SIMULATION

UDC 539.37:621.771.07

SIMULATION OF STRUCTURAL STATE AND STRESSES IN FORMING

ROLLS SUBJECTED TO HARDENING WITH INDUCTION HEATING

A. M. Pokrovskii,1 V. G. Leshkovtsev,1 A. A. Polushin,2 and E. B. Bochektueva3

Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 9, pp. 40 43, September, 2010.

Results of computer simulation of variation of temperature and structural state and of formation of stresses in

surface hardening of forming rolls heated by induction are presented. Two variants of surface hardening of

rolls with heating by commercial-frequency currents (CFC) used at machine-building plants are considered,

i.e., hardening with five-pass heating by CFC and hardening with one-pass heating by CFC and preliminary

furnace heating to 500C. The second variant of heat treatment is shown to be more efficient.

Key words: induction hardening, forming roll, residual stresses, mathematical simulation.

INTRODUCTION

Today, forming rolls are produced from steels of mar-

tensitic class with elevated hardenability. The thickness of

hardened layer in such steels is 50 70 mm, which ensures

high operating resistance of the rolls to contact stresses.

Martensitic structure in the surface layer of large rolls is

obtained by using induction heating and intense water cool-

ing of the surface. The process of hardening heating and

cooling gives rise to mechanical stresses. On one hand, these

stresses are connected with a high temperature gradient aris-

ing in the roll and on the other hand they are caused by the

change in the specific volume of the phases in the and

transformations that accompany the hardening. In

large parts like forming rolls these stresses may be quite con-

siderable and sometimes stimulate fracture of the parts al-

ready in the production process. This poses a technical prob-

lem of raising the strength of hardened parts and lowering of

self-balanced stresses arising in the hardening process (tem-

porary stresses) and after the hardening (residual stresses).

Tensile stresses are especially dangerous because they cause

the appearance and growth of cracks and fracture.

The aim of the present work consisted in choosing a ra-

tional mode of heat treatment for a forming roll in terms of

the criterion of minimum residual stresses given that all the

requirements of the specification are observed.

METHODS OF STUDY

The object of our study was a forming roll for cold roll-ing with a mass of 24.6 tons produced from steel 90Kh3MF

at the South-Ural Machine-Building Plant. The diameter and

the length of the functional part of the roll were 1350 and

1420 mm, respectively; the total length of the neck was

1520 mm, the maximum diameter of the conical part was

1000 mm and the diameter of the cylindrical part was

820 mm.

Preliminary heat treatment of such rolls includes double

normalizing with heating to 950C in the first operation and

to 850C in the second operation. Then the rolls are tempered

at 470C.

The final heat treatment consist of induction quenching

by commercial-frequency currents in a TPCh-1500 commer-

cial vertical induction installation. We studied two variants

of hardening, i.e., hardening with five-pass heating by CFCand hardening with one-pass heating by CFC and prelimi-

nary heating in the furnace to 500C.

In the first variant of heat treatment the roll was heated to

a surface temperature of 810C in the first four passes. In the

fifth hardening pass the surface of the roll under the inductor

was heated to 970C and then cooled by a sprayer. After the

passage of the functional part of the roll, the inductor was

stopped in the top position and water was fed to the surface

Metal Science and Heat Treatment Vol. 52, Nos. 9 10, 2010

442

0026-0673/10/0910-0442 2010 Springer Science + Business Media, Inc.

1N. . Bauman Moscow State Technical University, Moscow, Rus-

sia (e-mail: ampokr@mail.ru, leshkovtsev@bk.ru).2

South-Ural Machine-Building Plant (ORMETO-YuUMZ Com-

pany), Orsk, Russia.3

East Siberian State Technological University, Ulan-Ude, Russia.

of the barrel for 70 min. Then the roll was tempered in the

electric furnace for 60 h at 360C. The voltage in the induc-

tor was 390 V in all the five passes. The current in the induc-

tor and the speed of its motion are presented in Table 1.

In the second variant of heat treatment the roll was sub-

jected to preliminary through heating in an electric furnace to

500C. Then we performed a single quenching pass of the in-

ductor at a speed of 4.5 mmsec, in which water was fed onto

the surface of the roll heated to 970C from a sprayer at-

tached to the inductor. After heating the functional part of the

roll, the inductor was stopped in the top position and water

from the sprayer was fed to the surface of the roll for 70 min.

Then the roll was tempered in the inductor for 60 h at 360C.

The voltage and the current in the inductor were 380 V and

3500 A, respectively.

A rational mode of heat treatment for large parts like

forming rolls can be chosen only by mathematical simulation

of the thermal processes, of the processes of structure forma-

tion, and of the related processes of the appearance of

stresses. Simulation of these processes involves solution of

three problems, i.e., the problem of nonlinear nonstationary

heat conduction, simulation of structure formation, and com-

putation of stresses. These problems are interrelated, because

the thermophysical coefficients and the mechanical charac-

teristics depend not only on the temperature but also on the

structural state of the steel. In addition, the transfor-

mation is accompanied by absorption of heat and the

transformation is accompanied by emission of heat.

We resorted to step computation, which allowed us to

solve the problems of determination of the temperature,

structure, and stresses at each time step independently of

each other. At an arbitrary time step we first solved the prob-

lem of heat conduction with thermophysical characteristics

corresponding to the temperature and the structure of the pre-

ceding step. Then we modeled the structural changes with

the help of isothermal diagrams of the transformation of

supercooled austenite. In order to determine the structural

states appearing in continuous cooling we used the theory of

isokinetic reactions [1]. After this we computed the total co-

efficient of linear expansion, which allowed for the purely

temperature deformations and for the deformations related to

structural transformations. The temperature and the struc-

tural state obtained at a specific step was treated as initial

conditions for determining the stresses. The stresses were

computing by solving the elastic problem with allowance for

the rheological properties of the steel. All the three problems

were solved on the basis of the method of finite elements and

the appropriate software was created. The algorithm of the

simulation is described in detail in [2].

RESULTS AND DISCUSSION

The thermal computation has shown that the temperature

field arising due to induction hardening has a characteristic

form of a temperature torch (Fig. 1a ). Maximum tempera-

ture gradients arise in the surface zone between the inductor

and the sprayer and amount to 10 Kmm. Maximum surfacetemperature of 970C is attained in the fifth pass. This tem-

perature is detected in the zone lying right under the inductor.

The thickness of the layer heated above the austenization

temperature is about 60 mm. The thickness of the hardened

layer, where the content of martensitic components in the

structure exceeds 95%, is equal to 50 mm. The shaft of the

roll heats to only 30C even in the fifth pass.

Analysis of the stress state of the roll during surface

quenching has shown that the highest stress components are

normal axial stresses. We devoted special attention to tensile

stresses, because they cause opening and growth of cracks

and may result in failure of a roll in its production or ope-

ration.

In the case of five-pass hardening with CFC heating

(the first variant of heat treatment) maximum tensile axial

stresses attaining 625 MPa arise in the zone behind the

Simulation of Structural State and Stresses in Forming Rolls 443

TABLE 1. Modes of Induction Hardening with 4 Pre-

liminary CFC Heating Passes

Number

of pass

Speed of motion of the

inductor, mmsecInductor

current, A

1 4.5 3500

2 3.0 3500

3 2.5 3500

4 2.5 3500

5 1.1 4200

1

1

3

3

2

2

b

100

400

200

750

520 300

100

500

970

350

300300

250

100

120

30

320

Fig. 1. Distribution of temperatures (in C) (a) and axial stresses (in

MPa) (b ) in a longitudinal section of a backup roll in the fifth pass:

1 ) roll; 2 ) inductor; 3 ) sprayer.

sprayer at a distance of about 40 mm from the surface

(Fig. 1b ). The temperature in this region is about 300C. At

this moment the maximum tensile stresses on the shaft are

equal to 410 MPa and the temperature of this zone is about

35C. Maximum compressive stresses arise on the surface of

the roll cooled to about 100C, which is located behind the

sprayer, and are equal to 750 MPa.

When the roll is cooled to room temperature, the residual

stresses are self-balanced in its volume (Fig. 2). The stress

distribution is symmetrical with respect to the mid cross sec-

tion of the roll. A narrow zone of compressive stresses attain-

ing 850 MPa forms on the functional surface of the roll.

Maximum tensile stresses (430 MPa) arise near the mid sec-

tion at a distance of about 100 mm from the surface. Then

they damp rapidly to about 60 MPa and remain virtually in-

variable up to the shaft.

Computer simulation of the second variant of heat treat-

ment has shown that maximum temporary tensile axial

stresses appear in the roll at the moment when the inductor

almost reaches the upper face of the barrel (Fig. 3a ). Maxi-

mum tensile stresses equal to 608 MPa form in the surface

layers of the barrel lying behind the inductor; the tempera-

ture in this zone is 350C.

The residual stresses arising in the roll after hardening

with one-pass CFC heating (Fig. 3b ) are distributed over its

longitudinal section more uniformly than in the case of five-

pass hardening. For this reason the maximum tensile stresses

in this case are lower. They arise near the left and right end

faces in the zone of the edge effect and amount to 300 MPa.

In the neighborhood of the mid section of the roll the tensile

axial stresses do not exceed 240 MPa. Maximum compres-

sive stresses appear on the functional surface of the barrel

and amount to 885 MPa. On the shaft the stresses are tensile

and decrease from 170 MPa in the middle of the roll to

90 MPa near the necks. The thickness of the hardened layer

is 50 mm, just like after the first variant of hardening.

Comparing the results presented on Figs. 2 and 3b we

can infer that the distribution of residual axial stresses in the

case of one-pass CFC heating followed by sprayer hardening

is preferable to hardening with four preliminary heating

passes. The compressive stresses in the first case are not

much higher than in the second case (885 MPa instead of

850 MPa), but they should not be dangerous because it is

known [3] that such stresses raise the resistance of rolls to

contact fatigue.

In operation, cracks can grow only in the field of tensile

stresses [3]. The rate of growth of fatigue cracks is the higher

the greater the amplitude of the cyclically changing load. In

this connection special danger in operation of such rolls ap-

pears in the zones most distant from the neutral line, where

the cyclically changing bending rolling stresses have a non-

zero amplitude in contrast to the shaft zone, where the ampli-

tude is close to zero. In the case of hardening with CFC and

four preliminary heatings the maximum tensile stresses are

about 40% higher than in one-pass hardening (430 and

300 MPa, respectively). In addition, they are observed in a

region lying at a great distance from the shaft, where the ope-

rating stresses are the highest.

As for the maximum temporary stresses, they are virtu-

ally the same for both heat treatment variants and amount to

622 and 608 MPa, respectively. However, the second treat-

ment variant (hardening with one-pass CFC heating and pre-

liminary furnace heating) is preferable in the this case too.

The axial tensile stresses in the central shaft zone of the bar-

rel subjected to the first variant of heat treatment amount to

460 MPa. Though these stresses are not the highest, it should

be taken into account that maximum stresses arise in the sur-

face zone of the roll with martensitic structure. The rupture

strength of steel 90Kh3MF in this zone at a temperature of

350C is (r = 1800 MPa; in the shaft zone with pearlitic

structure (r = 900 MPa. The stress state in the roll is close to

a plane one, because the tangential and normal radial stresses

444 A. M. Pokrovskii et al.

8300

400100

50 50

2020

3030

60

Fig. 2. Distribution of residual axial stresses (in MPa) in longitudi-

nal section of a backup roll after hardening with 5 passes of CFC

heating and tempering.

1

3 2

b

550 400

200

100

30 20

20

30

300

860

10

295 300

235

200

10 10

90100

150

10090

Fig. 3. Distribution of temporary axial stresses (a) and residual axi-

al stresses (b ) in a longitudinal section of a backup roll after harden-

ing with one-pass CFC heating and preliminary heating (the values

are given at the curves in MPa): 1 ) roll; 2 ) inductor; 3 ) sprayer.

are an order of magnitude lower than the axial and hoop

stresses that are close in the value and have the same sign.

Thus, the equivalent stresses computed within the theory of

highest tangential stresses are equal to the maximum axial

stresses. The safety factor nr = (r(max for the shaft zone ofthe roll is equal to 2; in the surface zone it is equal to about 3.

Consequently, the strength of the shaft zone is lower than the

strength of the surface zone. In addition, the quality of the

steel with respect to the microstructure is much worse in the

shaft zone than in the zones distant from the shaft, and the

probability of formation of microcracks here is considerably

higher. In a roll heat treated by the second variant such dan-

ger in this zone does not arise.

CONCLUSIONS

1. The method of mathematical simulation has been used

for analyzing the behavior of the thermal field, the structural

state, and the stresses in backup rolls 1350 mm in diameter

fabricated from steel 90Kh3MF and heat treated by two vari-

ants, i.e., five-pass CFC hardening and one-pass CFC hard-

ening with preliminary furnace heating to 500C.

2. Application of one-pass CFC hardening with prelimi-

nary furnace heating to 500C to backup rolls should be pre-

ferred with respect to the criterion of minimum temporary

and residual stresses at the same thickness of hardened layer

equal to 50 mm.

The work has been performed within State Contract

No. 02.513.11.3487.

REFERENCES

1. J. Christian, The Theory of Transformations in Metals and Alloys.

Part 1. The Thermodynamics and The General Kinetic Theory

[Russian translation], Mir, Moscow (1978), 808 p.

2. R. K. Vafin, A. M. Pokrovskii, and V. G. Leshkovtsev, Strength

of Heat Treated Forming Rolls [in Russian], Izd. MGTU Im.

N. . Baumana, Moscow (2004), 264 p.

3. G. P. Cherepanov, The Mechanics of Brittle Fracture [in Rus-

sian], Nauka, Moscow (1974), 416 p.

Simulation of Structural State and Stresses in Forming Rolls 445