IN
DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2018,
Process optimization of
manufacturing of magnets by Electro Sinter Forging (ESF)
MARCO CAPECCIA
Preface and acknowledgements
This master thesis has been carried out at DTU in the materials and manufacturing department laboratories from february the 5th to july the 5th 2018, under previous agreement between DTU and KTH. A first thank goes to my supervisors at both universities, Associate Professors Chris Valentin Nielsen and Ove Bayard, together with the PhD student Emanuele Cannella and the lab technician Niklas: throughout the whole research they have always been available, with meetings or via email, for questions clarifying doubts and also for tutorials with all the equipment that has been used during the experimental part.Since the thesis agreement has been reached as an extension of an Erasmus programmes, administration offices of both universities have succeeded in arranging everything carefully and efficiently as concerns the required documentation, making the overall process as smooth as possible. For KTH, a thank goes to Tuija Venermo as international coordinator, to Anna Hellberg Gustafsson as Erasmus and mobility programmes coordinator and to Adisa Haliovic as economical administrator; for DTU, to Bjørn Sparre Jøhansson and to all the office for study programmes and international affairs. During my stay in Copenhagen, again abroad and in another country after a year spent in Stockholm, my mother Flores, grandmother Sofia and all my family has been supporting me from Milano cheering me up in the most troubled and harsh times all the year. A last special thank goes to the friend of mine Loic with whom I have been keeping in touch after last year when we were both at KTH, but also to the nice people I have met this year such as Alessandro, Gursharan, Mikey and others.
Abstract
Interest in powder metallurgy processes is nowadays continuously increasing due to several reasons such as less heavy manufactured parts, economical advantages and greater concern in environmental sustainability related to production. Electro sinter forging, ESF, belongs to them, being a
sintering technique characterized by high electric current intensity released for a very short lapse of time at low voltage on a powder green body, together with an applied load. After a brief description of the manufacturing process, its history and production background, relative density, hardness and load before tensile and compressive fracture are analyzed for disks sintered with different
combinations of electric current intensity, sintering time and applied force. A statistical univariate and factorial analysis is then performed on the achieved results so to give them robustness and trying to and out an optimal combination of input parameters leading to optimized properties of the disks, later to become magnets.
Sammanfattning
Nu för tiden ökar intresset för pulvermetallurgiska processer kontinuerligt. Detta beror på flera orsaker såsom tex att detaljerna som tillverkas idag är lättare, ekonomiska fördelar och att större hänsyn tages till miljön ur ett hållbarhetsperspektiv i samband med produktion. Elektro sinter smide, ESF, är en av dessa processer, varande en sintringsteknik som kännetecknas av att hög elektrisk strömintensitet frigörs under ett mycket kort tidsförlopp vid låg spänning på en pulvergrönkropp, samtidigt som en belastning anbringas. Efter en kort beskrivning av tillverkningsprocessen, dess historia och produktionsbakgrund analyseras relativ densitet, hårdhet och belastning före dragning och
tryckprovning för skivor sintrade med olika kombinationer av elektrisk strömintensitet, sintringstid och applicerad kraft. En statistisk envariabelanalys och flervariabelanalys utförs sedan på de erhållna resultaten för att ge dem robusthet och försöka få fram en optimal kombination av ingångsparametrar som leder till att optimerade egenskaper för skivorna erhålls, vilka senare ska bli magneter.
Contents
1 Introduction 7
2 State of the art 8
2.1 Previous attempts in modelling and simulating . . . 8
2.2 Sintering production advantages . . . 9
2.3 Latest developments in rare earth elements demand and supply . . . 10
3 Case study 12 3.1 Materials and equipment . . . 12
3.2 Manufacturing process . . . 14
3.3 Experimental procedure . . . 19
4 Experiments and results 20 4.1 Relative density . . . 20
4.1.1 Variable electric current intensity with fixed sintering time and applied force 20 4.1.2 Variable sintering time with fixed electric current intensity and applied force 25 4.1.3 Variable applied force with fixed sintering time and electric current intensity 26 4.1.4 Sintering time and applied force interaction . . . 27
4.1.5 Current intensity and applied force interaction . . . 30
4.1.6 Electric current intensity and sintering time interaction . . . 32
4.2 Hardness tests . . . 34
4.2.1 Measurements . . . 37
4.2.2 Intrasample hardness . . . 38
4.2.3 Nd Magnetostriction . . . 42
4.2.4 Hardness intersamples . . . 44
4.3 Compression and indirect tensile strength tests,idt . . . 47
4.3.1 Idt . . . 47
4.3.2 Compression tests . . . 52
5 Conclusions 56
6 Future works 58
7 Bibliography 59
A Nomenclature 62
B Material and equipment properties tables 63
Appendix63C Applied force settings 63
D ANOVA assumptions and mean difference tests 68
E Factorial ANOVA interactions effects 69
List of Tables
1 Data for samples sintered with variable current intensity and fixed sintering time and
applied force . . . 20
2 regression output . . . 22
3 curve intercept and coefficients with respective standard errors SE . . . 22
4 ANOVA output . . . 23
5 samples data for variable sintering time . . . 25
6 ANOVA output . . . 25
7 samples data for variable applied force . . . 26
8 ANOVA output . . . 27
9 data for samples sintered with variable AF and ST . . . 28
10 2 way factorial ANOVA output table . . . 28
11 Bonferroni output table . . . 29
12 Data for samples sintered with variable applied force and current intensity . . . 30
13 factorial ANOVA output . . . 31
14 Bonferroni output table . . . 31
15 Data for samples sintered with variable current intensity and sintering time . . . 32
16 factorial ANOVA output . . . 33
17 Bonferroni output . . . 33
18 HV data, sample sintered with 8,2kA, 1000ms and 5,1kN . . . 39
19 Kruskal Wallis descriptive statistics quantities . . . 39
20 Kruskal Wallis ranks . . . 39
21 Kruskal Wallis statistics tests . . . 39
22 Mann whitney descriptive statistics quantities . . . 39
23 Mann Whitney ranks . . . 40
24 Mann Whitney statistics tests . . . 40
25 Anova for samples sintered for 1000ms with variable applied force . . . 45
26 Kruskal Wallis descriptive statistics quantities . . . 45
27 Kruskal Wallis ranks . . . 46
28 Kruskal Wallis statistics tests . . . 46
29 Process parameters, relative density and maximum load for the analyzed samples . . 49
30 Process parameters, relative density and maximum load for the analyzed samples . . 55
31 matrix reporting, for each process parameter interaction combination, the optimal conditions resulting in a highest mean relative density . . . 56
32 process parameters, relative density, and maximum load withstood for IDT and com- pression test . . . 57
33 Shapiro Wilk output for relative density data; variable current intensity . . . 68
34 Brown Forsythe output for relative density data; variable current intensity . . . 68
35 Bonferroni means comparison test between groups with variable current intensity . . 71
36 Shapiro Wilk output for relative density data; variable sinteing time . . . 72
37 Brown Forsythe output for relative density data; variable sintering time . . . 72
38 Shapiro Wilk output for relative density data; variable applied force . . . 72
39 Brown Forsythe output for relative density data; variable applied force . . . 72
40 Shapiro Wilk output for relative density data; variable ST and AF . . . 72
41 Brown Forsythe output for relative density data; variable AF and ST . . . 72
42 Brown Forsythe output for relative density data; variable AF and CI . . . 72
43 Shapiro Wilk output for relative density data; variable CI and ST . . . 73
44 Brown Forsythe output for relative density data; variable CI and ST . . . 73
45 Shapiro Wilk output, sample sintered with 8,2kA, 1000ms and 7,3kN . . . 73
46 Brown Forsythe output, sample sintered with 8,2kA, 1000ms and 7,3kN . . . 73
50 Shapiro Wilk output for the intrasamaple hardness data, variable ST AF . . . 77
51 Brown Forsythe output for the intrasamaple hardness data, variable ST AF . . . 77
List of Figures
1 Multi-parts tool configuration[39] . . . 92 NdFeB magnet-to-magnet recycling, contribution of each stage to pollution [22] . . . 11
3 Svejsemaschine Expert . . . 12
4 electro sinter forging equipment . . . 13
5 assembly with most important dimensions, in mm . . . 13
6 Process operations diagram . . . 14
7 Applied force of 9,5kN as function of time during precompression . . . 15
8 how heat exchange occurs between two particles layers, 1), through the neck area, 3), in a direction schematically represented by the arrows 5), with spherical shaped radiations[32] . . . 16
9 inter and intra particle porosities characterizing crystallites structure [27] . . . 16
10 Applied force of 9,5kN and current intensity of 12kA as function of time during sintering 17 11 Ejection press . . . 18
12 electro sintered disk right after ejection . . . 18
13 Sartorius scale and inside of 3shape scanner . . . 21
14 A)disk after 3shape scanning, B)GOM mesh bridging C)final disk after GOM . . . . 21
15 second grade polynomial fitting curve for relative density data with variable current intensity . . . 23
16 residuals scatter plot against the fit y, relative density . . . 24
17 residuals scatter plot against the order of time with whom samples have been sintered 24 18 relative density scatter plot . . . 25
19 relative density scatter plot . . . 27
20 Hardness measurements microscope . . . 35
21 zoom on mycroscope and indentors, with a sample set on the platform . . . 35
22 indentations profiles for the first two samples analyzed; upper and central only in the upcoming sections . . . 36
23 Sample cross section . . . 37
24 2d cross section sketch with coordinate system set in the center . . . 37
25 indentations profiles for the first two samples analyzed; upper and central only in the upcoming sections . . . 38
26 Hardness as function of the indentation distance from the cross section core for upper, center and lower line . . . 38
27 a)upper and b)lower cross section of the analyzed sample sintered with 9,5kN of applied force and 200ms of sintering time . . . 40
28 5,1kN and 200ms, bottom . . . 41
29 5,1kN and 200ms, top . . . 41
30 5,1kN and 600ms, bottom . . . 41
31 5,1kN and 600ms, top . . . 41
32 5,1kN and 1000ms, bottom . . . 42
33 5,1kN and 1000ms, top . . . 42
34 7,3kN and 200ms, bottom . . . 42
35 7,3kN and 200ms, top . . . 42
36 7,3kN and 600ms, bottom . . . 43
37 7,3kN and 600ms, top . . . 43
38 9,5kN and 200ms, bottom . . . 43
39 9,5kN and 200ms, top . . . 43
40 9,5kN and 600ms, bottom . . . 44
41 9,5kN and 600ms, top . . . 44
42 particles orientation- sample sintered with 5,1kN and 600ms . . . 44
43 particle orientation-side of the sample sintered with 7,3kN and 1000ms . . . 44
44 Hardness values plotted as function of the indentation distance from the cross section core, samples sintered with 8,2kA, 9,5 kN and 200ms and 600ms . . . 47
45 horizontal setup between the press punches in case of compression test . . . 48
46 vertical setup between the press punches in case of IDT . . . 48
47 Load function of time for samples sintered with an applied force level of 5,1kN and sintering time 200,600 and 1000ms, whose respective curves are in black,red and green. 50 48 Load function of time for samples sintered with an applied force level of 7,3kN and sintering time 200,600 and 1000ms, whose respective curves are in black,red and green. 50 49 Load function of time for samples sintered with an applied force level of 9,5kN and sintering time 200,600 and 1000ms, whose respective curves are in black,red and blue. 51 50 Scatter plot of maximum load against relative density data . . . 52
51 horizontal setup between the press punches in case of compression test . . . 52
52 vertical setup between the press punches in case of IDT . . . 52
53 applied load function of time for compressed samples sintered for 600ms, with current intensity 5kA and applied force 5,1kN, 7,3kN and 9,5kN, respectively in black, red and green . . . 53
54 applied load function of time for compressed samples sintered for 600ms, with current intensity 5kA and applied force 5,1kN, 7,3kN and 9,5kN, respectively in black, red and green . . . 54
55 applied load function of time for compressed samples sintered for 600ms, with current intensity 8,2kA and applied force 5,1kN, 7,3kN and 9,5kN, respectively in black, red and green . . . 54
56 maximum peak function of relative density for the 9 nine analyzed sample . . . 55
57 NdFeB phisical properties . . . 63
58 Cu electrodes properties-1 . . . 64
59 Cu electrodes properties-2 . . . 65
60 Cu electrodes properties-3 . . . 65
61 Ceramic die properties . . . 66
62 regression line reporting how to convert in kN the applied force set with the poten- tiometer . . . 67
63 Relative density as function of af . . . 69
64 Relative density as function of st . . . 69
65 Relative density as function of af . . . 69
66 Relative density as function of ci . . . 69
67 Relative density as function of af . . . 70
68 Relative density as function of st . . . 70
1 Introduction
Electro sinter forging, ESF, is a powder metallurgy consolidation process belonging to the category of ECAS, electric current assisted sintering, which includes also ERS, electric resistance sintering, SPS, spark plasma sintering, PECS, pulsed electric current sintering, FAST, field-assisted sintering technique, plasma pressure compaction, PPC, and many other processes[6][1]. The first documented proof suggests the first resistance sintering apparatus has been used by Bloxam in 1906: later on, all of these names have referred to slightly different process still showing a similar principle behind, with a few variations and improvements that have been made in the years and a dramatic increase in the number of papers from the nineties on [2]. It has been believed that plasma formation was occurring among the powder inter particle pores even though this assumption has recently been proven to be wrong [3]. Compared to most of the other manufacturing processes, its development is quite recent in time and the related amount of papers being published is relatively low. It involves the application of a high intensity current discharge, which has been proven to help decreasing porosity of metal powders[4], with low voltage and for a very short lapse of time, on a green powder compact which has to be electrically conductive and that is inserted into a die clumped by two conductive electrodes connected to the main machine structure. A low voltage value and the absence of a capacitor which discharges current are the key features that distinguish it from the category of electric discharge sintering, EDS, in which the machine owns a capacitor bank which is able to store electromagnetic energy and then releases it in one or just a few heavy pulses. Again, different terms have been used in the case of high voltage since a universally acknowledged classification has not been established yet for any of them. Most of them are gathered by [5] and are electric pulse pressing, EPP, electric discharge compaction, EDC, pulsed electric discharge, PED, pulsed electric discharge, HREDC, EEDS, CDS, capacitor discharge sintering, PPS, HEHR and electric pulse consolidation,EPS. Another difference according to the classification made by [6] lays in the flow time of the electric current, respectively . As concerns the overall focus on the topic by researchers, Russia, US, Poland and Italy turn out to be the most interested countries with regard to the high voltage category in terms of number of papers published, as stated in [5]. No significant difference, instead, has been identified in the amount of applied pressure, even though it can be applied from both upper and lower electrode as for instance in the experimental apparatus of [7]. In this research it has been pursued an experimental approach by making an attempt of finding out the ESF process parameters conditions which could result in a final disk with optimized properties in terms of relative density, hardness and maximum stress before compressive and tensile fractures. All parts have been sintered with the same NdFeCoB powder alloy and different combinations of electric current intensity, sintering time and applied force, then examined by carrying out different tests. For relative density and hardness, statistical significance of results has also been provided with the analysis of variance ANOVA, in order to make conclusions as much general as possible.
2 State of the art
2.1 Previous attempts in modelling and simulating
When it comes to process parameters, the complex interaction of mechanical, thermal and electric phenomenon together with a very short duration makes it impossible, so far, to effectively monitor parameters such as temperature. A few attempts of modeling and simulating the process develop- ment have been made so far as well, with different approaches. Di Napoli et al. [15], for instance, have implemented in Comsol a model describing particles recrystallization and densification, where the thermal gradient is affecting the behaviour of both micro and macro parameters; in [16] has then been formulated a thermo mechanical model which eventually has not been solved due to the thermomechanical coupling in two out of the three of their process stages and the non linear differ- ential equations. Again, in [17] for CDS with circuit and SEI equations solved in Phyton, or in [18], who have formulated an ”equivalent simple cubic system” model representing the powder aggregate resistivity behaviour function of porosity. Nevertheless, most of papers related to ECAS, as it has been stated in [19], have been defined as ”property driven”: according to this classification, they have been aimed at identifying which input conditions could lead to a higher relative density of the sintered part,providing microstructure characterization and results of the measured properties.
On the other hand, though, many less are focusing on how each process parameter is affecting the overall phenomena and up to which extent.
The worst drawback of not being able to measure temperature directly is probably that it is not pos- sible to assess whether the alloy melting point has been overcome, which should be always avoided.
A destructive solution could be, for instance, to break the sintered part by cutting it and analyzing its cross section to check the crystallographic structure, but for obvious reasons it could not be implemented as a standard process monitoring technique in industry. A constraint which enables to homogeneously heat the sintered part and hence keep the temperature controlled has been pro- posed by [5] , stating that the pulse time should be longer than the magnetic field penetration time but also shorter than the one required for heating powder particles. An indirect way of measuring temperature is by monitoring a parameter called SEI, specific energy input, as it has been stated in [10]. Defined as the integral in the sintering time interval from 0 to the end T of the real part of voltage times density, normalized by the powder compact weight,it can be defined as the amount of electromagnetic energy dissipated through heat during the process, following the Joule effect prin- ciple.
SEI = 1 w
Z T 0
v(t)i(t)dt(1)
Due to the fact that it has been dealt with many problems in accurately measuring the voltage with the given equipment, it has been eventually decided not to take into account this parameter but just the current intensity, with whom it is still positively dependent. A few key similar features with this thesis research have been found out in [20] , in which it has been carried out an experiment with a neodymium magnetic powder alloy that does not slightly differ with mine in compositions except for the lack of cobaltum. Samples size of 1mm diameter and 8mm thickness is also comparable but on the other hand they have been produced with spark plasma sintering and the analysis has rather focused on the micro powder grains magnetic properties.
2.2 Sintering production advantages
Interest in all kinds of electric current assisted sintering processes is steadily increasing [8] also be- cause of the many advantages it provides the manufacturing industry from many points of views.
First of all, by making a comparison between a part electrically sintered and the same one firstly processed with a standard technique like casting, the cycle time would dramatically decrease from several minutes that it has to spend in a casting furnace within a mould to just a few seconds. The sintered part also requires less post processing , assuming that a cast one is later undergoing plastic deformation or machining operations. Therefore, the production rate would improve as well even though some thermal treatment may be needed at the end of the production cycle. One example can be the annealing and aging in order to, respectively, reduce the strain hardening due to the applied pressure and control the intermetallic compounds as suggested in [9] with regard to a biomedical application. Moreover, it does not need to be carried out in a controlled environment like in vacuum with the aim of preventing oxidation. Advantages can then be found with regard to the part in itself and the process parameters. The initial material powder properties do not have that much importance, a high heating rate takes place but with lower process temperatures than casting and it is easier to achieve powder consolidation as long as a reduced grain growth due to the very short duration. From a comparison with another more traditional powder metallurgy technique like metal injection moulding, there are again less operations, since after it is always performed a hot isostatic pressing aimed at increasing density [10]. When it comes to the shape, near net shape products can so far be manufactured, with the possibility of creating holes and cavities by placing an insert within the mould. Unlike many other processes, it also does not have any down scaling effect when being improved in a research laboratory, as a machine owns almost the same dimensions than an industrial one.
Nevertheless, there are still some constraints regarding the shape such as the sintered part ratio between thickness and height, which shall not overcome specific threshold depending on the equip- ment[11]. It is lastly not proven yet whether electric sintering leads to a saving in energy consumption or not compared to casting: even though when it comes to a single part it is undoubtedly less, it also works that here one, or just a few parts at a time would be produced for each press, whilst with casting many of them are being put in the furnace at the same time in a single mould as stated in [12] . A possible new tool design configuration in figure.. aimed at increasing production rate has been suggested by [14] thought for SPS but that can work with electro sinter forging as well:
more parts at a time can then be manufactured in just one sinterization by a machine designed with a serial, parallel or mixed configuration, solution still to be tested and investigated by researchers.
Nevertheless, this as long as many other powder metallurgy processes have already been recognized
Figure 1: Multi-parts tool configuration[39]
as green technologies, streamlining and optimizing the overall production and, for instance, minimiz- ing waste down to two or three percent. An original attempt of simultaneous sintering of different composites has recently been made by [13], so to try to see and evaluate the effects of extending the resistance sintering process to a sintered composite assembly. On the other side, some disadvantages and drawbacks have been pointed out as well. Firstly, size of parts has to be relatively small since the more it grows the more temperature difference between the core and the area closer to the surface increases.
2.3 Latest developments in rare earth elements demand and supply
Neodymium, the main component of the powder alloy used for sintering disks in this experimental research, is a rare earth element belonging to the lantanydes. Together with Dysprosium, it has been identified as the most critical rare element mainly due to its high performing functional requirements in terms of remanenece, coercitivity and maximum energy product in case of magnets, being widely used in many applications. Even though immediately after the sintered magnet invention by Sagawa et al. in 1983 its usage was restricted to costly devices only, it became more widespread with the years, for instance in medical appliances, households devices, hybrid cars, wind turbines and weapons. Nowadays, there can be observed a growing interest in trying to change these magnets lifecycle by recycling them with different methods or by finding substitutive solutions which can enable to cut down on it as much as possible, this trend due to several reasons. First of all the concern arose after the dramatic price increase of almost ten times of neodymium and almost all the other lantanydes which took place in 2011; even though it dropped significantly in the following years, its price is still thought to have a high volatility [15]. Then, also the main features of their worldwide supply and demand market mechanisms. If on one hand there have been discovered around the world many minal sites whose ores own high rare earth elements concentration, in fact just a few of them turn out to be exploitable at a large scale extraction rate, almost all of them located in China, Brazil, and other developing countries characterized by a rather unstable geopolitical context[16]. Among the unsuccessful cases of minal activity in spite of the ores rare earth richness it can be mentioned Mountain Pass in the US: the site has been permanently shut down in 2015 because of many factors, most of all the price fall already mentioned but also difficulties in keeping up with competitors such as China and wrong financial investments. Due to an increasing need of larger available amounts , together with a seek to become less dependant to China as a global supplier, new explorations have recently been intensified in Africa, Greenland and Canada to discover new sites[17]. In spite of that, in the short medium term this sites are not supposed to become capable of satisfying even a few percents of the global demand, mainly because of the scale advantages for chinese plants which makes their prices uncomparably more competitive. Moreover, their extraction shows many drawbacks in terms of environmental sustainability, carried out through large amounts of weak acids in case of chinese mines. Examples of other dangers and damages linked to it has been provided by [18], with cases of leucemia rates much over the average among population living nearby the mines.
Radioactive tailings also follow the extraction, since ores where rare earth elements are stuck into are rich in uranium and toryum radioactive isotopes. Recycle possible solutions present different features, first of all depending on the stage at which it is decided to implement: 25 percent of scraps not recycled at all so far are already generated during production, most of all in operations such as sintering, grinding, polishing or magnetization. Product size is then affecting the frequency with whom broken items can be collected. If it is estimated to be around 2 or 3 years for electronic devices, it can get extended up to 30 years for macro scale applications such as magnets for wind turbines.
The easiness with whom a broken product can be disassembled so to take out the rare earth at an industrial scale matters as well, usually less in micro electronic devices than in macro applications.
With this focus, the ”design for recycling” concept should become a more widespread best practice during product development[19], targeted at extending the product lifecycle by designing it so to simplify its disassembly. One of the first industrial scale attempts of scraps recycle has been made
a tiny percentage of virgin rare earth needs to be used in the order of 1 percent of the final product.
Nevertheless, even with a worldwide widespread network for collecting wastes that currently does not exist, recycle would still not be sufficient. With an annual demand growth rate expected to reach 6 percent in 2020[20]that overcomes the rare earth element available thanks to product substitution or breakage, recycle is forecasted to meet 50 percent of global demand just in 2100[21].
Lastly, it is interesting to analyze how the overall recycling process is affecting the environment and up to which extent. There can be estimated and represented in the hystogram in figure 2 the contribution of each stage [22], with electroplating and hydrogen mixing and milling having the average most consistent one. If taking into account just sintering, most of the energy consumption occurs during the electric discharge: a lot actually depends on the energy source used upstream to generate current in the country where a production plant is located, coal if in China.
Figure 2: NdFeB magnet-to-magnet recycling, contribution of each stage to pollution [22]
3 Case study
3.1 Materials and equipment
In figure 3 it can be seen the Svejsemaschine Expert sintering machine used for producing all sam- ples: thought and designed at first for welding purposes and based on MFDC, middle frequency direct current, it has later been adapted to sintering. The isotropic magnet powder alloy MQP-C-
Figure 3: Svejsemaschine Expert
20006-070 has been used to carry out the experimental research, mostly made up from Neodymium with lower percentages of Ferrum, Cobaltum and Borum; its physical properties are reported in appendix in figure 52. This kind of product has been so far the most widespread and chosen object of interest for researchers in relation to this process [25], in which sintered NdFeB permanent mag- nets have already been proven to own both high magnetocrystalline anisotropy and high saturation magnetization [21] . The most important features on which it has been decided to focus are high relative density, high hardness and relatively low brittleness, the second and the third one in trade off with each other, with the task of the experimental analysis that will be to identify which values intervals of current intensity, sintering time and applied force will enable to achieve the best final properties possible.
The neodymium powder alloy is poured into the cylindric hollow of the ceramic die, made of Alumina, Alpha Al2O3,99,5 , after having lubricated its inner surface with zinc stearate powder Zn[CH3(CH2)16CO2]2, containing ZnO at 12.5-14 percent. A further drop in friction between die and powder may be reached by mixing it, before sintering, with a tiny percentage of self-lubricating particles as it has been done in [27] with CDS, although this technique shows drawbacks like a more non homogeneous final agglomeration. Its most relevant features are being electrically and thermally insulating the way that the current flow through the conductive powder is being maxi- mized [1]. The stroke given by the upper electrode during compression, then, is not supposed to damage its structure by causing any breakage since there is always a bit of clearance in between
Figure 4: electro sinter forging equipment
Figure 5: assembly with most important dimensions, in mm
a good forgeability. Downspouts, gutters, roofing, gaskets, auto radiators, busbars, nails, printing rolls, rivets and radio parts are among their main applications beside the experimental one for tools here. The equipment and a 3d sketch of the die-tools assembly are illustrated in figure 4 and 5, with diameters and heights of each component reported, respectively, on left and right side. The disk thickness measure is missing since it has varied according to the amount of powder inserted at each sinterization.
As the number of disks sintered in this experimental thesis is too low compared to an industrial production volume, it would not have led to a reliable and accurate result finding out the optimal tool life conditions. In spite of that, it has still been reasonable to identify in which case a quicker electrodes wear occurs. For instance with too a high current intensity or too long sintering time, which would make the electrodes getting welded with the sintered part; the two intervals for the other two parameters are unknown in both cases, instead. Adhesion to the die surface can also occur, making the ejection more difficult and therefore increasing the risk of breakage.
3.2 Manufacturing process
Diagram in figure 6 depicts the main process stages: at each sinterization, the hollow die had to be first cleaned with an ethanol napkin to scratch away any adhesion residuals and then lubricated to simplify the ejection. The setup could then take place on the fixture set between the machine basement and ram, with powder insertion, upper electrode placement to close the die’s cavity, pre- compression, electro sintering, unloading and ejection to be manually carried out. Even though there
Figure 6: Process operations diagram
was not an automatized device which could insert every time exactly the same amount of powder, an attempt to keep the weight approximately constant around 2g has been made by using a plastic doser. Since a heavier disk would be bigger in size as well, the temperature difference between core and surface area would change as well with many other factors, making any comparison among samples less reliable. Once poured it with a tiny funnel into the die’s cavity and placed the upper electrode on top of it to close it, pre-compression takes place with the machine upper ram applying pressure on top of the upper electrode surface. An additional step carried out for instance in [18]
but not in this research consists in making the powder vibrating for a minute so to have equilibrium at a tap porosity state. Its main aim is to decrease the overall powder resistivity so to allow a more uniform current flow in the next stage,this by reducing the amount of pores within the green body.
An upper bound for a feasible value of applied force has been set as a technological constraint, corresponding to 9,5kN , as a higher value would lead to a manometer breakage. A specific lower bound, instead, cannot be fixed as long as the machine is releasing current. In case of a very soft compression, resistivity would still be high after, meaning there are still several air pores left within the green body: this structure would eventually increase the risk of spark formation during the current discharge. Compaction is assumed to be approximately uniform even though it depends on the contact surface area between particles and the oxide layer thickness surrounding them: on some, the applied pressure turns out to be higher than the one set in the machine, and on others instead lower [18]. Graph in figure 7 illustrates how force varies during pre compression: after a dramatic pulse shaped increase, it continues at the set constant value for approximately two seconds after the peak before the end of the operation.
0 2 4 6
0 2 4 6 8
1 0 1 2
t i m e [ s ]
a p p lie d f o rc e [N ]
Figure 7: Applied force of 9,5kN as function of time during precompression
As long as the machine is in condition of releasing current, then electric assisted sintering takes place.For the chosen sintering time, a current discharge whose intensity is measured by a Rogowski coil flows through the green body from upper to lower electrode. The Rogowski coil, already used in experimental researches such as [17], consists of an air coil wound which is placed around the conductive part through which current is flowing, in this case the lower electrode clumped to the lower ram. The device working principle revolves around the mutual inductance between primary and secondary circuit, which is linking output voltage and current intensity derivative in a directly proportional relation. Due to the fact that it is not made from any ferromagnetic material, it provides an extremely good linearity as long as a wide dynamic range [22]. On the other hand, many variables such as temperature, position of the conductor or electromagnetic disturbances can badly affect its accuracy, which makes it unsuitable for an industrial usage where accuracy must be approximately more than 99 percent [23]. Meanwhile, the same constant pressure of the pre compaction is kept on being applied, leading to a complex interaction between electric, thermal densification and deformation phenomena. The only source of heat is actually the powder compact, which dissipates thermal energy because of the Joule effect induced by the current flow. Unlike other processes where the graphite die is conductive and heats the powder, here is both thermally and electrically insulating as previously stated, the way that heat dissipation to the outside can almost occur just through the two copper electrodes. According to the heat transfer model proposed by [24]
not all the green body is being heated homogeneously. It is assumed the heat is being exchanged from one particle to the other through the necking areas, corresponding to 3) which can be of different shape according to the level of pressure previously applied, as in figure 8. Although the Neodymium alloy powder particles are characterized by a more polygonal shape rather than a spherical one, an approximation with the latter can still be made to show that each particle center turns out to be the coldest part of the green body
Resistivity is then expected to decrease in two different zones [25], at the contact areas and also at the surroundings, close to the die inner surface and the electrodes; in case of an excessively high applied force, though, powder resistivity can become almost the same as the one of the power supply circuit, behaviour which can make the current discharge not fully efficiently exploited. Five different stages occurring during the current flow have been identified by [5] : at first the slim oxide layer surrounding each particle starts getting destroyed thanks to the applied pressure, which makes the electric resistivity decrease and current flowing through the most conductive areas. Then it occurs a trade-off regarding resistivity during sintering, since the previous drop is counterbalanced by an overall increase of temperature up to different extents, which can eventually make it even rising.
After, the real sintering between particles takes place, with a surface layers breakage in both radial
Figure 8: how heat exchange occurs between two particles layers, 1), through the neck area, 3), in a direction schematically represented by the arrows 5), with spherical shaped radiations[32]
and vertical direction if referred to the system vertical axis of symmetry.
Current eventually flows through particles conductive necks until the end of the sintering time, and acts as a driver for the densification mechanisms which occurs in three different ways, counterbal- anced by grain coarsening: sintering, with a decrease of the surface curvature, plastic deformation and particle rearrangement[19]. The assumption behind is that there are two different kinds of porosity which decrease, one intraparticle and the other interparticle, illustrated in figure 9, since within the alloy powder it has been seen there are larger grains in which particles are gathered; the bonding strength or weakness depends on how high is the Arrhenius surface energy. The graph in
Figure 9: inter and intra particle porosities characterizing crystallites structure [27]
figure 10 eventually shows force and current pulse together in black and red, the latter generated immediately before the former drops, while sintering a sample with a current intensity of 12kA, ap- plied force of 9,572kN , current intensity 9kA and sintering time 150ms. Any variation in intensity will just make the pulse peak shifting upward or downward to the respective value on the y axis, whereas a change in sintering time will widen or shorten the pulse amplitude and hence also the time during which force and electricity are playing an active role simultaneously. The force curve after its peak, instead, can only be shifted along the y according to the value set with the potentiometer.
0 2 4 6 8
0 5
1 0 1 5
t i m e [ s ]
a p p lie d f o rc e [ k N ] 0 5
1 0 1 5
c u rr e n t in te n s it y [k A ]
Figure 10: Applied force of 9,5kN and current intensity of 12kA as function of time during sintering
even further increase in density. This operation did not turn out to be doable here because of two reasons. The available equipment does not allow to change the applied force during sintering: it could have been performed after when the disk has already cooled down, but then it would have become more similar to a material test. Also, the high alloy brittleness is making the post pressing much riskier, with fractures more likely to occur, whereas the aluminum alloy used in that paper had much better toughness properties. Ejection of the final disk in figure 12 has lastly been carried out manually with the press in figure 11.
A metallic pin is inserted into the die cavity leaving some clearance between them, and after, by pushing down the lever on the right, the press punch advances against the pin and makes it sliding until the sintered disk falls from the bottom and gets extracted. No disk breakage occurred apart from a few cases where there has been an adhesion phenomena with the die. A key factor enabling an effective ejection is the pinch effect in the sintering stage: the magnetic field arising due to current flow is generating a radial body contraction the way that the final diameter becomes smaller than the original one because of shrinkage, even though it is partially counterbalanced by the material springback effect. In figure 12 it can be seen the final sintered disk.
Figure 11: Ejection press Figure 12: electro sintered disk right after ejection
3.3 Experimental procedure
The three independent variables on which the research has focused among those that the equipment allows to change are current intensity [kA], sintering time [ms] and applied force [kN]: the first two could be set on the press control screen whereas the last one had to be manually regulated with a potentiometer on one side of the press. Their values have been changed with different combinations for each batch of sintered sample so to find out in which way they will be affecting relative density,hardness and maximum load before fracture, which can be assumed to be variables dependent from the previous ones. The chosen statistic tool providing robustness to results is the single and 2 way analysis of variance (ANOVA), which will be made in one or two factorial ways according to how many factors will change simultaneously during an experiment. A more complex but at the same time more accurate alternative could have been the analysis of covariance, not chosen in this case since the probability of finding out contradictions among different results would have been high with the restricted amount of data that has been possible to get in this context.
Its assumptions are that data of all its groups must be normally distributed and with homogeneous variance: these hypothesis have been respectively verified with Shapiro Wilk and Brown Forsythe test, whose output tables have all been reported in appendix. Among the normality tests, Shapiro Wilk has been prefered to Anderson Darling, Kolmogorov Smirnov, Lilliefors or others since it turns out to be one of the most powerful in case of small data sets as in this research: thought at first for less than 50, it exploits regression and linear correlation relations. It is expected that populations out of phisical measurements should almost always be normal, but in case they should not, instead of the homoschedastic ANOVA it has been implemented its non parametric version of Kruskal Wallis, which relies just on the variance homogeneity hypothesis. As post hoc tests for mean comparisons in case of significant results, it has been chosen Bonferroni, more accurate than similar tests such as Tukey, Fisher lsd or Scheff`e, for the former case and Mann Whitney for the latter, but Nemenyi or Dunn would have worked as well.
Current intensity is released from the machine and throughout the two conductive copper electrodes it flows into the disk. The minimum possible value which can be chosen is 3,8kA, whereas the maximum is far higher than the one required by the process and has never been applied to any sample. Different models have been proposed for the current flow across powder particles, suggesting a formation of paths shaped by the particles contact zone; the more the current flow is concentrated in these areas, the less it will be uniform. It is always linked to the electric resistivity the compacted powder body has, since if it is too high the machine will not release any current because of the high risk of sparks formation, phenomenon which occurs when current flows across porous cavities. The second one is the lapse of time during which the discharge occurs, whose values can be set from 1 to 7000 ms with a machine resolution of +1. Its increase or decrease is considered to affect mostly variables like hardness and brittleness rather than the relative density, thus being more important when it comes to hardness tests.The applied force then, determines the degree of compaction of the powder before sinterization and is set by rotating the machine potentiometer, whose scale is reported in appendix in section .
4 Experiments and results
4.1 Relative density
4.1.1 Variable electric current intensity with fixed sintering time and applied force As concerns the choice of the process parameter interval range, it has been pursued a trial and error approach since there were not formulas already available with whom calculating upper and lower bound; by analyzing the effect of just one factor treatment change at a time, its interval may have been later shortened or extended in case it was not wide enough to notice any significant influence on the output. For the first ANOVA, the minimum amount required of samples, 3, has been sintered for 11 levels of current intensity in between 3,8kA and 11kA with different increments, all reported in table 1.
Table 1: Data for samples sintered with variable current intensity and fixed sintering time and applied force
n CI [kA] V [mmˆ3] M[g] D [g/mmˆ3] Rd avg std dev
1A 3,8 310,860 2,1250 0,0068 88,55% 86,54% 2,19%
1B 3,8 326,640 2,1053 0,0064 83,49%
1C 3,8 234,920 1,5885 0,0068 87,59%
2A 4,5 272,330 1,8708 0,0069 88,98% 89,21% 0,60%
2B 4,5 254,069 1,7380 0,0068 88,61%
2C 4,5 257,067 1,7866 0,0069 90,03%
3A 5,5 282,710 2,0613 0,0073 94,45% 92,05% 1,73%
3B 5,5 280,660 1,9775 0,0070 91,27%
3C 5,5 265,360 1,8526 0,0070 90,43%
4A 6 236,890 1,7248 0,0073 94,31% 92,76% 2,62%
4B 6 318,120 2,1873 0,0069 89,06%
4C 6 251,290 1,8409 0,0073 94,89%
5A 7 221,500 1,5822 0,0071 92,53% 93,62% 0,77%
5B 7 273,640 1,9899 0,0073 94,20%
5C 7 223,750 1,6260 0,0073 94,13%
6A 8 233,940 1,6818 0,0072 93,12% 94,58% 1,11%
6B 8 236,650 1,7505 0,0074 95,82%
6C 8 269,220 1,9705 0,0073 94,81%
7A 9 256,740 1,9475 0,0076 98,26% 95,38% 2,26%
7B 9 225,530 1,6564 0,0073 95,14%
7C 9 288,480 2,0654 0,0072 92,74%
8A 9,5 271,020 1,9429 0,0072 92,86% 94,08% 1,46%
8B 9,5 255,580 1,8969 0,0074 96,14%
8C 9,5 313,520 2,2571 0,0072 93,25%
9A 10 301,140 2,1705 0,0072 93,36% 93,67% 1,43%
9B 10 295,590 2,1806 0,0074 95,56%
9C 10 282,510 2,0087 0,0071 92,10%
10A 10,5 300,300 1,9514 0,0065 84,17% 89,55% 3,81%
10B 10,5 288,740 2,0620 0,0071 92,50%
10C 10,5 280,700 1,9928 0,0071 91,96%
11A 11 285,050 2,0232 0,0071 91,94% 91,61% 0,71%
11B 11 263,600 1,8442 0,0070 90,62%
11C 11 312,080 2,2230 0,0071 92,27%
The electric current lower bound is a technological machine constraint since the Expert Maschinebau press could not release less , whereas the upper one has been fixed so not to release a far too high discharge, leading to possible damages such as electrodes excessive wear or welding with one side of the disk. If a variation of current intensity has occurred, sintering time and applied force have so far been kept fixed at 150 ms and 7kN, respectively. Given the theoretical powder alloy density of 0,00772g/mm3, relative density for each sample has been calculated with (1):
(1)rd =
M V
0, 00772
where m is the sintered disk mass and V its volume. The former has been calculated once weighted each of them with a Sartorius scale, instrument with a minimum resolution of +0,0001g, whereas the latter by laser scanning each sample in 3 shape; both devices are reported in figure 13. Developed by
Figure 13: Sartorius scale and inside of 3shape scanner
danish engineers and mostly used for a biomedical usage such as designing tooth implants or hearing aids devices, this device enables to reconstruct and display the 3D shape of the scanned object. It firstly needs to be placed inside the machine by opening it from one side and clumped to an internal oscillating platform through some adhesive wax.Then, parameters defining constraints such as the space range coordinates where the object is located, number of rotations around the object made by the beams and their angles have to be set before executing the scanning. It has been chosen 40, 0 and 30 mm for the first, referred to top, medium and bottom part, 10 for the second and 0, 40 and 80 for the third one, for a total scanning time of approximately five minutes. Since the 3D output always owns a cylindrical shell cavity on one side as the wax covered part could not get scanned, the file has been further processed in GOM inspect. Apart from closing the hole by applying a mesh grid, its usage has also been aimed at measuring each disk’s volume so to lastly find out its relative density. What happened at each stage can be seen in the diagram in figure 14.
Figure 14: A)disk after 3shape scanning, B)GOM mesh bridging C)final disk after GOM
Table 2: regression output
. relative density
Number of Points 33 Degrees of Freedom 30 Reduced Chi-Sqr 5,00E-04 Residual Sum of Squares 0,015
R Value 0,74729
Adj. R-Square 0,52901
Table 3: curve intercept and coefficients with respective standard errors SE
Intercept Intercept B1 B1 B2 B2 Statistics
Value SE Value SE Value SE Adj. R-Square
p 0,65045 0,04559 0,07421 0,01316 -0,00463 8,75692E-4 0,52901
An alternative way of measuring it is through Archimedes method as carried out in [10]: this methodology has not been chosen since it requires a waterproof coating for each disk, otherwise even a tiny water absorption would make the measurement unreliable. Once set the current intensity in kA on the x axis and the calculated relative density on the y axis, the literature has suggested in previous papers different curve patterns. In both cases an upward sloping branch of a parabola has been drawn, meaning that up to a current density threshold, relative density is positively dependent on it. A difference arises later on, since whereas in [12] the graph ends at a point reasonably assumed to be the parabola’s peak, in [5] it is presented the downward sloping branch as well, stating there is a current density value after which relative density starts decreasing dramatically. Moreover, the same parabolic pattern has been found out in the experiment carried out by [8], even though again with SPS and different materials for electrodes and sintered powder, which is supposed to explain why their peak is occuring in between 9 and 10 kA, a bit forward shifted compared to mine.
Figure 11 illustrates the scatter plot of gathered data, with relative density calculated by dividing the sample density by the specific one of the alloy. Data seem to follow that pattern [5] as well since an approximately continuous increase has been observed till sample 7A, the first one sintered at 9kA with a relative density of 98,26 , in percentage .After, assuming sample 10A an outlier, a slight decrease is observed, even though the relative density is still not dramatically falling down; it has been decided not to keep on increasing the current density and find out what may happen later because of the high likelihood of quickly damaging the equipment by doing so. Figure 15 illustrates a polynomial second grade fitting prediction model, whose regression parameters, intercept and coefficients are reported in tables 2 and 3.
The parabola peak occurs at a current intensity level of approximately 8kA even though the maximum relative density has been obtained for a sample sintered at 9kA. Sample 10A is to be considered as an outlier not consistently affecting the overall dataset, whose relative density is thus expected to keep on dropping with a further current intensity increase. In order to make
4 5 6 7 8 9 1 0 1 1 1 2
0 , 8 0 0 , 8 5 0 , 9 0 0 , 9 5 1 , 0 0
relative density
c u r r e n t i n t e n s i t y [ k A ]
Figure 15: second grade polynomial fitting curve for relative density data with variable current intensity
an assessment on the model bounty, the residuals have been plotted against the output response Y, relative density, and the order of time. From graph in figure 16 it can be seen the residuals are just slightly increasing over zero when the fitted relative density increases but they are overall distributed structureless without any evident relation with the x variable. Plot in the order they have been sintered as in figure 17, again no evident link can be established, meaning that throughout time the overall equipment conditions change is not relevantly affecting the output. Therefore, it cannot be found any factor which is dramatically affecting the machine variability, at least in the time bucket taken for sintering all the samples so far. Since just current intensity has changed from a group of samples to the other, it cannot be made any assessment on whether a change of two parameters at a time is affecting relative density positively or negatively. It can still be made a one way ANOVA analysis, though, whose result is reported in the table in figure 13. Each group consists in the three different disks sintered for each current intensity level, making the analysis a balanced draw. The F value found out from a Fisher with (10,22) degrees of freedom eventually turns out to be higher than the critical P value of 0,00397, sufficiently low to state that groups differ not only due to random effects and errors but also because of the effect of the treatment. The null hypothesis, therefore, is to be rejected with the meaningfulness below, meaning that both deviances within and between groups are affecting the total one; in other terms, a current intensity variation significatively affects relative density. The Bonferroni mean difference comparison test is reported in appendix in table 35.
Table 4: ANOVA output
. DF Sum of Squares Mean Square F Value Prob>F
Model 10 0,02163 0,00216 3,85546 0,00397
Error 22 0,01234 5,6097E-4
Total 32 0,03397
0 , 8 5 0 , 9 0 0 , 9 5 - 0 , 1 0
- 0 , 0 5 0 , 0 0 0 , 0 5
re g u la r re s id u a ls
F i t r e l a t i v e d e n s i t y
Figure 16: residuals scatter plot against the fit y, relative density
0 3 6 9 1 2 1 5 1 8 2 1 2 4 2 7 3 0 3 3
- 0 , 1 0 - 0 , 0 5 0 , 0 0 0 , 0 5
re g u la r re s id u a ls
o r d e r o f t i m e
Figure 17: residuals scatter plot against the order of time with whom samples have been sintered
4.1.2 Variable sintering time with fixed electric current intensity and applied force With a constant current intensity of 6kA and an applied force of 4-0 = 9,095kN, three samples have been sintered for four different levels of sintering time within the range [200 ; 350] ms and an increment of +50ms for a total of 12. The aim was to figure out whether variations within the interval taken into account were significantly affecting disks relative density or not. All the gathered data are shown below in table 5; normality and homoschedasticity tests are in appendix in tables 36 and 37.
Table 5: samples data for variable sintering time
ST[ms] V[mmˆ3] M [g] DENSITY[g/mmˆ3] RELATIVE DENSITY %
200 271,740 1,9670 0,007238537 93,76%
200 284,760 2,0566 0,007222222 93,55%
200 283,840 2,0573 0,007248098 93,89%
250 308,040 2,1901 0,007109791 92,10%
250 307,020 2,2170 0,007221028 93,54%
250 272,310 1,9614 0,00720282 93,30%
300 286,100 2,0409 0,00713352 92,40%
300 287,180 2,0843 0,007257817 94,01%
300 269,900 1,9544 0,0072412 93,80%
350 293,490 2,1405 0,007293264 94,47%
350 252,250 1,8247 0,007233697 93,70%
350 260,331 1,8863 0,007245776 93,86%
From the ANOVA output in table 6, a p-value of 0,73597 leads to state that within this sintering time interval there is no significant variation in groups mean relative densities.
Table 6: ANOVA output
. DF Sum of Squares Mean Square F Value Prob>F
Model 3 0,35151 0,11717 0,43187 0,73597
Error 8 2,17043 0,2713
1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 0
9 0 9 1 9 2 9 3 9 4 9 5
Relative density
S i n t e r i n g t i m e [ m s ]
Figure 18: relative density scatter plot
4.1.3 Variable applied force with fixed sintering time and electric current intensity The last batch of sample has been sintered covering the applied force interval of [4,8 ; 9,5]kN, with five different levels and a constant increment of 0,9kN except for the last one, where it has been of 2kN. Sintering time has been kept fixed at 150ms and current intensity at 6kA. Applied force is actually the only input parameter whose variations are directly modifying the powder aggregate particles structure, with particular regard to contact surfaces.The higher the pressure, the wider the necking areas through which current is assumed to flow for a chosen sintering time according to what stated for instance in [1] or in [19]. At the same time the green body resistivity is being affected as well, the way that at a low level compaction resistivity does not decrease that much since several air pores are still left in between particles: with more restricted necking contact areas, when current flows there it becomes more intensified leading to higher process temperatures. The opposite is worth with high compaction pressure, with a dramatic decrease in resistivity and particles being deformed in such a way that contact areas get larger, so that current flows more uniformly and at lower induced temperatures. A higher or lower sintering time or current intensity can thus be considered to play a key role but merely in enhancing or smoothing each effect previously described, since they modify the total amount of energy released due to Joule effect. It can eventually be said to counterbalance or catalyze the process temperature reached with a given average contact necking area supposed to be approximately the same one across the disk to be sintered, without taking into account that pressure may be distributed as a hill, with a peak in correspondence to the symmetry axis and decreasing values when getting further towards the side. The fact that an applied force variation turns out to affect process temperature has already been found out, for instance, in [2], experimentally and numerically for tungsten carbide powder. It is still unrealistic with the utterly limited knowledge available, though, to formulate an analytic model relying on phisical principles only able to describe this behaviour. Below in table 7 and 8 there are reported data and ANOVA output table togehter with a scatter plot of data in figure 19: the F value is just slightly greater than the critical one, high as well, and therefore at 95 percent of confidence a significative influence of applied force on relative density is to be rejected, with any variation occurring just due to randomness.
Table 7: samples data for variable applied force
AF[kN] M[g] V[mmˆ3] DENSITY[g/mmˆ3] RELATIVE DENSITY
4,8 1,8421 248,58 0,0074 95,99%
4,8 2,1148 292,49 0,0072 93,66%
4,8 1,7785 243,79 0,0073 94,50%
5,7 1,8927 256,39 0,0074 95,62%
5,7 1,9915 269,60 0,0074 95,68%
5,7 2,0122 277,15 0,0073 94,05%
6,6 2,1819 300,41 0,0073 94,08%
6,6 1,8651 254,59 0,0073 94,90%
6,6 1,8375 252,24 0,0073 94,36%
7,5 2,0020 273,83 0,0073 94,70%
7,5 1,9016 257,15 0,0074 95,79%
7,5 1,9518 269,53 0,0072 93,80%
9,5 2,0268 285,71 0,0071 91,89%
9,5 1,9000 273,80 0,0069 89,89%
9,5 1,8460 250,95 0,0074 95,28%
The p-value of 0,30629 leads to state that neither in case mean relative density is significantly changing between groups.
Table 8: ANOVA output
. DF Sum of Squares Mean Square F Value Prob>F
Model 5 0,0016 3,20E-04 1,41474 0,30629
Error 9 0,00203 2,26E-04
Total 14 0,00363
4 , 8 5 , 7 6 , 6 7 , 5 9 , 5
0 , 8 7 0 , 8 8 0 , 8 9 0 , 9 0 0 , 9 1 0 , 9 2 0 , 9 3 0 , 9 4 0 , 9 5 0 , 9 6 0 , 9 7
Relative density
A p p l i e d f o r c e [ k N ]
Figure 19: relative density scatter plot
4.1.4 Sintering time and applied force interaction
Once finished with the first set of experiments it can be stated that, by taking into account only one treatment effect at a time on each disk relative density, just an increase in current density has led to a significative improvement, whereas any change of sintering time or applied force within their explored ranges just leads to a relative density variation due to randomness. Hence, the next step will be aimed at finding out which combination of these two other parameters is providing the highest output values, if it exists. The chosen technique is a two way ANOVA, which has one more null hypothesis compared to the one way case: not only it will be calculated a p-value just for the single factor effect but also for the effect of their interaction, otherwise hard to quantify.
An unexpected outcome of an ANCOVA analysis carried out by [7] on samples capacitor discharge sintered is eventually stating that an increase in geometric density can be reached by increasing voltage but mostly by decreasing the applied initial pressure and thus force. It is still not clear why this behaviour occurs: what it is thought to happen is, with particular regard to electro sinter forging, whose applied current intensity is extremely high, that a lower pressure leads to an increase in resistivity, a drop of current flow, Joule heat, temperature and eventually density. By analyzing the effect of two treatments at three different levels, three different samples have thus been sintered in a balanced design of experiment draw for each of the possible nine combinations of treatments and levels for a total of 27 , all of them with the maximum current intensity of 8,2 kA found out from the polynomial fifth grade fitting of data reported in table 1. All disks have then been sintered following a complete randomization criteria, with a sintering time that has been extended up to 1000ms with the aim of analyzing the widest range possible. Difficulties have arisen when having to sinter samples with longest sintering time and lowest applied pressure: in this case a light compaction is still leaving many pores within the green body as long as a high resistivity, which are eventually making the process temperature increasing with a higher risk of welding between tool and sintered part. Adhesion can also occur between disk surface and the die’s cavity and the ejection eventually becomes less smooth with the disk more likely to get broken, also due to the high alloy brittleness. In both the other cases with a sintering time of a second it has still been observed a quicker electrodes wear and a system overheating due to the higher temperature reached during such a long time. Also,
their final shape shows a less accurate roundness probably due to the high friction with the die and pressure applied by the press through the pin. The remaining six did not lead to any particular problem. Table 9 reports all gathered data and relative density for a sintering time of 200, 600 and 1000 ms matched with three different level of applied force.
Table 9: data for samples sintered with variable AF and ST
AF[kN] ST[ms] V [mmˆ3] M [g] DENSITY [g/mmˆ3] RELATIVE DENSITY
5,1 200 266,741 1,9915 0,0075 96,71%
5,1 200 271,302 1,9988 0,0074 95,43%
5,1 200 260,604 1,9067 0,0073 94,77%
7,3 200 266,8 1,8112 0,0068 87,94%
7,3 200 280,05 1,9172 0,0068 88,68%
7,3 200 283,37 1,8963 0,0067 86,68%
9,6 200 251,342 1,8398 0,0073 94,82%
9,6 200 259,199 1,909 0,0074 95,40%
9,6 200 284,032 2,0758 0,0073 94,67%
5,1 600 260,34 1,8676 0,0072 92,92%
5,1 600 260,936 1,8669 0,0072 92,68%
5,1 600 255,001 1,8229 0,0071 92,60%
7,3 600 266,619 2,0061 0,0075 97,46%
7,3 600 279,008 2,0727 0,0074 96,23%
7,3 600 273,909 2,0598 0,0075 97,41%
9,6 600 229,522 1,6914 0,0074 95,46%
9,6 600 229,962 1,6601 0,0072 93,51%
9,6 600 239,322 1,7524 0,0073 94,85%
5,1 1000 260,234 1,8948 0,0073 94,32%
5,1 1000 294,433 2,1137 0,0072 92,99%
5,1 1000 229,671 1,6454 0,0072 92,80%
7,3 1000 256,085 1,8415 0,0072 93,15%
7,3 1000 262,906 1,9013 0,0072 93,68%
7,3 1000 254,168 1,8691 0,0074 95,26%
9,6 1000 218,182 1,5858 0,0073 94,15%
9,6 1000 267,877 1,9891 0,0074 96,18%
9,6 1000 237,872 1,7077 0,0072 92,99%
Table 10: 2 way factorial ANOVA output table
. DF Sum of Squares Mean Square F Value P Value
factor af 2 0,00135 6,75E-04 7,46437 0,00436
factor st 2 0,00182 9,09E-04 10,051 0,00117
Interaction 4 0,01304 0,00326 36,04572 2,30E-08
Model 8 0,01621 0,00203 22,4017 7,48E-08
Error 18 0,00163 9,04E-05 – –
Corrected Total 26 0,01784 – – –
The outcome from table 10 turns out to be partly in contradiction with the one found out in 4.2 and 4.3. By looking at the p-values column it can be stated that the group means significantly differ, with a mutual interaction between treatments sintering time and applied forces being the one which is influencing relative density the most. A glance at the P-values of the single factors leads
separately are influencing the output. Such a conclusion does not involve the one of paragraph 1.5 to be wrong, since here the sintering time interval has been extended up to 1000ms instead of the 350 upper bound of the previous interval, whereas the lower bound of 200ms is still the same. An applied force variation is significant as well even though of a less relevant impact, with the highest P value if making a comparison with the other ones; one possible explanation for a result which rather differs from the one in 4.2 can be that in the previous experiment the sintering time has been kept constant to 150ms. Here instead, even when analyzing the effect of just one treatment change at a time, the assessment is being formulated by looking three times at different values, for instance a force variation in case of 200, 600 and 1000ms. Due to the fact that the interaction fisher value is consistently higher than its P value, the final ANOVA output eventually enables to identify the input parameter conditions which are providing the best relative densities data for the samples sintered so far. Just by looking at the groups means, the highest one of 97,03391 percent with standard deviation 0,006982 comes out with a sintering time of 600ms and 7,3 kN, which are both means of the respective factors; such a percent ought to be regarded as successful since it is falling within the range between 95 and 98 percent reported to be an average one in [19]. Due to time constraints it has not been possible to make replications of this design of experiment which would ensure whether the maximum mean relative densities is still occurring with the same input parameters condition.
Therefore, it can be concluded so far that if trying to achieve again the highest relative density 600ms and 7,346kN may work better again, with an optimal current intensity of 8,2kA still worth.
An optimal medium level for both factors allows to achieve the highest relative densities probably because this match is optimally balancing the effects of each treatment. A sintering time of 600ms is thus supposed to be approximately the right time that a current intensity of 8,2kA needs to flow through the particles neck contact areas path being shaped by an applied force of 7, 3kN, together with a temperature which is not overcoming the alloy melting point with particular concern to the core. By giving a glance at the relative density variances and their means it can be noticed that the maximum levels of both sintering time and applied force, respectively 1000ms and 9,5kN, are not only resulting in lower relative densities, but make also process variability dramatically increase.
The two further steps of the design of experiment will involve two others two way ANOVA analysis which are aimed at evaluating a possible significative interaction between current intensity with sintering time and applied force by exploring again, for each, three different levels for a total of nine combinations.
Proven the relevance of the interaction between factors, a more in depth look at the 2 way ANOVA output can be given by making a multiple comparison Bonferroni test on the means, that enables to specifically assess which combinations of treatments change is significantly affecting the output, in this case relative density. The P value for each interaction is reported in table 11:
Table 11: Bonferroni output table
. MeanDiff SEM t Value Prob Alpha LCL UCL
7,3 5,1 -0,00971 0,00448 -2,16667 0,13177 0,05 -0,02154 0,00212 9,5 5,1 0,00756 0,00448 1,68717 0,32647 0,05 -0,00427 0,0194 9,5 7,3 0,01728 0,00448 3,85384 0,00349 0,05 0,00545 0,02911 600 200 0,02002 0,00448 4,46547 8,97E-04 0,05 0,00819 0,03185 1000 200 0,01157 0,00448 2,58085 0,05653 0,05 -2,61E-04 0,0234 1000 600 -0,00845 0,00448 -1,88462 0,2272 0,05 -0,02028 0,00338 When it comes to sintering time, the only significative variation occurs between 200ms and 600ms but not between 200ms and 1000 or 1000ms and 600ms; nevertheless it must also be noticed that the p value of 0,05653 is quite close to the null hypothesis rejection threshold and may change by making other replications. In case it should become less than 0,05, there would be a better evidence of a pattern where very short or very long sintering times are giving similar relative densities, definitely different from the ones with a medium one in better or worse, in this case 600ms. A constant change in sintering time is hence not giving a linear proportional variation in relative density: this behaviour might be explained stating that the densification mechanisms before and after a certain lapse of time
