SYSTEM FOR PROCESS ANALYSIS AND HARDNESS PREDICTION WHEN QUENCHING AXIALLY-SYMMETRICAL WORKPIECES OF ANY

SHAPE IN LIQUID QUENCHANTS Božidar Liščić

Faculty for Mech. Engineering, University of Zagreb, Ivana Lučića 5, 10 000 Zagreb, Croatia

e-mail: bliscic@fsb.hr

Keywords: Quenching, Heat Transfer Coefficient, Prediction of Hardness Distribution

Abstract. A new Temperature Gradient System has been designed for practical use when quench-ing real workpieces in any kind of liquid quenchants. The main hardware component of the system is a cylindrical probe of 50 mm Dia. × 200 mm assembled with three thermocouples, and the tem-perature data acquisition unit for automatic drawing of cooling curves. The accompanying software-package consists of three modules: The first one for calculation of the heat transfer coefficient, the second one for quenching process analysis by graphical presentation of different thermodynamic functions, and the third one for hardness distribution prediction on the axial section of axially-symmetrical workpieces of any complex shape. The hardness prediction 2-D program is based on a Finite Volume Method, by which cooling curves in every particular point of the axial workpiece section are calculated, and cooling times from 800 °C to 500 °C (t8/5) determined. Using the known relation between the cooling time (t8/5) and the distance from the quenched end of the Jominy specimen, for the relevant steel, the hardness can be predicted, at once, in every particular point of the axial workpiece section, which is the unique feature of this system. The system itself is designed to: record, evaluate and compare real quenching intensities during the whole quenching process, when different liquid quenchants with different conditions are used, and different quenching tech-niques have been applied.

Introduction The new Temperature Gradient System (TGS) is designed to be used when quenching real axially-symmetrical workpieces of any complex shape, in different liquid quenchants and different condi-tions. The main purpose of this system is: a) To calculate the real heat transfer coefficient as function of surface temperature and of time dur-

ing the whole quenching process. b) To analyze every quenching process by experimentally measuring and recording relevant cooling

curves and evaluating the quenching intensity during whole quenching process, expressed by dif-ferent thermodynamic functions. These functions enable to compare different quenching proc-esses in regard of: quenching intensity, dynamic of heat extraction, thermal stresses, and cooling rates in all points within the probe, where the thermocouples are placed.

c) Prediction of hardness distribution, at once, on the whole axial section of the workpiece after quenching, as well as after tempering. This enables every user to see at a glance whether or not adequate depth of hardening was achieved using concrete steel grade and quenching conditions. If the predicted results are not satisfactory, the user can repeat the simulation process using other steel grades and/or other quenching conditions. From the hardness distribution after tempering, mechanical properties (ultimate strength, yield strength, elongation) can be determined in each point of the section, depending on tempering temperature used, by means of an auxiliary dia-gram. The hardness prediction module of the system is applicable for those steels for which Jominy hardenability curve exists i.e. primarily for non-alloyed and low to medium alloyed structural steels.

Calculation of the Heat Transfer Coefficient (HTC) A real description of the heat transfer, as input value for calculation, is the fundamental prerequisite for a successful simulation of the quenching process. There is a big difference between calculating

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the HTC of a small laboratory test specimen (usually 12.5 mm Dia. × 60 mm) and of a real workpiece, where some inevitable influences occur, which are not relevant to labora-tory specimens.

First of all, as it is well known, quite big differences of the HTC are possible in different points over the entire sur-face of the workpiece, as it is shown in Fig.1. Other factors that affect the heat transfer at real workpieces, besides of the kind of quenchant, are: surface roughness, external flow field of the liquid and its turbulence. Taking into account only these factors, obviously some compromise has to be made when using the HTC for a real workpiece of complex shape.

Another very important question is: does the diameter of an axially-symmetrical workpiece, even a simple cylinder, have an influence on the HTC as function of surface tem-perature? Not knowing the answer on this ques-tion, one does not know in which span of diame-ters a calculated HTC may be used.

Fig.1 Heat transfer coeficients in different points of a flat ring quenched horizontally in still oil of 70 °C [1]

Fig.2 shows a HTC vs. surface temperature of a standard cylindrical laboratory test probe (12.5 mm Dia. × 60 mm), quenched in a fast quenching oil, having the maximum value of 4250 W/m2K. The calculation was based on an inverse heat conduction algorithm which uses an iterative procedure that begins with an initial guess to calculate the temperature dependent HTC [2]. In this case the thermocouple, which has recorded the time-temperature history, was placed in the geometric centre of the probe.

Fig.2 Calculated heat transfer coefficient of an ISO-9950 standard laboratory test probe (12.5 mm Dia. × 60 mm) quenched in a fast quenching oil [2]

Fig.3 shows the HTC vs. time and vs. surface temperature, when quenching the Liscic/Nanmac probe (50 mm Dia. × 200 mm) in a still mineral oil of 20 °C [3]. It is evident that the maximum value of the HTC is only 1400 W/m2K. The model for calculation of the HTC was based on the control volume numerical method [4]. In this case the surface temperature of the probe was directly measured using a special self-renewing thermocouple (U.S. Pat. No. 2.829.185). It is difficult to judge which of the following factors contributed more to the difference in HTC maximum values: the cylinder diameter, the calculation method, or the position of the thermocouple?

Fig.3 Heat transfer coefficient a) vs. time and b) vs. surface temperature when quenching the Liscic/Nanmac probe (50 mm Dia. × 200 mm) in a still mineral oil of 20 °C [3]

In order to investigate only the influence of the diameter on HTC, computer simulations have

been performed for cylinders of 20 mm diameter and 80 mm diameter by the HTC for 50 mm Dia.

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shown in Fig.3, using the same control volume method. The results of these simulations showed no difference in HTC vs. temperature, compared to Fig.3, but there was difference in HTC vs. time. As shown in Fig.4 the time to achieve the maximum value of the HTC is 10 seconds for 20 mm diame-ter, and 14 seconds for 80 mm diameter, Fig.5. Also the area under the HTC curve in case of 80 mm diameter is much bigger than in case of 20 mm diameter.

Fig.4 Heat transfer coefficient as function of time for acylinder of 20 mm Dia. × 80 mm, quenched in still min-eral oil of 20 °C, calculated by means of the heat transfercoefficient for cylinder of 50 mm Dia. × 200 mm [4]

Fig.5 Heat transfer coefficient as function of time for a cylinder of 80 mm Dia. × 320 mm, quenched in still mine-ral oil of 20 °C, calculated by means of the heat transfer coefficient for cylinder of 50 mm Dia. × 200 mm [4].

According to the Nukiyama curve for boiling [5], as shown in Fig.6, the HTC curve (α) follows

the heat flux density curve (q); accordingly the area under the HTC curves in Fig.4 and Fig.5 repre-sent also the heat extracted. From these simulations it can be concluded the following: If calcula-tions for smaller or bigger diameters are performed with a known HTC for a certain cylinder diameter, the maximum value of HTC will not change, but to find the difference, the curves HTC vs. time should be compared. These differences are in accordance with the cooling curves for dif-ferent cylinder diameters.

Fig.6 Nukiyama curve for boiling. A- free convection, B- nucleate boiling, C- transition boiling, D- film boiling [5]

Fig.7 Change in heat transfer coefficient at immersion cooling, due to wetting kinematics [6]

Finally, there is a phenomenon called wetting kinematics accompanied with every quenching

process in evaporable liquids [6], which can influence more or less the HTC. As shown in Fig.7 rewetting starts in those places on the workpiece surface, where the film boiling (vapour blanket) collapses and nucleate boiling starts. At every of these places at that moment a sudden increase of the HTC occurs. When cylinders with smooth surface are involved, rewetting starts usually at the lower end and moves gradually as a wetting front towards the upper end, as it is shown on the left side of Fig.8. Temperature inside the cylinder changes not only radially but also along the cylinder,

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as it is shown on the right side of the same figure. This case relates to immersion cooling of an AISI-4140 steel cylinder of 40 mm Dia. × 120 mm in water of 80 °C [7], which certainly are not conditions used in practice.

The rewetting process can have different forms and durations (from slowly moving wetting front at e.g. a quenching oil of high temperature, to abrupt explosion at some polymer solutions), so it can have smaller or big-ger influence on the local HTC. This phenomenon is today an object of scientific research in laboratory con-ditions, but it is not as yet been taken into consideration when calculating HTC of real workpieces.

Taking into account the factors which may influence development of the HTC during quenching real work-pieces, a cylindrical probe of 50 mm Dia. × 200 mm, instrumented with three thermocouples has been chosen for measuring and recording the temperature-time his-tory (cooling curve) at each quenching test. The dimen-sions of the probe were chosen in order to satisfy both: a) The ratio L/D = 4, which is enough to neglect the

heat extraction from both ends of the probe, and pro-vide for radial heat flow in the middle length cross-section, where the thermocouples are located.

b) To be representative for the diameter range between 20 mm and 100 mm, which is applicable to a great deal of workpieces in the metalworking industry. Fig.9 shows three cooling curves, measured at the

points: 1 mm below the surface, 4.5 mm below the sur-face and at the centre, where the thermocouples have been placed, when the probe is quenched in a high-speed mineral oil of 50 °C, without agitation [8]. Utmost care has been taken of temperature measurement, by minimiz-ing the possible errors regarding: damping effect; time lag and thermocouple response time. The mathematical method applied for calculation of the HTC, based on the cooling curve recorded at the point 1 mm below the surface is as follows:

Fig.8 Observed wetting kinematics (left) and temperature distribution (right), calculated usi-ng local heat transfer coefficients, when immer-sion cooling AISI-4140 steel cylinders of 40 mm Dia. × 120 mm, in water of 80 °C [7]

One dimensional heat conduction equa-tion, using temperature dependent physi-cal properties (density, specific heat capacity, heat conductivity), as a nonlin-ear inverse problem was first solved with measured temperature at the point 1 mm below surface, as Dirichlet boundary con-dition and extended the solution towards the surface of the cylinder. With the known surface temperature, the HTC was calculated by numerical differentiation, using the measured temperature of the quenching medium. Numerical solution of the heat conduction equation is done by the nonlinear implicit method, with simple

Fig.9 Experimentally obtained cooling curves (T-t) when quenching the 50 mm Dia. × 200 mm probe instrumented with three thermocouples, in a high-speed mineral oil of 50 °C,without agitation [8]

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iterations per time step, to adjust all physical properties to new temperatures. The solution extension and the calculation of the HTC by numerical differentiation is computed by local extrapolation, based on low degree polynomial least-squares approximation.

Analysis of the quenching process Each quenching process in evaporable liquids is a complex thermo-and fluiddynamic problem de-scribed in chapter 3 of [5], on which structure transformation, stress development (including resid-ual stresses), and distortion of quenched workpieces depend. Numerous factors can influence the process of quenching. Therefore, it is inadequate to describe this process by one sole number, as e.g. the Grossmann's value “H”.

The Temperature Gradient System (TGS) is based on the known physical rule that the heat flux at the surface of a body is directly proportional to the temperature gradient at the surface, multiplied by the thermal conductivity of the body material:

q = λ ∂T/∂x (1)

q = heat flux density [W/m2] λ = thermal conductivity [W/Km] ∂T/∂x = temperature gradient at the surface, perpendicular to it [K/m]

The heat flux density as function of time, and as function of surface temperature, Fig 10*, is physically the most accurate characteristic to describe the quenching intensity during the whole quenching process.

Fig.10 Heat flux density a) as function of time,and b) as function of surface temperature, when quenching the Liscic/Nanmac probe (50 mm Dia. × 200 mm) in still mineral oil of 20 °C. [3], p.378

The only difference between the Liscic/Nanmac probe and the actual probe is that the former had

thermocouples: at the very surface and at 1.5 mm below surface, while the latter has thermcouples at 1 mm and at 4.5 mm below surface, whereas the surface temperature has to be calculated.

With the actual probe the heat flux at the surface is calculated, but using the calculated surface temperature and measured temperatures in points 1 mm and 4.5 mm below surface, enables the cal-culation of the heat flux density also between these points and the surface. When comparing two different cases of quenching, the heat flux density curves enable at a glance to estimate which of them will result with greater depth of hardening. Another feature is that using the diagram: heat flux density vs. time, a delayed quenching process can instantly be recognized.

Other thermodynamic functions which are incorporated in the TGS software-package are: – Temperature differences ∆T = f(t) between centre and surface, as well as between centre and 4.5

mm and 1 mm below surface respectively, as function of time, Fig.11*a. This data are valuable when calculating thermal stresses during a concrete quenching process.

* Diagrams in Fig.10 and Fig.11 have been calculated from cooling curves measured with the Liscic/Nanmac probe (50

mm Dia.× 200 mm) having thermocouples at the very surface (n); at 1.5 mm below surface (i), and at the centre (c).

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Fig.12 Relation between time of cooling from 800 °C to 500 °C (t8/5) and the Jominy distance [11] – Integral ∫qdt vs. time, from beginning of the immersion until a selected time, represents the dynamic of heat extraction, Fig.11*b. – Cooling rate vs. temperature dT/dt [K/s] curves in all points where the thermocouples are located, obtained by differentiation of measured cooling curves, Fig.11*c. They can be a valuable information, particularly when special quenching processes as e.g. Intensive Quenching, are ap-plied.

Prediction of hardness distribution The software module 3 contains a 2-D computer programme developed by B.Smoljan, Tech. Fac-ulty, University of Rijeka, Croatia [9, 10], for prediction of hardness distribution within quenched axially-symmetric workpieces of any shape. The programme is based on the Finite Volume Method, and is suitable for use with Windows XP, as well as with older versions of Windows. It contains also the necessary subrou-tine for drawing a 2-D contour of every axially symmetric workpiece, and automatic generation of the FE mesh for a symmetrical half of it. By using temperature dependent heat transfer coeffi-

cient (HTC), calculated for each concrete case of quenching in module 1, cooling curves at every particular point of the axial workpiece section are calculated, and cooling times from 800 °C to 500 °C, t8/5 determined and stored. According to Rose [11] the time t8/5 is a relevant characteristic for phase transformation in most structural steels, and is accordingly decisive feature for resulting hardness after quenching.

Fig.11 Temperature differences vs. time a), ∫qdt = heat extracted vs. time b) and cooling curves vs. surface tempe-rature c), when quenching the Liscic/Nanmac probe (50 mm Dia. × 200 mm) in still mineral oil of 20 °C. [3], p.379

Because there is a fixed relation between the cooling time t8/5 and the distance from the quenched end of the Jominy specimen, for each time t8/5 the corresponding Jominy distance can be read, Fig.12. The next step is to read the hardness at the relevant Jominy distance from the Jominy harde-nability curve for the concrete steel in question. The whole procedure of conversion the cooling time t8/5 to the hardness at particular point of the workpiece section is shown schematically in

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Fig.13. The precision of the hardness prediction depends first of all on the Jominy curve, which further depends on the chemical composition of the particular batch, for every steel grade. There-fore the most precise hardness prediction can be expected when the Jominy curve for particular batch of the relevant steel grade is available.

Fig.14 shows the results of hardness prediction across a half of the axial section of a complex axi-ally-symmetric workpiece made of steel DIN-41Cr4, a) without central hole, b) with central hole, quenched in oil. This case clearly shows that the applied Finite Volume Method effectively simulates cooling not only at the outer radii and along the workpiece, but also at the inner radii in the hole.

Fig.13 An example of conversion the cooling time t8/5 to the hardness.

120

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2420

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3010

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As-quenched in oil H=0.5 As-quenched in oil H=0.5

Fig.14 Result of hardness prediction across a half of the axial section of a complex axially- symmet-ric workpiece made of steel DIN-41Cr4, quenched in oil, a) without central hole, b) with central hole of 20 mm diameter

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Fig.15 shows the comparison between the pre-dicted and experimentally obtained hardness dis-tribution for the workpiece shown in Fig.14. A statistical survey for this workpiece has shown that the average value of differences between predicted and measured hardness is – 0.372 HRC, and the standard deviation is 1.585 HRC.

The software package of the system contains two data files: – Data file of selected steel grades which consists

of: several international designations, chemical composition, and respective Jominy hardenabil-ity curves.

– Data file of heat transfer coefficients (HTC) calculated from the cooling curves recorded ex-perimentally by the probe.

Fig.15 Hardness distribution at the section of the workpiece shown in Fig.14: a) by mathematical mod-elling, b) by experiment [12]

Both data files are openly structured so that every user can add new grades of steel and/or new HTC's calculated for some other quenching conditions.

The two main purposes the modul 3 has to fulfil are:

1. To develop a general data bank for computer modeling of hardness distribution without perform-ing experiments with the probe in which both data files will be filled in with standard steel grades and enough HTC's for different quenchants and specified quenching conditions. It is par-ticularly important that all experiments for HTC calculations are performed using the same quenching probe. The Jominy curves in this data bank will be taken from literature, i.e. they will correspond to an average chemical composition, starting from an austenitization temperature shown in literature. By using this data bank the user can: a) Compare at a glance the real quenching intensities expressed by the mentioned thermody-

namic functions for all stored quenchants and specified quenching conditions. b) Perform an approximate hardness prediction for his concrete workpiece by using different

steel grades and /or different quenching conditions stored in the data bank. 2. To develop an own data bank based on own experiments with the probe. In this case the Jominy

curves stored should correspond exactly to the particular batch of the relevant steel grade, ob-tained by the Jominy test with the same austenitization temperature as it is used for hardening the concrete workpiece. The HTC should be calculated from cooling curves recorded in concrete quenching facilities and conditions. In this case a precise hardness prediction can be expected.

Conclusions While the real heat transfer coefficient is the most important prerequisite for every computer simu-lation of the quenching process, the whole process itself can be carefully analysed by different thermodynamic functions.

The Temperature Gradient System is applicable for all liquid quenchants (including salt baths and fluid beds), for different quenching conditions, and different quenching techniques (Immersion cooling, Spray cooling, Intensive Quenching).

Two main purposes of the system are: – To measure, record and evaluate a quenching process in order to compare it in respect of quench-

ing intensity and thermal stresses. – To predict the hardness distribution after quenching for every axially-symmetric workpiece of

any shape, by drawing the contour of its symmetric half and choosing a selected steel grade and quenching conditions, expressed by the calculated heat transfer coefficient.

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This possibility is intended to be used by practitioners in the heat treatment workshop to compare at a glance quenching processes performed in different media and different quenching facilities, in respect of possible depth of hardening. From the other side it is also a valuable tool for designers of new components, when optimum stell grade and quenching conditions are to be chosen.

The next important task for the described system is its application for quenching a batch of workpieces, where the probe itself should be placed at a representative place within the batch, to be heated and quenched together with it.

References [1] S.Segerberg, J.Bodin: Variation in the Heat Transfer Coefficient Around Components of

Different Shapes During Quenching, Proceedings First Intl. Conf. on Quenching & Control of Distortion, Chicago Ill, USA, 22-25 Sept. 1992.

[2] E.Troell, H.Kristoffersen, J.Bodin, S.Segerberg, I.Felde: Unique software bridges the gap between cooling curves and the result of hardening, HTM, 62 (2007) 3, pp.110-115.

[3] Steel Heat Treatment – Second Edition, Metallurgy and Technologies, G.E.Totten (Ed), Taylor & Francis Group, Boca Raton, USA (2007) p.382.

[4] Proprietary program: Simulation of Cooling a Cylinder in the Surrounding of Arbitrary Chosen Temperature, Faculty for Mech. Engineering, University of Zagreb, Croatia.

[5] B.Liščić, H.M.Tensi, W.Luty (Eds): Theory and Technology of Quenching, Springer Verlag (1992), p.43.

[6] H.M.Tensi: Wetting Kinematics in Theory and Technology of Quenching, (Eds): B. Liščić, H.M.Tensi, W.Luty, Springer Verlag, (1992), p.95.

[7] A.Majorek, H.Müller, E.Macherauch: Computersimulation des Tauchkühlens von Stahlzylindern in verdampfenden Flüssigkeiten, HTM 51 (1996) 1, pp. 11-18.

[8] By courtesy of Petrofer H.R. Fischer GmbH & Co. KG, Römerring 12-16, D-31137 Hildesheim, Germany.

[9] B.Smoljan: Numerical Simulation of As-Quenched Hardness in a Steel Specimen of Complex Form, Communications in Numerical Methods in Engineering,14 (1998), pp.277-285.

[10] B.Smoljan: Numerical Simulation of Steel Quenching, Journal of Materials Engineering and Performance, 11 (1) (2002), pp.75-80.

[11] A.Rose et al.: Atlas zur Wärmebehandlung der Stähle I, Verlag Stahleisen, Düsseldorf, 1958. [12] B.Smoljan: Mathematical Modelling of Residual Stress Distribution in a Quenched Steel

Specimen, Proceedings 12th IFHTSE Congress 29th Oct.-2nd Nov.2000, Melbourne, Australia, pp.217-222.