Theoretical Data vs. Experimental Data

The text in red below is taken from the paper "Report on a hot rolling formula" (A. Izzo, Iron and Steel International, Feb 1974, pages 47-54).

Before reading it you'd better go through some symbols and formulae illustrated in the first part of the paper. You can read them in the list below. ARC stands for Actual Rolling Conditions. SRC stands for Standard Rolling Conditions (click Roll Pressure to learn what we mean by Standard). At the end of this page you will find the reference literature taken from the paper.

      k_wi = roll pressure in ARC (Izzo) 
      k'_wi = roll pressure in SRC (Izzo) 
      k_wi = k'_wi a₁ a₂ a₃ a₄ a₅ (Izzo's formula) (5) 
      k_w = roll pressure in ARC 
      k'_w = roll pressure in SRC 
      k_w = k'_w a₁ a₂ (Siebel's formula) 
      h₀ and h₁ are entry and exit stock thickness 
      a₅ = function of h₁/d, KEM and temperature  
      h₁/d = exit stock thickness divided by roll diameter  
      KEM = (4.2 + C% + Mn% + 0.3 Cr%)/4.77

Something to remember, when you reach the diagrams: the curves refer to roll pressure measured in actual rolling conditions; only Siebel's diagrams give roll pressure in "his" standard rolling conditions (a₁=1 and a₂=1). Circled points always indicate calculated k_wi.

Calculated data versus measured data

Beside our own tests, six sources of information have been assumed as reference points for our calculations:

1. Siebel³
2. SKEFKO, 1947¹¹
3. SKEFKO, 1950¹²
4. Wallquist¹⁰
5. Wusatowski⁴
6. Leufvén¹³

Most of the calculations have been performed by our Univac 1108 electronic data processing unit; only Siebel's have been hand performed.
The input data were assumed according to the Author's prescriptions; if they were lacking (as for instance the roll surface hardness), approximate values have been assumed, based on the state of the knowledge at the time of the tests considered.
The output results of all the electronic calculations show an impressive agreement between measured and calculated data.
In this section some information about the test programs and the steel grades used is given, together with a synopsis of the input data and an examination of the test program.

Siebel's data
The theoretical points are calculated assuming "Standard Rolling Conditions", i.e. all the coefficients of formula (5) being equal to unity, except a₅ of course, because of the four grades of steel considered.
The four carbon steels considered were: 0.10% C (KEM=1.000); 0.28% C (KEM=1.058); 0.43% C (KEM=1.115); 1.03% C (KEM=1.152).

SKEFKO's data (1947 and 1950)
There is some difference, which was remarked also by Larke⁸, between the two sets of measured data collected at different times, but in the same conditions; this difference is still unexplained.
Values of KEM:
KEM = 0.950 (for low carbon steel with h0 = 2.2 or 4.4)
KEM = 1.010 (for low carbon steel with h0 = 3.3 or 5.5)
KEM = 1.148 (for high carbon steel)

Wallquist's data
Values of KEM:
KEM = 1.000 for low carbon steel (Wallquist's steel 1)
KEM = 1.152 for high carbon steel (Wallquist's steel 2)

Wusatowski's data
This set of measurements is interesting because it is the only one considering a 40 by 40 mm square which should give, according to Leufvén, a specific roll pressure about 20% lower than that given by flats.
Another peculiarity of this set is the very low rolling speed (0.2 m/s).
The composition of Cook and McCrum's¹⁴ low carbon steel has been considered: KEM = 1.052.

Leufvén's data
Values of KEM:
KEM = 1.000 for low carbon steel
KEM = 1.152 for high carbon steel

General input data
Table 1 Synopsis of the input data for each test program

Notes:
* Information not given by the author in the reference literature.
(1) var(n) means that h₁ is variable in order to get n values of
R (10, 20, 30... %) from each value of h₀.
(2) SKEFKO used 1110 °C only with high carbon steel.
(3) SKEFKO considered a strip width b_m instead of b₀.
[RBC indicates the coefficient a₂.]
[HSC is roll surface hardness]
[KSC is a code for roll material]

After a long, conceptual presentation, an American friend of mine told me: "I'm from Missouri: you've got to show me". Well, if you want to see the final results of this match, just click here.

References

1. Ekelund - Nagra dynamiska förhallanden vid valsning - Jernkontorets Annaler, 1927, 2, p.39
2. Mathea - Nomogramme zur Ermittlung von Walzkräften auf Grund der Gleichung von S. Ekelund - Stahl und Eisen, 1958, 78, p.1393
3. Siebel - Berechnung der Walzkraft und der Leistungbedarfes beim Walzen - Wälzlager in Walzwerken, Kugelfischer Georg Schäfer & Co., Schweinfurt, Firmendruckschrift.
4. Wusatowski - Fundamentals of rolling - Pergamon Press Ltd., London, 1969
5. Tselikov - Stress and strain in metal rolling - Mir Publishers, Moscow, 1967
6. Suppo, Izzo, Diana - Applicazione dell'elaboratore elettronico nei calcoli relativi alle calibrazioni (Computer application in calculations concerning roll passes) - La Metallurgia Italiana, 1972, 2, p.41.
7. Suppo, Izzo, Diana - Anwendung des elektronischen Rechners in der Planung der Kalibrierungen für Rundstahl - Conference held at the 8. Verformungskundliches Kolloquium, Rheinisch Westphälische Technische Hochschule, Aachen, BRD, March 1972. Der Kalibreur, Heft 19, Nov 1973 p3 and 47.
8. Larke - The rolling of strip, sheet and plate - Chapman and Hall Ltd., London, 1967.
9. Underwood - The rolling of metals - Chapman and Hall Ltd., London, 1952.
10. Wallquist - Calculation of roll pressure and energy consumption in hot rolling - J. Iron and Steel Institute, 1954, 177, p.142.
11. SKEFKO - Roll pressures and power consumption in steel strip hot rolling - The Ball Bearing Journal, 1947, 1, p. 13.
12. SKEFKO - New research into roll pressures and power consumption in the hot rolling of steel strip - The Ball Bearing Journal, 1950, 1, p. 3.
13. Leufvén, Iko, Bülow - Il calcolo della forza di laminazione nella laminazione a caldo (Calculation of roll force in hot rolling) - La Rivista dei Cuscinetti a Sfere, 1967, 149, p. 3.
14. Cook and McCrum - The calculation of load and torque in hot flat rolling - BISRA, London, 1958.