Alexander Dubček University of Trenčín Izhevsk State ... · single model of thin-rimmed gear was...

Alexander Dubček University of Trenčín

Izhevsk State Technical University

Publishing House:Alexander Dubček University of Trenčín

(The international scientific journal founded by two universities from Slovak Republic and Russian Federation)

This journal originated with kindly support of Ministry of Education of the Slovak Republic

Editor-in-Chief

Wagner Juraj, Dr.h.c., Assoc.prof., Ing., PhD., Alexander Dubček University of Trenčín

Science Editor

Dubovská Rozmarína, Prof. Ing., DrSc., Alexander Dubček University of Trenčín

Honorary Editors

Wagner Juraj, Dr.h.c., Assoc.prof., Ing., PhD., rector, Alexander Dubček University of Trenčín, Slovak Republic

Jakimovič Boris Anatoľjevič, Prof., DrSc., rector, Izhevsk State Technical University, Russian Federation

Members

Alexy Július, Prof. Ing., PhD. Gulášová Ivica, Assoc.prof., PhDr., PhD.Jóna Eugen, Prof. Ing., DrSc.Letko Ivan, Prof. Ing., PhD.Maňas Pavel, Assoc.prof., Ing., PhD. Mečár Miroslav, Assoc.prof., Ing., PhD.Melník Milan, Prof. Ing., DrSc. Obmaščík Michal, Prof. Ing., PhD. Zgodavová Kristína, Prof. Ing., PhD.

Jakimovič Boris Anatoľjevič, Prof., DrSc. Alijev Ali Vejsovič, Prof., DrSc. Turygin Jurij Vasiľjevič, Prof., DrSc. Ščenjatskij Aleksej Valerjevič, Prof., DrSc. Kuznecov Andrej Leonidovič, Prof., DrSc. Fiľkin Nikolaj Michajlovič, Prof., DrSc. Sivcev Nikolaj Sergejevič, Prof., DrSc. Senilov Michail Andrejevič, Prof., DrSc. Klekovkin Viktor Sergejevič, Prof., DrSc.Trubačev Jevgenij Semenovič, Prof., DrSc.

Alexander Dubček University of Trenčín Slovak Republic

Izhevsk State Technical UniversityRussian Federation

Editorial Office

Študentská 1, 911 50 Trenčín, Tel.: 032/7 400 279, 032/7 400 [email protected], [email protected]

Wagnerová Ružena, Ing.

Redaction

Publishing House

University Review No. 3Trenčín: Alexander Dubček University of Trenčín2007, 58 p.ISSN 1337-6047

Alexander Dubček University of Trenčín, Študentská 2, 911 50 Trenčín

3z SOLUTIONS - Zuzana Slezáková, www.3zs.sk

Graphic Design

Technical Information

© 2007 All rights reserved.Alexander Dubček University of Trenčín, Slovak Republic

�

Contributors

contents

45

50

33

29

21

2

Gordana MarunićModel For Stress Analysis of Spur Gear Blank

10 Maciej Bodnicki, Waldemar Oleksiuk, Wiesław MościckiExperimental Tests of Miniature Mechatronic Devices

39

Dean´s Foreword

5

Grzegorz Domek, P. KrawiecMethods of Designing of Timing Belts Pulley

Jaromír Drápala, Renata Kozelková, P. Kubíček, Ján Vřešťál, Aleš Kroupa

Interaction of Elements in the Copper/Indium – Tin Diffusion Joints at 400 and 600 °C

Marian Dudziak, Andrzej Kołodziej, Jacek Kroczak Numerical Analysis of State of Stresses And Strains in Splined Connections

Dariusz Dyja, Zbigniew Stradomski

The Salt Mist Corrosion Resistance of a Duplex-Type Ferritic-Austenitic Cast Steel

Hesham F. El-Maghraby, Ondrej Gedeon, Abdel Aziz Khalil

Formation and Characterization of Poly (Vinyl Alcohol-Co-Vinyl Acetate-Co-Itaconic Acid)/Plaster Composites, Part I: Characterization of Β-Hemihy-drate Plaster

Andreas Geiss, Markus Schinhaerl, Elmar Gregor Pitschke, Rolf Rascher, Peter Sperber, Fathima Patham Kadeer Mohideen, Juraj Slabeycius

Subsurface Damages Detecting On Standard Optical Glass by Dimple Method

Stanislav Holý, Jiří Jankovec, Petr Jaroš, Jaroslav Václavík, Otakar Weinberg

Experimental Calibration of Constants Used For Determining Residual Stresses From Hole Drilling Method Data

15

4

�

Gordana Marunić, University of Rijeka Faculty of Engineering, Rijeka, Croatiae-mail: [email protected]

contributors

Grzegorz Domek, Kazimierz Wielki University, Bydgoszcz, Polande-mail: [email protected]. Krawiec, Poznań University of Technology, Poznań, Poland

Maciej Bodnicki, Waldemar Oleksiuk, Wiesław Mościcki

Grzegorz Domek, P. Krawiec

Jaromír Drápala, Renata Kozelková, P. Kubíček, Ján Vřešťál, Aleš Kroupa

Marian Dudziak, Andrzej Kołodziej, Jacek Kroczak





Maciej Bodnicki, Waldemar Oleksiuk, Wiesław Mościcki,Institute of Micromechanics and Photonics, Warsaw University of Technology, Polande-mail: [email protected]: [email protected]: [email protected]

Jaromír Drápala, Renata Kozelková, Faculty of Metallurgy and Materials Engineering, Department of Non-ferrous Metals, Refining and Recycling, VŠB – Technical University of Ostrava, Ostrava, Czech Republice-mail: [email protected]. Kubíček, Na Čtvrti 14, 705 00 Ostrava – Hrabůvka, Czech RepublicJan Vřešťál, Masaryk University, Faculty of Science, Department of Theoretical and Physical Chemistry, Brno, Czech Republice-mail: [email protected]š Kroupa, Institute of Physics of Materials AS CR, Brno, Czech Republic e-mail: [email protected]

Marian Dudziak, Jacek Kroczak, Poznań University of Technology; Poznań, Polande-mail: [email protected]: [email protected] Kołodziej, Higher Vocational State School, Kalisz, Polande-mail: [email protected]

Dariusz Dyja, Zbigniew Stradomski, Institute of Materials Engineering, Czestochowa University of Technology, Czestochowa, Polande-mail: [email protected]

�

contributors

Reviewers

Prof. RNDr. Pavol Koštial, PhD.Prof. Ing. Ivan Letko, PhD.Prof. RNDr. Juraj Slabeycius, PhD.Prof. Ing. Miroslav Kopecký, PhD.Prof. Ing. Ján Vavro, PhD.Prof. RNDr. Ignác Capek, DrSc.

Prof. Ing. Eugen Jóna, DrSc.Prof. Ing. Vendelín Macho, DrSc.Prof. Ing. Martin Jambrich, DrSc.Prof. Ing. Ján Štefánik, PhD.

Hesham F. El-Maghraby, Ondrej Gedeon, Department of Glass and Ceramics, Institute of Chemical Technology, Prague, Czech Republice-mail: [email protected] e-mail: [email protected] Aziz Khalil, Department of Refractories, Ceramics, and Building Materials, National Research Centre, Cairo, Egypte-mail: [email protected]

Andreas Geiss, Markus Schinhaerl, Elmar Gregor Pitschke, Rolf Rascher, Peter Sperber, Fathima Patham Kadeer Mohideen,Deggendorf University of Applied Sciences, Deggendorf, Germanye-mail: [email protected] Slabeycius, Alexander Dubček University of Trenčín, Trenčín, Slovak Republice-mail: [email protected]

Stanislav Holý, Czech Technical University in Prague, Faculty of Mechanical Engineering, Department of Mechanics, Biomechanics and Mechatronics, Prague, Czech Republice-mail: [email protected]ří Jankovec, Jaroslav Václavík, Škoda Research Ltd., Dynamic Testing Laboratory, Plzeň, Czech RepublicPetr Jaroš, Techlab Ltd., Prague, Czech Republice-mail: [email protected] Weinberg, Škoda Research Ltd., Dynamic Testing Laboratory, Plzeň, Czech Republic e-mail: [email protected]

�

Dear colleagues, I would like to present you the special issue of Univer-sity Review oriented in material engineering. The problems of mate-

rial engineering, mechanics and design are still brisk and actual.

In this point of view we would like to present you some results of in-ternational cooperation of Faculty of Industrial Technologies in Púchov of Trenčín University of Alexander Dubček. We believe that presented papers could be the inspiration for readers to cooperate or participate on research with our fac-ulty.

Best regards

Prof. RNDr. Pavol Koštial, PhD. Dean of the Faculty of Industrial Technologies in Púchov

dean´s foreword

Prof. RNDr. Pavol Koštial, PhD.

�

The stress and deformation analysis of thin-rimmed gears with complex gear

blank based upon numerical approach, has been widely used method that overcomes the insufficiencies related to the application of conventional analytical methods pro-posed by the standards.

For the development of numerical mod-el that satisfies considering the accuracy, effort and time, first and important step comprises the decision about appropriate geometrical model.

The research into stress and strain state of thin-rimmed gear without web i.e. a gear with slots, was the first attempt towards the analysis of gear with complex blank consist-ed of thin rim, web and hub. The justifica-tion of a model angular extension and the number of teeth to be taken into account, have differed from author to author, and recommendations for adequate gear model have depended strongly on the aim of cer-tain research.

For the investigation of stress field in the root area of thin-rimmed gear without web,

ModeL for stress anaLYsis of sPur Gear bLanK

Gordana Marunić

The 3D models are developed for the stress analysis of a spur thin-rimmed gear blank ele-ments. Geometrical models are evaluated for the case of middle-web position and chosen facewidth value, by varying the values of two gear parameters i.e. the rim and web thick-ness. Through the using finite element method, the stress of rim and web joint is deter-mined for different models of pinion-wheel system. The accomplished stress comparison of maximum obtained stresses and their distribution in radial direction, offers the deci-sion whether or not the model simplification is possible from reliable gear blank elements stress determination point of view.

Abstract

3D modelling, spur gear, blank, FEM

Key words

�

all the meshing teeth of pinion-wheel sys-tem were represented in the model, along with one further tooth pair on both sides of the meshing teeth. The corresponding an-gular extension of the model was adopted of 120° [3]. The same spur meshing pinion-wheel system was utilised for the research into the effects of profile error and modi-fications on load sharing and distribution, and on tooth-root stress field, by the appli-cation of three-dimensional non-linear ap-proach [1].

The effects of gear rim thickness and in-fluence of web position on gear stresses for several positions on the meshing line, were studied based upon a single model sector corresponding to five teeth [5].

The influence of cylindrical gear blank upon load capacity was found for the gear body with middle web arrangement mod-elled as a single segment with three teeth [7]. The effect of rim and web thickness and number of teeth, on the deformation and stress of complex body elements, was es-tablished.

A hybrid approach was applied to study the load distribution and transmission error of thin-rimmed gears [9]. The finite element analysis was performed by use of a single gear sector usually of 60° to 90°, of gear with middle and end web position. A similar single model of thin-rimmed gear was de-veloped for parametric three-dimensional finite element analysis, to investigate the effects of gear geometry on the tooth-root stress field of spur gears, as well as to verify experimental results [2].

The deformations and stresses at every part of gear with offset web position were analysed in detail by use of finite element method and whole gear deformation model [6].

In this paper the attention is devoted to the modelling of pinion-wheel system geo-metrical model intended to develop into 3D FEM one, that enables proper evaluation of stress occurring in the elements of a spur gear structure. Maximum equivalent von Mises stress at the rim and web joint, and the stress distribution in radial direction in the area that covers maximum stress ap-pearance, are separated and compared for different models in order to simplify the pinion–wheel system. Two gear geometri-cal parameters, the rim and web, are varied and the evaluation of the obtained stresses is performed.

�d ModeLLinG of Pinion-wHeeL sYsteM

The research into the stresses of a spur thin-rimmed gear with middle web position is performed for three different models and by use of the FEM. The chosen geometri-cal data of gear pair are: number of teeth z1=z2=20, module m=10 mm, pressure angle α=20°, profile shift coefficient x1=x2=0, con-tact ratio εα =1,56, facewidth b=100 mm. Two gear geometrical parameters are taken into account: the rim thickness sR is varied from sR=3m, sR=2m, sR=1,5m to sR=m, and the web thickness takes two extreme values of sw=0,4b and sw=0,1b. For all considered cases, thin-rimmed wheel with complex body is mating with a solid pinion, in the highest point of single pair tooth contact.

Related to the utilised 3D FEM numeri-cal model, the material properties, mesh-ing and boundary conditions (loading, constraints, contact) are same ones as de-scribed in [8], for the model that satisfies in relation to the determination of tooth-root reliable stress field. Due to the geometry

�

and load symmetry, one half of facewidth is modelled for further FEM numerical model development.

There are modelled three models of pin-ion-wheel system, as follows.

Model 1 consists of pinion and wheel segment with angular extension corre-sponding to four teeth, and with three teeth above the rim.

Model 2 has pinion segment and the wheel formed as complete ring with three teeth above, as shown in Fig. 1. In order to take into account the influence of miss-ing teeth on the rim rigidity, the larger rim thickness of equivalent rigidity is calculated in accordance with [4].

Equivalent rim thickness sReq is obtained by increasing rim thickness sR for the value proportional to module:

sReq = sR + Am

A =0,19[1 + c/m – (2 + 17 (c/m))/z] +

+ (0,02x + x/z)

where A is dimensionless coefficient that takes into account the influence of teeth geometrical parameters on the rim rigidity, and c is bottom clearance.

coMParison of eQuiVaLent stress at riM and web Joint

For the described three models, maximum equivalent von Mises stress σeq is deter-mined at the rim and web joint, regardless of its location in radial direction, by means of finite element analysis. The obtained val-ues of equivalent stress are presented in Tab. 1.

Maximum equivalent stress of model 1 de-viates considerably from the correspond-ing one of model 3. This tress deviation is mostly expressed for the greatest rim thick-ness (sR/m=3), and increases severe going towards the thinnest web. For the thin-nest web (sw/b=0,1), the stress belonging to model 1 is more than twice lower than the stress of model 3. In the case of thinnest rim (sR/m=1), the stress deviation is about 30% for the thinnest web (sw/b=0,1). It is obvious that model 1 of pinion-wheel seg-ment cannot properly simulate the stress behaviour of gear body elements.

(1)

(2)

Fig. 1: The locations at the rim and web joint A where equivalent stress is determined in radial direction for the range of angle φ measured from the loaded tooth centre line (sectioned model 2 of segment pinion-whole wheel) Model 3 consists of wheel as described for model 2 and the pinion shaped as complete ring with three teeth above.

�

The comparison of maximum equivalent stress belonging to model 2 and 3, shows maximum stress deviation about 3,5% (Fig. 2). Therefore, the model 2 consisted of pinion segment and whole wheel can be adopted instead of model 3.

The obtained comparison of equivalent stress distribution in radial direction Fig. 3 a, b, that covers the area of maximum stress appearance, confirms too, unad-equate simplification introduced by model 1. The imposed constraints to model 1 with wheel segment, cause the shift of maximum equivalent stress location in relation to wheel whole model.

concLusions

The calculated equivalent von Mises stress at the rim and web joint of a spur thin-rimmed gear, and its distribution in radial direction, have been adopted as criteria for the evaluation of several pinion-wheel sys-tem geometrical models intended for the development of FEM numerical models.

The comparison of maximum equivalent stress and the insight into stress distribu-tion in radial direction, have pointed to the necessity of taking into account the defor-mations of gear under consideration, as a whole. In order to achieve reliable stress evaluation of thin-rimmed gear structure elements, complete gear is to be modelled, regardless of rim and web thickness.

Tab. 1: Maximum equivalent stress σeq [N/mm2] at rim and web joint

Model Web thickness sw/b

σeq [N/mm2]

Rim thickness sR/m

3 1

Model 1(segment+segment)

0,4 6,2 15,9

0,1 7,5 20,1

Model 2(segment+whole)

0,4 9,4 19,9

0,1 19,9 25,4

Model 3(whole+whole)

0,4 9,1 19,2

0,1 19,9 26,2

Model 2 (seg.+whole) Model 3 (whole+whole)

sw/b=0,1

0 1 2 3 0

20

30

N/mm2

eq

10

sR/m

sw/b=0,4

Fig. 2: Maximum equivalent stress σeq at rim and web joint for the model 2 (segment pinion and whole wheel), and model 3 ( whole pinion and wheel)

�

Baret, C. et al.: In: Proceedings of the International Gearing Conference. 1994, New-castle Upon Tyne, GB: UK National Gear Metrology, Univ. of Newcastle Upon Tyne, Brit-ish Gear Assn., 149.Blazakis, C. A., Houser, D. R.: Proceedings of the International Gearing Conference, UK National Gear Metrology, 1994, Newcastle Upon Tyne, Unated Kingdom: Univ. of Newcastle Upon Tyne, British Gear Assn., 41.Curti, G. et al.: Proceedings of MPT´ 91 JSME International Conference on Mo-tion and Powertransmissions, 1991, Hiroshima, Japan: JSME, 787.Dinovič, M. J., Šolomov, N. M.: Vestnik mašinostroenia, 6, 1975, 27.Kim, H. C. et. al.: Proceedings of International Congress - Gear Transmissions ´95, 1995, Sofia, Bulgaria: TUME-Bulgaria, 164.Li, S. : Journal of Mechanical Design, 124, 2002, 511.Linke, H., Mitschke, W. & Senf. M.: Machinenbautechnik, 32, 1983, 450.Marunić, G.: Proceedings of 5th International Scientific Conference RIM 2005, 2005, Bihać, Bosnia and Herzegovina, Univresity of Bihać, 317.Prabhu, M. S. & Houser, D. D. R.: VDI Berichte NR. 1230, VDI- Verlag, Düseldorf 1996.

1.

2.

3.

4.5.

6.7.8.

9.

Literature

Fig. 3: The comparison of equivalent stress σeq magnitude and location for the model 2 - segment pinion and whole wheel (a), and model 1 - segment pinion and wheel (b)

�0

There are more and more papers about devices of mechatronics presented on

scientific conferences. An effect of technical progress is the reason of this process. The in-telligence of the presented devices growth. The new scientific groups with different ba-sis areas work in area of mechatronics.

The miniature mechatronic devices are the specific. The knowledge of the fine me-chanics is in our opinion the fundamentally ones. On the design, test and diagnostics of such a equipment focused scientific interest of our Division of Design of Precision Devic-es, Faculty of Mechatronics.

Miniaturization is very often the most im-portant requirement. Small dimensions are indispensably in a number of applications: diagnostic medical equipment (e.g. port-able), space technique, multimedia etc. Small size could be useful from the market-ing point of view (an consumer prefers light, small devices).

The small devices need less energy. They work at less load and power. However at the same time small dimensions make difficult design and testing of such instruments.

eXPeriMentaL tests of Miniature MecHatronic deVices

Maciej Bodnicki, Waldemar Oleksiuk, Wiesław Mościcki

There are the special situations when physical experiments on miniature devices (or their units) need using of non-typical measuring procedures. Dimensions of object under tests eliminate often possibility of using of typical sensors – especially in transient state – be-cause of interaction and dynamic errors. This paper presents selected situations and exam-ples of optimisation of sensors structures and measuring procedures giving elimination of disadvantageous influences. The “sensorless” methods are taken into consideration, useful for control and testing of miniature intelligent electrical drive systems.

Abstract

mechatronic, experimental tests, miniaturisation, microdrives

Key words

��

The structure of the miniature mechatronic devices is “interdisciplinary”. They consist of mechanical, electric and electronic (sup-ply and sensors) and control (preferably by micro-controler) parts. Very often the most complicated ones are design by specialist from different areas and this interdiscipli-nary of teams gives the positive synergic effect.

This interdisciplinary character makes in some situations problems in modeling or ex-perimental testing of miniature mechatron-ics. We want to present selected problems on example of miniature electrical drives, on which focused our interest.

ProbLeMs of Miniature eLectri-caL driVes

Let the goal of the designer works is pro-grammable electric microdrive: with known load, speed and acceleration as well as gen-

eral time (action) characteristics. There are additional (useful) requirements: accuracy of the driven member while possibly small dimensions or weight (reduced moment of inertia) kept, consuming possibly low en-ergy (e.g. with battery suplly). Very offten the design process have to be short – so preferable is using of ready components as: micromotor, gear, sensors, and controler. The problems of fitting and optimization of gears is for example presented in [6].

The miniature DC motors are the popu-lar actuators in miniature mechatronic de-vices. The simply regulation of the angular velocity in a large range and high values of such speed, as well as high output power to size (weight) ratio. The information about usefully of the micromotor gives us the set of performance characteristics (an example – see Fig. 1). There are some disagreements between real and theoretical lines (curves) in effect of the armature influence [xx].

The control unit is an integrated part of the mechatronic drive. In analyzed type of mi-cromotor control procedure forms angular speed – continuously or pulse. The first type is realized by changes of voltage supply, in the second one by supply of the armature by constant amplitude and frequency but changing duty cycle. For the close-loop con-trol information about real value of velocity and direction is necessary.

The optimal selection of the motor from the commercial proposition is paradoxically not the simple. The performance characteristics taken from data catalogues of the manufac-tory should be source of the enough infor-mation, but very often those characteristics are simplified or presented without data about measuring methods.

Fig. 1: The set of performance characteristics of the separately excited permanent magnet DC motor [5]

Ia – armature current, Me – torque, n – angular speed, n0 – no load speed

��

Additionally, information about dynamics of the micromotor is especially important in case of mechatronic devices.

From the point of view of experimental setup, testing of electrical microdrives re-quires:

measurements of torque (to 1 Nm);measurements of angular velocity (up to tens thousands of rpm); precision applying of load (e.g. by special torque-motors [7]; measuring (or stabilization of tempera-ture); independent (separately) measurements of electrical quantities (e.g. voltage and current of armature in the same time); dynamic data acquisition.

Methods, transducers and test rigs useful in the case of the classical micromachines may disturb the correct operation of a mini-ature motor. So, it should be considered to propose special transducers of mechanical quantities as well as unconventional meas-uring methods. Dimensions of the studied objects determine low values of the mo-ments of inertia of the rotors, what makes the designer of the measuring system care-fully consider the possibility of attaching to them any additional elements. Values of the parasitic torque of losses in typical measur-ing transducers and the loading units within the test rigs (e.g. brakes) exceed the maxi-mal values of the torquere developed by the miniature motors.

eLiMination of tHe additionaL Load “Produced” bY sensors of tHe test stand

There is possible to show two ways of re-duction of additional loading (by torque and moment of inertia) performed by sensors of the test rig.

The first group of methods is called „sen-sorless“ measurement. In fact instead of di-rectly measurement the values of detected quantity the calculation from other signals is proposed. The natural way is looking for elimination of directly worked transduc-ers of the mechanical quantities (torque, speed, velocity) by relative easy measure-ment of electrical signals. The knowledge of the mathematical model of the object un-der test is often necessary (but sometimes only basic dynamic rules are used [2, 3]). The good example are developed in our Di-vision experimental setups for such tests of DC micromotor:

determination of full setup of load char-acteristics without directly speed meas-urement (calculated from velocity) or on basis only current measurement; application of effects of commutation phenomena in DC micromotors for cal-culation of angular displacement.

Especially the performance of commuta-tion pulses of current (synthetic presented on Fig. 2) could be useful for control proce-dures.

The second group of method based on using of non-contact (preferable optoelec-tronic) sensors of displacements. Signals of speed and velocity are then calculated as the derivative of displacement. Values of the forces and torque’s are also combined with displacement by deformation of elastic element.

��

Fig. 2: The proposed structure of the transducer process-ing the current pulses into the typical TTL encoders signal [2]LEM – Hall-effect based current/voltage transducer (without galvanic connection to the supply circuit of the micromotor), F1 – low-pass filter (for elimination of nois-es), F2 – high-pass filter (for elimination of the constant component), P – trigger digitizing the signal

aGGreGates – inteGration of tHe Parts of inteLLiGent Micro-driVes

The aggregates are the joint units offered by manufacture, consist of micromotor, sensors and gear. There are mainly kinds of miniature sensors in this case (data taken from [1, 4]:

D.C. generator (speed transducer) – characterized by voltage signal directly (linearly) proportional to speed, small moment of inertia, small parasite torque and silent work (the parameters of dis-tinguish small one: mass – 13 g, diameter – 16 mm, length – 16.8 mm, M.I. – 0.31

gcm2, range: 500–5000 rpm with inaccu-racy – 0,2%;synchronous generator (for less values of the speed, the amplitude of gener-ated voltage is used, characterized by pulsed load torque added to micromotor (the parameters of distinguish small one: mass – 14 g, diameter – 22 mm, length – 13.9 mm, M.I. – 0.4 gcm2, range: up to 15000 rpm); encoder based on Hall effect (the param-eters of distinguish small one: mass – 10 g, diameter - 10 mm, length – 13.3 mm, M.I. – 0.09 gcm2, 10 pulses on full turn); encoder based on optoelectronic cou-ples (the parameters of distinguish small one: mass 14 g, diameter – 22 mm, length – 19.5 mm, M.I. – 1,2 gcm2, 60 pulses on full turn);

The view of the some aggregates is shown on Fig. 3.

suMMarY and concLusion

Miniaturization of the mechatronic electrical drives is constant tendency. In effect – also the methods of testing of such an objects continually are developed. Also the new so-lutions of integrated sensors are proposed. In every case the new methods of determi-nation of static and dynamic properties of new drive units are necessary. The physi-cally experiments have to support building of new mathematical models of drives and give us possibility of comparison of various products.

The trends in area of testing are no doubt methods eliminating additional loads on miniature device, preferably non-con-tact or sensorless. Also for control of the re-ally miniature motors (e.g. characterized by diameter 8 mm with M.I. of rotor 0,03 gcm2

��

Fig. 3: The examples of shapes of miniature aggregates [4]a) with DC tachogenerator, b) with magnetic encoder c) with optoelectronic encoder

[4]) it means less then described generators and encoders, the traditional transducers could be eliminated. These methods have to be repeatability and reliable.

Avago Technologies Limited: www.avagotech.comBodnicki M., et al.: Metody pomiaru wielkości mechanicznych charakteryzujących pracę miniaturowych silników elektrycznych. (Grant Raport nr 4 T10C 005 25), IMiF, Warszawa, 2006Bodnicki M., Pochanke A., Czerwiec W.: in Proceedings of the 5. Polish-German Me-chatronic Workshop „Tools of Mechatronics”,2005, Serock, Poland: Sensorless measure-ment in testing of miniature actuators. MINIMOTOR. Faulhaber DC Motors: www.minimotor.chOleksiuk et al.: Konstrukcja przyrządów i urządzeń precyzyjnych. WNT, Warszawa, 1996Oleksiuk W.: Przekładnie zębate w miniaturowych motoreduktorach. Zeszyty Naukowe Politechniki Opolskiej, 68, 2001, 271Wierciak J., Igielski J.: Problems of applying load torque in tests of mechatronic drive systems. Elektronika, 8/9, 2004

1.2.

3.

4.5.6.

7.

Literature

��

Grzegorz Domek, P. Krawiec

Easy production technology of pulleys without necessity to maintain high

workmanship accuracy is one of the advan-tages that contribute to development of belt gears. In modern gears, it is important to take the production accuracy of pulleys into account, but also a state of surface as in most cases frictional steam of belts and pulleys occurs. Gears with cogbelt have been recognised and still mistakenly are as gears, where only profile coupling occurs [1,5]. The frictional and profiling character of cogbelt coupling with pulleys and the im-portance of surface state and workmanship accuracy of pulleys for the coupling quality have not been taken into account. In case of toothed cylindrical gears, operation tests have shown a huge significance of not only workmanship accuracy of pulleys, but also the technology of their working. Application of these experiences on gears with cogbelts

contributes to another quality progress in intermeshing of belts with pulleys[2]. Series of cogbelt pulley production technologies, the new machine tools and a broad selec-tion of materials applied in production con-tribute to it. Pulley teeth may be located freely along a pulley width and an axially placed guiding wedge starts to be applied more often. The difference in production technology makes the belt pulleys of the same type and the same producer differ in dimensions and surface state [3,4].

beLt PuLLeY ProfiLe ProbLeMs

By shaping belt pulleys, the design engineers applied experiences obtained in other gear structures. Structures of chain, toothed, cy-lindrical and other gears were developed. A pulley had to assure staying on track and proper ratio and coupling in a gear. Round

The work treats about problem of designing of timing belt pulleys depending on expected character of ratio. There are many different ways of non-uniform gear ratio in gears with timing belts where different support of belt tooth on the tooth space of the pulley occurs. Analysis of this problem will let for wider use of this type of gears.

Abstract

pulleys, gears with timing belts

Key words

MetHods of desiGninG of tiMinG beLts PuLLeY

��

belts, V-belts, splines belts and polygo-nal belts have got a problem with staying in track. The problem required a solution within flat belts and cogbelts. There are three structures that can be distinguished, out of which each makes up a solution to this problem, they are however adapted to specific operating conditions in a gear. Pro-duction of a belt pulley in a profile of a bar-rel generates various linear velocities on a pulley surface. The points of contact on a surface with greater diameter move faster, what pulls a belt always into the pulley cen-tre. Special profile of the running side, e.g. application of a guiding wedge allows plac-ing the belt on the pulley basing on special slot. This is a good solution for belts moving with low linear velocity on pulleys with a di-ameter not causing an excessive bending of a belt with a wedge. There is also a possibil-ity to apply edge discs and belt work-rests, however this solution often causes mechan-ical damage of a belt.

One may come across automatic adjust-ment systems in case of slow-moving belts, used in control systems. These systems are applied in gear structures, where the cost of instrumentation is not considerable in comparison with the cost of the entire plant. Belt gear ratio may be: fixed, variable or non-uniform and may cover reduction and growth of revolutions of intermeshing drive-shafts. A belt may intermesh with one pulley, most often with a pair of pulleys, but also with numerous pulleys of different cou-pling character. In case of gears with fixed ratio, various profiles assure various instan-taneous and average efficiency. Gears with a variable ratio mainly include wedge gears and wedge-toothed gears. In these struc-tures, ration change is obtained through approaching and moving away of surfaces intermeshing with belt sides. Intermeshing

with a pulley at different diameter allows obtaining different ratios. Gears with non-uniform ratio are the gears, in which pulleys are placed eccentrically or their external profile is not a pulley. Location in this type of gears changes during one shaft revolu-tion. Series of parameters essential for belt coupling with pulleys may be distinguished here, such as: profile of belt and pulleys, sur-face state, barrel profile, whip and parallel-ism of shafts. The profile of belt and pulley has a significant impact on coupling in gear with V-belt and toothed belt. Modification of belt profile is a problem, because such belts have been produced in large numbers and have created great confusion among users. Necessity to apply mechanical char-acteristics of belt material as well as belt bending on pulleys has been documented in many works [].

Taking essential changes into account is possible in structure change of pulleys, which are produced in shorter series and often on individual design engineer’s de-mand. The surface state and structural fea-tures, often omitted, such as gear tooth and tip rounding radius is dependant on a pro-duction technology. Pulley setting on shafts is considered here however. The solutions, such as bearing adapter sleeves or collets considerably improve repeatability of pul-ley setting.

tootHed beLt PuLLeYs

The problems of toothed belt pulley struc-tures cover such areas as in the remaining gear types. The frictional and profile cou-pling character makes optimal solutions of some of them difficult. Belt guiding on pul-leys is usually conducted through edge discs on pulleys or special profile of the running side. Barrel-profiled pulleys are not occur-

��

ring in this group. These gears are highly efficient. Production of gears with variable and non-uniform ratio is possible.

Fig.1: Belt bending on the pulley

In order to assure correct belt coupling with pulleys, it is necessary to consider mechani-cal properties of a belt and profile changes of teeth caused by bending and belt pres-sure on pulleys. Free belt bending allows observing profile change of teeth within the bent zone. The pressed material below the base is pushed out inside teeth and depend-ing on their type, a change of their basic parameters is visible. In case of trapezoid teeth, one may observe evident rounding of side surfaces and the tip. In coupling with a pulley, the belt material is pressed between the base and the pulley surface. Therefore, belt pulleys should consider belt tooth pro-file change at arc of contact other than in case of belts leaning on the tips of pulley teeth and belts leaning on bottom lands of pulleys (Fig.1).

A small layer of belt material is pressed in gears leaning on tooth tips and this case is similar to free bending. A ratio of tooth rounding undergoes a considerable change out of the parameters determining char-acteristic features of belt tooth. The re-maining features, such as tooth volume, height and surface ratio also undergo slight change; however it does not have an impact on coupling in gear. Belt pulley space profile does not have an impact on tooth belt pro-file. Material push out in the central part of tooth and side rounding create worsening situation within the tooth root. It is more

imposed on notch effect, what worsens tooth falling into pulley space even more. It is recommended to increase the angle be-tween the sides of the neighbouring teeth in relation to the angle of belt tooth sides. In case of the T10 type belt, the difference is 10% and inaccuracy in this scope is often the case, what however does not have an impact on gear durability.It partially consid-ers a change of tooth profile due to bending and improves meshing with belts during op-eration. It is important to maintain accura-cy of tip diameter and pulley pitch in gears with such character of intermeshing of belt with pulleys. In connection to belt deforma-tion within the zone between the base and pulley leaning surface, it is recommended to increase pulley tip diameter. There are three groups of belts of this kind: belts with trapezoid and involute teeth with margin, belts with rounded teeth and belts with especially profiled tooth tip. The belts with flat tooth tip lean on the space, the round-ing of which corresponds to the diameter of tooth roots Rf . The belt material is pressed between space surface and the base with rounding by radius Ra which make up the fragments of two coaxial rolls.

The radiuses of these rolls decrease with pulley diameter drop. It is generally thought that the bottom land of gear rounded by ra-dius have an impact on polygon effect re-duction, yet the flat profile of the bottom land of gear would have an impact on pol-ymeric chain arrangement in a belt tooth. Such profile may be changed without any cost. It is possible to slightly lean the bottom land of gear or profile in such a way that a tooth is more pressed on the load carrying side on driving pulley. Incorrect adoption of belts’ mechanical properties was the prob-lem of belt pulley profile. Different way of intermeshing of belts with driving pulleys

��

with driven pulleys has not been taken into account. In case of a gear with two pul-leys, the conditions undergoing on arcs of contact have been recognized as symmet-ric. Therefore, all profiles of pulley straight teeth are also symmetric. In other words, pulleys may move in all directions. This is partially true, because the pulley function change from driven to driving causes a change of conditions undergoing on the arc of contact and the coupling and decoupling zones. Similarly to car tyres, also in belt pul-leys, in order to obtain optimum intermesh-ing conditions of belt and pulley, it is neces-sary to design pulleys adapted to direction. A pulley mounted in a gear as driving shall be perfectly operating as driven in opposite direction. Pulleys with straight symmetric teeth shall still be applied in reverse drives, however in these cases; the loads for both directions are rarely the same.The problem also concerns pulleys with rounded and in-volute teeth, whereas in case of these belts, attempts are made to obtain such profile of belt pulleys to obtain a intermeshing with the pulleys provided both with STD and ITD teeth.

Flexibility is only one of the directions to seek new structures, other is to seek opti-mum intermeshing and the pulleys with the CTD tooth profile or POLYCHAIN may be an example of this. Shaping belt tooth in such a way to create proper pressure layout within belt tooth when leaning on the bottom land of gear, may be presented on an example of RPP belts leaning on HTD and STD pulley. Belt tooth structure, which was to make belt tooth tip more flexible in order to improve coupling with pulley, had contributed to a positive effect for belt durability by chang-ing leaning way on pulleys. Introduction in the case asymmetric bottom land of gear would improve the coupling conditions.

Accuracy of pulley make is a substantial problem of a gear structure. Series of meas-urements have been conducted on belt pul-leys, the most important of which include: roughness, pith accuracy and rectilinearity of teeth. Single and total deviations of left and right side of belt pulley as well as ra-dial run-out deviation have been presented on the measurement result sheet. The ta-ble presenting the measured values, below the measurement curves, illustrates inaccu-racy of pulley make. It shall cause an extra changeability of coupling conditions [1,3], contact stresses shall be different in belt pulleys as well as their distortion. Adopting this in average coupling formula, it gives us:

where: S1,S2 – stresses in wrapping connec-tors, z- tooth number on pulley arc of con-tact, p- pitch, Δpk- pulley pitch error, Δlz- belt tooth distortion.

The features, which have been taken into account in measurements, also include: deviation of adjacent pitches, irregularity of pitches and total deviation of pitches. The last feature has been considered in the stud-ies on belt pulley diameter amendment. The term total pitch in case of a toothed belt is important for changes made in relation of a toothed belt pitch to a pulley, it is also important when totaling pitch errors of pul-leys with a large number of teeth.

where: Ro- pulley(roots) radius, ho- belt tooth height, k- height change of cord axis.

The test results show different accuracy of pulley make. This difference is not caused by a tooth profile as it does not have an im-

oz

z

kp

plzf

SS

12

1 ,

o

z

zk

o

oo

z

p

z

khRp

o

122

,

(1)

oz

z

kp

plzf

SS

12

1 ,

o

z

zk

o

oo

z

p

z

khRp

o

122

, (2)

��

pact on the pitch accuracy. These pulleys were made of different materials, what has a huge importance for the surface state of these pulleys, as well as in most cases deter-mine a working technology. Steel pulleys, such as the tested HTD pulleys are made by hobbing, yet aluminum pulleys (the tested AT pulleys) are made by profile milling. Such method selection is not imposed by a desire to obtain specific accuracy of make, but by economic reasons. It has been accepted that a hop would be a better steel working tool than a profile miller. It should be emphasized here however that this type of division is not fulfilled, particularly when it cymes to small producers of pulleys, who are provided with machine tools of one type. Producers of pulleys often try to engage all machine tools in a production. Different production tech-nology also leads teeth differing in struc-tural details. Produced pulleys have various roughness, tooth rounding at tip and root of different radiuses, tooth contour line is not the same. Measurement of tooth line show considerable irregularities in this part of a pulley tooth, which has a first contact with belt in the coupling process. HTD type steel pulleys feature greater irregularity. Profile errors in this field determine a considerable volume wear of belt teeth and at the same time worsen coupling conditions in the en-tire utilization process.

The belts with teeth irregularly distrib-uted at a belt width are one of the last structures. These structures try to imitate toothed cylindrical gears, so as to trans-fer their advantages to belt gears. Belts of the following teeth are produced: curved, canopy, diagonal and conical. Tooth profile in transverse cross-section to a tooth side has not been changed and in case of curved teeth, this is AT profile, canopy teeth –HTD, diagonal –CTD and conical -AT. Space pro-

file of belt pulleys reflects the same profiles of teeth without considering torsion and upsetting of teeth on the arc of contact. Proper belt structure taking the properties of polymers applied in a production of belts into consideration is a problem for pro-ducers. Internal friction inside upset teeth causes dissipation of a considerable part of energy. A material in an increased tem-perature is imposed to greater deformation caused both by pressure as well as bending. Belt expansion is added to this type of belts, what causes deformation of teeth at width.

The problem of deformation of teeth is being solved by using composite fibres in teeth, covering fabrics or excluding the cen-tral part of a belt from profiled coupling us-ing a guiding wedge as in the case of BATK type belts. Partially the problem is solved by increasing a gap between belt teeth and pulley, what worsens however the coupling conditions. In effect, the belts with irregu-larly distributed teeth at width do not trans-fer greater torques. The gears of this type are working emitting less noise. Thanks to the increase of cover ratio, a greater number of teeth is taking part simultaneously in the coupling process, and the points of belt teeth are not striking the points of pulley teeth.

suMMarY

Cutting teeth according to the profiling method is the most frequently applied method in the production of belt pulleys, what causes a low pulley make quality observed in the tests. Unfortunately, the number of mills used for a production of an entire range of teeth is limited and not all pulleys are provided with an optimal tooth profile. The structure of pulleys with teeth

�0

Dudziak M., Domek G., Gear with timing belts in mechatronic drives, Machine Dynam-ics Problems 2004, Vol 28, No 3, Warsaw University of Technology, s. 83-88, ISSN 0239-7730.Domek G., Malujda I.,, Stan powierzchni i wymiarów pasów zębatych, Mechanik 2/2006, s. 130-132Domek G., Dudziak M., Dissipation of energy in gear with timing belts, Progress in Ma-terial Engineering, Zeszyty Naukowe TU Ostrawa, cislo 1,rok 2005, s. 53-59Domek G., Dudziak M., Kołodziej A., Ocena błędów kształtu pasów i kół zębatych Inżynieria chemiczna 3 /2005, s. 20-21Domek G., Dudziak M., Kołodziej A., Błędy kształtu w przekładni z pasem zębatym, Mechanik 3/2005, s. 174-175

1.

2.

3.

4.

5.

Literature

irregularly distributed at width should cover deformation of the central belt caused by maintaining a belt on track. Analysis of also these kinds of barrel-shaped pulleys is pur-poseful here.

��

interaction of eLeMents in tHe coPPer / indiuM – tin diffusion Joints at �00 and �00 °c

Jaromír Drápala, Renata Kozelková, P. Kubíček, Jan Vřešťál, Aleš Kroupa

The Cu-In-Sn ternary system is one of the possible systems which should be stud-

ied from the point of view of interaction of solder with substrates. The study of equi-librium phases in the paper W. Köster et al. [2] was the first attempt to study of phase equilibria in this ternary system. Although X.J.Liu et al. [4] optimized thermodynamic parameters and phase equilibrium data in this ternary system, critical evaluation of the literature data in the frame of the COST531 program as well as new experimental phase equilibrium encouraged us to perform the reassessment of the Cu-In-Sn system.

dissoLVinG of soLid PHase in MeLt

According to the fundamental law of the physical dissolving kinetics the following linear dependence holds for the substance flux density j from the solid phase surface between this flux and the melt unsaturated concentration c

j = k (co – c),

where k is the velocity constant of dissolv-ing and co is the saturated concentration in the melt. According to Nernst theory a dif-

Interaction of lead-free solders with copper substrate represents an important phenom-enon in the issue of reliability of solder joints. New experimental data describing phase equilibria in the Cu-In-Sn system after long-time diffusion annealing at the 400 °C and 600 °C will be presented. The composition of solders was: 100 % Sn, 75 % Sn + 25 % In, 50 % Sn + 50 % In, 25 % Sn + 75 % In, 100 % In. We study an interaction between copper wire and indium or tin alloys in liquid state too. The fast quenching method was employed to freeze thermodynamic equilibrium after annealing, followed by metallography, micro-hardness measurements, SEM (Scanning Electron Microscope) and WDX (Wave Dispersive X-ray) analysis. New phase equilibrium data, together with the data from literature, represent the best existing experimental description of phase equilibria in the system in question. The obtained experimental results of the phase equilibria were compared with the ther-modynamic modelling by the CALPHAD (Calculation of Phase Diagrams) method and with other authors.

Abstract

reaction diffusivity, copper – indium – tin ternary system

Key words

(1)

��

fusion layer of the thickness δ creates on the solid and liquid phases interface and the gradient of concentration is expressed by the relation

It follows from relations (1) and (2)

where Ds is the diffusion coefficient of the solid phase in melt. The diffusion layer thick-ness δ depends on the flow velocity of melt, i.e. on the velocity of melt agitation, and it can vary in the range of δ = 5 ÷ 100 μm. It is expressed by Nusselt criterion Nu

where l is the characteristic dimension of the dissolving body. The Nusselt number magnitude is expressed by means of Rey-nolds and Prandtl numbers

where vk is the rate of convections; v is the kinematic viscosity. For Re < 1, Pr >> 1 holds e.g. Nu

These problems are concerned in more details in the monograph [1].

There are convections in the experiments when the melt is seemingly stationary. They are caused e.g. by a very small temperature gradient, by the difference of the solid and liquid phases densities, imperceptible vibra-tions, shakes, etc. These factors then have a very negative influence, e.g. when studying diffusion in liquids and melts applying capil-lary methods [3], where just these factors influence negatively the accuracy of deter-mination of the values of diffusivity in liquid phase. At the flow rates of vk < 1 μm/s and times of experiments observing dissolving of metals in melts in order t = 105 ÷ 106 s, the melt homogenisation is almost perfect.

The description of the time dependence of the solid phase dissolving in melt, i.e. the and the following can be written for the melt concentration during dissolving kinet-ics of dissolving, is formally performed ana-logically to the description of the chemical reaction kinetics. In our case we proceed from the following relation

where dc/dt is the time change of concen-tration of the solid phase in melt. We will concern the case when the interface bound-ary is plane and the interface boundary shift is perpendicular to this plane. This case will be called one-dimensional dissolving unlike the situation when the melt column is cylin-drical and the solid phase forms the cylin-der walls. This will be the cylindrical course of dissolving where the interface boundary shift is different from the one-dimensional dissolving. One-dimensional dissolving can be observed experimentally e.g. when both the solid phase and melt are placed in a ce-ramic capillary that is inert to the melt. Let us perform the dissolving mathematical de-scription by means of fig. 1 when solid Cu is dissolved in molten Sn. The interface bound-ary has in the time t = 0 the coordinate x = 0 and the height of molten Sn column above solid Cu is lo. It holds for the time change of the melt concentration with the interface boundary movement

Fig. 1: Scheme of plane dissolving of solid phase in melt

grad c = (c – co) / k = Ds / ,Nu = l /

Re = vk l / Pr = / Ds,3 PrRe .

dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(2)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(3)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(4)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(5)grad c = (c – co) /

k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(6)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(7)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

��

and the following can be written for the melt concentration during dissolving

where X(t) is the interface boundary shift. From relation (8) we receive

Inserting relation (9) into equation (7) we obtain an explicit expression of the first-or-der differential equation. After integration and arrangements we obtain the following relation for the interface boundary move-ment X(t)

When deriving relation (10), the volume changes in the melt at dissolving were not taken into account, i.e. we assumed an ideal solution. In the first phase of dissolving the melt decrement due to the diffusion into the solid phase, in our case Sn → Cu, is usu-ally negligible compared to the amount of copper dissolving in tin and therefore this factor was not taken into consideration in the material balance. In the time period when the melt concentration approaches to the saturation, i.e. c(t) → co, the dissolvent diffusion into the solid phase plays a more significant role in the material balance.

It follows for short times from relation (10)

and the interface boundary movement is then a linear function of time. We receive from relation (10) for the interface bound-ary maximal shift

In fig. 2 the interface boundary movement courses X(t) according to relation (10) are presented for illustration for the selected value of the velocity constant of dissolving k = 5.10-7 and various values of the saturated concentration co. Inserting relation (10) into relation (8), we obtain time dependence of the course of concentration c(t) of the solid phase dissolving in melt at the perfect ho-mogenisation of melt and c(t) = co holds.

Fig. 2: Time courses of the interface boundary movement X(t) at the solid phase dissolving in melt for the velocity constant of dissolving k = 5.10-7 in dependence on the relative mass of saturated concentrations co of the solid phase in melt.

eXPeriMent

Experimental alloys were made using pure metals Cu (99.95 %), In (99.995 %), and Sn (99.995 %). The composition of solders in diffusion couples was: 100 % Sn, 75 % Sn + 25 % In, 50 % Sn + 50 % In, 25 % Sn + 75 % In, 100 % In. Solders were inserted in the cop-per block with cylindrical hole of 10 mm or 30 mm diameter and sealed by Cu lid. Phase equilibria in the diffusion couples Cu/In-Sn after diffusion annealing at the 400 °C/50 hours, 600°C/310 hours and 600 °C/48 hours were studied. The quenching method into water was employed to freeze thermo-dynamic equilibrium after annealing, fol-lowed by metallography, micro-hardness

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(8)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(9)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(10)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(11)

grad c = (c – co) / k = Ds / ,Nu = l /


dc / dt = k [co – c(t)],

dtd

ddc

dtdc

(7)

olt

ttc21

1

; 1 = Cu; 2 = Sn,

2taa

ddc

; a = lo 2 / 1.

tak

o

ot

ak

ec

cet 111 / .

(t) co k t . . . t << a / k

o

o

ccat

1

.

Cu

t = 00

x(

t) l o Sn

0

2

4

6

8

10

12

0 20 40 60 80 100distance [m]

In, S

n co

nten

t [at

. %]

In Sn

Cu

600 °C / 48 h Cu

Cu

hole

solder

(12)

��

measurements, SEM (Scanning Electron Microscope). Equilibrium compositions in multi-phase specimens were determined by WDX (Wave Dispersive X-ray) spectroscopy using standard calibration method.

A capillary method was used for further experiments. The aim of this test was to dis-cover the character of dissolving and influ-ence of convection in the diffusion joint Cu / (Sn, In). When Cu substrate comes in contact with the melt of pure Sn or In and/or with the alloy Sn-In, the reactive diffusion among individual components happens, besides the Cu preferential dissolving in the solder melt, resulting in formation of new phases, mostly in the solid. An important role plays a convection in the melt, which may nega-tively influence the character of diffusion processes. Therefore the specimens were subjected to various temperature and time conditions. Before the experiment itself the Cu wire, diameter 2.8 mm and length about 10 mm, with the front surface modi-fied metallographically, was placed in the lower part of quartz capillary, inner diam-eter 2.8 to 3 mm. The solder specimens were prepared in the form of cylinders by sucking the melt in the corresponding capil-lary to ensure the contact solder / Cu wire. The lengths of the solder specimens were gradually 2, 4, 6, 8 and 10 mm. The heat treatment was executed in laboratory fur-naces at the temperatures 400 and 600 °C and at three different times, 24, 48 and 72 hours under the protective atmosphere of argon. The furnace, however, was not her-metic tight and surface oxidation of speci-mens occurred. Cooling of specimens was carried out by free cooling out of the fur-nace (at outdoor temperature) or the speci-mens were kept in the ampoule and graph-ite crucible in the furnace till cooling down. Some of the specimens were annealed in a

vacuum furnace at 110 Pa and then cooled in vacuum during about 24 hours.

resuLts

The results of WDX analysis are listed in Ta-ble 1.

As an example, the concentration profile of In an Sn in Cu region and microstructure of the sample Cu/25 at. % In-75 at. % In after annealing 600 oC / 48 hrs is shown on the Fig. 3. By interaction of the solder melt with Cu grows the β (BCC) phase on the Cu sur-face. With respect to the large concentra-tion difference between pure Cu and Cu in phase β (BCC), the concentration profile in the region adjacent to the phase interface Cu/β phase during annealing is created. This profile is dependent on the values of diffu-sion coefficients of individual components. On the phase interface the concentration corresponding to respective isotherm of phase diagram is established. In the same time in the melt the dissolving Cu is increas-ing its concentration up to saturation of the melt by Cu. With respect to the large vol-ume of melt, the enrichment of melt by Cu proceeds in the neighbouring region of melt to the substrate only. Dissolution of Cu in the melt is influenced substantially by the temperature and convections. In the case of enough long annealing time, all existing reactions in the isothermal section should be established. The observed jumps in the concentration profile are important infor-mation on respective existing phase. Region between individual concentration jumps brings information on the domain of exist-ence of given phase. The role of the three orders higher diffusion coefficient in liquid phase than in solid phase need to be taken into account.

��

Concentrations of elements in given lo-calities determined by the WDX method correspond very well to concentrations of phases according to the equilibrium binary diagrams of Cu – Sn and/or Cu – In systems, see Fig. 4 and Fig. 5. The Cu wire dissolving by the Sn and/or In melts happened both on the wire front and surface. With increas-ing volume of the Sn and In melt the area

of pure Cu strongly decreased and it often retained just the wire central part, which was caused by high convection in the melt. In addition, high capillarity of In and Sn led to their transport even into the lower area of capillary.

Tab. 1: Experimental results of WDX analysis.

Content Sn [at. %] Sample Annealing

Cu liquid Cu - 100 % Sn* 400 °C / 50 h 2.9 19.2-21.9 21-24 40-42.5 96-99 Cu - 100 % Sn 400 °C / 50 h 6.4 20.4 24.8-25.8 44.5 96-99 Massalski [5] 400 °C 8.1 20.5 24.5-25.1 43.5 84.7

Content Sn [at. %] Sample Annealing

Cu liquid Cu - 100 % Sn 600 °C / 48 h 9 14.8-15.2 not found 21.7-22.5 24.5-26.2 94-98 Cu - 100 % Sn 600 °C / 310 h 9 15 Massalski [5] 600 °C 9.1 14.9 16.1-20.2 21.7-22.6 24.7-26.1 55

Content In [at. %] Sample Annealing

Cu liquid Cu - 100 % In 600 °C / 310 h 11 19.8 Massalski [5] 600 °C 10.8 19.5-21.8 29.1-30.9 63

Sample Content In/Sn [at. %] Cu - In/Sn Annealing

Cu or liquid in liq. Cu - 25 / 75 400 °C / 50 h 0.1/1 6.3/16.7 5.3/21 12.8/28.4 25/72 12/30 Cu - 25 / 75 400 °C / 50 h 0.2/0.3 10.6-8/13.4-16 11.6/28.7 Köster [2] 400 °C 1.4/4.1 5.4-5.8/16-17 6-7/18-19 10-11/30-32 23/67


Cu liquid Cu - 25 / 75 600 °C / 48 h 3.4/6.3 6.1/10.7 not found 5.4/21.5 Cu - 25 / 75 600 °C / 310 h 1.5/8 2-3/13.5-14.5 not found 3/23 Köster [2] 600 °C 2.2/7.1 4-4.2/12-12.6 4.4-6/13-17 10.5/30


Cu liquid Cu - 50 / 50 600 °C / 310 h 5.9/4 9.5-10/7-7.5 11-12/9.5-10 Köster [2] 600 °C 4.3/4.7 8.7-9.2/8.4-9 10-13/10-13 22.5/22.5


Cu liquid Cu - 50 / 50 600 °C / 310 h 7/3 14.5/5.5-6 Köster [2] 600 °C 8/2.5 14-15/4.4-4.7 20-22/6.2-7 25-27/8 58/17 * air cooling Cu – fcc solid solution of copper, – bcc Cu17Sn3 and – bcc Cu-In, – Cu4Sn and – Cu-In, –Cu41Sn11 and – Cu7In3, – Cu6Sn5, Cu-In and Cu17Sn3 Cu0.545(Cu,In,Sn)0.122(InSn)0.333, – Cu10Sn3, – Cu3Sn [? ? ? 1,2,11].

��

It would be possible to determine interdif-fusion coefficients of Sn and Cu from the concentration profiles of Sn in (Cu) and con-centration jump into the adjacent phase δ. Applying the surface analysis of secondary solidified melts In(Cu) and Sn(Cu), it will be possible to determine an approximate com-position of liquidus at given conditions of annealing, which may be a suggestion for continuing the study of phase diagrams Cu – In – Sn. On the basis of the melt global behaviour, where a significant role at Cu

dissolving is played by convection, which is among others dependent on the liquid phase volume, it would be convenient to propose a theoretical model of dissolving and to describe the entire process kinetics.

Considering the discovered structural and phase transformations at the proc-ess of specimen cooling (mostly several hours) and favourable results when apply-ing vacuum, We propose to perform fur-ther experiments according to the follow-

Fig. 3: Sample Cu/25 at. % In – 75 at. % Sn – annealing 600 °C/48 h + quenching, concentration profile of In and Sn in α Cu and microstructure.

Fig. 5: Isothermal sections in the Cu-In-Sn system at 600 and 400 °C with experimental results.

��

ing procedure: put specimens into the silica glass capillaries with the metal wire in the lower part of semi-closed capillaries. Place an appropriate low-melting alloy above this wire and ensure the contact of both mate-rials. Then evacuate the silica capillary and let proceed annealing. The cooling phase has to be as short as possible, in the order of seconds, which is hardly executable in practice. However, the given specimen di-mensions and volume enable to solve this problem by quenching into water or liquid CO2. The method of decantation would be the most convenient for preserving the melt composition after annealing, which is, however, hardly feasible in this case of closed ampoule. Turning the ampoule by 180° in the moment of quenching presents a certain hope. In this way the rest of melt divides from the solid phase and it will be easily analysed chemically by classical pro-cedures.

Application of capillary methods known from the study of diffusion in molten met-als and melts enables to reduce significantly

or even nearly eliminate convections in the melt at reactive diffusion if the ceramic cap-illary diameter is suitably opted. The con-vection elimination results in deceleration of the solid phase dissolving and, moreover, it is possible to determine the value of dif-fusion coefficient of metals in solid phase. For this purpose it would be convenient to use so-called method of „long capillary“ po-sitioned vertically. A cylinder of Cu about 1 cm long would be inserted on the capillary bottom and a column of melt (Sn), height h ≈ 5 ÷ 10 cm, above it. Considering the con-vection elimination, it is suitable to opt the capillary inner diameter of about 0.25 cm. In case of smaller diameters the surface dif-fusion can show itself more significantly.

concLusions

In this work, results of experimentally ob-tained phase equilibria by means diffusion annealing of joints copper/indium, tin alloys will be presented. The experimental results

Fig. 4: Concentration profile of Cu and Sn after annealing 600 °C/24 h (WDX analysis).

Cu (Cu) δη

ε

Cu / Sn joint, 600 °C / 24 hours

distance

��

will be compared with thermodynamic calcu-lation of the Cu-In-Sn ternary system accord-ing to CALPHAD method.

Aksemrud, G.A., Molchanov, A.D.: Rastvorenie tverdykh veshchestv. Ed. „Khimia“, Mos-cow 1977.Köster, W. Gödecke, T., Heine, D.: Z. Metallkde, 63, 1972, 802.Kubíček, P., Pepřica, T.: Methode and experimental results of a study of diffusion of al-loys and deoxidation elements in liquid iron. International Metals Reviews, 28, 1983, 3, 131-157.Liu, X. J. et al.: J. of Electronic Mater., 30, 2001, 1093.Massalski, T.B.: Binary Alloy Phase Diagrams. ASM Metals Park, Ohio 1987.

1.

2.3.

4.5.

Literature

��

nuMericaL anaLYsis of state of stresses and strains in sPLined connections

Marian Dudziak, Andrzej Kołodziej, Jacek Kroczak

Involute splined connection are more and more frequently used, especially in au-

tomotive and aircraft industry, because in comparison to other splined connections they are characterized by higher static and dynamic strengths of teeth and proper fa-tigue strength. It enables to decrease of connection dimensions and getting of bigger compactness of connections. General ten-dency in developing of geometrical features of this kind of connections is increasing of teeth number in toothing and decreasing of tooth depth. It is done by the considerable improvement of toothing manufacturing quality.

Geometric form and machining accuracy of involute splined connections are normal-ized [3, 4]. In standard [1] there were es-tablished normalized pressure angles (300, 37.50 and 450), accuracy classes (4, 5, 6, 7) and fitting types for stationary connections (H/k, H/js) and movable connections (H/h, H/f, H/e, H/d). Fittings mentioned in stand-ard concern fittings on teeth side surfaces only (side fits). Teeth flank surfaces transmit the drive and simultaneously create the co-axial connection.

Splined connections are calculated for contact stresses between hub and shaft reasons:

During designing and calculating of splined connections simple designing formulas are used. These, are not taking into account the influence of applied machining tolerance classes for stress distributions in the analysed connections. Even after the accurate machining the sur-faces of machine elements do not adhere together in ideal way. Roughness, waviness and form deviations are the main reasons for irregular contact on the entire nominal contact surface. The authors have carried out the numerical analysis of stresses and strains state that were the results of assembling of external and internal spline.

Abstract

splined connection, stress, strain, contact elements, design

Key words

�0

where: F – circumferential force, Ad = zhl – pressure surface, pa – allowable stress; z – number of teeth, h – active tooth depth, l – connection’s length.

In philosophy of new approach to designing and manufacturing the essential perform-ance direction is taking into account the real geometric structure (form deviation) and surface structure (topography) of ex-ternal and internal splines:

where: Ar – real pressure surface.

Taking into account the actual measuring technique achievements (e.g. coordinate measuring machines) as well as calculation techniques (FEM analysis) enables the accu-rate valuation of load in the connection.

caLcuLation ModeL of inVoLute sPLined connection

For determining of values and distribution of contact stresses and strains, basing on contact mechanics, there was elaborated the non-linear model of involute splined connection 12zx5mx30RxH7/k6. Numerical calculations were carried out for the case where the connection was not loaded and nascent stresses were resulted only from negative allowance on teeth flank (fitting H7/k6). For solution of this problem there was used the computer system I-DEAS. All input data, necessary to carrying out of analysis, were loaded to software with the aid of the adequate procedures.

In the pre-processor there was prepared three-dimensional FEM model of the con-nection together with boundary conditions: restrained lateral surface of hole in shaft and outside hub surface (Fig. 1). Referring to spatial analysis of the problem there were used solid elements. From among all accessible from library solid elements there were selected elements of cuboidal shape with 8 nodal points, so-called brick elements. These finite elements were taken mainly because of their better representa-tion of contact surface and more accurate results of calculations in stress concentra-tion zones. FEM mesh was concentrated near places of contact of integral keys flank surfaces for solution accuracy increasing. In analysis there were not taken into account material plastic strain.

For analysis purposes there were used also contact elements of type surface-to-surface defined between cooperating sur-faces of teeth and keyways. On basis of car-ried out numerical tests there were selected optimal parameters controlling of contact procedures, such as: normal and tangential penalty factors. For solving of contact prob-lem there was taken the implemented in the software augmented Lagrange method.

nuMericaL resuLts of contact anaLYsis

Problem of contact between spline flank surfaces was solved using finite elements method in software I-DEAS. Obtained re-sults of spatial contact stress distribution and strains for examined connection are shown in Fig. 2 and 3. There were obtained uniform distributions on each teeth flanks.

(1)

(2)

ad

pAFp ≤=

ar

pAFp ≤=

��

a)

Fig. 1: FEM calculation model: a) general view, b) enlarged view

b)

Fig. 2: Spatial contact stress distribution

Fig. 3: Three-dimensional strain distribution

��

Fig. 2: Spatial contact stress distribution

Fig. 3: Three-dimensional strain distribution

suMMarY

Knowledge of obtained distributions is nec-essary for correct evaluation of splined con-nection operation. The showed results may serve as the representation of assumed ideal state of analysed connection.

Presented chosen numerical results con-firm the complexity of presented contact problem. For taking into consideration ad-ditional effects connected to form and posi-tion deviations influence and external load there should be carried out further numeri-cal researches, which authors are going to carry out in the nearest future.

PN-ISO 4156+A1: Połączenia wielowypustowe ewolwentowe walcowe osiowane na bokach zębów. Wymiary, tolerancje i sprawdzanie.Bober, A., Dudziak, M.: Zapis konstrukcji, PWN, Warszawa 1999.Humienny, Z.: Specyfikacje Geometrii Wyrobów (GPS) – podręcznik europejski, WNT, Warszawa 2004.Jezierski J.: Analiza tolerancji i niedokładności pomiarów w budowie maszyn, WNT, Warszawa 2003.

1.

2.3.

4.

Literature

��

tHe saLt Mist corrosion resistance of a duPLeX-tYPe ferritic-austenitic cast steeL


Duplex stainless steel (DSS) represent an important and expanding class of stain-

less steels with an attractive combination of mechanical properties and corrosion re-sistance. Ferritic-austenitic cast steels com-bine the qualities of each phase: the ferrite guarantees the strength and resistance to intercrystalline corrosion and the austenite ensures ductility and resistance to general corrosion [4].

The chemical composition and the heat treatment temperature have the most im-portant influence on the precipitation be-haviour of duplex cast steel. At the temper-ature of ~ 4800C the ferrite may decompose

into an iron-rich BCC phase (α) and a chro-mium-enriched BCC phase (α’) either by nucleation and growth of α’ precipitates or by spinodal decomposition [5]. This leads to a hardening of the ferrite and subsequent loss of impact toughness and corrosion re-sistance [2].

After annealing at temperature 600-9000C, DSS will precipitate a number of in-termetallic phases in ferrite, such as �, χ, γ’, M23C6 etc., in which damage of � phase is most severe. Preferential growth of � phase into the ferrite is mainly result of the higher Cr and Mo concentration in ferrite matrix. A fundamental reason why the � phase pref-

The paper presents the results of metallographic examination and corrosion resistance testing in a salt mist atmosphere of a concentration of 5% NaCl for a duplex-type cast steel (with different carbon content) after various heat treatments operations (solution heat treatment, quench ageing, annealing). Testing results show that the the cast steel structure after the solution heat treatment changes substantially with increasing carbon content. It has been found that the cast steel both as solutioned as well as quench aged has similar corrosion resistance in the salt mist atmosphere. The highest mass loss was exhibited by the cast steel as annealed after solutioning.

Abstract

duplex steel, heat treatment, sigma phase, ε-Cu phase, corrosion resistance

Key words

��

erentially grows into the ferrite is that the ferrite is thermodynamically metastable at the temperature where the � phase precipi-tates so that the ferrite phase should de-compose into an equilibrium state [3].

In addition to the basic ferrite- and austenite-forming elements, part of the duplex cast steel grades contain also Cu. Quench ageing of DSS with copper addition at a temperature of 4800C causes precipita-tion of ε-Cu phases in ferrite matrix. Copper rich ε-Cu precipitates in duplex cast steel cause a reduction in corrosion resistance by disrupting the integrity of the passive film, and stimulate the formation of pits [1].

The purpose of the present work was to find out the effect of the solution heat treatment, quench ageing and annealing on the properties of the ferritic-austenitic du-plex cast.

MateriaLs & MetHodoLoGY re-searcH

The chemical composition of the ferritic-austenitic duplex cast steel used for the present work is listed in Tab. 1. For the pur-pose of the optimisation of the structure and service properties of duplex cast steel, the following heat treatment processes were carried out:

solution heat treatment in water af-ter 2h of soaking at a temperature of 10800C,quench ageing of the cast steel for 4h at a the temperature of 4800C,annealing for 10h at a temperature of 8000C.

Tab.1: Chemical composition of the investigated cast steel

Heat No.

Element, %

C Cr Ni Cu Mo Mn Si S P Fe

1 0,040 24,7 6,74 3,11 2,22 0,88 0,88 0,01 0,017 bal.

2 0,055 24,4 6,71 3,08 2,40 0,14 0,81 0,02 0,020 bal.

3 0,060 24,7 6,91 3,00 2,90 0,14 0,73 0,02 0,019 bal.

4 0,090 24,0 8,02 2,60 2,25 0,24 1,05 0,01 0,016 bal.

The microscopic investigations were per-formed on the optical microscope Zeiss Ax-iovert 25. Specimens for optical metallogra-phy (OM) were chemically etched in a 30g potassium ferricyanide + 30g potassium hy-droxide + 60ml distilled water.

Corrosion resistance was tested in a salt spray chamber with an artificial salt mist atmosphere of a concentration of 5% NaCl in 0,1 M CH3COOH and at a temperature of 350C. The conditions of the environment were selected so at to reproduce the cor-

rosion mechanisms existing during service, but progressing at an accelerated rate. Prior to being placed in the salt spray chamber, the specimens had their surface polished and cleaned with acetone, and the charac-ter and degree of surface damage during the corrosion test and after its completion were assessed from the mass losses and metal-lographic observations of the specimens. A single testing cycle took 6 hours.

��

resuLts and discussion

Examples of cast steel microstructure after the solution heat treatment from 1080oC/2h/water are presented in Fig. 1 and Fig. 2. Cast steels from heat 1 and 2, contain-ing Cmax=0.055% feature a two-phase fer-ritic-austenitic structure (Fig. 1a). In the structure of solution heat treated cast steel with increased carbon content (heat 3 and 4) a carbide eutectic, non-dissolved during the heat treatment, is observed (Fig. 1b). Quench ageing hasn’t caused the micro-structural changes which can be observed using light optical microscopy. As a result

of isothermal holding at 480oC, the spinoi-dal decomposition of ferrite to Fe-rich α and Cr-rich α’ phases and fine-dispersion Cu-rich ε phases have occurred, which has been extensively described in the authors’ works [x].

Fig. 2 presents microstructural changes in a duplex cast steel resulting from anneal-ing at 800°C/10h/air. High temperature of soaking caused an eutectoidal decomposi-tion of ferritic matrix and creation of signifi-cant amounts of σ phase and of secondary austenite γ’ according to the reaction δ → σ + γ’ (Fig. 2b).

Fig. 1: The microstructure of the cast steel after the solution heat treatment: a) heat 1, b) heat 4.

Fig. 2: The microstructure of the cast steel after the soaking at 800oC/10hrs/air.

a) b)

a) b)

��

The results of the salt spray chamber inves-tigation of the cast steel after, respectively, the solution heat treatment, quench ageing and the annealing are summarized in Table 2. The specimens were placed in the salt spray chamber at an angle of 150-300 in re-lation to the vertical plane in such a manner as to their surface was positioned in parallel to the direction of salt mist flow, while be-ing freely exposed to the circulating sprayed mist. It was found from the performed cor-rosion tests that the cast steel both as su-persaturated as well as quench aged had similar corrosion resistance in the salt mist atmosphere. Of the cast steels under analy-sis, as heat treated in different manners, the highest mass loss was exhibited by the cast steel as annealed after the solution heat treatment – after approx. 200 hours of test

the mass loss amounted to about 0.5 mg and was 10 times higher compared to the solutioned cast steel.

The metallographic examination of the supersaturated and quench aged cast steels revealed that the attack of pitting corrosion only occurred after 48 hours of test, and the number and size of pits had not undergone any significant changes after the complete time of specimen exposure in the solution of 5% NaCl in 0.1M CH3COOH at a tempera-ture of 350C (Fig. 3a). The surface of the su-persaturated and annealed cast steel exhib-ited greater tendency to pitting corrosion – pits were observed already after 12 hours of test, and their number increased with the time of the test, whereas their size had un-dergone any significant changes (Fig. 3b).

SpecimenNo.

Heat treatment Specimen mass mass loss�m, [mg]

before test[g]

after the test[g]

Heat 1

1_1 10800C/2h/ water 15,81939 15,81933 0,06

1_2 10800C/2h/ water + 4800C/4h/air 15,13353 15,13349 0,04

1_3 10800C/2h/ water + 8000C/10h/air 15,71836 15,27836 0,44

Heat 2

2_1 10800C/2h/ water 15,79513 15,79508 0,05

2_2 10800C/2h/ water + 4800C/4h/air 15,32128 15,32122 0,06

2_3 10800C/2h/ water + 8000C/10h/air 15,93253 15,93204 0,49

Heat 3

3_1 10800C/2h/ water 15,58275 15,58267 0,08

3_2 10800C/2h/ water + 4800C/4h/air 15,89748 15,89748 0,06

3_3 10800C/2h/ water + 8000C/10h/air 15,93353 15,93307 0,46

Heat 4

4_1 10800C/2h/ water 16,49472 16,49468 0,04

4_2 10800C/2h/ water + 4800C/4h/air 16,03375 16,03369 0,06

4_3 10800C/2h/ water + 8000C/10h/air 16,39461 15,87461 0,52

Tab. 2: The mass losses of specimens during the corrosion test in a salt spray chamber with an artificial salt mist atmos-phere of a concentration of 5% NaCl in 0,1 M CH3COOH and at a temperature of 350C.

��

Fig. 3: An example of the surface of the supersaturated cast steel upon exposure in the salt mist atmosphere after a time of 192 h (a) and corrosion pits on the surface of the cast annealed at 8000C/10h for an exposure time of 24 h (b); heat No. 2

Corrosion products in the form of envelopes could be visible around the pits. In the super-saturated and annealed cast steel, uniform corrosion was also observed to progress fastest, which manifested itself in etching of the structure constituents. The structure of this cast steel, as revealed as a consequence of corrosion, showed that all pits were lo-cated within the eutectoid region.

concLusions

The investigation carried out has enabled the following findings and conclusions to be formulated:

The cast steel structure after the solu-tion heat treatment changes substantial-ly with increasing carbon content. Cast steels containing Cmax=0.055% feature a ‘clean’ two-phase ferritic-austenitic structure. In the structure of solution heat treated cast steel with increased carbon content a carbide eutectic, non-dissolved during the heat treatment, is observed. Annealing at 800°C caused an eutectoidal decomposition of ferritic ma-trix and creation of significant amounts of σ phase and secondary austenite γ’.

1.

The highest corrosion resistance is exhib-ited by exclusively supersaturated cast steel. The quench ageing treatment and the associated process of precipitation of the ε-Cu phase did not cause any ap-preciable impairment in corrosion resist-ance. The metallographic examination showed that the attack of pitting corro-sion only occurred after 48 hours of test, and the number and size of pits had not changed significantly after the complete time of specimen exposureThe largest mass loss was exhibited by cast the steel annealed after the solu-tion heat treatment, with an austenite/eutectoid structure (after the salt spray chamber test, the mass loss being 10-times higher compared to the supersatu-rated cast steel). The surface of the an-nealed cast steel exhibited also greater tendency to pitting corrosion – pits were observed already after 12 hours of test, and their number increased with the time of the test.

2.

3.

a) b)

��

Banas J., Mazurkiewicz A.: Mat. Science and Eng. A, 277, 2000, 183-191.Dyja D., Stradomski Z, Pirek A: Proceedings of the International Conference –Metal2006, Czech Republic.Huang C.-S., Shih C.-C.: Mat. Science and Eng. A, 402, 2005, 66-75Smuk O., Hanninen H., Liimatainen J.: Mat. Science and Tech., 20, 2004, 641-644Stradomski Z., Dyja H.: Mat. Engineering (SK), 5, 2006, 32-36

1.

2.3.4.

Literature

��

forMation and cHaracteriZation of PoLY (VinYL aLco-HoL-co-VinYL acetate-co-itaconic acid)/ PLaster coM-Posites, Part i: cHaracteriZation of Β-HeMiHYdrate PLaster


Gypsum plaster is widely used in con-struction; mainly for coating interior

surfaces. Huge and extensive amounts of gypsum raw materials are spread allover the world. In Egypt, a high grade gypsum deposits occur at the Gulf of Suez, Red Sea, and Mediterranean Coastal localities [8]. Ancient Egyptians had recognized some of them which were used for production of the desired plaster that was used for plas-tering the indoors of the Ancient Egyptian

pyramids [13]. Gypsum-based composites have received increased extensive applica-tion in the development of new wall interior materials. Composite formation with poly-mers is one of the new routes in this regard. Various investigators studied the effect of varying the grain size of the original gypsum raw material on the phase constitution of the calcination products [1, 9-11]. Others investigated the effect of polymers addi-tion to β-hemihydrate plaster on the micro-

X-ray fluorescence (XRF), thermal analysis (DTA, TG), and X-ray diffraction (XRD) were im-plied to clarify the chemical and mineral constitution of the tested gypsum plaster. Moreo-ver, physical properties including normal consistency (N.C.) and setting time (S.T.) in addition to mechanical properties such as compressive strength (C.S.) and bending strength (B.S.) were determined. Results revealed that the purity of the tested plaster was calculated to be around 96 % CaSO4.½H2O with minute siliceous material along with slight of calcium and magnesium carbonates. The carbonates were calculated to be 1.34 and 1.9 % for MgCO3 and CaCO3, respectively. Thermal analysis results confirmed the presence of carbonates which were identified as a dolomite rather than MgCO3 and CaCO3 binary phases. XRD re-sults of the tested plaster indicated a bassanite pattern free from any gypsum, anhydrite, or carbonate contaminations. Absence of carbonates in the XRD results confirms that their existence was below 5 %, the limits of sensitivity of the tool. The plaster sample blended 46 % water and gave long setting time and moderate mechanical properties.

gypsum, plaster, composites

Abstract

Key words

�0

structure and mechanical properties of the formed polymer / β-hemihydrate plaster composites [6, 7]. However, the evaluation of the β-hemihydrate plaster before being blended with polymers, have received little attention.

The present study reports the charac-terization of a commercial-grade gypsum plaster using X-ray fluorescence (XRF), dif-ferential thermal analysis (DTA), and X-ray diffraction (XRD). In addition, normal con-sistency (N.C.), setting time (S.T.), compres-sive strength (C.S.), and bending strength (B.S.) of the starting gypsum plaster were measured.

eXPeriMentaL

A commercial-grade gypsum plaster (CaSO4.½H2O), (BPB Formula Gmbh, Ger-many) was used in this study. The chemical composition of the starting plaster was in-vestigated by X-ray fluorescence (XRF) using an ARL 9400 XP sequential WD-XRF spec-trometer with a Rh anode end-window X-ray tube type 4GN fitted with 75 µm Be win-dow. The obtained data were evaluated by standardless software Uniquant 4. Differen-tial thermal and thermogravimetric analy-ses for the plaster powder were performed over a temperature range from room tem-perature up to 900oC, in a simultaneous TG/DTA instrument (Model SETARAM-SETSYS Evolution-1750 TG-DTA/DSC-18) with mass spectrometer (Pfeiffer Balzers Thermostar) in an air atmosphere at a heating rate of 10oC min-1.

The phase composition and the degree of crystallinity of the plaster was studied by X-ray powder diffraction (XRD) using an automated diffractometer (X’Pert PRO θ-θ), with a step size of 0.02o, counting time

of 0.3 s / step and a scan range from 5 to 65o 2θ. A Cu Kα tube operated at 40 kV and 20 mA was used for X-rays generation. XRD patterns were manipulated and interpreted using the “High Score Plus” software pack-age.

In the light of the ASTM No.C 472-90, both the normal consistency and setting time of the plaster were determined using modified and normal Vicats, respectively. Setting time was measured using Vicat appa-ratus blending water amounting to the pre-determined N.C. Samples for both compres-sive and bending strengths were prepared using the predetermined N.C. and tested after one, three, and seven days of aging. To measure compressive strength, 2.5 cm x 2.5 cm x 2.5 cm cubes were tested using a uni-versal testing machine (FPZ100/1, HECKERT/THURINGER INDÜSTRIEWERKE, Germany) at a crosshead speed of 0.56x10-4 m.s-1. Three-point bending strength measured using 17.2 cm x 2.3 cm x 2.3 cm bars samples tested using universal testing machine (FM250, HECKERT/THURINGER INDÜSTRIEWERKE, Germany) at a crosshead speed of 0.45x10-4 m.s-1 and span of 10 cm. An average of five measurements for each test was recorded and considered.

resuLts and discussion

XRF results of the investigated plaster, Table (1), show that it consists mainly of CaSO4.½H2O. The CaO-SO3 ratio suggests the high grade quality of the plaster. More-over, the CaSO4/H2O ratio demonstrates the absence of either gypsum or anhydrite phases contaminations which confirm the high purity grade of the plaster.

��

Type SiO2 R2O3 CaO MgO SO3 *H2O *CO2 NaCl

Wt. % 0.44 0.02 38.53 0.64 53.55 5.28 1.54 Trace

Mol % 0.43 8.96 x 10-3 40.41 0.93 39.18 16.99 2.05 Trace

Tab.1: XRF data of the tested plaster

*Both H2O and CO2 were determined by weight loss at 240 and 1000 oC respectively.

The XRF results in Table 1 also revealed that the plaster sample contained minute amounts of either SiO2 or R2O3 due to minor impurities in the mother gypsum rock used for the production of the plaster. Results, however, show some MgO and CO2 con-tent, suggesting the presence of magnesite, MgCO3 impurities (1.34 %). The CaO-SO3 ra-tio, on the other hand, clarifies the existence of trace amounts of calcite, CaCO3 as con-taminations (1.9 %). The existence of CaCO3 and MgCO3 may be as two separate min-eral phases or single dolomite [CaMg(CO3)2] phase. Phase calculations based on XRF data show that the carbonate phases lie around 3.2 % which in addition to the siliceous im-purities may indicate a purity of the plaster to be around 96 % CaSO4.½H2O.

Figure 1 shows the thermal analysis (DTA&TG) results of the tested plaster. It is clear from the figure that on heating the β-hemihydrate plaster it gave three notice-able thermal effects; a low-temperature large endotherm at 170oC, a small exotherm at 360oC, and a small high-temperature en-dotherm at about 720 oC. The endotherm at 170oC denotes the transformation of the β-hemihydrate plaster into soluble anhydrite (γ-CaSO4) which, in turn, was converted into the insoluble (β-CaSO4) phase giving rise to the small exotherm at 360 oC. Both the low-temperature endotherm and the exotherm are the characteristic thermal peaks of the hemihydrate plaster [2, 3, 5, 12]. The presence of one single endotherm at 170 oC strongly indicates the absence of

gypsum CaSO4.2H2O phase in the tested β-hemihydrate plaster. Anhydrite phase, on the other hand, is a thermally-inert phase which is hardly detected with the calorimet-ric tools. The obtained endotherm at 720 oC is due to the decomposition of dolomite [CaMg(CO3)2] forming the corresponding CaO and MgO with the evolution of carbon dioxide gas [4]. It is also clear from the TG curve that the plaster denotes two weight loss stages, a large step at 150-180 oC and a small one at 660-740 oC. The first one cor-responds to the evolution of the water of crystallization of plaster to form γ-CaSO4. The second one is due to the liberation of CO2 from the carbonate contaminations. Both TGA steps confirm the DTA findings and the XRF results as well.

X-ray diffraction pattern of the β-hemihy-drate plaster is given in Figure 2, from which the interlattice spacing (dÅ) and relative intensities (I/Io) were calculated and com-pared with the ASTM data of the expected phases. Calculations clarify that the tested plaster consists of the mineral phase bas-sanite (CaSO4.½H2O) as the sole constituent. The XRD data revealed the absence of any gypsum or anhydrite confirming the previ-ously mentioned thermal analysis results. It should be mentioned that the XRD pattern did not reveal any carbonate phases, al-though it were suggested from XRF and DTA results. These findings may denote that the carbonate impurity is below 5 %, which is the limit of sensitivity of XRD tool.

��

Fig. 1: TG and DTA curves of plaster.

Fig. 2: XRD of tested plaster.

Table 2 shows the physicomechanical prop-erties of the tested β-hemihydrate plaster. It is clear that the tested plaster blends 46 ml of H2O for each 100 g of plaster powder. It is calculated that the stoichiometric amount of water needed for hydration of pure plas-ter amounts to 18.6 %. The determined normal consistency of the plaster is 46 % which means that an extra amount of water of workability was used for plaster consist-ency. The tested plaster showed somewhat long setting time. Extended setting time is mainly attributed to the excess amount of

water used for workability. Moreover, the setting time results of the plaster confirm its constitution which was suggested from the DTA findings that it is free from gypsum phase. The existence of minute amounts of gypsum is known to accelerate the setting time of plaster sharply [14].

��

Mechanical Properties Normal Consistency

(%)

Setting Time (min)

Compressive Strength (MPa) Bending Strength (MPa) Initial Final one day 3 days 7 days one day 3 days 7 days

46 26’ 30” 30’00” 8.5±0.9 17.7±1.3 18.2±1.2 4.3±0.2 6.7±0.2 8.7±0.2

Tab.2: Physicomechanical properties of the tested plaster

Mechanical properties of the tested plas-ter, as given in Table 2, confirmed the high purity of the plaster under investigation [9, 10]. Data also demonstrate that the early aged samples gave lower strength values which were doubled on aging for three days and slightly improved with further aging for seven days. The progressive increase in the strength of the plaster is due to the comple-tion of its hydration as well as the evapora-tion of excess water blended, that was used for workability. The latter is a common hy-dration criterion met with all hydraulic ce-ments and plasters [12].

In the light of the obtained results, it is recommended that the high grade indus-trially-produced β-hemihydrate plaster CaSO4.½H2O that was evaluated in this work could be used technologically as a starting material for the formation of plaster com-posites for different applications.

concLusion

We have investigated a commercial grade gypsum plaster sample to clarify its chemi-cal and mineral constitution using X-ray flu-orescence (XRF), thermal analysis (DTA, TG), and X-ray diffraction (XRD). Results revealed that the purity of the tested gypsum plaster sample was calculated to be around 96 % CaSO4.½H2O with small amount of siliceous materials and carbonates. The carbonates were calculated to be 1.34 % of MgCO3 and 1.9 % of CaCO3. Thermal analysis re-sults confirmed the presence of carbonates

which were identified as a dolomite rather than MgCO3 and CaCO3 binary phases. The investigated gypsum plaster sample blend-ed 46 % water and gave long setting time with moderate mechanical properties.

acKnowLedGeMent

This work was a part of the project No 2A-1TP1/063, “New glass and ceramic materi-als and advanced concepts of their prepa-ration and manufacturing”, realized under financial support of the Ministry of industry and trade. It was also a part of the research programme MSM 6046137302 Preparation and research of functional materials and material technologies using micro- and na-noscopic methods.

��

Literature

1. Combe, E. C., Smith, D. C.: J. Appl. Chem., 18, 1968, 307. 2. Dweck, J., Bucher, P. M., Coelho, A. C. V., Cartledge, F. K.: Thermochim. Acta, 346, 2000, 105. 3. Dweck, J., Andrade, B. F., Monteiro, E. E. C., Fischer, R.: J. Thermal Anal. & Calorimetry,

67, 2002, 321. 4. Enayetallah, M. E., Khalil, A. A., Gagalla, A. M.: Sprechsaal, 110, 1977, 194. 5. Enayetallah, M. E., Khalil, A. A., Gagalla, A.M.: Trans. & Brit. Ceram. Soc., 76, 1977,

95. 6. Eve, S., Gomina, M., Gmouh, A., Samdi, A., Moussa, R., Orange, G.: J. Eur. Ceram. Soc.,

22, 2002, 2269. 7. Eve, S., Gomina, M., Ozouf, J.-C. Orange G.: J. Eur. Ceram. Soc., 27, 2007, 1395. 8. Khalil, A. A., Gad, G. M.: J. Appl. Chem. Biotechnol., 22, 1972, 697. 9. Khalil, A. A., Hussein, A. T., GAD, G. M.: J. Appl. Chem., 21, 1971, 314. 10. Khalil, A. A., Hussein, A. T.: Trans. Brit. Ceram. Soc., 71, 1972, 67. 11. Khalil, A. A., Trans. Brit. Ceram. Soc., 71, 1972, 217. 12. Khalil, A. A.: J. Appl. Chem. Biotechnol., 22, 1972, 703. 13. McDowell, S. J.: Bull. Am. Ceram. Soc., 14, 1935, 229. 14. Ridge, M. J., Hill, R. D.: Austral. J. Appl. Sci., 11, 1960, 180.

��

subsurface daMaGes detectinG on standard oPticaL GLass bY diMPLe MeHtHod


The usage of advanced materials has been increasing in high-technology ap-

plications, which are progressive and use sophisticated principles. In the recent years materials like optical glass N-Bk7 as well grouped in the material science as an ad-vanced material or ceramics are becoming more important for such applications. One of this high-technology applications may be found in the optical sector. In this sector the advanced materials are mainly used as com-

ponents like e.g. lenses, mirrors mount in medical equipment such as implants and en-doscopes or others e.g. collision avoidance devices, transportation industry, scientific testing devices, projectors, telescopes and lithography.

The requirements on these materi-als have been increasing and in the recent years, the material properties of the supe-rior surface are becoming more important. Even slight defects in the bulk material and

The requirements on the materials used in the optical sector have been increasing and the material properties of the superior surface are becoming more important. A cracked layer near the surface distinguishes the material properties e.g. of standard optical glass N-Bk7. This layer is formed during the machining and known as subsurface damage (SSD). For the final usage of the optical surface these cracks must be minimized and eliminated in order to avoid failures. Therefore measurements have to be done. For the analysis of the near surface cracks, different nondestructive and destructive evaluation methods are known. The dimple method has proved to be an effective, inexpensive technique for accurately measuring the damage in advanced materials. The dimple technique requires only polish-ing and etching of a small spot on the superior surface by using acid solution. The focus of this work is to provide an insight into the preparation of standard optical glass N-Bk7 for damage detection by using the dimple method. Therefore, it features an overview of the setting parameters and displays different measurements of subsurface damages on the surface of N-Bk7.

subsurface damages, SSD, dimple method, optical material, standard optical glass N-Bk7

Abstract

Key words

��

primarily on the surface can cause it to fo-cus the light improperly, reduce the con-trast, increase the diffusion, absorb laser energy, destroy the smooth surface, lead to damage of the coatings or the interface of the coatings with the substrate and make it ineffective for its intended usage [1]. Due to the sophisticated applications of optical

components and tools high technical re-quirements on the superior surface and on the glass material composition, has to be fulfilled. Table 1 exemplifies the composi-tion of standard optical glass, which con-sists mainly of silicon dioxide in noncrystal-line form and additional oxygen compound to set the optical parameters.

Tab.1: Elements and the corresponding proportion of ingredients of N-Bk7 [4]

SilicaSiO2

Boron oxideB2O3

Titanium oxideTiO, Ti2O3

Barium oxideBaO

Sodium oxideNa2O

60% to 70% 10% to 20% <1% 1% to 10% 1% to 15%

Potassium oxideK2O

Calcium oxideCaO

Antimony trioxideSb2O3

Zinc oxideZnO

5% to 15% <1% <1% <1%

subsurface daMaGes

Manufacturing process like grinding, lap-ping and polishing introduce different kinds of damages or defects, including fractures, scratches, sleeks, microcracks and residual stresses. The cracked layer near the ma-chined surface is known as subsurface dam-age (SSD) and may be explained by the hill model of plasticity [2]. This damaged layer must be minimized and eliminated, in order to avoid failures in the final device produc-tion like damaged coatings or unusable de-vices. Generally subsurface damages reduce the quality and life time of the workpieces because of the surfaces age faster and be-come dull. The single crystal characteristics are not given any longer and coatings may split. Therefore it must be guaranteed that these depth damages are removed for the final usage of the optical surface in order to avoid failures in the final device.

Figure 1 indicates the layers after cold processing of advanced materials. The de-fect layer may be easily superficially smeared by simply polishing and a small polishing

layer is generated on the leading surface. After that polished layer, the damages are not visible any more. Subsurface damages are contained in the defect layer, which is located under the surface and distinguishes from other regions in both composition and micro structure. The deformed layer, defect layer and polished layer overlapped succes-sively in the defect free bulk material. The subsurface damage layer in optical glasses for example is unsymmetrical; every ion is not fully coordinated from the subsurface layer to the surface layer. Due to the high requirements in the optical field, the defect layers must be eliminated therefore the treatment and measurement of subsurface damages is a major topic.

��

Fig. 1: Schematic of subsurface damages

diMPLe MetHod

Subsurface damages and the correspond-ing defect layer may be measured by using fracture mechanics, measuring etch rates or other destructive techniques [5]. Origi-nal destructive methods for determining the damage require a polished shape to be placed on the surface and passes from the defect free bulk through the other lay-ers. A possibility to make the necessary preparation is the dimple method [3]. This technique has proved - in comparison with other techniques - to be an effective, inex-pensive technique for accurately measur-ing the coating thickness in materials. The dimple technique for damage detection re-quires etching a small spot on the surface or the whole surface using hydrohalic acid solution. For example for optical glasses hydrofluoric (HF) solutions of ten weight percent acid in distilled water are used for about ten seconds to expose the damages. After the etching, a dimple is inserted into the leading surface. Afterwards the sample is again etched.

Figure 2a) indicates the procedure of the sample preparation. The dimple is lapped into the exposed surface by a spherical ball and abrasive slurry. The sample is fixed

in the support of the workpiece at an ad-equate angle. The angle must be chosen depending on the sample geometry and the ball size. Once the sample is in position, the spherical steel ball of known diameter is placed between the sample and the driv-ing shaft. Due to the weight, the steel ball presses against the etched sample surface with a constant load. The abrasive slurry is dropped to the contact zone between the sphere ball surface and the sample surface. The rotating driving shaft provokes the ro-tation of the steel ball because of the fric-tion between the ball and the shaft. Once the sphere rotates the polishing slurry leads to the material removal in the contact zone. Depending on the material properties of the tested materials, the depth of the lay-ers, polishing slurry and used sphere size, the number of revolutions and the on-time must be selected. Table 2 gives an overview of the used setting parameters for the sam-ple preparation of N-Bk7.

Figure 2b) displays the model for the geo-metric relation of the polished dimple. Once the necessary penetration depth past the subsurface damages is achieved, the dimple is finished. The purpose of the dimple is to be able to visually determine the defect lay-er thickness like Figure 3 exemplifies. Knowl-

Tab.2: Overview of the setting parameters

Parameter Value range Unit

Shaftspeed 1200 – 2000 rpm

Polishing time 100 – 300 sec

Sphere diameter 20 – 25 mm

Slurry grain size 1 – 3 µm

Etching time 10 – 30 sec

Neutralisation time 30 – 60 sec

Dimple depth < 20 µm

Polished layer

Defect layer

Elastic deformedlayer

Defectfree bulk

��

Tab.2: Overview of the setting parameters

edge of the radius of the steel ball and the curvature radius are essential. Furthermore measurements of the inner and outer diam-eter must be done by an adequate meas-urement method, for example light micro-scope or scanning electron microscope. At the beginning of the defect free bulk or at

the last traces of the subsurface damage at the position φ the measurement of the in-ner diameter should take place. When eve-rything is done, the depth of the damage can be calculated using the equation 1 for the geometry.

(1)

a)

Fig. 2: Principle a) and model b) of the dimple method

resuLts

The introduced damages and the corre-sponding crack layer at the near surface are detected like Figure 3 displays. The cracks are visible in the light microscope image of a standard optical glass N-Bk7, which was machined in point kinematics with a D46 disc wheel. The root mean square surface roughness Sq before the preparation was 758 nm. The lapped dimple was produced with a diameter 20 mm sphere ball and the resulting dimple depth amounts 17 microns. The figure indicates that the most cracks are near the leading surface up to a depth of 5 microns. Between 5 and 15 microns the amount of the cracks decreases. Therefore the crack density increases from the bulk material to the surface. The last trace of the SSD was detected at 15 microns from the ground surface. Such measurements were applied on N-Bk7 surfaces with different initial surface conditions.

Figure 3 shows the results of the damage layer depth in comparison to the root mean square surface roughness Sq of optical glass N-Bk7. The different properties are achieved through disc wheel grinding with D15 and D46 grains and point kinematics. It shows that the damage layer thickness increase with the surface roughness. Therefore to minimize the cracks the surface roughness has to be on certain low level. Due to the load during processing and the brittle frac-ture of the material a plastic deformation depth of 5 microns remain at the substrate at a certain low roughness level.

concLusion

The increasing requirements on advanced materials necessitate measurements of the superior surface, which comprised a cracked layer known as subsurface damage (SSD). Destructive evaluation methods like

��

Fig. 3: Light microscope image of a dimple in N-Bk7

Fig. 4: Correlation between surface roughness Sq and depth of the damage layer at N-Bk7

Collier D., Schuster R.: Superpolishing deep - uv optics. In Photonics Spectra, Laurin Publishing, 1996Lambropoulos J. C. et al.: Subsurface Damage in Microgrinding Optical Glasses. In Advances in Fusion and Processing of Glass II, Volume 82, pages 469-474, 1998Randi J. A. et al.: Determination of subsurface damage in single crystalline optical mate-rials. In Medical Imaging 2003: Volume TD02, pp. 84-86, pages 84–86, 2003.Schott Glass: Material safety datasheet N-Bk7, 2001Shen J. et al.: Subsurface damage in optical substrates. In Optik - International Journal for Light and Electron Optics, Volume 116, Issue 6, Elsevier Science, pages 288–294, 2005.

1.

2.

3.

4.5.

Literature

the dimple method have proved to be an ef-fective, inexpensive technique for accurately detection of damages in amorphous glass materials like standard optical glass N-Bk7. This work provides an insight into the prepa-ration for damage detection using dimple lapping and etching of the surface. At this, it features an overview of suitable setting parameters and displays different measure-ments of subsurface damages.

acKnowLedGMents

The authors would like to thank the mem-bers of the faculty of mechanical and electri-cal engineering of the Deggendorf University of Applied Sciences and the Faculty of Indus-trial Technologies in Puchov of the Alexander Dubcek University of Trencin. This work has been supported by the ”PraeziForm” project of the InnoNet series of the BMWi. They are also grateful for the Fraunhofer Institute for Production Technology and the participating companies for their assistance.

�0

eXPeriMentaL caLibration of constants used for de-terMininG residuaL stresses froM HoLe driLLinG MetH-od data


Residual stresses exist in the object with-out the application of any service or oth-

er external loads. The most common causes of residual stresses are the manufacturing processes, as casting, welding, machining, molding, heat treatment etc. The residual stresses may also be induced later in the service life. Identification of residual stress-es in the structure is very important for es-timation of the structure service or residual service life. Especially their positive values

are predominant factor contributing to fa-tigue and other structural failures. Negative residual stresses however can increase the fatigue life in some cases. In many cases the determination of residual stresses is used for controlling the manufacture proc-ess directly (controlling of maximum avail-able surface stresses induced by machining, determination of sufficient negative value of residual stress induced by rolling or shot penning) or indirectly (checking of the core

Residual stresses arise due to technology processes or during operation, particularly due to overloading. They are present in parts even when no external forces act. In the super-position with stresses caused by loading give total stress value. Their existence often nega-tively affects the part safety and its lifetime. Thus the determination of residual stresses is very important. The hole drilling strain-gage method is widely used and is based on drilling a small hole in the special rosette centre which causes partial residual stresses release The corresponding strains are measured and then related to relieved principal stresses (magni-tude and orientation) through a series of equations using dimensionless constants a, b [1], [2], [3]. The constants a, b are obtained by FEA calculations for normalized dimensions of rosettes produced in USA and mostly used in all the world. But other producers of special rosettes for determining residual stresses exist. In presented work, the experimental set-up is described for deriving of these constants for uniform stress field for three rosette types from two producers and given results of experimental calibration are discussed. The constants are derived using proposed method and are compared with those, obtained us-ing FEA model.

residual stress measurement, constants a, b, FEA, uni-axial tensile loading

Abstract

Key words

----

��

residual stresses of large forgings induced by heat treatment process through measur-ing the surface residual stresses).

The most widely used method for meas-uring residual stresses is the hole drilling method. The method involves attaching generally rectangular three-element strain gage rosette to the surface, drilling a blind hole in the vicinity of the gages and measur-ing the relieved strains at individual counter clockwise marked strain gauges ε1, ε2, ε3. The measured strains are then related to relieved principal stresses through a series of equa-tions using dimensionless, almost material-independent constants a, b . This method is the basics of ASTM E837 [4] standard. The constants a, b are given in [4] as the func-tion of basic geometrical parameters - nor-malized hole depth z/D and normalized hole diameter D0/D for three common types of rosettes, as they are function of dimensions of the strain gage grid of individual rosette. Here, D0 is the real hole diameter, z is the real hole depth and D is the mean diameter of the strain gage rosette. The procedures, used in [4] for residual stress determina-tion are valid only for those stresses, which are uniformly distributed within the whole drilled hole depth. The standard gives tables for particular constants a, b for eight hole depths. However, stress evaluation at these depths should serve only for demonstration of stress uniformity; the history of relieved strains should correspond to typical char-acteristics for relieved uniform stress field. These characteristics have typical shapes in coordinates z/D0 and relative relieved strain measured in every of the three directions. The shape of plots is modified only by the basic geometrical parameter D0/D. The re-sidual stress is then computed as an aver-age value in the depth 0,4 D with the help of power series method in [4].

Goal of presented work is to derive the con-stants a, b for the types of residual strain gage rosettes, not involved in [4], especially for those, produced by Co. Hottinger Bald-win Messtechnik (HBM), using FEA model and for commonly used experimental set-up with the help of experimental calibra-tion. Another goal of these investigations was to compare the experimental and com-puted values for getting some correction factors for residual stress evaluation using computed constants.

ModeLLinG tHe HoLe driLLinG usinG finite eLeMent anaLYsis (fea)

The FE-simulation was performed using the PC-version of FE-software COSMOS/M, ver. 2.9. For both the pre-processing and post-processing the COSMOS/M module GeoS-tar has been utilized. The analyzed area was a block of size 100 x 77 x 24 mm (length, width, height). In the Figure 1a) we can see meshes in 4 areas (No. 1 is the area lying between strain gauges, No. 2 is area of the hole, No. 3 is area of strain gauges, No. 4 is area connecting the strain gauges to the area No. 2 and to the No. 5 - area where the element size is growing). The iterative PCG-solver was used to solve the linear elastic problem. The average strains computed from the virtual fibers of each strain-gauge were the results from these calculations. These values were used for evaluation of calibrating coefficients. For the illustration the resulting nodal radial stress field at the end of the hole-drilling process is in the Fig. 1b).

The FE analysis was carried out for follow-ing types of strain gage rosettes: 125RE (MM Vishay), RY21 (HBM) and RY61 (HBM). Series of relived strains ε1, ε2, ε3 at given depth and

--

--

--

--

��

with given hole size has been calculated us-ing FEA for above mentioned types of strain gage rosettes. The same steps for depth pa-rameter z/D and hole diameter parameter D0/D were used similarly to [4]. In addition

to this, the computation was performed di-rectly for the same hole diameter and the hole depth used during experimental cali-bration, which are standardly also used dur-ing service measurement.

a) b)Fig. 1: FEA meshes and radial stress distribution around the drilled hole

Evaluation of the coefficients a, b was per-formed for each step of computation ac-cording following relations

Resulted series of computed coefficients using FEA are given in Table 1 to Table 3. How can be seen from these tables, the co-efficients differ from each to the other for the corresponding dimensional parameters for individual strain gage rosettes. There is also difference when comparing the rosette 125RE with the standard [4] coefficient val-ues. The difference becomes higher with increasing the hole diameter (D0/D). The reason is, that the calculation of ASTM co-efficient probably was performed for the strain gage centre rather than using integra-tion of the relieved strain along constituent rosette wires. Explanation can be given by Figure 2. Here, the map of coefficients a, b is drawn, as they have been calculated

for individual points of rosette having one strain gage grid (8 points in radial direction, 9 points in tangential direction to the drilled hole). Numbering of radial direction points growth with increased radial distance from the hole. You can see high non-linearity of drawn surface notably for the coefficient b, which growths in direction to the hole cen-tre.

The calculated values for the coefficients using integration along strain gauge meas-uring grid gives constants a = 0.099, b = 0.205, while the corresponding values for the grid centre are a = 0.105, b = 0.266. The ASTM gives following values a = 0.101, b = 0.227. Figure 2. also serves as the notion how important is the accuracy of coeffi-cient and strain gage position statement, to receive the satisfactory error of the residual stress calculation.

(1)

--

--

-

--

----

��

Table 1: Coefficients a, b for the strain gage rosette 125RE, MM Vishay

Table 2: Coefficients a, b for the strain gage rosette RY21, HBM


--

--

--

��

Table 1: Coefficients a, b for the strain gage rosette 125RE, MM Vishay



eXPeriMentaL caLibration

The calibration for coefficients a, b was carried out by installing three above men-tioned types of residual stress strain gauge rosettes on the uni-axially stressed tensile specimen of the cross section 77 × 24 mm and length of 250 mm. Specimen material was the carbon steel of Czech Standard ČSN 11 520, equivalent to DIN St 52). Before the calibration, the specimen surfaces were grinded and specimens were annealed for reliving the residual stresses. Strain gage rosettes were bonded using HBM adhesive

EP 250 and hardened at the temperature up to 60°C. All specimens were loaded in the hydraulic testing machine Schenck 400 kN, the measured level force was F = 225 kN. Orientation of the strain gauge rosettes was according Figure 3, the strain gage “1” was aligned parallel to the loading direction. Re-moving of the particular layers was made using standard hole-drilling device common with the MM Vishay RS 200 without remov-ing the specimen from the loading machine. The end-mill drilling set-up has been used. Special two-edged widia eccentric hole cut-ters were used for drilling the holes.

Fig. 2: Map of coefficients a, b above the grid surface for the rosette 125RE; z/D = 0.2, D0/D = 0.3

Fig. 3: Set-up for experimental calibration

--

--

��

According [4] and [6], the drilling of the hole may to be performed at unloaded speci-men. However, on the real structure, the material is always prestressed. That is why it was decided, to perform the experimen-tal calibration twice for each strain gage rosette. First with drilling to the unloaded specimen followed by loading and second with drilling of the loaded specimen. In both cases the specimen was first loaded with-out drilling the hole, to measure the main strains εmax, εmin and calculate the Poisson’s ratio μ. For the first type of calibration, the hole was drilled at unloaded specimen. After having applied the load F = 225 kN strain gage readings were performed. The relieved strain was then taken as the strain difference after each drilling minus before all drillings for the loaded specimen. For the second type of calibration, the hole was drilled for each depth step at the loaded specimen without unloading it, just direct-ly obtaining the stress differences at each drilled depth as the difference of un-drilled and drilled specimen.

Example of typical measured shapes of relative relieved strain for the free and loaded rosette HBM RY21 drilled with ø4 mm and ø6 mm mills are in Fig. 4, where the comparison is made with results, ob-tained by FEA. Here the common fact ob-served during the whole calibration process is presented, that the coincidence between experimental and FEA results is better for larger hole diameters. The second visible fact is, that for each rosette type the relived strain is higher, when the rosette is drilled under load. This is a serious finding, be-cause it puts relatively large systematic er-ror to the residual stress calculations. Nev-ertheless, the obtained stresses are always higher then presented in the structure, when this shift has not been corrected. This

difference could be explained by originated plastic deformations at stress concentra-tions along the hole (maximum tangential stress is near the strain gauge 1, where the difference is greatest) due to superimposi-tion of milling process, where due to the chip forming process the plastification has to occur. Obtained results for the strain gauge rosette MM Vishay 125RE are com-mon to the mentioned diagrams. However, the relived strains, obtained for small ro-sette RY61, drilled with ø 1.5 mm mills have very high dispersion and are not suitable for coefficient calculations. It has been found, that mills of similar small diameter are not suitable for the hole drilling method, as they bring high plastic deformation to the speci-men. That is why, the results are not pre-sented here. There are non-smoothed raw measured data given in Figure 4.

The coefficients a, b were calculated from the experimental relieved strains again according the relation (1). Example of calculated coefficients for HBM RY 21 ro-sette are in Fig. 5 for the drilled hole D0 = 4 mm and in Fig. 6 for the drilled hole of diam-eter D0 = 6 mm. The calculated coefficients for all drilled steps are given in Table 4 for strain gage rosettes HBM RY21 and MM Vishay 125RE, drilled with the D0 = 4 mm. The curves given in mentioned charts and Table 4 were smoothed using polynomial approximation.

--

��

Fig. 4: Relative relived strains for strain gauge rosette HBM RY21

Fig. 5: Coefficients a, b for strain gage rosette HBM RY21 and drilled hole D0 = 4 mm

Fig. 6: Coefficients a, b for strain gage rosette HBM RY21 and drilled hole D0 = 6 mm

--

--

��

concLusions

Calibration coefficients a, b for the hole drilling method have been derived for most used residual stress strain gauge rosettes HBM RY21, RY61 and MM Vishay 125 RE us-ing FEA and experimental calibration. New method for residual stresses evaluating along the depth has been presented here.

Realized investigations have shown, that experimentally obtained coefficients differ from those obtained with FEA, if the drilling is performed to the loaded specimen. Their real value is always higher, which means, that the residual stresses, evaluated by us-ing ASTM coefficients, are always higher in comparison with the stress in real specimen. The agreement of experimental and stand-ard coefficients a and b is better for higher hole diameters. It has also been found, that the end mill process for the small diameter rosette HBM RY61 is not quite suitable, as obtained strain relived profile differs from typical shape and estimated coefficients are quite away from expected values.

An additional part of this paper which will be presented at the Conference deals with the evaluation of residual stresses in large tur-bine rotor forging, where the residual stress induced due to heating treatment may be taken along the drilled hole as uniform, but it is influenced of superimposed surface stress involved due to machining. The inte-gral method according Schajer [5] and our proposed method based on improvement of Kelsey s method [7] are used in this case and they are compared with results, given from power series method [4].

acKnowLedGMents

The research was supported by the Ministry of Industry and Trade of the Czech Republic, project No FT-TA/026 and No. FT-TA2-019.

Table 4: Coefficients a, b for rosettes HBM RY21 and MM Vishay 125RE based on experimental calibration--

--

��

Kobayashi, A. S. “Handbook on Experimental Mechanics”, Prentice-Hall, Inc., N.J., (1987)Kelsey, R. A.”Measuring Non-uniform Residual Stresses by Hole Drilling Method”, Proc. SESA, IX, No. 1, (1956)Rendler, N. J., Vigness, I “Hole-Drilling Strain-Gage Method of Measuring Residual Stresses”, Experimental Mechanics 6, No. 12, (1966)ASTM E 837-01 Standard Test Method for Hole-Drilling Strain Gage Method, American Society for Testing and Materials, (2002)Schajer, G. S. “Measurement of Non-uniform residual stress using the hole drilling method,” Journal of Engineering materials and technology, Vol 110, No.4, (1988), Part 1: pp. 338-343, Part II:pp. 344-349Vishay, M. G. “Measurement of Residual Stresses by the Blind Hole Drilling Method”, Tech Note TN-503, (1981)Jaroš, P. “Unified Data Reduction Procedure for Both Standard and Hole-Drilling Strain Gauge Rosettes”, Experimental Techniques, Jan/Feb 1995Flaman M. T., Boag J. M. “Comparison of Residual-stress Variation with Depth-analysis Techniques for the Hole-drilling Method”, Experimental mechanics, Dec 1990.Schwartz, T., Kockelmann, H. „Die Borlochmetode - ein für viele Anvendungsbereiche optimales Verfahren zur experimentellen Ermittlung von Eigenspannungen“, Messtech-nische Briefe HBM MTB 29,(1993).

1.

2.

3.

4.

5.

6.

7.

8.

9.

Literature

Alexander Dubček University of Trenčín Izhevsk State ... · single model of thin-rimmed gear was...

Documents

Transcript of Alexander Dubček University of Trenčín Izhevsk State ... · single model of thin-rimmed gear was...