executed for all these teeth. The first step in the simulation process is the positioning of the cutting edge on the 3D space.

This positioning is repeated along the path that is covered by the cutting edge. The profiles that arise are combined in order to form a 3D surface. The next step is the creation of an assembly that includes the workgear and the 3D surface. Afterwards, Boolean operations are used in order to generate the 3D chip and the 3D gap. The above described process is repeated for all active teeth in every rotation of the cutting tool. Finally, after the end of the simulation process the cutting forces on every one of the active teeth of the hob are calculated. These forces are added up and the total cutting forces are calculated.

4. HOB3D Formulation

4.1. Simulation Formulation

In HOB3D all the movements involved in the process are transferred to the hob cutting tooth motion. Furthermore, the simulation process is carried out on one gap of the gear thus reducing the simulation time. In order to identify the cutting teeth, those are numbered. The tooth which has the local axis Y1 parallel to local axis X2 when it passes through the center of the gap is named Tooth 0, the tooth that passes after that is named Tooth 1 and the tooth previous to that is named Tooth-1 and so on.

The simulation process is illustrated on Fig. 3. As it is presented, the hob profile according to DIN3972 [10] must be designed first. This profile is presented on the top left frame of Fig. 3 and positioned on the 3D space, as illustrated on the next frame of fig. 3. The positioning is repeated for a series of times until the tooth is out of the cut.

After this step, there is a series of profiles correctly positioned on the 3D space. Every profile represents a revolving position of the hob and its positioning includes hob rotation, workpiece rotation and feed rate. All these profiles are combined in order to form a 3D surface like the one seen in the last frame of the first line of fig. 3. Then, the 3D surface is assembled with the 3D gap produced from the previous tooth. The final stage of the simulation process is the extraction of the final gap geometry and the non-deformed chip geometry. This is achieved with the aid of Boolean operations, as supported by the used CAD environment.


Fig. 3 HOB3D simulation process.

4.2. Force Component Calculation Formulation

After the simulation is completed, the cutting forces can be calculated. The

force calculation code is performed in accordance with Kienzle-Victors equations. The calculation process is based on sections made on every one of the solid chips.

A series of sections are made for every chip. Each section is made in the plane of the hobs cutting edge. The planes are visible on the top left frame of Fig. 4. After the creation of the section on the 3D chip, the crossection is discritised along the cutting edge. This discritisation is presented on the top right frame of fig. 4.

The three force components are calculated according to the elementary chip width and thickness for every elementary chip section. The three force components are rotated in order to match the local coordinate system (1) and then added up in order to produce the total cutting forces on every crossection. After all the sections are calculated the total forces on the tooth are obtained, as presented on the bottom of Fig. 4.


Fig. 4 Force calculation algorithm.

4.3. Simulation Results

HOB3D has been used in order to produce the 3D solid chips in the full cut phase of gear hobbing. These chips were analysed so that the cutting forces are calculated. The crossections made on the chip are presented on the right side of Fig. 5 whereas the chip thickness on six of the crossections is illustrated on the left side of the same figure.


Fig. 5 Chip thickness of the solid chip.

The cutting forces components for the above chip are presented in the next Fig. 6 which are calculated in accordance with the system 1.

Fig. 6 Cutting forces on one generating position.


5. Verification

The verification of the force calculation module was conducted in two

phases. First, the cutting forces simulated on specific teeth were compared to the ones measured by B o u z a k i s [4] while other cutting forces calculated by HOB3D were compared to the ones measured by G u t m a n n [5]. Fig. 7 illustrates the results of the first phase of the verification. As it can be seen, each column of the figure illustrates the measured and calculated cutting forces on one generating position measured on the coordinate system of the 3D gap (2). In most of the cases the simulation code predicts not only the form but also the magnitude of the cutting forces.

Fig. 7 Comparison between calculated and measured cutting forces.


The second step of the verification is the comparison between measured and calculated forces for all the cutting teeth simultaneously. Fig. 8 presents the comparison between the measured and the calculated cutting forces in all three directions of the coordinate system, as illustrated on the top left side of the figure.

Fig. 8 Comparison between calculated and measured cutting forces.

4. Conclusions

1. A novel simulation model for gear hobbing, developed in a commercial CAD environment is presented in this paper. The model can simulate the manufacturing of helical as well as spur gears

2. The developed model can predict the cutting forces components with great accuracy. The calculated forces have been verified with the aid of cutting experiments. Received: March 10, 2010 Technical University of Crete,

Department of Production Engineering&Management, Chania, Crete, Greece,

e-mail: [email protected]


R E F E R E N C E S

1. D i m i t r i o u V., V i d a k i s N., A n t o n i a d i s A., Advanced Computer Aided Design Simulation of Gear Hobbing by Means of 3-Dimensional Kinematics Modeling, ASME J. of Manuf. Science and Eng., 129, 911-918., (2007).

2. D i m i t r i o u V., A n t o n i a d i s A., CAD-based Simulation of the Hobbing Process for the Manufacturing of Spur and Helical Gears, Int. J. of Advanced Manuf. Technology, 41, 3-4, 347-357 (2008).

3. F r i d e r i k o s O., Simulation of Chip Formation and Flow in Gear Hobbing Using the Finite Element Method, Ph.D. Thesis, Aristoteles University of Thessaloniki, Greece 2008.

4. B o u z a k i s K. D., Konzept und technologishe Grundlagen zur automatisierten Erstellung optimaler Bearbeitungsdaten beim Waelzfraese, Habilitation, TH Aachen 1980.

5. G u t m a n n P., Zerspankraftberechnung beim Waelzfraesen, Ph.d. thesis, TH Aachen, 1988.

6. A n t o n i a d i s A., Determination of the Impact Tool Stresses During Gear Hobbing and Determination of Cutting Forces During Hobbing of Hardened Gears, Ph.d. thesis, Aristoteles University of Thessaloniki, 1989.

7. A n t o n i a d i s A., V i d a k i s N., B i l a l i s N., Fatique Fracture Investigation of Cemented Carbide Tools in Gear Hobbing. Part 1: FEM Modeling of Fly Hobbing and Computational Interpretation of Experimental Results. ASME J. of Manuf. Science and Engineering, 124, 4, 784-791, 2002.

8. A n t o n i a d i s A., V i d a k i s N., B i l a l i s N., Fatique Fracture Investigation of Cemented Carbide Tools in Gear Hobbing. Part 2: The Effect of Cutting Parameters on the Level of Tool Stresses A Quantitative Parametric Analysis, ASME J. of Manufacturing Science and Engineering, 124, 4, 792-798, 2002.

9. B o u z a k i s K., K o m p o g i a n n i s S., A n t o n i a d i s A., V i d a k i s N., Gear Hobbing Cutting Process Simulation and Tool Wear Prediction Models. ASME J.of Manuf. Science and Engineering, 124, 1, 42-51 2002.

10. D I N 3972, Bezugsprofile von Verzahnwerkzeugen fuer Evolventenverzahnungen Nach DIN 867, 1981.

DETERMINAREA PRIN SIMULARE CAD A COMPONENTELOR

FOREI DE ACHIERE LA FREZAREA DANTURILOR

(Rezumat)

Unul dintre cele mai uzuale procedee de prelucrare a danturilor, n special a celor exterioare, este frezarea. Optimizarea acestui tip de proces de danturare prezint la ora actual o importan deosebit n industrie. Lucrarea prezint un nou program de simulare, numit HOB3D, care permite simularea procesului de achiere ntr-un mediu CAD comercial, cu rezultate optime n ceea ce privete precizia de prelucrare. Elementele rezultante ale programului de simulare se refer att la achia 3D i la geometria golului dintre dinii frezei, ct i la nivelul forelor de achiere dezvoltate, elemente care au fost validate experimental.




CONTRIBUTIONS CONCERNING THE COMPUTER AIDED CONTROL OF THE FELLOWS' CUTTER

BY

EUGEN STRJESCU1, CONSTANTIN DOGARIU1, OLIMPIA PAVLOV2 and DUMITRU DUMITRU3

Abstract. In the paper are presented the bases of a methodology for the determination of all the geometric and constructive elements of the cutting tools for the fellows cutter, tools having curve edges, starting from the getting of a solid model 3D of the measured tool. There are shown the possibilities to obtain a 3D model and the mathematical model of the geometric parameters control.

Key words: fellows' cutter, control, cutting tools, 3D model, geometry, curved edges.

1. Introduction

Preoccupations concerning the increase of the standard, standard type and special cutting tools production and preoccupations concerning new tools with superior constructive functional performances represent a major tendency in the manufacturing of machines. The software resources implicates the existence in the system of a collection of organized information in order to assure not only the complete design of the cutting tool but also the analysis, the syntheses, comparison, modeling, simulation optimization, visualization, the optional presentation of the partial results etc. So the modern design is made in order to obtain a solid 3D model that is later automatically detailed in sections and views 2D. The existence of the solid model signify the spectacular increase of the information's number permitting practically the total knowledge of the positions of any point or surfaces from the elements construction and of the angles between directions or planes. This demarche ameliorates the tackling of the cutting tools' design by means of the concurrent engineering.

32 Eugen Strjescu et al.

The modern means for the assisted design (Catia, Solid Works, Ideas, Solid Edge) are capable to make automatically sections in any point and after any direction, pointing automatically distances between points or angles values.

In this way we can avoid the situations in which we are choosing for the cutting tool a value for an angle at a peak, but in other sections or points the real values are outside the domain of availability. Starting from these observations, we want to develop a new method for the control of the manufactured cutting tool, starting from the idea of the obtention of a solid model.

This demarche is extremely utile in the admission of the concurrent engineering.

2. Using the Solid Model for the Cutting Tools' Control

2.1. Possibilities to obtain the 3D Models of the Real Pieces 2.1.1. The getting of the 3D model of the cutting tool by photography. The software D Sculptor presents a relative new in the large landscape of the CAD software and the software for treatment of the images and corps 2D and 3D. It permits the creation on the computer photorealistic models for a large game of objects using habitual photos, easy and fast. We do not need special hardware

elements, but only a normal computer and a photo camera. A digital camera is required, but it is possible to use scanned photos. The main screen of the program is presented in the fig. 1.

Fig. 1 The main screen of D Sculptor software.

The basic processes for the models construction are presented down: it is positioned the object to

acquire the model on the calibration plane;

it is photographed the object from many angles;

the photos are imported in the software D Sculptor;

D Sculptor detects automa-ticaly the model; D Sculptor is calculating the three-dimensional model. The obtained three-dimensional model (3D) (fig. 2) can be used with software. In time D Sculptor 2.0 was improved at a technical level and from the point of view of the interface.


It is possible to create models faster than before, and the last version of D Sculptor 2.0 Professional has a superior accuracy.

2.1.2. Generation of the 3D model by scanning. A 3D scanner is a modern device, intense developed during the last years, device that analyses a real object or an average in order to collect data concerning the form, the texture and the color of the object. The acquired data can be used to digitally construct 3D models, utile for a large game of applications. In the most situations, a single scanning do not produces a complete model of the subject. Multiple scanning, some time hundreds, from many directions are necessary usually to obtain information about all the sides of the object. These scans must be introduced in a common reference system, processes named usually alignment or recording. The scans will fusion in order to create a complete model.

Now the scanners are of two types: scanners 3D with contact and without contact. The scanners non contact can be active or passive. It exists a large gamut of technologies for the two categories. In techniques are imposed the non contact scanners, with laser.

The essential problem of the getting of a 3D model by scanning is represented by the great number of necessaries scans and by the possible necessity to complete the acquired model using programs for assisted design (Catia, SolidWorks etc.). This last activity is more necessary if the

form of the scanned tool is more complex.

Fig. 2. The solid model resulted after the images treatment.

For these reasons we can affirm that for the simple tools the proposed method is not efficient, because the completion of the model need too much time for routine measurements, but becomes very efficient for the complex cutting tools, measurable with difficulties, at which we obtain the geometric parameters baffling to measure (and in the main cases with a low accuracy).

3. The Control of the Geometry Based on the 3D Model

After the getting of the 3D model using the software D Sculptor 2.0 or by scanning, the model is exported in the Solid Works software, resulting the up presented (fig. 2).


On the obtained model are choose points on the main edge and on the secondary one and there are given command for the construction of the planes in which are measured the requested geometric elements.

3.1. The Determination of the Fellows' Cutters' Geometry.

The fellows' cutters are tools destined to the manufacturing by mortising the internal and external gear of the spur gears with right, inclined of "in V" teeth, representing from that reason a high degree of universality, as consequence of the cutting edges' access in areas inaccessible for other kind of tools (for example, side mills, hobbing cutters, etc.). Also, the fellows' cutters are the single cutting tools that can machine cylindrical gear wheels with interior denture, by rolling. 3.1.1. Geometric parameters. The clearance angle at the tooth' peak presents a big importance, because from that value depends the bigness of the profile correction in time after successive sharpening.

Also, by the value of this angle depends the size of the lateral clearance angle on the two flanks of the tooth that result much more little. So, it is considered the lateral clearance angle at the level of the divided circ, respectively if the tooth is cut after the division cylinder, the intersection curve between this cylinder and the involute clearance angle of the tooth will be a helix. Because the disposition on the involute flanks of the points in which the values of the angles , , and are determined, it results that in any point we obtain different values that must very between convenient limits.

The actual methods do not permit the determination of these angles, but

20

3031'

Fig. 3 The determination of the angles v and v at the peak.

Bul. Inst. Polit. Iai, t. LVI (LX), f. 2, 2010 35 only of the values from the peak of the tooth (Fig. 3). The minimal values (that must have a specified value) are determined on the base of mathematical rela

the tooth is realized (posterior planes, Fig. 4), we

the

le to draw a chart

O. The determination ns are similar with the before precise conditions.

tions, but the real angles' variations not controlled. If the intersection of the tooth with planes parallel with a medial plane of

obtain different values for the angles p and p (the plane Pp - Pp) in the points of intersection between these planes and the cutting edge from the involute flank. The points in which the determination is made can be however dense (from example 0.01 mm), but such frequency is not necessary, because the variation limits and the variation mode can be observed in only some points, and that fact simplify determination operations. The Solid Works compu-ter program, by the facilities that are offered, give directly under the form of a quote the values obtained for the angles determined in these planes. Using a program that permits the drawing of the mentioned planes at determined distances, with a pre established step, becomes possible to obtain the desired values in every point on the edge, and with these values it is possib

Fig. 4 e tooth with paralel planes. The intersection of th

(Fig. 6). Similarly, it is possible to construct normal planes at the cutting edge's tangent in the anterior determined points on

that edge, or orthogonal planes (Fig. 5). Obviously, in these planes are determined the angles n and n, or the angles O and

Fig. 5 Intersectio orthogonal planes. ns with

conditio


2 2.11

3.31

4.27

3.31 3.31 3.31 3.31

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

p

p

p 2 2.11 3.31 4.27

p 3.31 3.31 3.31 3.31

M1 M2 M3 M4

Fig. 6 Variation chart of the angles p and p along the cutting edge on the involute flank of the fellows' cutter.

ions

the Fig. 8 and Fig. 10 are presented in the charts from the Fig. 9 and Fig. 11.

Excepted the presented determinations, that are essential for a good service

of the fellows' cutter, it is possible to determine another angles, e,g. in sect

2

0.94

2.522.24

3.31

2.91

0.95 0.97

0

0.5

1

1.5

2

2.5

3

3.5

n n

n 2 0.94 2.52 2.24

n 3.31 2.91 0.95 0.97

M1 M2 M3 M4

Fig. 7 Variation chart of the angles O, O (noted in the figure with n, n).

with quidam planes, as in Fig. 8, or with front planes (Pf - Pf) as in Fig. 10. In this case too, the angles are directly posted by the Solid Works computer program. The values for the angles for the determinations from


Fig. 8 Sections with certain parallel planes with the intersections' presentation

2.02

2.91

4.44

6.44

3.36 3.38 3.31 3.52

0

1

2

3

4

5

6

7

0

0

0 2.02 2.91 4.44 6.44

0 3.36 3.38 3.31 3.52

M1 M2 M3 M4

We can observe the anomaly of the variation of the normal back rake angle O. A lot of verification proves that the model is correct, so it is to research the real situation.

Fig. 9 The charts of the angles O and O

A proposal for a complete control of cutting tools made on the basis on the getting of a 3D solid model is new and brings the first advantage that it is possible to obtain all the angles searched at any point of the cutting edges or active planes.


Fig. 10 Intersections with frontal planes in different points.

2.32

2.05 2.01 1.93

0.48 0.560.62

0.74

0

0.5

1

1.5

2

2.5

f

f

f 2.32 2.05 2.01 1.93

f 0.48 0.56 0.62 0.74

M1 M2 M3 M4

Fig. 11 Values for the angles f i f in frontal plans Pf - Pf.


4. Conclusion The method is especially useful for complex tools, small, with the active

surfaces and curved cutting edges, to which access control with current instruments is very slowness or impossible and where the definition of theoretical planes control angles is difficult to apply. The other method of obtaining the 3D model through photography has its limits. Further research will develop methodologies for control of complex tools for very large or very small, with curved surfaces, methodologies able to change the angles of the long edges or surfaces with steps as small. Received: March 25, 2010 1"POLITEHNICA" University from Bucharest , Department of Machines and Production Systems e-mail: [email protected] 2S.C. MUNPLAST S.A. e-mail: [email protected] 3"VALAHIA" University from Targoviste e-mail: [email protected]

R E F E R E N C E S . 1. M i n c i u C . , S t r j e s c u E . , .a., Scule achietoare, ndrumar de proiectare.

Editura Tehnic, Bucureti, 1995. 2. S t r j e s c u , E . , Proiectarea sculelor aschietoare, Litografia I.P.Bucureti, l984. 3. E n a c h e , t . , S t r j e s c u , E . , M i n c i u , C . , Metode i programe pentru

proiectarea asistat a sculelor achietoare. Litografia I.P.Bucureti, 1988. 4. S t r a j e s c u E . , P a v l o v O . , Metodologie de control asistat de calculator al

sculelor achietoare pe baza unor metode neconvenionale de obinere a modelelor 3D. Conferina ICEEMS, Braov, 2005.

5. S t r j e s c u E . , P a v l o v O . , D u m i t r u , D . , C ontributions Concerning the Informatic Control of the Cutting Tools, International Conference on Manufacturing Science and Education - MSE Sibiu, 2009.

CONTRIBUII PRIVIND CONTROLUL INFORMATIZAT AL CUITELOR ROAT

(Rezumat)

n lucrare se prezint bazele unei metodologii pentru controlul informatizat al tuturor

elementelor geometrice i constructive ale sculelor achietoare n general, i al cuitelor roat pentru mortezat roi dinate cilindricve n special. Metodologia are la baz obinerea unui model solid, iar acest lucru se poate face fie prin fotografiere, folosindu-se programe potrivite, fie prin scanare 3D, fie n faza de proiectare. Metoda propus permite controlul absolut al tuturor parametrilor geometrici i constructivi, n orice punct i n orice plan, precum i trasarea graficelor de variaie. Se poate imagina o metod prin care un program de proiectare asistat de tipul Solid Concept, parametrizat, s modifice unghiurile sculei pornind de la valoarea admisibil a unui anume unghi ntr-un anume plan.




CONTRIBUTIONS TO THE ELABORATIONS OF A GRAPHICAL METHOD FOR PROFILING OF TOOLS

WHICH GENERATE BY ENVELOPING

I. ALGORITHMS

BY

SILVIU BERBINSCHI, VIRGIL TEODOR, NICOLAE DUMITRACU and NICOLAE OANCEA

Abstract. The generation of the ordered curls profile (surfaces) associated with the centrodes of the rack-gear tool represent an fundamental problem for the profiles reciprocally enveloping associated with a couple of rolling centrodes. The knowing, in principle, of the generating rack-gear allow the construction of the tool and, also, the determination of the axial profile of the worm mill for the ordered curl profiles generation. They are known and used more solutions for the solving of this problem: analytical solutions, based on the fundamentals theorems of gearing; complementary theorems, obtained from the fundamentals theorem; graphical methods based on graphical environments capabilities. In this paper, is proposed an algorithm for the approach of issue of ordered curl profiles based on the CATIA design environment capabilities. It is proposed a general algorithm which allows making applications, ended with the numerical determination of the rack-gear reciprocally enveloping with ordered curl profiles. They are solved profiles known in discrete form, substituted by spline approximation. The method allows drawing the gearing lines as so as the interference trajectories. The obtained results are comparing with results obtained by analytical methods.

Key words: enveloping surfaces, rack-gear tool, graphical design method.

1. Introduction

The profiling of tools which generated by enveloping by the rolling method rack gear tool and gear shaped tool may be make by some methods:

42 Silviu Berbinschi et al - analytical methods, based on fundamental methods of surfaces enwrapping

first Olivier theorem, Gohman theorem, normals method, W i l l i s [1], [2]; - complementary analytical methods minimum distance method, the

substitutive circles family method, the in-plane generating trajectories method [3]-[5];

- graphical-analytical methods [6]; - graphical methods, using the capabilities of CAD software [7]. We mention that the methods proposed and used for the study of

reciprocally enveloping surfaces respect the enveloping fundamental theorem. The proposed solutions leads to comparable results, in most cases

identically, for the crossing profile tools shape, which generated by rolling ordered curls profiles associated with a couple of rolling centrodes.

Literature include multiples applications for various domains as methods of tools profiling, revolution surfaces, for generating helical surfaces [8]; the modelling of the cylindrical surfaces with disk tools [9]; generation of the helical compressors rotors [10].

In this paper, is proposed a method for profiling of the rack-gear tools reciprocally enveloping with ordered curl profiles, based on the capabilities of the CATIA design environment.

2. Generation Kinematics

In principle, the tools profiling determination problem for rack-gear tool

reciprocally enveloping with an ordered curls profile, associated with a circular centrode, assume to respect the kinematics of the generating process, see figure 1.

Fig. 1 Couple of rolling centrodes.

The two rolling centrodes, C1 circle, associated with the profiles ordered curls and C2 straight line, associated with the rack-gear tool, are in rolling movement, so, is respected the condition:


(1) 1rpR = , where is the linear velocity in the translation of C2 centrode;

1rpR the value of velocity in point O1the gearing pole, from C1 centrode, in the rotation movement around z axis;

1 variable angular parameter. In the rotation of C1 centrode the translation movements along the C2

centrode and the rotation around Z axis are evenness. They are defined the reference systems: xyz is the global reference system, with z axis overlapped to the rotation axis

of the C1 centrode; XYZ mobile reference system, initially overlapped to the global reference

system, joined with the ordered curls profile ; mobile reference system, joined with C2 centrode of rack-gear tool,

with axis parallel and of the same sense with the global reference system xyz. The kinematics of the rolling process of the two centrodes, C1 and C2,

tangents in point O1 gearing pole presume that the velocities of points belongs to the two centrodes, temporally situated in point O1, to be equals.

In this way, the global motion of the reference system, joined with centrode C2, is described by the transformation,

(2) x a= + ,

where:

(3) ; x

x yz

= = represent the matrix of the current points in the space , respectively xyz;

(4) 0

rp

aR

=

is the matrix formed with the coordinates of point O1, in the global reference system, with instantaneous velocity in the translation movement of C1 centrode and Rrp the value of circular centrode C1 (rolling radius).

Also, the revolution movement of C1 centrode is described by transformation

44 Silviu Berbinschi et al

(5) ( )1 1Tx Xy Yz Z

=

where XYZ

is the matrix of the current point in space XYZ, and

(6) ( ) ( ) ( )( ) ( )1 1 1 11 1

1 0 00 cos sin0 sin cos

=

is the rotation transformation matrix, around X axis, with angle 1 (counterclockwise rotation).

The assembly of equations (3) and (6), with the respect of rolling condition (1), determine the relative motion,

(7) ( ) ( )( ) ( )1 11 1

1 0 0 00 cos sin0 sin cos rp

XYZ R

=

while the profile, belongs to the profiles ordered curl, associated with the C1 centrode, in form,

(8) ( )( )0

Y uZ u

= with u variable parameter, describe a profiles family in the rack-gear space:

(9) ( )( )( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( )1

1

1 1 1

1 1 1

, 0;

, cos sin

, sin cosrp

rp

u

u Y u Z u R

u Y u Z u R

1;

.

= = +

= +

The enveloping of the profile family (9) represents the rack-gear tools

profile.


Often, the profile (8) may be replaced by the equations of one surface, cylindrical or cylindrical helical,

cm_fasc.2_2010

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