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BULETINUL

INSTITUTULUI

POLITEHNIC

DIN IAŞI

Volumul 62 (66)

Numărul 4

Secția

CONSTRUCŢII DE MAŞINI

2016 Editura POLITEHNIUM

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI PUBLISHED BY

“GHEORGHE ASACHI” TECHNICAL UNIVERSITY OF IAŞI Editorial Office: Bd. D. Mangeron 63, 700050, Iaşi, ROMANIA

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

Editorial Board

President: Dan Caşcaval, Rector of the “Gheorghe Asachi” Technical University of Iaşi

Editor-in-Chief: Maria Carmen Loghin,

Vice-Rector of the “Gheorghe Asachi” Technical University of Iaşi

Honorary Editors of the Bulletin: Alfred Braier,

Mihail Voicu, Corresponding Member of the Romanian Academy,

Carmen Teodosiu

Editors in Chief of the MACHINE CONSTRUCTIONS Section

Radu Ibănescu, Aristotel Popescu

Honorary Editors: Cătălin Gabriel Dumitraş, Gelu Ianuş

Associated Editor: Eugen Axinte

Scientific Board

Nicuşor Amariei, “Gheorghe Asachi” Technical University of Iaşi Dirk Lefeber, Vrije Universiteit Brussels, Belgium

Aristomenis Antoniadis, Technical University of Crete, Greece Dorel Leon, “Gheorghe Asachi” Technical University of Iaşi

Virgil Atanasiu, “Gheorghe Asachi” Technical University of Iaşi James A. Liburdy, Oregon State University, Corvallis, Oregon, USA

Mihai Avram, University “Politehnica” of Bucharest Peter Lorenz, Hochschule für Technik und Wirtschaft, Saarbrücken,

Nicolae Bâlc, Technical University of Cluj-Napoca Germany

Petru Berce, Technical University of Cluj-Napoca José Mendes Machado, University of Minho, Guimarães, Portugal

Viorel Bostan, Technical University of Chişinău, Republic of Moldova Francisco Javier Santos Martin, University of Valladolid, Spain

Benyebka Bou-Saïd, INSA Lyon, France Fabio Miani, University of Udine, Italy

Florin Breabăn, Université d’Artois, France Gheorghe Nagîţ, “Gheorghe Asachi” Technical University of Iaşi

Walter Calles, Hochschule für Technik und Wirtschaft des Saarlandes, Vasile Neculăiasa, “Gheorghe Asachi” Technical University of Iaşi

Saarbrücken, Germany Fernando José Neto da Silva, University of Aveiro, Portugal

Caterina Casavola, Politecnico di Bari, Italy Gheorghe Oancea, Transilvania University of Braşov

Miguel Cavique, Naval Academy, Portugal Dumitru Olaru, “Gheorghe Asachi” Technical University of Iaşi

Francisco Chinesta, École Centrale de Nantes, France Konstantinos Papakostas, Aristotle University of Thessaloniki,

António Gonçalves-Coelho, Universidade Nova de Lisboa, Portugal Greece

Cristophe Colette, Université Libre de Bruxelles, Belgium Miroslav Radovanović, University of Niš, Serbia

Juan Pablo Contreras Samper, University of Cadiz, Spain Manuel San Juan Blanco, University of Valladolid, Spain

Spiridon Creţu, “Gheorghe Asachi” Technical University of Iaşi Loredana Santo, University “Tor Vergata”, Rome, Italy

Pedro Manuel Brito da Silva Girão, Instituto Superior Técnico, Enrico Sciubba, University of Roma 1 “La Sapienza”, Italy

University of Lisbon, Portugal Carol Schnakovszky, “Vasile Alecsandri” University of Bacău

Cristian Vasile Doicin, University “Politehnica” of Bucharest Nicolae Seghedin, “Gheorghe Asachi” Technical University of Iaşi

Valeriu Dulgheru, Technical University of Chişinău, Republic of Filipe Silva, University of Minho, Portugal

Moldova Laurenţiu Slătineanu, “Gheorghe Asachi” Technical University of

Gheorghe Dumitraşcu, “Gheorghe Asachi” Technical University of Iaşi Iaşi

Dan Eliezer, Ben-Gurion University of the Negev, Beersheba, Israel Alexandru Sover, Hochschule Ansbach, University of Applied

Michel Feidt, Université Henri Poincaré Nancy 1, France Sciences, Germany

Cătălin Fetecău, University “Dunărea de Jos” of Galaţi Ezio Spessa, Politecnico di Torino, Italy

Mihai Gafiţanu, “Gheorghe Asachi” Technical University of Iaşi Roberto Teti, University “Federico II”, Naples, Italy

Radu Gaiginschi, “Gheorghe Asachi” Technical University of Iaşi Ana-Maria Trunfio Sfarghiu, Université Claude Bernard Lyon 1,

Bogdan Horbaniuc, “Gheorghe Asachi” Technical University of Iaşi France

Mihăiţă Horodincă, “Gheorghe Asachi” Technical University of Iaşi Suleyman Yaldiz, “Selçuk University”, Konya, Turkey

Soterios Karellas, National Technical University of Athens, Greece Stanisław Zawiślak, University of Bielsko-Biała, Poland

Grzegorz Królczyk, Opole University of Technology, Poland Hans-Bernhard Woyand, Bergische University Wuppertal, Germany

B U L E T I N U L I N S T I T U T U L U I P O L I T E H N I C D I N I A Ş I

B U L L E T I N O F T H E P O L Y T E C H N I C I N S T I T U T E O F I A Ş I Volumul 62 (66), Numărul 4 2016

Secția


Pag.

ANA MARIA BOCĂNEȚ, IRINA COZMÎNCĂ și CRISTIAN CROITORU,

Cercetări experimentale privind componentele forţei de aşchiere la

frezarea frontală simetrică (engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . .

9

MIHAIL AIGNĂTOAIE, Studiu CAD-FEA a influenţei formei CHAMFER

asupra fenomenului de concentrare a tensiunilor într-un sistem de ţevi

ramificate în T (engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

MIHAIL AIGNĂTOAIE, Studiu CAD-FEA a influenţei formei FILLET asupra

fenomenului de concentrare a tensiunilor într-un sistem de ţevi

ramificate în T (engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

DANIEL MĂRGUȚĂ, Planificarea experimentelor la tăierea cu jet de apă a

pieselor din ,,lemn lichid” (engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . .

35

FLORENTINA MOCANU, Calculul momentului încovoietor corespunzător

forţei centrifuge (engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

EMILIAN PĂDURARU și CĂTĂLIN GABRIEL DUMITRAȘ, Conceperea

unui sistem de prehensiune flexibil pentru un braț robotic industrial

(engl., rez. rom.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

DAN SCURTU și DORU CĂLĂRAȘU, Curgerea laminară a fluidului

magnetoreologic printr-un tub de curent cu secțiune circulară (engl.,

rez. rom.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

S U M A R

B U L E T I N U L I N S T I T U T U L U I P O L I T E H N I C D I N I A Ş I

B U L L E T I N O F T H E P O L Y T E C H N I C I N S T I T U T E O F I A Ş I Volume 62 (66), Number 4 2016

Section

MACHINE CONSTRUCTION

Pp.

ANA MARIA BOCĂNEȚ, IRINA COZMÎNCĂ and CRISTIAN CROITORU,

Experimental Researches Regarding Cutting Forces in Symmetrical

Face Milling (English, Romanian summary) . . . . . . . . . . . . . . . . . . . . . .

9

MIHAIL AIGNĂTOAIE, CAD-FEA Study on the Influence of CHAMFER on

Stress Concentration in a Pipe T Shape (English, Romanian

summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

MIHAIL AIGNĂTOAIE, CAD-FEA Study on the Influence of FILLET on

Stress Concentration in a Pipe T Shape (English, Romanian

summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

DANIEL MĂRGUȚĂ, Planning Experiments for Water Jet Cutting of the Parts

Obtained from “Liquid Wood” (English, Romanian summary) . . . . . . .

35

FLORENTINA MOCANU, Calculus of Bending Moment Corresponding to

the Centrifugal Force (English, Romanian summary) . . . . . . . . . . . . . . .

47

EMILIAN PĂDURARU and CĂTĂLIN GABRIEL DUMITRAȘ, Designing a

Flexible Gripping System for an Industrial Robotic Arm (English,

Romanian summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

DAN SCURTU and DORU CĂLĂRAȘU, Laminar Flow of

Magnetorheological Fluid Flowing in Current Pipes (English,

Romanian summary) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

C O N T E N T S

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Publicat de

Universitatea Tehnică „Gheorghe Asachi” din Iaşi

Volumul 62 (66), Numărul 4, 2016

Secţia


EXPERIMENTAL RESEARCHES REGARDING

CUTTING FORCES IN SYMMETRICAL FACE MILLING

BY

ANA MARIA BOCĂNEȚ, IRINA COZMÎNCĂ

and CRISTIAN CROITORU

“Gheorghe Asachi” Technical University of Iaşi,

Faculty of Machine Manufacturing and Industrial Management

Received: November 1, 2016

Accepted for publication: December 23, 2016

Abstract. Knowing the forces values in metal cutting is an essential

requirement due of their connection with the cutting tool design, energy and

tools consumption, vibrations in process, workpiece machinability and accuracy

of the final product. This study presents an experimental investigation of the

cutting forces occurring in symmetrical face milling, taking into account different

working conditions, both in terms of variation of milling specific elements (radial

depth of cut, number of teeth that simultaneously cut, contact angle between cutter

and workpiece) and cutting regime (feed per tooth).

Keywords: symmetrical face milling; analytical models; forces

measurement; forces analysis.

1. Introduction

The large number of theoretical and experimental researches in the field

of face milling shows the importance that this process has within the specific

technologies in machines manufacturing. Theoretical and experimental studies

related to the dynamic of face milling process were intended to evaluate the

cutting forces and moments and the influence that they have on the

technological system stability (Sekulić et al., 2007; Salguero et al., 2013; Zheng

Corresponding author; e-mail: [email protected]

mailto:[email protected]

10 Ana Maria Bocăneț et al.

Minli et al., 2008). Also, the forces in face milling have been extensively used

in the study of several aspects of the cutting process such as the manner that

they could be used for controlling the cutting process, detecting the wear and/or

breakage of the cutting tool and the development of new types of tools and

milling machines (Kuljanic and Sortino, 2005; Korkut et al., 2007; Guzeev and

Pimenov, 2011; Bhattacharyya et al., 2008). The cutting forces developed

during processing and because of them, the quality of the machined surface, are

influenced by a number of factors, including the feed rate, depth and width of

cut, the cutting geometry, hardness of the material being cut, the cutter’s

number of teeth and the relative position between tool and workpiece. Thus,

most analytical models for calculating cutting forces in face milling include

these parameters and also the rotational movement of the cutter (Bhattacharyya

and Sengupta, 2009; Aykut et al., 2007; Sekulić et al., 2007; Budak, 2006;

Cozmîncă, 1995; Kaymakci et al., 2012; Kumar Pradeep Baro et al., 2005;

Yang Yang et al., 2013).

This study is intended to experimentally verify the theoretical models

for the evaluation of cutting force components in symmetrical face milling

which are considering, in addition to the parameters described above, the

specific elements of each variant milling, such as symmetrical full (complete)

and incomplete milling, the number of teeth that simultaneously cut and the

relative position between the cutting teeth and part, such as cut-up and cut-down

milling (Bocăneţ and Cozmîncă, 2014).

2. Methodology of Experimental Researches on Cutting Force’s

Components in Symmetrical Face Milling

The methodology of experimental researches carried out in order to

verify the proposed theoretical models of symmetrical face milling forces is the

same used in a previous study related to verifying the cutting forces in

asymmetrical face milling (Bocăneţ and Cozmîncă, 2015). The universal

milling machine CNC DMU 50 eco and face milling cutter from ZCC-CT

Company, equipped with inserts, type APMT11T3DSR-MM, were used in order

to process the part and the dynamometer Kistler, 9257BA type, was used for

measuring the three components of cutting force. Some experimental

measurements were performed in order to verify the valuation models of forces

in symmetrical face milling, both in cut-up and cut-down milling, for three

different values of feed rate. For both types of milling, namely full and

incomplete, the adopted working regime was the following one: speed n = 505

rpm; cutting velocity (peripheral velocity) vc = 100 m/min; axial cutting depth

ap = 1 mm; feed per tooth f1 = 0.10 mm/tooth; f2 = 0.14 mm/tooth; f3 = 0.18

mm/tooth. The processing variables are the radial depth of cut (ae), the number

of teeth that simultaneously cut (zs) and the contact angle (Ψ) between cutter

and workpiece, so one had the following values: ae = 49 mm, Ψ = 124.5°, zs = 2.5

Bul. Inst. Polit. Iaşi, Vol. 62 (66), Nr. 4, 2016 11

– calculated (Cozmîncă et al., 2010) for incomplete symmetrical face milling,

ae = 63 mm, Ψ = 180°, zs = 4.5 – calculated (Cozmîncă et al., 2010) for

complete (full) face milling. The machining was performed using coolant.

Fig. 1 illustrates some images captured during the experimental tests.

a

b

Fig. 1 – Symmetrical face milling: a ‒ complete (full); b ‒ incomplete.

As in the previous study (Bocăneţ and Cozmîncă, 2015) the positioning

and fastening of the part on dynamometer were made using four screws which

required the construction of four holes, with negative impact on the

measurement of force’s components in milling. Also, between the orientation

and positioning of coordinates systems, namely the orientation of cutting force’s

components from the normal plane to cutter’s axis, according to which the

models for evaluating FZ, FX and FY were developed (Bocăneţ and Cozmîncă,

2014), and respectively, the orientation of dynamometer’s coordinates system

according to which the dynamometer is measuring the force’s components,

there are differences and therefore, in order to correctly appreciate the forces

values, equalization of the two systems is necessary. To experimentally verify


the analytical models for face milling forces evaluation, a set of data was

registered, where the tangential force Fy is corresponding to component FZ, Fx is

the radial force corresponding to component FX and Fz is the axial force

corresponding to component FY in face milling (Bocăneţ and Cozmîncă, 2015).

3. Results Regarding the Cutting Force’s Components

in Symmetrical Face Milling

A preliminary form of registered data is presented in Fig. 2 and the

analysis of the resulted graphic highlights the following:

‒ the time for measuring the forces was 30 seconds;

‒ due to the presence of holes for positioning and fastening the part on

dynamometer, in order to measure the minimum, maximum and mean values of

forces, a period of time from 1 to 4.5 seconds was chosen (depicted in Fig. 3),

when the process is considered to be stabilized;

‒ registrations show the evolution of forces for every cutting in or out of

the insert;

‒ the shape of evolutionary forces diagrams shows the complex nature

of the milling process, since many factors are involved during processing, both

of technological system and of milling process (shocks generated by the entry

and exit of the cutting inserts, appearance and removing the material deposition

on the cutting edge, changes of tool geometry due to wear, chip thickness

variation, etc).

Fig. 2 – Forces variation in incomplete symmetrical cut – down face milling, using

fz1 = 0.1 mm / tooth for a measuring period of time of 30 s.


Some of the results are presented below.

Fig. 3 − Detail on Fig. 2 in the stabilized area of cutting

Cutting conditions: vc = 100 m/min; fz1 = 0.1 mm / tooth; ae = 49 mm;

ap = 1 mm; workpiece material: C 45.

Fig. 4 − Variation of cutting forces in full symmetrical cut-up face milling, feed per

tooth fz1 = 0.14 mm/tooth.

Cutting conditions: vc = 100 m/min; vf2 = 565 mm/min; ae = 63 mm; ap = 1 mm;

workpiece material: C 45.


4. Comparative Analysis of the Forces Analytical Models in Symmetrical

Face Milling and Measurement Results

Furthermore, some comparison charts between the values obtained using

the analytical models for the evaluation of forces in symmetrical face milling

(Matei (Bocăneţ), 2012; Bocăneţ and Cozmîncă, 2014) and those obtained by

measuring, were conducted (Figs. 5-7).

Fig. 5 − Values of tangential component FZ of the force, theoretically and

experimentally determined.

Fig. 6 − Values of radial component FX of the force, theoretically and



Fig. 7 − Values of axial component FY of the force, theoretically and


When calculating the theoretical values of face milling forces, there were

considered the cutting forces acting on an insert, working conditions of the tests

(radial cutting depth ap, feed rate f, cutting velocity vc), geometrical parameters of

the cutter and chips contraction coefficient Cd, both theoretically and


The comparison charts show that the calculated values of forces

components FZ, FX and FY are positioned between the maximum and minimum

experimental values of forces, but because of the multiples factors which may

interfere, in some cases they exceed this limits.

Some possible causes of these differences come from the hypothesis

used for developing the analytical models, such as it was considered a mean

value of the cutting force acting on an insert, a value equal for all the inserts that

were simultaneously in cut and the average value of chip’s thickness was used

(Cozmîncă, 1995; Bocăneț and Cozmîncă, 2014; Bocăneț and Cozmîncă, 2015),

while in practice the chip’s thickness varies along the contact angle.

5. Conclusions

The comparison charts of the values obtained by theoretical calculation

and experimental values obtained for symmetrical face milling force’s

components, show that, in most of the cases, the theoretical values are

positioned on one side or another of the mean experimental value, approaching


to the maximum or minimum values according to the different influences that

occur during processing.

It was shown that this fact appears due to using of an average value for

the force acting on an insert, but also because of using the average value of 1.5

for the exponent “n” of the chip’s contraction coefficient Cd from the

relationship of deformation force.

Since the exponent “n” takes different values for each component of the

force, depending on the variant of milling and feed per tooth, for a proper

appreciation of its value an experimental verification is required. In order to do

this correction it is necessary to carry out a new set of experimental

measurements for face milling using a cutter with a single tooth.

REFERENCES

Aykut Ș., Gölcü M., Semiz S., Ergür H.S., Modeling of Cutting Forces as Function of

Cutting Parameters for Face Milling of Satellite 6 Using an Artificial Neural

Network, Journal of Materials Processing Technology, online at

www.elsevier.com/locate/matdes (2007).

Bhattacharyya P., Sengupta D., Estimation of Tool Wear Based on Adaptive Sensor

Fusion of Force and Power in Face Milling, International Journal of

Production Research, 47, 3, online at http://www.informaworld.com (2009).

Bhattacharyya P. et al., On-Line Tool Condition Monitoring in Face Milling Using

Current and Power Signals, Int. J. Prod. Res., 46, 4, online at

http://www.informaworld.com (2008).

Budak E., Analytical Models for High Performance Milling. Part I: Cutting Forces,

Structural Deformations and Tolerance Integrity, International Journal of

Machine Tools & Manufacture, 46, online at www.sciencedirect.com, 1478-

1488 (2006).

Bocăneţ A.M., Cozmîncă I., Experimental Researches Regarding Cutting Forces in

Asymmetrical Face Milling, Bul. Inst. Polit. Iaşi, s. Construcţii de Maşini, LXI

(LXV), 4, 11-20 (2015).

Bocăneţ A.M., Cozmîncă M., Theoretical Contributions to the Developement of New

Valuation Models of Face Milling Forces, Bul. Inst. Polit. Iaşi, s. Construcţii

de Maşini, LX (LXIV), 1, 17-24 (2014).

Cozmîncă M., Cutting Basis (in Romanian), Publishing House “Gheorghe Asachi”, Iaşi,

1995.

Cozmîncă M., Poenaru S., Voicu C., About the Cutting Forces at Face Milling, Bul.

Inst. Polit. Iaşi, s. Construcţii de Maşini, LVI (LX), 1, 13-18 (2010).

Guzeev V.I., Pimenov D. Yu., Cutting Force in Face Milling with Tool Wear, ISSN

1068_798X, Russian Engineering Research, 31, 10, online at

www.sciencedirect.com, 989-993 (2011).

Kaymakci M. et al., Unified Cutting Force Model for Turning, Boring, Drilling and

Milling Operations, International Journal of Machine Tools & Manufacture,

54-55, online at www.sciencedirect.com, 34-45 (2012).


Korkut I. et al., The Influence of Feed Rate and Cutting Speed on the Cutting Forces,

Surface Roughness and Tool–Chip Contact Length During Face Milling,

Materials and Design, online at www.elsevier.com/locate/matdes (2007).

Kuljanic E., Sortino M., Tool Wear Estimation Method – TWEM Using Cutting Forces

in Face Milling, International Journal of Machine Tools and Manufacture,

online at www.sciencedirect.com (2005).

Kumar Pradeep Baro et al., Modeling of Cutting Forces in a Face-Milling Operation

with Self-Propelled Round Insert Milling Cutter, International Journal of

Machine Tools & Manufacture, online at www.sciencedirect.com (2005).

Matei (Bocăneţ) A.M., Theoretical and Experimental Contributions to Mathematical

Modeling of Cutting Forces in Face Milling (in Romanian), Ph. D. Diss.,

“Gheorghe Asachi” Technical University of Iaşi (2012).

Sekulić M. et al., The Influence of Machining Conditions Change of Cutting Forces in

Face Milling, PSU-UNS International Conference on Engineering and

Environment – ICEE, online at www.sciencedirect.com (2007).

Salguero J., Batista M., Calamaz M., Girot F., Marcos M., Cutting Forces Parametric

Model for the Dry High Speed Contour Milling of Aerospace Aluminium

Alloys, Procedia Engineering 63, online at www.sciencedirect.com, 735-742

(2013).

Yang Yang, Xinyu Li, Liang Gao,, Xinyu Shao, A New Approach for Predicting and

Collaborative Evaluating the Cutting Force in Face Milling Based on Gene

Expression Programming, Journal of Network and Computer Applications,

online at www.sciencedirect.com, 1540-1550 (2013)

Zheng Minli et al., Research on Dynamic Cutting Performance of High Speed Face

Milling Cutter, Key Engineering Materials, Vols. 375-376, online at

www.scientific.net (2008).

CERCETĂRI EXPERIMENTALE PRIVIND COMPONENTELE FORŢEI DE

AŞCHIERE LA FREZAREA FRONTALĂ SIMETRICĂ

(Rezumat)

Studiile teoretice și experimentale legate de dinamica procesului de frezare

frontală urmăresc evaluarea forțelor și momentelor de așchiere, influența pe care o au

acestea asupra stabilității sistemului tehnologic. Forțele la frezarea frontală au fost

intens utilizate și în studierea altor aspecte ale procesului de așchiere așa cum sunt

modul în care pot fi utilizate pentru controlul și reglarea procesului de așchiere,

detectarea uzurii și/sau ruperii sculei așchietoare, dezvoltarea unor noi tipuri

constructive de scule așchietoare și mașini de frezat.

Din diagramele de comparaţie între valorile obţinute prin calcul teoretic cu

ajutorul modelelor analitice şi valorile experimentale obţinute pentru componentele

forţei la frezarea frontal simetrică, se poate observa că, în majoritatea cazurilor, valorile

teoretice se situează de o parte şi de alta a valorilor medii experimentale, apropiindu-se

de valorile maxim sau minime în funcţie de diferitele influenţe care apar în timpul

prelucrărilor.


Publicat de



Secţia


CAD-FEA STUDY ON THE INFLUENCE OF CHAMFER

ON STRESS CONCENTRATION IN A PIPE T SHAPE

BY

MIHAIL AIGNĂTOAIE


Faculty of Mechanical Engineering,

Department of Mechanical Engineering, Mechatronics and Robotics



Abstract. Piping systems are basic components of many mechanical

systems. They frequently include pipe T shapes. The paper presents a CAD

(Computer Aided Design) and FEA (Finite Element Analysis) study of such an

element. The CAD model of the pipe T shape is generated automatically by use

of Salome-Meca pre/post processor (EDF-France). The FEA processor Code-

Aster, included in Salome-Meca, evaluates the stress concentration. The paper

studies a possibility of reduction of the stress concentration. The initial basic

model was used to generate 4 different additional study cases. In each and every

additional case a different CHAMFER was added on the initial CAD model, on

the external edges generated by the intersection of the main pipe with the

incident pipe. A comparison of the von Mises stress distribution is made in order

to analyze the evolution of the stress concentration in the studied models.

Keywords: FEA; Salome-Meca; Stress concentration; CHAMFER; Pipe T Shape.

1. Introduction

Many practical applications in Mechanical engineering include pressure

vessels and piping systems. Their theoretical design is based on analytical


20 Mihail Aignătoaie

formulas from the theory of thin-walled vessels or thick-walled vessels (Boresi,

et al., 2003). There are also methods using specific codes, (Moss, 2004), based

on ASME Code, Section VIII, Division 1. In this case the design follows

specific rules and does not require a detailed evaluation of all stresses.

Frequently the piping systems have complicated shapes. For a limited number

of cases, the literature, (Young et al., 2002), recommends specific formulas for

the correct evaluation of stresses in the vicinity of the stress concentrators: the

areas with rapid geometrical changes. These cases do not include the

intersection between two pipes with rectangular axes. For such situations the

most popular and convenient recommended solution is FEA. The paper presents

a CAD and FEA study for stress concentration reduction in a T-shape pipe.

Fig. 1 − The initial full CAD model.

2. The CAD-FEA Study

The CAD model, Fig. 1, was automatically generated by use of

SALOME-MECA (EDF, France), as part of the Open-source package

CAELINUX-2013, (*** CAELINUX, 2016). SALOME-MECA was used as

CAD editor for defining the geometry of the created models and also as pre/post

processor for the FEA study.

The T shape pipe was created with the following specifications, defined

within SALOME-MECA:

R1 ‒ Radius of the main T-shape pipe = 80 mm

W1 ‒ Thickness of the main T-shape pipe = 20 mm

L1 ‒ Length of the main T-shape pipe = 960 mm

R2 ‒ Radius of the incident T-shape pipe = 50 mm

W2 ‒ Thickness of the incident T-shape pipe = 20 mm

L2 ‒ Length of the incident T-shape pipe = 960 mm.


Fig. 2 − The definition of the simplified CAD model.

The initial CAD model, Fig. 1, has two symmetry planes (xOz and

yOz), Fig. 2. For efficiency reasons of the FEA study it is more convenient to

use a simplified model that is a quarter of the initial one, Fig. 2.

Fig. 3 − Mesh details of the FEA model (case study 1: no CHAMFER).

Fig. 4 − Mesh details of the FEA model (case study 3: H = 30; W = 15).


The area in the vicinity of the junction of the main pipe and the incident

pipe, due to the rapid changes in form, represents a stress concentrator. In order

to study the possibility of reducing the stress concentration four options of

CHAMFER were considered. Salome_Meca CAD editor can automatically

generate for Pipe T-Shape CHAMFERS defined by the parameters H, and W

defined as:

H ‒ Height of the chamfer along the incident pipe.

W ‒ Width of the chamfer along the main pipe.

The CHAMFER options were applied on the exterior edge resulted

from the intersection from the two pipes. The additional four study-cases and

the corresponding values of the H and W parameters of the CHAMFER are

indicated in Table 1 and Table 2.



The boundary conditions for the symmetry planes implies free Degrees

Of Freedom, DOFs within each and every symmetry plane and blocked DOFs

normal to these planes. The basic meshing parameters for the studied models are


presented in the Table 1. The load of the FEA model is a pressure p = 10 MPa,

uniformly distributed on the interior faces of the T shape pipes.

Table 1

Basic Parameters of the FEA Study

Study

case

CHAMFER

HxW [mm]

Finite Elements TETRA10

[Quadratic tetrahedrons]

Nodes DOFs

1 No CHAMFER 136567 237371 740289

2 20x10 136993 238126 742476

3 30x15 138279 239947 748141

4 40x20 143528 247899 772167

5 60x30 144332 249087 776285

Fig. 7 − Details of σvon Mises distribution (case study 1: no CHAMFER).

Fig. 8 − Details of σvon Mises distribution (case study 2: H = 20; W = 10).


Details of some meshed models are presented in Figs. 3-6. Figs. 7-11

show the distribution of the σvon Mises stresses in practically all the studied test-

cases. Table 2 indicates σvon Mises stresses versus CHAMFERs used in the study.

Table 2

Maximum Value of the von Mises Stresses in Stress Concentration Area

Study case CHAMFER

HxW [mm]

σvon Mises

[MPa]

1 No CHAMFER 215.665

2 H=20; W=10 210.205

3 H=30; W=15 205.700

4 H=40; W=20 199.639

5 H=60; W=30 185.819

3. Discussions and Conclusions

‒ The adopted values of the L1/L2 parameters (the lengths for

main/incident pipes) were sufficient large in order to avoid the influence of the

boundary conditions applied at the end of the pipes on the stress concentration

area, Figs. 7 and 8.

‒ The maximum stress concentration (evaluated by the σvon Mises stress)

produces in all cases on the interior edge resulted from the intersection of the

main and incident pipe, closer to the longitudinal symmetry plane xOz, Fig. 2.

‒ According to Table 2 σvon Mises was reduced in case study 5 with 13.83%

by comparison with the initial, no CHAMFER case.

The use of CHAMFER might be an efficient solution for reducing the

level of stress concentration.

The best decision should probably consider manufacturing costs versus

the imposed safety conditions.

‒ Future studies could be extended to other solutions (classical or

modern) for modifying the shape of the edges in the stress concentration area.

REFERENCES

Boresi Arthur P., Schmidt Richard J., Advanced Mechanics of Materials, 4th Ed., John

Wiley & Sons, Inc., Hoboken, 389-399, 502-542, 2003.

Moss Dennis R., Pressure Vessel Design Manual: Illustrated Procedures for Solving

Major Pressure, 3rd Ed., Gulf Professional Publishing, Burlington, USA, 1-7,

255, 2004. Young Warren C., Budynas Richard G., Roark’s Formulas for Stress and Strain, 7th

Ed., McGraw-Hill, New York, 73-79, 553-688, 771-797, 2002.

**

* CAELINUX, www.caelinux.com, accessed 1.01.2016.


STUDIU CAD-FEA A INFLUENŢEI FORMEI CHAMFER ASUPRA

FENOMENULUI DE CONCENTRARE A TENSIUNILOR

ÎNTR-UN SISTEM DE ŢEVI RAMIFICATE ÎN T

(Rezumat)

Sistemele de conducte sunt o componentă de bază pentru multe sisteme

mecanice. În mod frecvent sunt folosite ţevi ramificate în T. Lucrarea prezintă un studiu

Computer Aided Design, CAD- Finite Element Analisis, FEA a unui astfel de element.

Modelul CAD a ţevii ramificate în T este generat automat cu ajutorul Salome-Meca,

pre/post processor dezvoltat de EDF, Franţa. Evaluarea stării de tensiune a fost realizată

cu ajutorul Code-Aster, processor FEA inclus în pachetul Salome-Meca. Lucrarea

studiază o posibilitate de reducere a fenomenului de concentrare a tensiunilor. Modelul

de bază iniţial a fost utilizat pentru a genera 4 cazuri de studiu suplimentare. În fiecare

din aceste cazuri suplimentare, pe modelul iniţial CAD, pe muchiile exterioare rezultate

din intersecţia dintre ţeava principală şi ţeava incidentă, s-au adăugat diferite valori

pentru forma CHAMFER. Este realizată o comparaţie a valorii maxime a tensiunilor

von Mises în toate modelele studiate, pentru a analiza evoluţia fenomenului de

concentrare a tensiunilor.


Publicat de



Secţia


CAD-FEA STUDY ON THE INFLUENCE OF FILLET

ON STRESS CONCENTRATION IN A PIPE T SHAPE

BY

MIHAIL AIGNĂTOAIE


Faculty of Mechanical Engineering,




Abstract. Many mechanical systems include piping systems using frequently

pipe T shapes, which represent stress concentration areas. The paper analyzes a

possibility to reduce the stress concentration by use of the FILLET shape. The

study was performed by use of Salome-Meca (EDF France) under Linux Xubuntu,

used as CAD editor and also as pre/post processor for the FEA study. FEA

processing was performed by use of Code-Aster, included in Salome-Meca.

Salome-Meca has generated automatically the CAD model of a pipe T shape as a

basic initial model. 8 alternative study cases were created. In each and every case a

FILLET, varying within 5-40 mm, was added on the external edge resulted by the

intersection of the main pipe with the incident pipe. A comparison between all the

nine study cases is made considering the distribution of the von Mises stresses in

order to analyze the stress concentration evolution.

Keywords: FEA; Salome-Meca; Stress concentration; FILLET; Pipe T Shape.

1. Introduction

Practical applications in the field of Mechanical engineering often

include complex pressure vessels and piping systems. Their classical design is



based on analytical formulas known from the theory of thin-walled vessels or

thick-walled vessels (Boresi et al., 2003). The literature also presents practical

methods using specific codes, (Moss, 2004), based on ASME Code, Section

VIII, Division 1. Such a design procedure follows specific rules and does not

implies a detailed evaluation for all stresses. Piping systems might have

occasionally complicated shapes. For a rather limited number of cases, there

were developed, (Young et al., 2002), specific formulas for the correct

evaluation of stresses in the vicinity of the areas with a significant geometrical

changes also known as stress concentrators. None of these cases include the

intersection between pipes with rectangular axes. Usually such problems could

be studied by use of Finite Element Analysis, FEA. The paper presents a

Computer Aided Design, CAD and FEA study on the possibility of stress

concentration reduction in a T-shape pipe by use of the FILLET shape.

Fig. 1 − The initial CAD model: full model (left) and simplified model (right).

2. The CAD-FEA Study

The study was performed by use of the open-source system

CAELINUX-2013 (*** CAELINUX, 2016) developed under Xubuntu. This

package includes Salome-Meca (EDF, France), a CAD editor and pre/post

processor, able to automatically define a T shape pipe. The initial model was

created with the specifications defined within SALOME-MECA:

R1 ‒ Radius of the main T-shape pipe = 80 mm

W1 ‒ Thickness of the main T-shape pipe = 20 mm

L1 ‒ Length of the main T-shape pipe = 960 mm

R2 ‒ Radius of the incident T-shape pipe = 50 mm

W2 ‒ Thickness of the incident T-shape pipe = 20 mm

L2 ‒ Length of the incident T-shape pipe = 960 mm.


This is considered the “case study 1”, or “no FILLET”, a reference

model, Fig. 1, (left). The full model has two symmetry planes (xOz) and (yOz).

For an efficient use of the hardware resources during FEA processing,

the FEA study uses a simplified model, Fig. 1, (right) which represents a quarter

of the initial one.

Table 1

Basic Parameters of the FEA Study

Study

case

FILLET

R [mm]

Finite Elements, TETRA10

[Quadratic tetrahedrons]

Nodes DOFs

1 No FILLET 136567 237371 740289

2 5 136111 236715 737913

3 10 136285 236991 739053

4 15 136162 236755 738545

5 20 135605 235872 735546

6 25 136306 236792 738332

7 30 136163 236575 738015

8 35 137219 238290 743426

9 40 138403 239941 748069

Fig. 2 − Mesh details of the FEA model (case study 1: no FILLET).

Fig. 3 − Mesh details of the FEA model (case study 4: R = 15mm).


The geometry resulted from the intersection between the main pipe and

the incident pipe is very complex and could be considered a stress concentrator.

The study analysed the possibility of reducing the stress concentration,

considering eight additional study-cases, by use of the FILLET shape option.

On the initial CAD model, “case-study 1”, there were applied FILLETS, within

Salome-Meca, in the range 5-40 mm on the exterior edge generated by the

intersection between the main pipe and the incident pipe. The corresponding

study-cases and values of FILLETS are described in Table 1 and Table 2.



The boundary conditions for the simplified FEA model implies free

Degrees Of Freedom, DOFs within each and every symmetry plane and blocked

DOFs normal to these planes. The most important meshing parameters for all


the studied models are presented in the Table 1. The FEA model was loaded

with a pressure p = 10 MPa, uniformly distributed on all the interior faces of the

T shape pipes.

Fig. 6 − Details of σvon Mises distribution (case study 2: R = 5).




Table 2

Maximum Value of the von Mises Stresses in Stress Concentration Area

Study case FILLET

R [mm]

σvon Mises

[MPa]

1 No FILLET 215.665

2 5 215.472

3 10 214.876

4 15 214.189

5 20 213.264

6 25 212.417

7 30 211.329

8 35 210.142

9 40 208.786

Details of some selected meshed models are presented in Figs. 2-5.

Figs. 6-10, show the distribution of the σvon Mises stresses in some of the studied

test-cases. Table 2 compares the maximal values for σvon Mises stresses in the

stress concentration area versus FILLETs used in test case-studies 1-9.

3. Discussions and Conclusions

‒ The values for the L1/L2 parameters (the lengths for main/incident pipes)

were sufficient large in order to avoid the influence of the boundary conditions

applied at the end of the pipes on the stress concentration area, Figs. 6-10.


‒ The maximum stress concentration was evaluated by use of σvon Mises

stress. The maximum values, in all cases, were observed on the interior edge

resulted from the intersection of the main and incident pipe, within the area

closer to the longitudinal symmetry plane xOz.

‒ According to Table 2 σvon Mises was reduced in case study 9 with 3.18%

by comparison with the initial, no FILLET case.

The use of FILLET shape is probably not a very convenient solution for

reducing the level of stress concentration. The manufacturing costs for generating

such surfaces might also not be an advantage for adopting this solution.

‒ Future studies could be extended to other possibilities (classical or

modern) for improving the shape of the edges in the stress concentration area.

REFERENCES

Boresi Arthur P., Schmidt Richard J., Advanced Mechanics of Materials, 4th Ed., John

Wiley & Sons, Inc., Hoboken, 389-399, 502-542, 2003.

Moss Dennis R., Pressure Vessel Design Manual: Illustrated Procedures for Solving

Major Pressure, 3rd Ed., Gulf Professional Publishing, Burlington, USA, 1-7,

255, 2004. Young Warren C., Budynas Richard G., Roark’s Formulas for Stress and Strain, 7th

Ed., McGraw-Hill, New York, 73-79, 553-688, 771-797, 2002.

**

* CAELINUX, www.caelinux.com, accessed 1.01.2016.

STUDIU CAD-FEA A INFLUENŢEI FORMEI FILLET

ASUPRA FENOMENULUI DE CONCENTRARE A TENSIUNILOR

ÎNTR-UN SISTEM DE ŢEVI RAMIFICATE ÎN T

(Rezumat)

Multe sisteme mecanice includ reţele de conducte care folosesc frecvent ţevi

ramificate în T, care reprezintǎ zone de concentrare a tensiunilor. Lucrarea analizeazǎ

posibilitatea de a reduce fenomenul de concentrare a tensiunilor prin utilizarea formei

FILLET. Studiul a fost realizat cu ajutorul pachetului Salome-Meca (EDF Franţa) sub

Linux Xubuntu, utilizat ca editor CAD dar şi ca pre/post processor pentru studiul FEA.

Procesarea FEA a fost realizatǎ cu ajutorul programului Code-Aster, inclus în Salome-

Meca. Modelul CAD al unei ţevi ramificate în T a fost generat automat cu ajutorul

Salome-Meca. Au fost considerate 8 cazuri de studiu, ca opţiuni alternative pentru

reducerea fenomenului de concentrare a tensiunilor. În fiecare din aceste cazuri pe

muchiile exterioare rezultate din intersecţia ţevii principale cu ţeava incidentǎ s-a aplicat

opţiunea FILLET, valoarea acesteia variind în domeniul 5-40 mm. Este prezentatǎ o

comparaţie între valorile maxime a distribuţiei tensiunilor von Mises pentru toate

cazurile studiate, pentru a analiza evoluţia fenomenului de concentrare a tensiunilor.


Publicat de



Secţia


PLANNING EXPERIMENTS FOR

WATER JET CUTTING OF THE PARTS OBTAINED FROM

“LIQUID WOOD”

BY

DANIEL MĂRGUȚĂ


Faculty of Machine Manufacturing and Industrial Engineering



Abstract. In the context of the technological developments of the last

decades the scientific community and the world economic reality required the

development and optimization of new processes and technologies that enable the

sustainable production of recyclable modern materials, biocompatible and

biodegradable from renewable natural resources. One of these resources is

certainly the vegetable material such as lignin. As a result of increasing demand

for biodegradable materials, it has developed a new material with the trade name

“liquid wood” (100% biodegradable), by a team of German researchers

(Technical Institute of Chemistry of Fraunhofer with the company Tecnaro

GmbH). This material meets all the above conditions and is consistent with

chemistry and “green” engineering also. “Liquid wood” can be found in three

different forms: “Liquid Wood” named ARBOFORM®, wood with plastic

composite named ARBOBLEND®, wood with composed biopolymer named

ARBOFILL® (Nagele et al., 2014). The paper aims planning experiments using

the Taguchi method for water jet cutting of the pieces obtained by injection from

liquid wood.

Keywords: liquid wood; water jet cutting; Taguchi method; plastic

injection; Quality of the cutting surface.


36 Daniel Mărguță

1. Introduction

The main challenges in obtaining and industrial conversion for

materials from bio resources are durability, sustainability, compatibility and

accessibility to such new material. Environmental integrity and social

equilibrium is attained when an enduring developments happened and this meet

the basic human needs (Nagele et al., 2014; Shah et al., 2008).

“Liquid wood” is a thermoplastic material of high quality, that can be

processed like any plastic (injection moulding, extrusion, calendering, blow

moulding, thermoforming or pressing to obtain semi-finished products, sheets,

films or profiles), non-polluting the air and does not affect the human health.

This material decays (breaks down) in water, humus and carbon dioxide, as well

as the natural wood, which makes it more eco-friendly than plastics materials

which by combustion releases a lot of toxic gases (Shah et al., 2008; Eggins and

Oxley, 2001). Also, since lignin is a residue - product of paper industry can be

used from this source and thus is not necessary to cut other trees to get this

natural material.

Considering the special properties of “liquid wood” (mechanical,

physical, electrical, structural, thermal) using of this type of material has

expanded in many fields, successfully substituting the conventional plastic

materials. Thus, we find using this material in automotive industry, construction,

electronics, large consumer goods and others (http://www.tecnaro.de). In recent

years they developed some research on the behaviour of liquid wood (Nedelcu et

al., 2016; Nedelcu et al., 2013a; Nedelcu et al., 2013b; Nedelcu et al., 2015a;

Nedelcu et al., 2015b; Constantin, et al., 2015; Plăvănescu, 2014) but lacks

research on the processing of liquid wooden parts.

Water jet cutting is, undoubtedly, the most spectacular and modern cutting

process. This technology, included among unconventional technologies, is less

used in our country and as a result, researches in this area are relatively modest.

This technology relies on the use of concentrated energy of a high

pressure water jet or a water jet with abrasive particles and allows machining of

every contour on one machine at any surface quality requirements.

Water jet cutting machines is a tool that achieves high precision:

0.01mm. The maximum size of the material is cut up to 300x1500x200 mm.

Water jet cutting technology is the latest technology, enjoying the

advantages that ensure the needs of the most demanding customers: excellent

quality of cut surface, the possibility of cutting the three-dimensional shapes

and lack of deformations (Hashish, 2002; http://www.grafex.ro).

This paper summarizes the process of issues implementation of water

jet machining for liquid wood parts, presenting considerations on technological

parameters and economic issues depending on the type and the thickness of the

cutting material.


2. The Principle of Processing

Processing principle is based on the particular mode of behaviour of

materials under stress from shock. In these situations it is essential that strikes at

high-speed body another body. Water is sent, in this case, the material at high

speed and it the moment of impact, a material becomes “stiff” more “tough”

than the material to which it is sent and can thus produce penetration (Fig. 1,

Mistodie et al., 2007).

Fig. 1 ‒ Working principle of water jet cutting process.

Compared to laser cutting, can be seen that the cuts with water jet are

made from two to three times wider, but still narrow and especially with a

constant width. As a result, scheduling the numerical control equipment with a

correction radius equal to half width of the cut, can be achieve very precise

contours.

The basic elements of a water jet cutting machines are (Fig. 2): the

water jet cutting machines with CNC command, the cutting head, control panel,

recirculation water reservoir; high-pressure pump; abrasive supply hopper;

drying facility for abrasive; spent abrasive collector.

Cutting wear

Deformation wear

Striated surface

Smoth

surface


Fig. 2 ‒ The components of the water jet cutting machine.

The experimental results will be made on either a water jet cutting

machine produced by the American company OMAX Corporation as shown in

Fig. 3.

Fig. 3 ‒ Water jet cutting machine MAXIEM 2030.

The equipment contains three main parts of operation: the MAXIEM

table of the machine with: Z, Y and Z system of axes; nozzle and abrasive

recovery tank system and cutting table surface; control bench with monitor,

keyboard, mouse, USB port and Soft Basic Intelli-MAX; MAXIEM pump

group: with high-pressure pump and load pump.

The cutting head (Fig. 4, Mistodie et al., 2007) for abrasive water jet is

more complex from construction point of view, using materials such as ruby,

sapphire and diamond in its construction. Sapphire is the most often used in

pure water jet cutting, because of his low price (15-30) $ lasting life of 50-100 h.

For abrasive water jet cutting is used Ruby, this having the same lasting life but


higher price, and Diamond that has a lifetime of 800-2000 h and a price of 20

times higher than Sapphire, so it can by used intensively for 24 h. The cutting

headwear depends on the work mode and also on the quality of water and

abrasive materials. For this reasons it was complex surveyed to establish the

correlations between all involved factors. The abrasive used is sand, tough and

very fine grain.

3. Quality of the Surfaces Obtained by

Abrasive Water Jet Cutting

The surfaces quality processed with this technological process is given

by several factors as: material thickness; physico-chemical properties and in-

process machine parameters (pressure, cutting speed, range correction, the

technical condition of equipment and special nozzle).

Generally, by using this method are obtained very good quality of the

cutting surface in comparison with the other cutting methods. A very important

aspect is that the taper of the cutting area, how relates to the inclination at edges

of the material obtain during the water jet or abrasive water jet cutting process.

Because this method naturally occurring erodes the processed material, leads to

the appearance of a taper in the cutting area, because the peaks of the material

are exposed to the water jet for different periods of time.

There are different types of taper from cutting shown in Fig. 5,

(Mistodie et al., 2007).

Fig. 4 ‒ The cutting head.


a

b

c

d

Fig. 5 ‒ Different Types of jet. The quality of the cut surface.

Tapered V shape (Fig. 5a), occurs where the tip of the cut is wider in

the jet penetration area than in the base of the material. This is happened when

the jet spending enough time in an area to erode the material more than the base.

The jet tends to erode the margins.

The inverse conical shape (Fig. 5b), occurs where the tip of the cut is

narrower than the base. This tends to happen with soft materials when the

material is quickly eroded or when cutting is very slow.

Tapered barrel shape (Fig. 5c), result when the middle of the cut is

wider than the top or bottom. This form tends to occur in very thick materials.

Tapered diamond or trapezoidal shape (Fig. 5d), is actually tapered V

which was tilted because the nozzle is not at right angles to the material. This

conical shape is actually very small, very little is visible to the naked eye. Its

occurrence is by increasing cutting speed or in the case of thin materials by

stacking them.

All the five qualities obtained by water jet cutting are presented in Table 1,

(Mistodie et al., 2007): Q5, it is the highest-quality, the piece is smooth, ribbed

with great accuracy; Q4 is a very good quality with very fine striations; Q3, is a

good quality, but streaking appear at the bottom; Q2, is a poor quality that


accentuates the ribbed bottom, the exit jet area; Q1, poor quality, high ribbed

over the entire cutting.

Table 1

Quality Classes of Surfaces

Material

thickness Inclination Deviations from the straight line

Q5 Q3 Q5 Q3

0.12 0.002 0.005 +/-0.003 +/-0.005

0.25 0.0035 0.0075 +/-0.005 +/-0.005

0.5 0.003 0.01 +/-0.007 +/-0.005

0.75 0.0035 0.012 +/-0.010 +/-0.020

1 0.004 0.014 +/-0.015 +/-0.030

1.5 0.006 0.016 +/-0.020 +/-0.040

2 0.008 0.018 +/-0.025 +/-0.045

3 0.01 0.02 +/-0.030 +/-0.050

It follows from the presented show that the cut surface quality is

variable depending on the chosen cutting regime. In terms of industrial use,

state of wear of the nozzles should be closely monitored and observed their

lifetimes. We intend in the future to investigate how wear changes the shape of

the water jet and how this affects the quality of the cut surface.

This study involves shooting ultrafast the abrasive jet, while monitoring

the operating parameters.

In this sense we use modern equipment of shooting at high-speed

synchronous for measurement of parameter involved in the cutting process.

4. General Aspects Looking at

Planning Experiments

Optimizing cutting regime parameters is very important to get a quality-

cost report as good. This is done taking into consideration the most about

significant factors how influencing the cutting process. Optimisation is making

so that the surface quality to be the best in terms of high cutting speeds, suitable

thickness of parts and materials and obtain a minimum cutting widths. Analysis

of the results is done by statistical methods or plans experiences. The main

parameters that can influence the process of abrasive water jet cutting are

presented in Fig. 6 (Patel et al., 2015).


Fig. 6 ‒ Process parameters that can influence the abrasive water jet cutting.

The process parameters include the hydraulic parameters related to the

abrasive, mixture of water and abrasive for the quality of the cut. The

parameters that must be highlight correlated are: water jet pressure; cutting

speed; abrasive flow; the particle size of the abrasive; abrasive nature; the

mixing room parameters and the number of passes.

In the experimental research will consider the following input

parameters: advance (mm/min); pressure (bar) and abrasive flow rate (g/min)

and next, as output parameters: roughness; depth and speed of material removal.

During the tests is considered one variable at a time, while other variables are

kept fixed. It can be study these issues on the output parameters: speed crossing

effect; jet pressure effect; abrasive flow effect and stand-off distance effect. The

values of some influence factors are presented in Table 2.

To reduce the number of experimental determinations, needed for

verification, and rapid and accurate interpretation of the results of a theoretical

model, it has resorted to methods of planning the experiments.


Table 2

Values of Factors Influence

Coded

values

Water

pressure

[bar]

Abrasive

Flow

[g/min]

Cutting

speed

[mm/min]

Distance

nozzle – material

[mm]

1 2000 60 500 1.0

2 2500 100 1000 1.5

3 3000 150 1500 2.0

4 3500 200 2000 2.5

5 4000 250 2500 3.0

In the experimental research will be used Taguchi method. The method

is well known and used mainly having the advantage of providing the best

accuracy using a reduced number of experimental tests. The experimental plan

is presented in Table 3 type Taguchi L27 (313

) for a process expressed by an

equation defined by Eq. (1):

Y=M+A+B+C+D+AB+AC+AD+BC+BD+CD (1)

Table 3

Experimentation Plan

Crt.

No. Factors Materials tested

No.

attempt

s 1 2 3 4 5 4x5=20

1 Water jet pressure, [bar] 2000 2500 3000 3500 4000 A

2 Abrasive flow, [g/min] 60 100 150 200 250 B

3 Cutting speed, [mm/min] 500 1000 1500 2000 2500 C

4 Distance nozzle –

material, [mm] 1.0 1.5 2.0 2.5 3.0 D

Total attempts 80

Taguchi method requires also the checking of orthogonality and the

number of freedom degrees and finis with assigning independent factors columns.

5. Conclusion

The method of using water jet cutting allows a very good quality of the

cutting surface than other cutting processes. In the process, parameters are

interrelated and should highlight the pressure jet of water; cutting speed;

abrasive flow and the distance nozzle – material, factors that will be considered

in the plan experimental propose in the paper. It will be studied both

independent factors influences and interactions of these factors on roughness,

depth of cut and on the rate of material removal.


REFERENCES

Constantin C., Plăvănescu S., Nedelcu D., Impact Comparative Study of Phone

Carcasses Behavior by FEM, IOP Conf. Series: Materials Science and

Engineering, 87, pp. 012100 (2015).

Eggins H.O.W., Oxley T.A., International Biodeterioration and Biodegradation, 48, pp.

12 (2001).

Hashish M., Abrasive-Waterjet (AWJ) Studies, 16th International Conference on Water

Jetting, Aix-en-Provence, France, 16-18 October, 2002.

Mistodie L., Ghiță E., Mircea O, Consideratii tehnico-economice la tăierea cu jet de

apă abraziv, Proceedings of Tehnologii inovative pentru îmbinarea

materialelor avansate, pp. 1-8 (2007).

Nagele H., Pfitzer J., Ziegler L., Inone-Kauffmann E.R., Eckl W., Eisenreich N., Lignin

Matrix Composites from Natural Resources - ARBOFORM®

, Bio-Based

Plastics: Materials and Applications, First Edition. Edited by Stephan Kabasci,

John Wiley & Sons. Ltd. Published 2014 by John Wiley & Sons, Ltd. (2014).

Nedelcu D., Ciprian Ciofu, Nicoleta Monica Lohan, Microindentation and Differential

Scanning Calorimetry of “Liquid Wood”, Composites Part B: Engineering, 55,

11-15 (2013a).

Nedelcu D., Investigation on Microstructure and Mechanical Properties of Samples

Obtained by Injection from Arbofill, Composites Part B: Engineering, 47, 126-

129 (2013b).

Nedelcu D., S. Plavanescu and V. Paunoiu, Study of microstructure and mechanical

properties of injection molded Arboform parts, Indian Journal of Engineering

& Material Processing, 22, 534-540, (2015a).

Nedelcu D., L. Santo, A. Santos and S. Plavanescu, Mechanical Behaviour Evaluation

of Arboform Material Samples by Bending Deflection Test, Materiale Plastice,

52, 4, 423-426 (2015b).

Nedelcu D., Lohan N.M., Volf I., Comăneci R., Thermal Behaviour and Stability of the

Arboform®

LV3 Nature Liquid Wood, Composites Part B: Engineering, 103,

84-89 (2016).

Patel J.K., Shaikh A.A., The Influence of Abrasive Water Jet Machining Parameters on

Various Responses - A Review, Int. J. Mech. Eng. & Rob. Res. (2015).

Plăvănescu S., Biodegradable Composite Materials - Arboform: A Review, International

Journal of Modern Manufacturing Technologies, 6, 2, 63-84 (2014).

Shah A., Hasan F., Hameed A., Ahmed S., Biotechnology Advanced, 26, pp. 266

(2008).

http://grafex.ro/Servicii/?gclid=Cj0KEQiA2uDEBRDxurOO77Cp-

7kBEiQAOUgKV1wXttEOvMh6LHAnlg__kDzzjoqyfnKeMfrJRSxQEcMaAtA

u8P8HAQ#taiere-jet-apa.

http://www.tecnaro.de/english/willkommen.htm?section=we.

http://grafex.ro/Servicii/?gclid=Cj0KEQiA2uDEBRDxurOO77Cp-7kBEiQAOUgKV1wXttEOvMh6LHAnlg__kDzzjoqyfnKeMfrJRSxQEcMaAtAu8P8HAQ#taiere-jet-apa




PLANIFICAREA EXPERIMENTELOR

LA TĂIEREA CU JET DE APĂ A PIESELOR DIN ,,LEMN LICHID”

(Rezumat)

În contextul evoluților tehnice din ultimile decenii, comunitatea științifică și

realitatea economică mondială a necesitat dezvoltarea și optimizarea de noi procese și

tehnologii, care să permită producția durabilă de materiale moderne reciclabile,

biocompatibile și biodegradabile din resurse naturale regenerabile. O astfel de resursă o

reprezintă materialele vegetale, precum lignina. Ca urmare a cererii tot mai mari de

materiale biodegradabile, a fost dezvoltat un nou material, cu numele comercial de

,,lemn lichid” (100% biodegradabil), de către o echipă de cercetători germani (Institutul

Tehnic de Chimie din Fraunhofer împreună cu compania Tecnaro GmbH). Acest

material, îndeplinește toate condițiile de mai sus fiind în concordanță cu chimia și

ingineria ,,verde”. ,,Lemnul lichid”, se poate găsi sub trei forme diferite: „Lemn lichid”

ARBOFORM®, compozit plastic cu lemn ARBOBLEND

®, compus biopolimeric

ARBOFILL® (Nagele et al., 2014). Lucrarea își propune planificarea experimentelor

utilizând metoda Taguchi la tăierea cu jet de apă a pieselor din lemn lichid obținute prin

injecție.


Publicat de



Secţia


CALCULUS OF BENDING MOMENT CORRESPONDING TO

THE CENTRIFUGAL FORCE

BY

FLORENTINA MOCANU





Abstract. The paper offers an original contribution for calculus of bending

moment corresponding to the centrifugal force in a bar as a truncated cone form

with a specific elliptical section.

Keywords: centrifugal force; bending moment; curve bar; elliptical section.

1. Introduction

The paper presents in a unitary way some specific aspects, as resistance

corresponding to the centrifugal force, for elastic deformations, for a specific

bar design. On considered for bar a form as a truncated cone with a specific

elliptical section.

2. Centrifugal Force

2.1. Vertical Part of the Bar

The specific bar design is composed from two main parts:

‒ vertical part, parallel with the bar’s rotation axis;


48 Florentina Mocanu

‒ curved part.

The horizontal part, perpendicular on the bar’s rotation axis, represents the

joint element between the bar which we are analysis and other element of structure

(Fig. 1). The bar has a truncated cone form with a specific elliptical section.

The expression of the elementary centrifugal force corresponding to an

elementary volume separated at the distance x is:

Fig. 1 – The specific bar.

dxRba

RdxARdVRdmdF

xx

xcx

2

222

(1)

where: ρ – density of the bar; ω – angular speed; Ax – transversal section area of

the elementary volume; ax, bx – semi axes of the elliptical section; dx – thickness


of the elementary volume; R – distance between the rotation axis of the bar and

the arm’s vertical section axis (Buzdugan, 1986).

The linear variation law of the semi axes can be written as follows:

xkbb

xkaa

x

x

21

11

1

1

(2)

with

Lb

bbk

La

aak

1

122

1

121 ;

where: a1, a2 – the big semi axes of the elliptical transversal section

corresponding to the sections 1-1 respectively 2-2; b1, b2 – the small semi axes

corresponding to the same ellipses; L – the length of vertical part of the bar.

By replacing the relations (2) in the relation (1) is results:

1122 dxbaBxAxRdF

xc (3)

The expressions for the coefficients A, B are:

12112112122

1;

1aabbba

LBbbaa

LA (4)

The expression of centrifugal force can be determined by integrating the

relation (3).

LL

cc dxbaBxAxRdFFx

0

1122

0

After all the calculus it results:

121212

2

2a2a6

babaRL

Fc

(5)

2.2. Curved Part of the Bar

To establish, in a current section from the curve bar, the expression of the

centrifugal force it is necessary to be isolated an infinite small element of

elementary thickness. The element is obtained by sectioning on a radial

direction by two successive sectioning under the angles α, respectively α+ dα

from the horizontal axis (Fig.2).

It is considered the elementary volume:

dSAdV (6)

where: Aα – the aria of the transversal section of the curve bar; dS – the

elementary length of the bar portion limited by two sections.

In Eq. (6) we have:

baA

drdS

(7)


where: aα and bα – the large semi axis, respectively the small semi axis of the

elliptical transversal section (Mocanu, 2011).

Fig. 2 – The curve bar.

The expression of the elementary centrifugal force is:

drrba

rdSArdVrdmdFc

2

222

(8)

Concerning Fig. 2:

cos drr (9)

Replacing the relation (9) in Eq. (8) it results:

cos2 ddrrbadFc (10)

The linear variation law of the semi axes can be written as follows:

42

32

1

1

kbb

kaa

with

2

2

2

234

2

233

b

bbk

a

aak

where: a2, a3 – the large semi axis, b2, b3 – the small semi axes of the elliptical

transverse section corresponding to the sections 2-2 respectively 3-3.

By replacing the last relations in Eq. (10) it is obtained:

cos2222

ddrbaDCrdFc (11)

Where C, D are calculated by the expressions:


23223223232

2;

4aabbbaDbbaaC

(12)

2.3. Bending Moment to the Centrifugal Force

In a current section from the curve bar (β section) the bending moment

corresponding to the centrifugal force can be written as having two components:

21 MMM (13)

where: M1(β) – the bending moment given by the centrifugal force

corresponding to the vertical part of the bar; M2(β) – the bending moment

corresponding to the centrifugal force on the curve part of the bar.

The bending moment given by the centrifugal force corresponding to

the vertical part of the bar can be calculated as:

xxLFM Gc 1 (14)

where: Fc – the centrifugal force corresponding to the vertical part of the bar

given by Eq. (5); xG – the coordinate of the center weight; xβ – the vertical

distance from section β to the section 2-2 (Fig. 1) (Mocanu, 2011).

For the calculus of the position of the center weight of the vertical part

of the bar it is used the relation:

V

dV

x

L

x

G

0 (15)

where: dVx – the elementary volume obtained by successive sectioning at the

distances x and x+dx; V – the volume of the entire vertical part of the bar (the

volume of a truncated cone with an elliptical section).

But:

dxbaBxAxdxxkbxkadxbadxAdV xxxx 112

2111 11 (16)

where A, B are calculated with the relations (4).

On the other hand:

121212 2a2a6

babaL

V

(17)

Replacing the relations (16) and (17) in relation (15) and doing the

integration and all the necessary calculus it is obtained:

11122122

11122122

22

3

2 babababa

babababaLxG

(18)

Concerning Fig. 2 the vertical distance from section β to the section 2-2

can be geometrically expressed as follows:


sinrx (19)

Is replaced the relations (5), (18) and (19) in relation (14). After all the

necessary calculations it is obtained the expression of the bending moment

under the next form:

sin12

22

1 RL

M (20)

with: 121212

11122122

2a2a2

3

babaL

r

babababa

The bending moment of the elementary centrifugal forces in β section

(

2,0

) on the curve part of the bar has the expression (Mocanu, 2011):

brdFdM c

2 (21)

In relation (21) br is the arm of the elementary centrifugal force.

Concerning Fig. 2 this arm can be geometrically expressed as follows:

sinsinsinsin rrrbr (22)

By replacing in Eq. (21) the relations (11) and (22) it is obtained:

sinsincos22222

2 ddrbaDCrdM

The bending moment corresponding to the centrifugal force on the

curve part of the bar can be written follows:

0

22222

0

2 sinsincos ddrbaDCrdMM

After integration the last relation and executing all calculus it is obtained:

drrrM 2223232 (23)

with:

222 sin2

ba

2cos2sin2cos4

1sin

8

3

4

32sin

22sin

22

22

CCD

DCDC

2222

2223

cossin

cossinsin2

sin3

babaD

DbaDC


In β section the bending moment of the centrifugal forces M(β) is

obtained by adding the relations (20) and (23).

Section 3-3 is dangerous section for the studied bar. The maximum

bending moment could be determined by particularization of the expression of

M(β). After replacement and performing all calculations is obtained the

maximum value of the moment:

22232323223222

232323223223

2223

1212122

111221222

2

max

57.015.052.0

425.0363.0

22a2a

6

3122

babbaaaabbbadr

bbaaaabbbar

barbabaRr

L

babababaRL

MM

(24)

It takes into account the particular situation when the transversal section

of the bar is constant (an elliptical section with a and b large semi axis,

respectively small semi axis). In this case the maximum value of the moment is

obtained by the particularization of the last relation and has the next expression:

232max' 14.12

2drrrLLR

abM

(25)

REFERENCES

Buzdugan Gh., Rezistenţa materialelor, Edit. Academiei, Bucureşti, România (1986).

Mocanu F., Rezistenţa materialelor, Vol. 2, Edit. Tehnopress, Iaşi, România (2011).

CALCULUL MOMENTULUI ÎNCOVOIETOR CORESPUNZĂTOR

FORŢEI CENTRIFUGE

(Rezumat)

Lucrarea prezintă o abordare originală privind calculul momentului ȋncovoitor

corespunzător forţei centrifuge. Calculul momentului s-a efectuat pentru bara cu o

formă specifică formată dintr-o porţiune dreaptă, verticală, paralelă cu axa de rotaţie şi o

porţiune curbă sub formă de arc de cerc. Se consideră forma barei ca fiind cea a unui

trunchi de con cu o secţiune transversală eliptică, variabilă pe lungimea barei. S-a

stabilit expresia momentului ȋncovoietor ȋntr-o secţiune curentă a barei, dar şi valoarea

maximă a acestuia ȋn secţiunea periculoasă. Prin particularizare s-a determinat valoarea

maximă a momentului ȋncovoietor dacă secţiunea transversală a barei este constantă şi

are formă eliptică.


Publicat de



Secţia


DESIGNING A FLEXIBLE GRIPPING SYSTEM FOR AN

INDUSTRIAL ROBOTIC ARM

BY

EMILIAN PĂDURARU and CĂTĂLIN GABRIEL DUMITRAȘ



Received: October 14, 2016


Abstract. The paper summarizes the researches on specialized literature

and designing a gripping system capable of meeting the current requirements of

flexible manufacturing systems and industrial robots, namely handling a variety

of parts with different shapes, sizes and weights. The first part of the paper

contains general information about current state of researches in gripping system

application field and gripping forces analysis and methods of calculation. The

second part of the paper contains my own contribution. From studies I choose

gripping system that is capable to configure for achieving several tasks. It is

designed with four parallel fingers and two pneumatic cylinders. The primary

cylinder drives the fingers to grab objects like an ordinary gripper. My main

contribution is by introducing the second cylinder who changes the position of

the fingers, transforming the system from a four finger gripper to a two finger

gripper, through this, expanding the range of seized objects.

Keywords: gripper; gripping system; gripper design; prehension; finite

element analysis.


56 Emilian Păduraru and Cătălin Gabriel Dumitraș

1. Introduction

The gripping mechanisms are complex mechatronic structures used by

industrial robots, which are aimed to realize gripping operations of parts in order to

handling, transfer or assembly in a robotised technological process (Khoo, 2008).

Gripping mechanism are designed to replace the human hand because they

are very effective in repetitive cycles, can handle heavy objects and can operate in

extreme ambient conditions and temperatures (Monkman and Hesse, 2008).

There are numerous of parts with different shapes and sizes that must be

handled, that is why it is impossible to design a gripper suitable for all parts.

Most gripper researches utilize electric motors or pneumatic cylinders and two

fingers, because those are designed for one specific job. However, new

technological developments have given the opportunity to develop universal

gripping systems (Burak, 2010).

A gripping system must meet the following properties (Rajput, 2008):

• Optimal adjustments of gripper structure at performed operations;

• Adjustments to a wide range of openings and prehension options of

different shapes and sizes parts;

• Safety in handling parts (stability in positioning and orientation of the parts);

• Optimum characteristics in terms of clamping force;

• Systems with small weight and size;

• Avoiding damage and deformation of parts during prehension;

• Position on objects precisely;

• Variation in gripping possibilities based on weight, size and shape;

• The possibility to grip an object, when this is near to another object;

• Fast change/adapt of gripping system according to the next part to be

manipulated;

• Changes in clamping force according to the part weight.

In Table 1 are presented comparison criteria between electrical,

pneumatic and hydraulic operating (Deaconescu, 2008).

Table 1 Comparison Between Electrical, Pneumatic and Hydraulic Operating

Comparison criteria Type of acting

Pneumatic Hydraulic Electrical

Availability ** * ***

Long distance transport possibility ** * ***

Storage cost of the working environment *** ** *

Level of environmental pollution *** * **

Components cost *** * ***

Speed of movement in execution element ** * ***

The size of obtained forces ** *** *

Lifetime *** ** **

Working parameters adjustments *** ** *

Where: *** = very good; ** = good; * = satisfactorily


Nowadays, there are researches to transform a simple gripper, who can

accomplish a single task, to a multipurpose gripper. These can handle a variety

of object, but are to complex with a large number of components and linkages.

Some of these adaptive gripper designs are presented as follows: in Fig. 1 is a

two finger adaptive gripper, in Fig. 2 is a three finger adaptive gripper.

Fig. 1 – Two finger adaptive gripper Fig. 2 – Three finger adaptive gripper

(http://robotiq.com/products). (http://robotiq.com/products).

Another research is based both adaptive and flexible gripper. Not only

the position of fingers are changing, but the fingers are flexible and can mold

around the objects (Fig. 3).

Fig. 3 – Multi choice gripper

(https://www.festo.com/group/en/cms/10221.htm).

Researches are made in order to drive way of fingers. In Fig. 4 is

represented the drive mode of fingers where “tendons” are used to operate them.

Fig. 4 – Tendons operating finger

(http://yameb.blogspot.ro/2014/04/mit-meche-deflorez-competition-entry.html).

http://robotiq.com/products


https://www.festo.com/group/en/cms/10221.htm

http://yameb.blogspot.ro/2014/04/mit-meche-deflorez-competition-entry.html


2. Personal Contributions

Following the researches in the first part of the paper and considering

the current trends in gripping systems development, I designed a gripping

mechanism with four fingers, opening/closing parallel and pneumatic drive.

This acts like a normal gripper with concentric clamp (Fig. 5). Because the

necessity of a flexible gripper who can grab various types of parts, I added a

second cylinder connected to a flange (Poz. “b” in Fig. 6) and a linkage system

connected between the flange and fingers (Poz. “a” in Fig. 6) that can change

the fingers configuration, transforming the mechanism from four finger grippe

to a two fingers gripper with parallel clamp. The operating principle of the

second cylinder and the way it changes the fingers position is represented in Fig. 7.

Fig. 5 – Design of four fingers gripper. Fig. 6 – Design of two finger gripper.

Fig. 7 – The gripping system changing mode from four fingers to two fingers.

As we can observe, this solution bring many benefits regarding the

variety of shapes and dimensions of parts that can be handled, but increase the

complexity of the system, making it unstable and expensive to produce. The

main future objective is to reduce the number of components making it more

rigid and with lower production costs.

a

b


3. Conclusions

After researches I concluded that the technology is in great progress in

the development of more flexible industrial robot which requires designing of

more flexible grippers to handle a huge variety of parts.

Another trend in robotic development is to create a gripper that is

capable to send a lot of information from the object like weight, temperature,

the grabbing pressure and automatic positioning the robot arm on the parts.

My experimental gripper designs extend only the range of shapes and

dimensions of the objects.

The future directions of my researches is to reduce the component parts

of the gripper, to be less expensive to produce, to try different types of fingers

configurations to extend the range of objects shape.

Another direction I am looking for is to test different materials for

gripper component parts, to reduce the weight and to increase the strength, such

as fiber glass, aluminium alloys or other materials.

Acknowledgements. I want to thank to my scientific coordinator Prof. Univ.

Dr. Ing. Cătălin Gabriel Dumitraș for his constant guidance, support and

encouragement. I want to particularly thank for his contribution in my development as a

person, the advices given and especially for the trust given to me throughout the studies.

REFERENCES

Burak D., Development of a Two-Fingered and a Four-Fingered Robotic Gripper,

Middle East Technical University (2010).

Deaconescu A., Contribution to the Behavioral Study of Pneumatically Actuated

Artificial Muscle, 6th

International Conference of DAAAM Baltic Industrial

Engineering, Tallinn, Estonia 2008, Vol. 1.

Khoo S., Design and Analysis of Robot Gripper for 10 kg Payload, Universiti Teknikal

Malaysia Melaka (2008).

Monkman G., Hesse S., Robot Grippers, WILEY-VCH Verlag GambH & Co. KGaA,

Weinheim (2007).

Rajput R.K., Robotics and Industrial Automation, S. Chand & Company Ltd., New

Delhi (2008).








CONCEPEREA UNUI SISTEM DE PREHENSIUNE FLEXIBIL PENTRU

UN BRAȚ ROBOTIC INDUSTRIAL

(Rezumat)

În această lucrare se prezintă o sinteză a literaturii de specialitate în domeniul

sistemelor de prehensiune. Plecând de la cerințe, a fost creat un sistem de prehensiune

nou capabil a îndeplini criteriile domeniilor de prelucrare flexibile și a roboților

industriali. Prima parte a lucrării conține informații generale referitoare la stadiul actual

al dezvoltării în domeniul sistemelor de prehensiune, a analizei forțelor și a metodelor

de calcul a lor. În partea a doua se prezintă contribuția proprie. Analiza sintetică a

literaturii de specialitate a condus la definirea unui sistem care să îndeplinească mai

multe sarcini. În construcția lui au fost utilizați doi cilindri pneumatici și patru degete

paralele. Primul cilindru asigură deplasarea degetelor ca într-un sistem clasic. Al doilea

cilindru asigură schimbarea poziției degetelor transformând astfel sistemul dintr-un

sistem prehensibil cu 4 degete într-unul cu două degete, asigurându-se astfel extinderea

gamei de utilizare.


Publicat de



Secţia


LAMINAR FLOW OF MAGNETORHEOLOGICAL FLUID

FLOWING IN CURRENT PIPES

BY

DAN SCURTU and DORU CĂLĂRAȘU





Abstract. Magnetorheological fluids are Bingham type non-Newtonian

fluids. In motion, the kinematic and energetic characteristics of the Bingham

type fluid flow differ from the ones of the Newtonian fluid. MR fluids are

energized by an external magnetic field influencing the slip stress. Bingham-type

MR fluids form a central plug region moving at constant velocity. This

paperwork analyzes the effect of external magnetic field on the flow velocity of

magnetorheological fluids. The numerical modeling of the phenomenon shows

that the magnetic field value has a significant influence on the fluid flow

velocity.

Keywords: magneto rheological fluid; plug, velocity; magnetic induction.

1. Introduction

Magnetorheological fluids are Bingham type non-Newtonian fluids that

can be classified as smart fluids.

In motion, the kinematic and energetic characteristics of the Bingham

type fluid flow differ from the ones of the Newtonian fluid. The variation of the


62 Dan Scurtu and Doru Călărașu

unit tangent friction factor is defined by the equation0

dV

dz , in which 0

is deformation and dV

dz is shear stress.

Magnetorheological fluids are energized by an external magnetic field

influencing the slip stress.

Bingham-type magnetorheological fluids form a central plug region

moving at constant velocity.

Considering the complex dynamics of the magnetically controlled

fluids, it is hard to analyze them fully. To study the flow, mathematical models

from the dynamics of real fluids plus mathematical models specific to

electromagnetism is employed.

The paperwork shows theoretical results obtained from studying the

effect of the intensity of applied magnetic field H, respectively of magnetic

induction B on the pressure differences of MR fluid flow in a pipe.

2. Mathematical Models Used in Theoretical Research of

Magnetorheological Fluid Flow

MR fluids are non-Newtonian plastic fluids Bingham (Craig, 2003; Siginer et al., 1999; Chilton and Stainsby, 1998) characterized by the relation:

0

dV

dz 0 (1)

In which: ‒ shear stress, 0 0 ( )B ‒ deformation stress, .ct ‒ fluid

dynamic viscosity.

Considering that the magnetic induction B H , in which is

environment permeability [ 0 1 ], it results that the total friction of the

MR fluid depends on the size of the magnetic induction B by the term 0 B .

If we assume that by using a coil a magnetic field is obtained, the

magnetic induction value depends on the current I induced in N loops of the coil

with length l, namely B B I .

I NB

l

(2)

It results that MR fluid can be controlled if it flows in a circular pipe

equipped with a coil run by current I. By regulating the intensity of current I,

the deformation stress values vary.

The Herschel-Bulkley model (Herschel and Bulkley, 1926)


] is employed to calculate the stress τ for magnetic induction values B > 0.

1

0 11 tanh tanh

n

(3)

For the laminar flow, Chilton and Stainsby (1998) propose a formula (4)

to calculate pressure drop. The equation needs an iterative solution

2 3

4 8 3 1 1 1

4 1 1

n n nP K V n

L D D n X aX bX cX (4)

4

yLX

D P

,

1

2 1

a

n,

2

1 2 1

nb

n n,

22

1 2 1

nc

n n

For the turbulent flow, the authors propose a method that needs

knowing wall shear stress, but they do not provide a formula for it. The model

was perfected by Hathoot:

2 34 1

3 1

perete

n VD aX bX cXR

n

(5)

1/

1 1/

1

perete pere

n

te

nK

X ,

4

perete

D P

L

3. Theoretical Model of Bingham-Type MR Fluid

Flow Dynamics in a Circular Pipe under the Influence of an

External Magnetic Field

In the case of Bingham type bodies, the kinematic and energy

characteristics of the flow differ from those of the Newtonian fluids. According

to the variation of the unit tangent friction factor, 0

dV

dz , the distribution

of velocities in the cross section of the pipe includes two sub-fields (Kciuk and

Turczyn, 2006). In the central area of 0

r radius, the unit factor has a lower value

that the flow limits . The fluid travels as a rigid system, apparently non-

deformable, like a cylindrical plug. The solid plug travels with a constant

velocity with no modification in its geometry.


The value of the 0

r radius, which is the barrier between the two sub-

fields, depends on the rheological characteristics of the fluid.

In the sub-field 0;r r R , the stress exceeds the value of

0 and the

character of the flow changes, Fig. 1.

Fig. 1 ‒ Domains of the flow.

The description of the laminar motion of fluids is made by using the

Navier-Stokes equations written in cylindrical coordinates ( , , )r z .

2

2 2

2 2

1 2,

1 1 2,

1

r r r rr z r r

r rr z

z z zr z z z

v vv v v vv pv v f v

r r z r r r r

v v v v v v vvpv v f v

r r z r r r r

vv v v pv v f v

r r z z

(6)

, , , , , , , ,

r r zV r z v r z e v r z e v r z k

2 2 2

2 2 2 2

1 1

r r r r z. (7)

in which , ,V r z is the flow velocity of the real fluid being in permanent

motion with the kinematic viscosity .

The continuity equation in cylindrical coordinates is:

1 1

0

z

r

v vr v

r r r x

(8)


It is considered the unidirectional and axially symmetrical flow with the

velocity of V , in a cylindrical pipe with radius R and length l under the action

of a pressure gradient. In these conditions, 0; 0; 0 r zv v v V .

If mass forces are neglected, 0 r zf f f , and continuity equation

is used in the required conditions, the equation of dynamic equilibrium results:

2

2

1

d V dV p

r dr zdr (9)

Taking into account the expression of the friction factor for non-

Newtonian fluids 0 dV

dr , it results that

p

r r z

(10)

In the sub-field (1), the shear velocity is high and the fluid tends to have

a Newtonian behavior.

In the sub-field (2), the fluid moves with a constant velocity as a solid

plug without being subject to shear.

The relations of the flow velocities in the two areas under the action of

the pressure gradient are determined by applying the limit conditions (barrier)

for the flow velocity V .

The solution of the Eq. (1) is:

2 01 2ln

4

DpV r r r c r c

l

(11)

For 0r r (plug barrier)

0

dV r

dr

2

0 0 01 0

2

r Dp rc

l

(12)

The c1 constant results and V r has the expression:

2 20 00 0 2ln ln

4 2

Dp DpV r r r r r r r c

l l

(13)

For r R (at the wall) 0V R :


2

2 00 0 2ln ln 0

2 2

Dp Rr R R r R c

l

The velocity, V r 0;r r R has the expression

2 2

2 00 0ln ln

2 2 2

Dp r R R RV r r r R r

l r r

(14)

For determining the 0r radius of the plug, we consider inside the pipe a

cylinder of 0r radius being in equilibrium under the action of the pressure and

friction forces (Fig. 1).

From the equation of the dynamic equilibrium of forces,

21 2 0 0 02p p r r l the following expression results for the plug radius:

00

2

lr

Dp

(15)

The traveling velocity 0V of the fluid plug is obtained from the relation

of the velocity V r with the condition 0r r

2 220 0

0 0 0 0

0 0

ln ln2 2 2

rDp R R RV r r R r

l r r

(16)

4. Theoretical Results Obtained by Numerical Simulation

The numerical modeling was carried out for a MRF 132 magnetorheological

fluid, Fig. 1 in the following conditions:

Pipe diameter D = 0.025 m;

Pipe length L = 0.015 m;

Pressure difference of the flow: DP1 = 12 KPa, DP2 = 15 KPa,

Magnetic induction B [0 – 0.4] T

Fluid viscosity dynamic coefficient = 0.112 Pas

Shear velocity dV r

dr [s

-1] 1000

0 = 39.721B4 ‒ 132.358 B

3 + 119.0925 B

2 + 10.280 B + 0.10815

the deformation for the MR132 fluid, 0 , [KPa] (Han et al., 2009; Hong

et al., 2008).


In Fig. 2, deformation varies depending on the size of the magnetic

induction B.

Fig. 2 ‒ Variation of the deformation stress depending on the size

of the magnetic induction B.

The plastic deformation 0 increases as the magnetic induction B

increases. The increase gradient is higher in high inductions.

Fig. 3 presents the variation of the fluid plug radius for two constant

pressure values of the flow, depending on the magnetic induction B value.

Fig. 3 ‒ Variation of the fluid plug radius.

The r0 radius of the fluid plug increases as the magnetic induction B

increases at a constant pressure difference. The increase is determined by the

size of the stress 0 .


At constant values of the magnetic induction B, the r0 radius of the fluid

plugs decreases as the pressure difference increases.

Fig. 4 presents the velocity variation of the fluid plug for two constant

pressure values of the flow, depending on the size of the magnetic induction B.

Fig. 4 ‒ Variation of the fluid plug velocity.

The travel velocity V0 of the fluid plug decreases as the magnetic

induction B increases, at constant values of the pressure difference.

At constant values of the magnetic induction B, the V0 decreases as the

pressure difference determining the flow increases.

Figs. 5 and 6 present the variation of local flow velocity V(r) of the

magnetorheological fluid in relation to radius r for two constant pressure values

of flow, depending on the size of the magnetic induction B.

Fig. 5 ‒ Variation of the local velocity V(B,r).


Fig. 6 ‒ Variation of the local velocity V(B, r).

The local flow velocity V(r) in the space between the fluid plug and the

pipe wall has an approximately parabolic variation in relation to current radius r

and decreases as the magnetic induction B increases.

For a magnetic induction B = cst.; r = cst. the local velocity V(r)

increases as the pressure difference increases.

5. Conclusions

The rheological character of the fluid is strongly influenced by the

magnetic induction value.

The r0 radius of the fluid plug increases as the intensity of the applied

magnetic field rises, and for constant magnetic induction values, it decreases as

pressure difference rises.

The travel velocity V0 of the fluid plug is influenced both by the

magnetic induction value and by the pressure difference of the flow.

The local flow velocity of the fluid V(r) in the space between the fluid

plug and the pipe wall has an approximately parabolic variation in relation to

the current radius r. At a constant pressure difference, the velocity V(r)

decreases as the magnetic induction B increases.

For a magnetic induction of B = cst., at the radius r = cst., the velocity

V(r) increases as the pressure difference increases.


REFERENCES

Chilton R.A, Stainsby R., Pressure Loss Equations for Laminar and Turbulent non-

Newtonian Pipe Flow, Journal of Hydraulic Engineering, 124, 522 (1998).

Craig B., One Fluid, Multiple Viscosities - Numerous Applications, Active Fluids are

Changing Damping Technology Forever, AMPTIAC Quarterly, 7, 2, 15-19

(2003).

Han Y.M., Kim C.J., Choi S.B., A Magnetorheological Fluid-Based Multifunctional

Haptic Device for Vehicular Instrument Controls, Smart Materials &

Structures, 18, 1, 015002, January 2009.

Herschel W.H., Bulkley R., Konsistenzmessungen von Gummi-Benzollösungen, Kolloid

Zeitschrift, 39, 291-300 (1926).

Hong S.R., Wereley N.M., Choi Y.T., Choi S.B., Analytical and Experimental

Validation of a Nondimensional Bingham Model for Mixed-Mode Magneto

Rheological Dampers, Journal of Sound and Vibration, 312, 3, 399-417, May

2008.

Kciuk M., Turczyn R., Properties and Application of Magneto Rheological Fluids,

Journal of Achievement in Material and Manufacturing Engineering, 18, 127-

130 (2006).

Siginer D.A., De Kee D., Chhabra R.P., Advances in the Flow and Rheology of non-

Newtonian Fluids, 8, Elsevier (1999).

CURGEREA LAMINARĂ A FLUIDULUI

MAGNETOREOLOGIC PRINTR-UN TUB DE CURENT CU

SECȚIUNE CIRCULARĂ

(Rezumat)

Fluidele magnetoreologice sunt nenewtoniene de tip Bingham. În cazul

mișcării acestora, caracteristicile cinematice și energetice ale curgerii diferă de cele ale

fluidului Newtonian. Lichidele magnetoreologice sunt caracterizate de faptul că

energizarea acestora se realizează prin intermediul unui câmp magnetic exterior care

influențează efortul de alunecare. Specific mișcării fluidelor magnetoreologice de tip

Bingham este formarea unui dop fluid în zona centrală care se deplasează cu viteză

constantă. Lucrarea are ca scop analiza influenței câmpului magnetic exterior aplicat

fluidului magnetoreologic asupra vitezei de curgere a acestuia. Modelarea numerică a

fenomenului, arată că mărimea câmpului magnetic are influență considerabilă asupra

vitezei de curgere a fluidului.

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