Comprehensive Optimization Control Technology of Rolling Energy and Oil Consumption in Double Cold Rolling

Abstract

In double cold rolling process, rolling energy and oil consumption is normally controlled separately, thereby causing a high comprehensive cost. This study investigated a calculation model of plate-out oil film thickness on strip surface, oil film thickness in deformation zone, friction coefficient, bite angle, forward slip, rolling force, rolling power, rolling energy consumption, and rolling oil consumption. Subsequently, the effect of emulsion flow and concentration on rolling energy and oil consumption comprehensive cost was quantitatively analyzed. On this basis, an objective function of rolling energy and oil consumption comprehensive cost was proposed, and the corresponding comprehensive optimization control technology for rolling energy and oil consumption was developed. Through a field application of this technology, the reduction of rolling energy and oil comprehensive consumption cost was achieved by optimizing emulsion flow and concentration comprehensively. Thus, a significant economic benefit was created with further popularization and application values.

1. Introduction

In recent years, the steel industry market competition has become increasingly aggressive. Packaging tinplate steel strips are steadily shifting to thin-gauge and high-strength double reduced products for minimizing material consumption and product body weight, thereby contributing to environmental preservation. The double reduced products are manufactured through double cold reduction rolling. This process is a second cold rolling operation performed after a first cold reduction rolling and annealing operation. The rolling process is performed on a two-stand double cold reduction mill, the first stand reduces strip thickness and enhances strength, whereas the second stand transfers strip roughness and controls strip flatness (Fig. 1).

Fig. 1.

Schematic diagram of the configuration of a double cold reduction mill.

In cold rolling, oil in water emulsions are generally used as lubricants. These emulsions are supplied by either a recirculated system or a direct application system. In recirculation systems, low-concentration and high-flow emulsions are supplied to the roll bite and rolls for lubrication and cooling. The advantage of recirculation systems includes low oil consumptions, which are preferably applied to tandem cold rolling mills. In direct application systems, high-concentration and low-flow emulsions are supplied to the strip surface for lubrication at the upstream of the roll bite; in addition, a roll coolant spray system is provided separately at the delivery side. The advantage of direct application systems includes favorable lubricity and cleanness. These advantages are preferably applied to double cold rolling mills with thin gauge, high strength, favorable flatness, and clean surface. However, disposable use of emulsion inevitably causes high oil consumption and large treatment of waste lubricants. Energy and oil consumption are the main components of double cold rolling production cost. Moreover, emulsion flow and concentration are the key influencing factors of these consumptions.

Many scholars have conducted numerous studies for emulsion rolling lubrication technology. Kimura and Fujita^1,2,3) established an estimation model of plate-out oil film after experimentally investigating the influences of plate-out time, emulsion flow, emulsion concentration, and oil droplet size on plate-out oil film formation characteristics through laboratory tests; then, these authors developed a hybrid lubrication system by combining recirculation and direct application systems. Azushima^4,5) proposed a numerical estimation method for oil film thickness during cold rolling by combining conventional starvation and plate-out models. Nakanishi⁶⁾ determined the relationship between introduced oil volume and emulsion particle size, emulsion concentration, and rolling velocity on a test mill. Matsubara⁷⁾ discussed the lubricant oil behavior and numerically analyzed the introduced oil film in hot rolling. Moreover, Lo⁸⁾ claimed that rolling speed and supply concentration determines the pattern of pressure distribution in an inlet zone, and a large oil droplet pressurizes the lubricant. Bai⁹⁾ developed a set of optimization technology of the relationship between emulsion flow and rolling velocity to minimize the overall fluctuation of rolling pressure during velocity acceleration and deceleration in the rolling process. Wu¹⁰⁾ developed a theoretical model for mixed lubrication on the basis of the average volume flow and asperity flattening models and the lubricant volume flow rate and outlet speed ratio; this model could determine total pressure, lubricant pressure, film thickness, and real contact area at any point within the work zone. However, these studies have focused on the lubrication property and stability improvement of recirculation systems in tandem cold rolling mills. Influences of emulsion flow and concentration on rolling energy and oil consumption of direct application systems in double cold rolling mills have not been studied well. The energy and oil consumption were separately controlled and not well balanced, thereby resulting in high comprehensive cost. Therefore, a comprehensive control of rolling energy and oil consumption through emulsion flow and concentration optimization provides significant values.

2. Comprehensive Optimization Control Technology of Rolling Energy and Oil Consumption

2.1. Plate-out Oil Film Thickness on the Strip Surface Calculation

In double cold rolling, the strip surface shows lipophilic and hydrophobic properties; thus, oil droplets in emulsion preferentially spread and plate-out a certain thickness of oil film on the strip surface (Fig. 2). Plate-out oil film thickness is determined by emulsion flow, emulsion concentration, emulsion flow residual rate, emulsion concentration plate-out rate, and entry rolling velocity. Emulsion flow residual rate is the proportion of emulsion that remains at the strip surface and mixes in the oil film plate-out process. It is influenced by the emulsion amount on per square of strip surface and plate-out time. Emulsion concentration plate-out rate is the proportion of plate-out oil amount in the emulsion and is closely related to oil wettability, emulsion concentration, and plate-out time. Thus, the plate-out oil film thickness on the strip surface is defined in Eq. (1).   

$$\{\begin{array}{l}{\xi }_{\text{2}}=1\mathrm{\hspace{0.17em} }000{\eta }_C{\eta }_Q\frac{QC}{B{v}_0}\\ {\eta }_Q=exp\left(-{\delta }_{t}t-{\delta }_Q\frac{Q}{B{v}_0}\right)\\ {\eta }_C={\eta }_{C0}+{\lambda }_{w}tanh\left({\lambda }_{t}t\right)\cdot exp\left(-{\lambda }_{C}C\right)\end{array}$$(1)

where ξ₂ — Plate-out oil film thickness on the strip surface (μm);

  Q — Emulsion flow (L/min);

  C — Emulsion concentration (%);

  B — Strip width (m);

  v₀ — Entry rolling velocity, $v_0\text{=}\frac{v_1{h}_1}{h_0}$ (m/min);

  v₁ — Exit rolling velocity (m/min);

  h₀ — Entry thickness of strip (mm);

  h₁ — Exit thickness of the strip (mm);

  η_Q — Emulsion flow residual rate;

  η_C — Emulsion concentration plate-out rate;

  t — Emulsion plate-out time, $t=\frac{L}{v_0}$ (min);

  L — Emulsion plate-out distance (m);

  δ_t — Time coefficient of the emulsion flow residual rate (min⁻¹);

  δ_Q — Flow coefficient of the emulsion flow residual rate (mm⁻¹);

  η_C0 — Emulsion initial concentration plate-out rate by emulsion-strip crash;

  λ_w — Wettability coefficient of the concentration plate-out rate;

  λ_t — Time coefficient of the emulsion concentration plate-out rate (min⁻¹);

  λ_C — Concentration coefficient of the emulsion concentration plate-out rate.

Fig. 2.

Schematic diagram of the oil film formation and variation mechanism in double cold rolling.

In Eq. (1), the coefficients of the emulsion flow residual rate and concentration plate-out rate are affected by emulsion nozzle spray conditions, oil properties, and strip surface characteristics. These six coefficients can be determined by optimal regression through a series of laboratory tests.

2.2. Oil Film Thickness in Deformation Zone Calculation

At the rolling inlet zone, plate-out oil film on the strip surface enters the geometrically wedge-shaped region formed by work roll and strip. The oil film is introduced to the roll-bite with the increase in pressure and decrease in thickness. When the oil film pressure reaches the strip deformation resistance, the strip enters the deformation zone and begins to deform. The increased behavior of the oil pressure is indicated by combining Reynolds and Barus viscosity equations,⁴⁾ as expressed in Eq. (2).   

$$\{\begin{array}{l}{\displaystyle \frac{dp}{d\xi }}=-{\displaystyle \frac{6\eta }{\alpha }}\cdot {\displaystyle \frac{\left(v_0+v_r\right)}{60}}\cdot {\displaystyle \frac{\left(\xi -{\xi }_0\right)}{{\xi }^3}}\\ \eta \text{=}{\eta }_{0}exp\left(\theta p\right)\end{array}$$(2)

where p — Oil pressure (MPa);

  ξ — Oil film thickness (μm);

  ξ₀ — Oil film thickness at the entry of the deformation zone (μm);

  η — Oil kinetic viscosity (Pa·s);

  η₀ — Initial kinetic viscosity (Pa·s);

  θ — Pressure viscosity coefficient (MPa⁻¹);

  α — Rolling bite angle (rad);

  v_r — Work roll velocity, $v_r=\frac{v_1}{1+f}$ (m/min);

  f — Forward slip (%).

At the entry and exit of the inlet zone, the boundary conditions of Eq. (2) are described in Eq. (3).   

$$\{\begin{array}{l}p=0\text{ at }\xi ={\xi }_2\\ p=K_0-{\sigma }_0\text{ at }\xi ={\xi }_0\end{array}$$(3)

where K₀ — Entry deformation resistance, K₀=1.155σ_s0 (MPa);

  σ_s0 — Entry yield strength (MPa);

  σ₀ — Back tension (MPa).

By a definite integration of Eq. (2) with the boundary conditions of Eq. (3), the oil film thickness at the entry of the deformation zone can be expressed in Eq. (4).   

$${\xi }_0={\left(\sqrt{{\displaystyle \frac{5\alpha \left[1-e^{-\theta \left(K_0-{\sigma }_0\right)}\right]}{\theta {\eta }_0\left(v_0+v_r\right)}}{\xi }_2^2+{\xi }_2}-\sqrt{{\displaystyle \frac{5\alpha \left[1-e^{-\theta \left(K_0-{\sigma }_0\right)}\right]}{\theta {\eta }_0\left(v_0+v_r\right)}}}{\xi }_2\right)}^2$$(4)

In the deformation zone, the oil film thickness decreases due to the extension of strip surface area in rolling. Assuming that the oil volume is incompressible in accordance with the oil film mass flow constant condition, the oil film thickness at the exit of the deformation zone can be defined in Eq. (5).   

$${\xi }_1=\frac{v_0+v_r}{v_1+v_r}{\xi }_0$$(5)

where ξ₁ — Oil film thickness at the exit of the deformation zone (μm).

Furthermore, the average oil film thickness in the deformation zone is expressed in Eq. (6).   

$$\overline{\xi }=\frac{{\xi }_1+{\xi }_0}{2}$$(6)

where $\overline{\xi }$ — Average oil film thickness in the deformation zone (μm).

2.3. Friction Coefficient, Bite Angle, Forward Slip, Rolling Force, and Rolling Power Calculation

A mixed lubrication regime is assumed to exist in the deformation zone of double cold rolling. The regime contains boundary lubrication and hydrodynamic lubrication. The contact ratio between work roll and strip decreases with the increase of the oil film thickness in the deformation zone. Furthermore, the ratio of boundary lubrication decreases, and the ratio of hydrodynamic lubrication increases. Thus, the friction coefficient decreases. The relation between friction coefficient and oil film thickness in the deformation zone of the double cold rolling is described in Eq. (7).¹¹⁾   

$$\mu ={\mu }_h+\left({\mu }_b-{\mu }_h\right)\cdot exp\left(\beta \overline{\xi }\right)$$(7)

where μ — Friction coefficient;

  μ_h — Friction coefficient of hydrodynamic lubrication;

  μ_b — Friction coefficient of boundary lubrication;

  β — Attenuation index of friction coefficient (μm⁻¹).

Subsequently, on the basis of rolling theory,^12,13) the bite angle, forward slip, rolling force, and the rolling power of double cold rolling can be obtained using Eq. (8).   

$$\{\begin{array}{l}P=\left(Q_f\text{+}{\displaystyle \frac{2}{3}}\sqrt{{\displaystyle \frac{1-v^2}{E}}K{\displaystyle \frac{h_1}{\mathrm{\Delta }h}}}\right)\left(K-\sigma \right)B\sqrt{R_y\mathrm{\Delta }h}\\ N=\text{2}P\mathrm{\Psi }\sqrt{R_y\mathrm{\Delta }h}{\displaystyle \frac{v_r}{60R}}\\ f=\left(1-{\displaystyle \frac{h_1}{2R_y}}\right){\displaystyle \frac{\mathrm{\Delta }h}{4h_1}}{\left[1-{\displaystyle \frac{1}{2\mu }}\left(\sqrt{{\displaystyle \frac{\mathrm{\Delta }h}{R_y}}}-{\displaystyle \frac{{\sigma }_{1}B{h}_1-{\sigma }_{0}B{h}_0}{P}}\right)\right]}^2\\ \alpha =\sqrt{{\displaystyle \frac{\mathrm{\Delta }h}{R_y}}}\end{array}$$(8)

where P — Rolling force (kN);

  N — Rolling power (kW);

  Q_f — Influence coefficient of friction, $Q_f=1.08+1.79\frac{\mathrm{\Delta }h}{h_0}\mu \sqrt{\frac{R_y}{h_0}}-1.02\frac{\mathrm{\Delta }h}{h_0}$;

  R — Radius of work roll (mm);

  R_y — Flattening radius of work roll, $R_y=R\left[1+\frac{16\left(1-{\nu }^2\right)P}{\pi E\mathrm{\Delta }hB}\right]$ (mm);

  K — Equivalent deformation resistance, $K\text{=}\frac{K_0+K_1}{2}$ (MPa);

  σ — Equivalent tension, σ=0.7σ₀+0.3σ₁ (MPa);

  Δh — Strip reduction, Δh=h₀−h₁ (mm);

  K₁ — Exit deformation resistance, K₁=1.155σ_s1 (MPa);

  σ_s1 — Exit yield strength (MPa);

  σ₁ — Forward tension (MPa);

  E — Elastic modulus of work roll (MPa);

  v — Poisson ratio of work roll;

  Ψ — Arm coefficient, Ψ=0.2–0.4 in cold rolling.

2.4. Rolling Energy and Oil Consumption Comprehensive Cost Calculation

On the basis of calculated rolling power, the rolling energy consumption per ton of strip is obtained using Eq. (9).   

$$W={10}^6\cdot \frac{N}{60\rho B{h}_1{v}_1}$$(9)

where W — Rolling energy consumption per ton of steel (kW·h/t);

  ρ — Density of steel (kg/m³).

Similarly, the rolling oil consumption per ton of strip is expressed in Eq. (10).   

$$V={10}^6\cdot \frac{2QC}{\rho B{h}_1{v}_1}$$(10)

where V — Rolling oil consumption per ton of steel (L/t).

Given the unit energy and unit oil consumption cost, the rolling energy and oil consumption comprehensive cost per ton of strip is obtained using Eq. (11).   

$$U=e_{\text{1}}W+e_{2}V$$(11)

where U — Rolling energy and oil consumption comprehensive cost per ton of steel (CNY/t);

  e₁ — Unit energy consumption cost (CNY/kW/h);

  e₂ — Unit oil consumption cost (CNY/L).

2.5. Comprehensive Control Model of the Rolling Energy and Oil Consumption

In double cold rolling, given the mill equipment configuration, rolling schedule, oil property, strip grade, and specification, the rolling energy and oil consumption are dominated by emulsion flow and concentration. Therefore, the main control objective is to minimize the rolling energy and oil consumption comprehensive cost by optimizing the emulsion flow and concentration in a certain range under the constraint condition of rolling force, rolling power, and forward slip. Thus, the objective function of rolling energy and oil consumption comprehensive control model is expressed in Eq. (12). The calculation flowchart is illustrated in Fig. 3.   

$$\{\begin{array}{l}F(X)=U=e_{\text{1}}W+e_{2}V\\ P<{\phi }_1{P}_{max}\\ N<{\phi }_2{N}_{max}\\ f<{\phi }_3{f}_{max}\\ Q_{min}\le Q\le Q_{max}\\ C_{min}\le C\le C_{max}\\ X=\left(Q,C\right)\end{array}$$(12)

where F(X) — Objective function of rolling energy and oil consumption comprehensive control model;

  X — Optimizing vector variable of emulsion flow and concentration;

  P_max — Maximum allowable rolling force (kN);

  N_max — Maximum allowable rolling power (kW);

  f_max — Maximum allowable forward slip (%);

  Q_min — Minimum emulsion flow (L/min);

  Q_max — Maximum emulsion flow (L/min);

  C_min — Minimum emulsion concentration (%);

  C_max — Maximum emulsion concentration (%);

  φ₁ — Safety factor of the rolling force, normally φ₁=0.8–0.9;

  φ₂ — Safety factor of the rolling power, normally φ₂=0.8–0.9;

  φ₃ — Safety factor of the forward slip, normally φ₃=0.8–0.9.

Fig. 3.

The calculation flowchart.

3. Quantitative Analysis of the Effects of Emulsion Flow and Concentration on Rolling Energy and Oil Consumption Comprehensive Cost

To quantitatively analyze the effects of emulsion flow and concentration on rolling energy and oil consumption comprehensive cost, a typical TH620 product of a 1220 double cold reduction mill is used to simulate the variation tendency of rolling energy consumption, oil consumption, and their comprehensive cost with emulsion flow and concentration, as depicted in Figs. 4, 5, 6. The mill equipment configuration and capability parameters, the rolling oil property parameters, the model calculation coefficient parameters, and the rolling parameters of the typical TH620 product are listed in Tables 1, 2, 3, 4, correspondingly.

Fig. 4.

The variation tendency of rolling energy consumption with emulsion flow and concentration.

Fig. 5.

The variation tendency of rolling oil consumption with emulsion flow and concentration.

Fig. 6.

The variation tendency of rolling energy and oil consumption comprehensive cost with emulsion flow and concentration.

Table 1. Mill equipment configuration and capability parameters.

Work roll radius R/mm	165
Elastic modulus of work roll E/MPa	210000
Poisson ratio of work roll v	0.3
Emulsion plate-out distance L/m	0.5
Maximum allowable rolling force Pmax/kN	10000
Maximum allowable rolling power Nmax/kW	3000
Maximum allowable forward slip fmax/%	15.0
Minimum emulsion flow Qmin/(L/min)	5.0
Maximum emulsion flow Qmax/(L/min)	20.0
Minimum emulsion concentration Cmin/%	2.0
Maximum emulsion concentration Cmax/%	15.0

Table 2. Rolling oil property parameters.

Initial kinetic viscosity η0/Pa·s	0.023
Pressure viscosity coefficient θ/MPa−1	0.012

Table 3. Model calculation coefficient parameters.

Time coefficient of the emulsion flow residual rate δt/min−1	21.96
Flow coefficient of the emulsion flow residual rate δQ/(mm−1)	9.56
Emulsion initial concentration plate-out rate by emulsion-strip crash ηC0	0.136
Wettability coefficient of the concentration plate-out rate λw	0.785
Time coefficient of the emulsion concentration plate-out rate λt/min−1	218.5
Concentration coefficient of the emulsion concentration plate-out rate λC	6.243
Friction coefficient of hydrodynamic lubrication μh	0.012
Friction coefficient of boundary lubrication μb	0.136
Attenuation index of friction coefficient β/μm−1	−6.253
Arm coefficient Ψ	0.35
Density of steel ρ/(kg/m3)	7850
Unit energy consumption cost e1/(CNY/kW/h)	2.0
Unit oil consumption cost e2/(CNY/L)	10.0

Table 4. Rolling parameters of the typical TH620 product.

Strip width B/m	0.948
Entry thickness of the strip h0/mm	0.237
Exit thickness of the strip h1/mm	0.160
Exit rolling velocity v1/(m/min)	803
Entry yield strength σs0/MPa	300
Exit yield strength σs1/MPa	620
Back tension σ0/MPa	109
Forward tension σ1/MPa	190

Figures 4, 5, 6 demonstrate the following scenarios:

1) The rolling energy consumption per ton of steel decreases with the increase in emulsion flow and concentration given the improved lubrication in the roll bite. However, the decrease in gradient gradually slows down and stabilizes at high emulsion flow and concentration given the decrease in the emulsion flow residual rate and the concentration plate-out rate.

2) The rolling oil consumption per ton of steel increases linearly with the increase in emulsion flow and concentration considering the disposable use of emulsion.

3) The rolling energy and oil consumption comprehensive cost per ton of steel first decrease with the increase in emulsion flow and concentration; then, the comprehensive cost increases and reaches a minimum value at a certain emulsion flow and concentration. When the emulsion flow and concentration are low, the emulsion flow residual rate and concentration plate-out rate are high. Furthermore, the rolling energy consumption cost decreases faster than the increase in the rolling oil consumption cost. Thus, the rolling energy and oil consumption comprehensive cost per ton of steel decreases. By contrast, when the emulsion flow and concentration are high, the emulsion flow residual rate and concentration plate-out rate are low. Moreover, the rolling energy consumption cost decreases slower than the increase in the rolling oil consumption cost. Consequently, the rolling energy and oil consumption comprehensive cost per ton of steel increase.

4) Under a fixed rolling oil consumption condition, the rolling energy consumption varies with different combinations of emulsion flow and concentration setting values, thereby causing different gradients of emulsion flow residual rate and concentration plate-out rate, thereby leading to the variation in the rolling energy and oil consumption comprehensive cost per ton of steel.

4. Field Application

To validate the practical application effects of the comprehensive optimization control technology of rolling energy and oil consumption further, four typical steel grade products are selected for the experiment in a 1220 double cold reduction mill. The rolling energy consumption, oil consumption, and their comprehensive cost are compared with the original and optimal control technology of rolling energy and oil consumption, as displayed in Figs. 7, 8, 9. The rolling parameters of the four typical steel grade products and the emulsion flow and concentration setting values of the four typical steel grade products with the original and optimal control technology are listed in Tables 5 and 6, respectively. The photo of the test scene are presented in Fig. 10.

Fig. 7.

Comparison of rolling energy consumption with original and optimal control technology.

Fig. 8.

Comparison of rolling oil consumption with original and optimal control technology.

Fig. 9.

Comparison of rolling energy and oil consumption comprehensive cost with original and optimal control technology.

Table 5. Rolling parameters of the four typical steel grade products.

	TH520	DR8CA	TH580	TH620
Strip width B/m	0.927	0.921	0.968	0.948
Entry thickness of the strip h0/mm	0.207	0.213	0.230	0.237
Exit thickness of the strip h1/mm	0.170	0.170	0.170	0.160
Exit rolling velocity v1/(m/min)	687	653	686	803
Entry yield strength σs0/MPa	310	300	300	300
Exit yield strength σs1/MPa	520	550	580	620
Back tension σ0/MPa	102	100	119	109
Forward tension σ1/MPa	168	155	181	190

Table 6. Emulsion flow and concentration setting values of the four typical steel grade products with the original and optimal control technology.

Items	Emulsion	TH520	DR8CA	TH580	TH620
Original	Flow/(L/min)	8.5	8.2	12.9	13.6
	Concentration/%	2.5	3.5	9.1	11.4
Optimal	Flow/(L/min)	8.4	8.6	9.9	11.7
	Concentration/%	5.7	6.2	6.9	8.8

Fig. 10.

Photo of the test scene. (Online version in color.)

Figures 7, 8, 9 illustrate the following details. After the practical application of the comprehensive optimization control technology of rolling energy and oil consumption, the TH520 steel rolling energy consumption decreases from 16.20 kW·h/t to 9.914 kW·h/t; rolling oil consumption increases from 0.503 L/t to 1.134 L/t; and rolling energy and consumption comprehensive cost decrease from 37.43 CNY/t to 31.17 CNY/t, which is reduced by 16.72%. The DR8 steel rolling energy consumption decreases from 16.68 kW·h/t to 11.31 kW·h/t; rolling oil consumption increases from 0.715 L/t to 1.329 L/t; rolling energy and consumption comprehensive cost decrease from 40.51 CNY/t to 35.91 CNY/t, which is reduced by 11.36%. Moreover, the TH580 steel rolling energy consumption increases from 9.792 kW·h/t to 13.08 kW·h/t, the rolling oil consumption decreases from 2.649 L/t to 1.542 L/t; rolling energy and consumption comprehensive cost decrease from 46.07 CNY/t to 41.58 CNY/t, which is reduced by 9.75%. The TH620 steel rolling energy consumption increases from 13.78 kW·h/t to 16.29 kW·h/t; rolling oil consumption decreases from 3.243 L/t to 2.154 L/t; and rolling energy and consumption comprehensive cost decrease from 59.99 CNY/t to 54.12 CNY/t, which is reduced by 9.78%.

In addition, after using the technology in the field, the average rolling energy consumption is reduced by 16.2%, the average rolling energy consumption is reduced by 9.6%, and the average rolling energy and oil consumption comprehensive cost per ton of steel is reduced by 10.7% on the basis of the tracking statistics results over one year. Therefore, the comprehensive optimization control technology of rolling energy and oil consumption can effectively reduce the rolling energy and oil consumption comprehensive cost.

The optimal emulsion flow and concentration setting values are decided by the strip reduction, entry and exit yield strength, rolling velocity, back and forward tension. They increase with the increasing of strip reduction, entry and exit yield strength, rolling velocity and the decreasing of back and forward tension. Moreover, the emulsion flow residual rate increases with the increasing of rolling velocity. Therefore, a higher emulsion flow is preferred in high rolling velocity under a fixed rolling oil consumption condition.

The TH520 and DR8CA steels are not easy to excess the maximum allowable value of rolling force, rolling power and forward slip because of their low reduction and exit yield strength. But the TH580 and TH620 steels are easy to excess the maximum allowable value of rolling force, rolling power and forward slip because of their high reduction and exit yield strength.

With the original control technology, the main control principle of emulsion flow and concentration setting is to reduce the oil consumption in TH520 and DR8CA steels rolling, while it shifts to prevent the exceed of the allowable value of rolling force, rolling power and forward slip in TH580 and TH620 steels rolling. Therefore, the rolling energy consumption in TH520 and DR8CA steels rolling and the rolling oil consumption in TH580 and TH620 steels rolling are too high. Consequently, the minimum rolling energy and oil consumption comprehensive cost cannot be achieved.

With the optimal control technology, the main control principle of emulsion flow and concentration setting is to minimize the rolling energy and oil consumption comprehensive cost under the constraint condition of rolling force, rolling power, and forward slip. Therefore, the high rolling energy consumption in TH520 and DR8CA steels rolling and the high rolling oil consumption in TH580 and TH620 steels rolling are corrected. The rolling energy and rolling oil consumption increase respectively with the increasing of strip reduction and exit yield strength in the sequence of TH520, DR8CA, TH580 and TH620 steels. Thus, the minimum rolling energy and oil consumption comprehensive cost is achieved.

5. Conclusion

On the basis of plate-out oil formation mechanism on the strip surface, hydrodynamic theory in the inlet zone, mixed lubrication regime characteristics and rolling theory, plate-out oil film thickness on the strip surface, oil film thickness in the deformation zone, friction coefficient, bite angle, forward slip, rolling force, and rolling power was calculated. Subsequently, the relationships among rolling energy consumption, rolling oil consumption, rolling energy, and oil consumption comprehensive cost per ton of steel were established. Thus, a comprehensive optimization control technology of rolling energy and oil consumption in double cold rolling was developed.

The effects of emulsion flow and concentration on rolling energy and oil consumption comprehensive cost were quantitatively analyzed. With the increase in emulsion flow and concentration, the rolling energy and oil consumption comprehensive cost per ton of steel first decreased and then increased until reaching a minimum value at a certain emulsion flow and concentration.

After the practical application of the comprehensive optimization control technology, the rolling energy and oil consumption comprehensive cost of the four typical steel grade products reduced by values within the range of 9.75%–16.72%. Furthermore, on the basis of the tracking statistics results over one year, the average rolling energy consumption, the average rolling energy consumption, and the average rolling energy and oil consumption comprehensive cost per ton of steel reduced by 16.2%, 9.6%, and 10.7%, correspondingly. Thus, a significant economic benefit was created for enterprises.

Acknowledgements

This work is supported by the Natural Science Foundation of Hebei Province (Grant No. E20160203385) and the Heavy Machinery Collaborative Innovation Program (Grant No. ZX01-20140400-05). A few experiments were made in Baosteel Tinplate Plant. The authors gratefully acknowledge the technical support of Baosteel.

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