In today’s competitive manufacturing environment, it is extremely important to improve metallurgical production quality, especially for high-demand products such as thick steel plate.

Despite the success of modern science and manufacturing in improving the flatness of steel plate, several new, stricter quality standards for rolled-metal stock have made it necessary to develop and implement the efficient technology.

Domestic hot-rolled thick steel plate production is currently most advanced at the following mills: the 2350, 4500, and 5000 mills at the Magnitogorsk Metallurgical Combine (MMK); the 2800/1700 and 5000 mills at the Izhora Metallurgical Plant, Severstal; the 5000 mill at the Vyksa Metallurgical Plant; the 2300/1700 mill at the Chelyabinsk Metallurgical Combine; and others. The MMK 5000 mill produces hot-rolled plate with thickness 8–100 mm and widths of 1500–4800 mm from carbon steel, low-alloy steel, and alloy steel; the Severstal 5000 mill (manufactured by Izhora Metallurgical Plant) produces plate with thickness 70 mm and maximum width 4800 mm from F500W high-strength steel; the Vyksa Metallurgical Plant 5000 mill produces plate with thickness 40–80 mm and maximum widths of 4800 mm. All these mills are equipped with plate straighteners.

When straightening steel plate, the primary difficulties involve determining the mean deformation stress during hot straightening operations (which reduces the calculation accuracy of bending moment and torque calculations for modernization of plate straighteners) as well as determining the geometric parameters of the plate being straightened. The purpose of this paper is to develop techniques for calculating the aforementioned parameters when straightening plates on a roller straightening machine (RSM).

In Russia, the primary standard for thick steel plate is GOST 19903-2015. However, many metallurgical firms in Russia produce plate to Eurostandard EN 10029-91 and US standard ASTM A6/A6M-91. Under GOST 19903-74, the maximum deviations from flatness are 5, 8, 10, and 12 mm over a 1 meter baseline. Under Eurostandard EN 10029-91 and US standard ASTM A6/A6M-91, flatness is measured over the full width of the plate and over a 4000 mm baseline along the long axis of the plate. Under Eurostandard EN 10029-91, the normal flatness N of a class varies from 5 mm to 8 mm, depending on plate thickness [1].

In hot rolling shops, plate is commonly straightened while hot. Hot straightening of plate is performed as the temperature decreases from the temperature at the end of the rolling process (850–900°C) to a temperature of 100–500°C [2]. This is accomplished by feeding the plate from the last stand of the rolling mill via a roller table to a roller straightening machine.

In hot forming, the mean strain resistance is determined using the method of thermomechanical coefficients [3]:

$$ {\upsigma}_{SC}={\upsigma}_0{k}_{\upvarepsilon}{k}_u{k}_t, $$
(1)

where σ0 is the basic yield strength; and kε, k и , and k t are coefficients that take into account the amount of deformation, the deformation rate, and the temperature at which the deformation occurs.

Under the method described in [3], the coefficients kε, k и , and k t for each metal or alloy are determined using graphs of the functions kε = ƒ(ε), k u = ƒ(u), and k t = ƒ(t).

The mean strain resistance for 45 steel may be calculated using the equation [4]

$$ {\upsigma}_{SC}={A}_1{\upsigma}_0{\left(10\upvarepsilon \right)}^{A2}{u}^{A3}{\left(T/1000\right)}^{-A3}, $$
(2)

where σ0 = 88 MPa is the basic yield stress of the metal obtained for ε = 0.1, u = 1.0 sec–1, Т = 1000°С, А1 = 1.0, А2 = 0.173, А3 = 1.143, and A4 = 3.05.

When the plate is straightened using an RSM, the relative deformation can be written as

$$ \upvarepsilon =z\left(1/{r}_0-1/r\right), $$
(3)

where z is the vertical distance from the neutral axis of the plate cross-section to the fiber under consideration, r0 is the initial radius of the section of plate prior to straightening, and r is the bending radius of the sheet on the rollers.

The rate of plastic deformation during straightening u = ε/t (t is the time required to straighten the plate in the RSM). The time required to straighten the plate t = m/v p (m is the spacing between RSM rollers, and v p is the linear straightening speed).

Practical experience in straightening is known to cause the plastic deformation rate for the straightening process to vary from 0.01 sec–1 to 1.2 sec–1. When a deformed section of a rectangular cross-section plate is straightened in an RSM, the plastic bending moment is given by the formula

$$ {M}_{\mathrm{pl}}=\frac{Bh^2}{4}\frac{2}{{\left({\upvarepsilon}^{\ast}\right)}^2}\underset{0}{\overset{\upvarepsilon^{\ast }}{\int }}\upsigma \upvarepsilon d\upvarepsilon, $$
(4)

where B and h are the width and thickness of the plate; ε* is the relative deformation of the extreme fibers in the transverse section of the plate; and σ is the stress, which varies over the vertical cross section of the plate.

If the quantities σ and ε in Eq. (4) are represented in the form of mean values σ* and ε*, the latter equation may be written in the form

$$ {M}_{\mathrm{pl}}=\frac{Bh^2}{4}\frac{2}{{\left({\upvarepsilon}^{\ast}\right)}^2}\underset{0}{\overset{\upvarepsilon^{\ast }}{\int }}\upsigma \upvarepsilon d\upvarepsilon ={W}_S{\upsigma}_{SC}^{\ast }, $$
(5)

where W S = Bh2/4 is the drag torque for a plate of rectangular cross-section, and \( {\upsigma}_{SC}^{\ast } \) is the yield strength of the plate.

The total torque due to the RSM tractive force MΣtor is the sum of the following torques: the torque Mtor(1) from bending the sheet over the rollers, the torque Mtor(2) required to overcome roller friction against the surface of the plate, and the torque Мtor(3) required to overcome friction in the trunnions for the non-driven rollers [5, 6].

The torque required to overcome roller friction against the surface of the plate is given by

$$ {M}_{\mathrm{tor}(2)}= Pf\left(2v/D\right), $$
(6)

where ƒ1 is the coefficient of rolling friction for the rollers against the surface of the plate, v is the linear straightening speed, and D is the roller diameter. For hot straightening, the coefficient of rolling friction ƒ1 = 1.0–1.5 mm [1].

The torque required to overcome friction in the trunnions for the non-driven rollers is given by the formula

$$ {M}_{\mathrm{tor}(3)}=\sum \limits_1^n{P}_i{f}_2\frac{D}{2}\upomega, $$
(7)

where P i is the straightening force for the ith roller, ƒ2 is the coefficient of sliding friction for the roller trunnions in the bearings, and ω is the roller angular rotation velocity.

The RSM electric motor power is determined as follows:

$$ N={M}_{\Sigma \mathrm{tor}}v/102D\upeta, $$
(8)

where MΣtor = Mtor(1) + Mtor(2) + Mtor(3) is the total torque, and η is the efficiency of the motor used in the machine.

The straightening force is given by the formula

$$ P=2{M}_{\mathrm{pl}}/m. $$
(9)

We then rewrite Eq. (3) in slightly different form:

$$ {\upvarepsilon}^{\ast }=\frac{h}{2}\left(\frac{1}{r_0^{\ast }h}+\frac{1}{rh}\right)=\frac{1}{2}\left(\frac{1}{r_0^{\ast }}+\frac{1}{r}\right), $$
(10)

where \( {r}_0^{\ast } \) is the initial radius of the plate prior to straightening, and r is the bending radius of the sheet on the rollers.

Table 1 lists experimental values of r/h for specific values of r0/h for plate made from 10 steel, 20 steel, and 45 steel [5].

Table 1. Relative Bending Radii for Plate
Full size table

Table 1 can be used to determine the values of r/h if we know the relative initial radius of a section of plate prior to straightening r0/h. Equation (10) was used together with the quantities r0/h and r/h to determine the relative deformation at the second roller \( {\upvarepsilon}_2^{\ast } \). The deformation at the third \( \left({\upvarepsilon}_3^{\ast}\right) \) and subsequent RSM rollers was determined in a similar manner.

Table 2 lists the calculated bending torques for 45-steel plate as a function of deformation speed (u) and temperature.

Table 2. Calculated Torques for Straightening 45-Steel Plate for Various Deformation Temperatures and Speeds on a 10-Roller Straightening Machine (h = 20 mm, B = 2000 mm)
Full size table

In Table 2, M2pl–M10pl are the plastic bending torques at RSM rollers 2, 3, ..., 10 calculated using Eq. (4).

Analysis of the results in Table 2 revealed the following:

1) the bending torque each roller increase with increasing temperature from 20 to 300°C, and then decrease as the temperature increases to 500°C. If the data in Table 2 are used to graph the bending torque as a function of temperature, the resulting graphs will appear to be similar to those for strain resistance as a function of temperature [3];

2) higher deformation speeds mean larger bending torques on all rollers;

3) the bending torques decrease from roller No. 2 through roller No. 10 as the plate passes through the RSM.

The calculation presented above is for hot straightening of thick steel plate (45 steel) after rolling on the 2300/1700 combination mill at the Chelyabinsk Metallurgical Combine, with the straightening machine immediately following the 2300 stand group. The technical specifications of the 2300 mill roller straightening machine are as follows:

Plate width, mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

800–2100

Plate thickness, mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6–20

Straightening speed, m/sec . . . . . . . . . . . . . . . . . . . . . . . . .

2

Number of straightening rollers. . . . . . . . . . . . . . . . . . . . . .

7

Diameter of straightening rollers, mm. . . . . . . . . . . . . . . . .

400

Length of straightening rollers, mm . . . . . . . . . . . . . . . . . .

2300

Roller spacing, mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

410

Diameter of supporting rollers, mm . . . . . . . . . . . . . . . . . .

400

For a 45 steel plate with relative initial radius \( {r}_0^{\ast }=10.0 \) (see Table 1), we obtain a relative plate bending radius r* = 130.

Substituting these values into Eq. (10), we obtain

$$ {\upvarepsilon}^{\ast }=1/2\left(1/{r}_0^{\ast }+1/r\right)=0.053. $$
(11)

The calculated plate straightening parameters at 400°С obtained from Eqs. (3), (4), (9), and (10) are listed in Table 3.

Table 3. Calculated Straightening Parameters for 45-Steel Plate (h = 20 mm, B = 2000 mm)
Full size table

Analysis of the data provided for 45 steel in Table 3 indicated that ε* decreases from 0.053 to 0.0029, the deformation rate u decreases from 0.106 sec–1 to 0.006 sec–1, the bending torque М decreases from 104·103 to 40·103 N·m, and the straightening force decreases from 650.0 to 310.0 kN from roller No. 2 to roller No. 10.

In addition, the improved plate straightening quality in hot straightening compared with cold straightening is due to enhanced structural modification of the metal throughout the entire cross section. The plate has improved surface quality because the combination of alternating bends and cooling removes the scale.

The straightening efficiency of the ten-roller straightening machine for 45-steel plate (h = 20 mm, В = 2000 mm) was determined using the formula

$$ \mathrm{E}=\frac{1/{r}_0-1/{r}_1}{1/{r}_0}100,\%. $$
(12)

The straightening parameters for the 45-steel plate are listed in Table 4.

Table 4. Straightening Parameters for 45-Steel Plate (h = 20 mm, B = 2000 mm)
Full size table

The data in Table 4 imply that the parameter А lies within the range 20.0 to 40.0 mm and the parameter l lies within the range 800 to 1000 mm; after straightening, А lies within the range 4.0 to 10.0 mm, and l lies within the range 800 to 1000 mm; the straightening efficiency is therefore 75–86.0%.

Conclusion

1. We performed a theoretical study of the process for hot straightening of steel plate via alternate bending of metal over rollers, taking temperature and bending speed into account, and also determining the parameters for this process.

2. The calculations performed for this paper indicate that temperature and bending speed have a substantial impact on bending torque and straightening force, which must be taken into account in the design and operation of RSMs.

3. The calculations showed that for a 45-steel plate (h = 20 mm, B = 2000 mm) straightened on a roller straightening machine, ε* decreases from 0,053 to 0,0049, the bending speed u increases from 0,106 to 0,011 sec–1, the bending torque М decreases from 104·103 to 70·103 N·m, and the straightening force decreases from 650 to 437.6 kN.