2013 Volume 53 Issue 4 Pages 690-697
Universal rolling of channel sections has various advantages in both productivity and product quality. However, research on deformation in channel universal rolling appears to be inadequate. In particular, the effect of rolling conditions such as thickness reductions on deformation behavior is still unknown. To investigate the influence of rolling conditions in detail, a model rolling experiment and finite element analyses of channel universal rolling were conducted. The results showed that flange spread displays a linear relationship against the reduction balance, which was defined as the difference of the flange and web thickness strains. Similar linear behaviors of the flange depth and bulge height against the reduction balance were also demonstrated. The results of a non-steady-state finite element simulation showed that the friction force between the flange inside surface and the horizontal roll side surface caused asymmetric flange deformation, decreasing flange depth and increasing bulge height. The results of this research indicate the importance of the reduction balance for controlling flange deformations, and in particular, for reducing bulge height. Finally, the suitable range of the reduction balance considering other phenomena was discussed.
Hot-rolled channels are commonly used in many construction applications and are generally produced using the 2-high mill. Channels are produced various shapes and sizes depending on the intended application. Many roll pass designs for producing these channel sections have been presented in the literature.^{1,2,3)}
Universal mills are widely used in the production of H-beams. After universal rolling of H-beams was successfully realized, universal mills were also applied to channel rolling. Several roll pass designs for different mill layouts have been reported.^{4,5,6,7,8,9,10,11,12)}
Universal rolling of channels has many advantages in both productivity and product quality.^{7,11,12)} First, a smooth product surface can be obtained. In 2-high groove rolling, the surfaces of the outer flanges are wiped by the sides of the groove and often become rough. On the other hand, the vertical rolls of the universal mill move in a linear direction with the channel bar, and as a result, channels produced by universal rolling have smoother outside flange surfaces.
Second, universal rolling improves roll life. Because of the agreement of the stock and roll movements, roll wear is smaller. Moreover, wear of the vertical rolls can be easily compensated by adjustment of the roll position.
Third, rolling mill energy consumption is smaller in universal rolling for the same reason that roll wear is smaller.
Fourth, constant flange thickness products, i.e., so-called parallel flange channels (PFC), can be manufactured.^{9,11)}
In spite of these advantages of universal rolling, the application of this method to commercial section mills is not particularly common. In universal rolling of channels, it is reported that overfill at the outside corners often occurs, as if two new flanges are created.^{7,12)} Although control of this overfill is very important for producing an excellent section shape, deformation in channel universal rolling had not been investigated in detail. In particular, the effect of rolling conditions on flange deformation was still unknown.
In previous work, the authors investigated the influence of rolling conditions on deformation behavior in H-beam and Tbar universal rolling.^{13,14)} That research indicated that the balance between the thickness reductions of web and flange was an important factor in universal rolling deformation.
In the present research, the fundamental deformation behavior in channel universal rolling was investigated in a laboratory rolling experiment. Next, non-steady-state finite element (FE) simulation was carried out to investigate the mechanism of overfill formation at the outside corners. The effect of the web and flange thickness reductions was also discussed using the results of another FE analysis with a steady-state model. Finally, suitable rolling conditions for reducing bulge height were discussed.
First, reduced-scale model experiments were carried out to investigate the general behavior of rolling deformation. Figure 1 shows a schematic diagram of the channel universal rolling experiment. In many cases of actual universal mills for channels, the width of the horizontal roll in contact with the web outside surface is usually wider than that of the inside horizontal roll to restrain overfill of the outside corner. ^{11,12)} However, in order to observe the outside corner deformation more clearly, horizontal rolls having the same widths were used in the laboratory mill. In addition, because the rolls in Fig. 1 have the same configuration as H-beam rolls, the common use of rolls between different products is also possible.
Universal rolling of channel.
Pure lead was used as the model material in all rolling experiments. It has been reported that the deformation behavior of pure lead is similar to that of hot carbon steel at elevated temperatures.^{15)} Because these experiments were carried out at room temperature, the effect of temperature distribution on rolling deformation was eliminated.
A constant reduced-scale of one-fifth was assumed in the experiments. The horizontal rolls of the mill were driven and the vertical rolls were undriven. The dimensions of the rolls and workpiece section are shown in Table 1 and Fig. 2. The workpiece length was set at 300 mm. The geometry in this experiment corresponds closely to that of an intermediate pass of a parallel flange channel of PFC400 × 130, that is, a PFC with a web height of 400 mm and flange width of 130 mm.
Roll diameter (mm) | Horizontal roll | 180 |
Vertical roll | 140 | |
Horizontal roll rotation speed | 7 rpm | |
Flange inclination angle | 6 deg. |
Dimensions of inlet section for rolling experiment.
The specimen is expected to turn up upon delivery, resulting upward curing. To deliver straight rolled channels, web guides were applied at both the entry and exit sides, as shown in Fig. 3.
Guide and table for rolling experiment.
In order to examine the effect of rolling conditions on channel rolling deformation behavior, several combinations of web thickness reduction r_{w} and flange thickness reduction r_{f} were tested. With the universal mill, it is possible to set the horizontal and vertical roll gaps individually. A target r_{w} of 15% and three target r_{f}, 12%, 18% and 24% were selected. As a result, the target range of the thickness reduction difference (r_{f} – r_{w}) was –3% to 9%.
2.3. Modeling of Universal Rolling DeformationIn research on H-beam universal rolling, the spread of flange width B has been studied in detail,^{13,16)} and it has been shown that the difference between the flange and web thickness strain strongly influences flange spread. The same relationship was also reported in T-bar universal rolling.^{14)} Therefore, a similar influence was expected in channel universal rolling.
Flange spread behavior in H-beam universal rolling is expressed by the following equation:^{13,16)}
(1) |
(2) |
(3) |
The flanges of channels are located on only one side of the web. Because of the unique rolling deformation creating new two flanges, the bulges at outside corner shown in Fig. 4 were expected. To investigate the asymmetric deformation of these flanges, in addition to the flange width B, the flange depth d and bulge height h were measured before and after rolling. The relationships between the reduction balance and changes in these dimensions were then investigated to validate the possibility of modeling as shown in Eq. (1).
Bulges at outside corners.
The rolling experiment was completed without any problems. Three or four specimens were rolled for each target rolling condition. In total, eleven channels were rolled with the laboratory universal mill. Although all the rolled channels displayed upward curling at the top end, the web guide enabled delivery of the channels in a straight condition to the tail end. Figure 5 shows a photograph of a rolled pure lead specimen.
Example of rolled pure lead specimen (r_{w} =14.8%, r_{f} = 18.5%).
The dimensions of the channels before and after rolling were measured at the center of length, and these measurements were used in calculating the actual thickness reductions, strains and flange deformation parameters. Figure 6 shows the actual web and flange thickness reductions. The range of r_{w} was 14.0% to 17.5%, while r_{f} was 11.1 to 24.0%. These reductions covered the three target rolling conditions, and a wide range of (r_{f}–r_{w}) from –4.7% to 9.6% was examined. Flange deformation parameters of width, depth and bulge height were also evaluated using the measurements.
Actual thickness reductions in experiment.
Figure 7 shows the initial section and three rolled sections of pure lead specimens that were close to the target thickness reductions. As can be seen in this figure, bulging deformation occurred in universal rolling, and the bulges became larger with higher flange thickness reduction.
Sections before and after rolling.
Figure 8 shows the relationship between the reduction balance and flange spread parameter ln(B_{1}/B_{0}). A linear relationship can be seen between the two parameters. This means that the flange spread model in Eq. (1) is applicable to channel universal rolling.
Reduction balance and flange spread parameter.
To investigate asymmetric flange deformation, the change of flange depth Δd and bulge height Δh were evaluated. Figure 9 shows the tendencies of Δd and Δh against the reduction balance. The flange depth Δd decreased in universal rolling, but the influence of the reduction balance was very small. Unlike Δd, Δh increased in universal rolling and changed in a linear manner against the reduction balance. Thus, it can be understood that the influences of the reduction balance on both Δd and Δh can be expressed by the right side of Eq. (1). The inclinations a and intercepts b of the regression lines are presented in Table 2.
Reduction balance and variations of flange depth and bulge height.
Inclination | Intercept | |
---|---|---|
Width spread parameter ln(B_{1}/B_{0}) | 0.528 | –0.001 |
Flange depth Δd | –1.06 | –1.46 |
Bulge height Δh | 16.84 | 2.10 |
The results of the experiment clearly demonstrated the trend of new flange creation reported in some studies. Moreover, the influence of the reduction balance was also quantitatively presented. These characteristics of channel universal rolling deformation were not known before, and are presented for the first time in this paper.
However, the cause of this asymmetric flange deformation had not been clarified. Therefore, a numerical simulation was performed to investigate the mechanism of this particular rolling deformation.
To investigate the deformation behavior in channel universal rolling in detail, a three-dimensional numerical simulation was conducted. A dynamic explicit FE code, ABAQUS Explicit Ver.6.11, was used for the numerical analysis. Because a channel has a symmetrical section shape, a half channel was modeled for the analysis. Solid brick reduced integration elements (C3D8R) were used for the modeled channel, and the element number was approximately 470000. The rolls were assumed to be analytical rigid surfaces. In all cases, a non-steady-state model was used. The horizontal rolls were driven, and their rotation speed was set at 40 rpm. The vertical rolls were defined as undriven free rotation parts.
Real rolling geometries corresponding to the model rolling experiment in Chapter 2 were used in the numerical simulation. The dimensions in the experiment were multiplied by 5 times for conversion to the actual rolling geometry. Because the three-dimensional simulation requires a rather long calculation time, three rolling conditions were simulated. Table 3 lists the combinations of web thickness reduction and three flange reductions, together with the other geometrical and numerical conditions. For example, Coulomb friction was assumed between rolls and materials, and a friction coefficient of 0.4 was used. The web guides and tables in Fig. 3 were also constructed in the numerical model to avoid extreme upward curling in the simulation.
Product size of channel | 400 × 130 | |
---|---|---|
Inlet material size (mm) | Web height; H | 477 |
Flange width; B | 150 | |
Web thickness; tw | 22.5 | |
Flange thickness; tf | 39 | |
Roll diameter (mm) | Horizontal roll | 900 |
Vertical roll | 700 | |
Horizontal roll width (mm) | 400 | |
Horizontal roll rotation speed | 40 rpm | |
Flange inclination angle | 6 deg. | |
Target thickness reduction | Web; r_{w} Flange; r_{f} |
r_{w} = 15% r_{f} = 12, 18, 24% |
Friction coefficient | Stock – roll Stock – table & guide |
0.4 0.0 |
Young’s modulus | 100000 N/mm^{2} | |
Poisson ratio | 0.3 |
A flow stress curve for hot carbon steel^{17)} was used to create flow stress data for the analysis.
(4) |
The FE simulations of the three target conditions were executed successfully. Figure 10 illustrates a simulated rolling deformation with the target flange reduction of 18%. In the FE simulation, the target thickness reduction corresponded to the roll gap setting, and the resulting thicknesses might be different from the roll gap. Therefore, the thickness reductions and deformation parameters were calculated by the same method as in the experiment using the geometries before and after rolling simulation. In Fig. 11, the flange spread parameters ln(B_{1}/B_{0}) are plotted against the reduction balance with the experimental results. The results of the FE simulation agreed well with the experimental results. Figure 12 shows the relationship between the reduction balance and Δd, and Fig. 13 presents the results for Δh. In these graphs, the FE results are located at the center of the scatter ranges of the experiment and display similar trends against the reduction balance. The agreement between the FE analyses and the experimental results demonstrates the accuracy of the FE simulation.
Rolling deformation and equivalent plastic strain (non-steady-state FEM).
Flange spread parameter (non-steady-state FEM).
Change of flange depth (non-steady-state FEM).
Change of bulge height (non-steady-state FEM).
Both the experimental results and the results of the FE simulation show that the flange depth decreases while the bulge height of the outside corner increases. This deformation behavior indicates the existence of downward force at the flanges.
It was expected that downward force might occur at the inside flange surfaces in contact with the side surfaces of the upper horizontal roll. The side surfaces of the horizontal roll move both forward and downward at the entry side of the universal mill. On the contrary, the flanges of the channel move mainly in the forward direction. As a result, the flanges are subject to downward friction forces at the areas of contact between the flanges and the horizontal roll. It was expected that the larger downward friction force created a higher outside corner bulge.
The downward friction shear forces were calculated using the numerical results. Vertical components of nodal shear forces in the contact area were picked out, and the summation of the vertical components was used as the downward friction shear force. Figure 14 shows the relationship between the reduction balance and the vertical friction shear force. Minus friction force means downward force, while a plus value means upward force. It can be seen that a larger reduction balance creates a larger downward friction shear force. As shown in Fig. 13, Δh becomes larger as the reduction balance increases. Thus, these results validated the hypothesis that the friction force between the flanges and the horizontal roll causes downward deformation of the flanges.
Vertical friction shear force by non-steady-state FEM.
The finite element simulation in Chapter 3 showed good accuracy and excellent agreement with the experimental results. However, because the time required for these calculations is on the order of days, an extremely long time would be necessary to simulate many rolling conditions.
In previous research, the authors applied a steady-state FE model to simulate universal rolling of H-beams and T-bars. The calculation time for the steady-state simulation is on the order of a few hours. Therefore, the application of this steady-state simulation to channel universal rolling was examined with the aim of investigating deformation behaviors under a wide range of rolling conditions.
4.1. Steady-State Model and Numerical ConditionsThe steady-state model was a Lagrange multiplier three-dimensional rigid-plastic FE analysis, namely, the CORMILL System.^{18)} Many rolling passes of various sections, including universal rolling, have been analyzed successfully with this simulation system.^{13,14,18)} Its implicit calculation method can provide highly accurate results for deformation, stress and strain.
A half part of the channel was modeled for the analysis. In our previous research on H-beam universal rolling, suitable element numbers were investigated by careful numerical trials.^{13)} The same element numbers as employed in the research were also used in the present FE simulation, the element numbers being 6 and 30 in the thickness and width directions, respectively. The element number in the rolling direction was determined to be a total of 28 from the entry section to the exit section.
The conditions of the steady-state simulation were substantially similar to those of the non-steady-state simulation in Chapter 3. The numerical conditions are presented in Table 4. More combinations of web and flange thickness reductions were simulated. For the series of steady-state simulations, two groups of thickness reductions were planned. The five conditions in the constant r_{w} group correspond to the conditions of the experiment and non-steady-state simulation. The conditions of the constant r_{f} group have the same r_{f} of 18% and five different r_{w} from 9 to 21%. In total, nine different rolling conditions were simulated.
Product size of channel | 400 × 130 | |
---|---|---|
Inlet material size (mm) | Web height; H | 477 |
Flange width; B | 150 | |
Web thickness; tw | 22.5 | |
Flange thickness; tf | 40 | |
Roll diameter (mm) | Horizontal roll | 900 |
Vertical roll | 700 | |
Horizontal roll width (mm) | 400 | |
Horizontal roll rotation speed | 40 rpm | |
Flange inclination angle | 6 deg. | |
Target thickness reduction Web; r_{w}, Flange; r_{f} | r_{w} constant | r_{w} = 15%, r_{f} = 12, 15, 18, 21, 24% |
r_{f} constant | r_{w} = 9, 12, 15, 18, 21%, r_{f} = 18% | |
Friction coefficient | 0.4 |
The flow stress curve for hot carbon steel^{17)} was also applied to the steady-state analysis with a minor modification as follows:
(5) |
The constant 0.02 was added to the original flow stress Eq. (4) to avoid calculating abnormally small flow stress in the pre-deformation part in the FE model. A constant rolling temperature of 1000°C was assumed in the stock.
4.2. Boundary Conditions of Steady-State ModelThe boundary conditions of the steady-state analysis were similar to those in other researches.^{13,14,18)} Uniform velocities throughout the cross sections of the entry and exit boundaries were assumed; this boundary condition restricts the curling of the rolled channel without guides and tables. At the same time, forces and bending moments at the entry and exit cross sections are necessary to balance the global equilibrium of force.
In the steady-state simulation, the height of the entry section should be given as an initial condition. The height requiring minimum vertical force at the entry boundary section was considered to be the suitable height of the inlet section. The heights of each condition are listed in Tables 5 and 6.
r_{w} | r_{f} | Inlet section height /mm |
---|---|---|
15% | 12% | –1.0 |
15% | –2.0 | |
18% | –3.4 | |
21% | –5.0 | |
24% | –6.0 |
r_{w} | r_{f} | Inlet section height /mm |
---|---|---|
9% | 18% | –5.0 |
12% | –4.5 | |
15% | –3.4 | |
18% | –2.1 | |
21% | –1.5 |
A rolling deformation in a steady-state FE simulation is presented in Fig. 15 with the distribution of equivalent plastic strain. The thickness strains and flange deformation parameters were calculated using the simulated thicknesses and flange dimensions. In Fig. 16, ln(B_{1}/B_{0}) in the constant r_{w} group are plotted against the reduction balance with the results of the experiment. The tendency of the simulated flange spread parameter was substantially in agreement with the experimental results.
Deformation in steady-state FE simulation (r_{w} = 15%, r_{f} = 18%).
Flange spread parameter (steady-state FEM and experiment).
Figures 17 and 18 show Δd and Δh against the reduction balance. Although both parameters show trends similar to the experiment, offsets of approximately 5 mm can be seen. These differences were caused by the inadequate inlet section height. To make the simulated results closer to the experiments, more downward shift of the inlet section is necessary. However, the implicit calculation did not reach conversion when the inlet section was too low, and it was difficult to find a more adequate method for better determination of the inlet height.
Flange depth variation (steady-state FEM and experiment).
Bulge height variation (steady-state FEM and experiment).
In spite of the existence of some level of offset, the simulated results showed tendencies similar to the experimental results, demonstrating that it is possible to investigate the characteristics of deformation behavior using the steady-state FE simulation. Based on this conclusion, the rolling conditions in the constant r_{f} group were also simulated, and their deformations were compared with those of the constant r_{w} group.
Figure 19 shows ln(B_{1}/B_{0}) of all nine conditions against the reduction balance. Other flange deformation results, Δd and Δh are also presented in Figs. 20 and 21. The results of both groups show good agreements. These results demonstrate that the reduction balance (λ_{f} – λ_{w}) is the most important parameter for rolling deformation, even if the values of the individual thickness reductions are different. As a result, the importance of the reduction balance for deformation behavior in channel universal rolling was clearly demonstrated. This also means that Eq. (1) is a useful model for predicting the flange deformations in channel universal rolling.
Flange spread parameter (steady-state FEM).
Flange depth variation (steady-state FEM).
Bulge height variation (steady-state FEM).
The results of the experiment and FE simulations clearly demonstrated the influence of the reduction balance on channel rolling deformation. It was shown that a smaller reduction balance reduces the bulges at the outside corner. However, to determine suitable universal rolling conditions, the effect of the reduction balance on other phenomena should also be considered.
When the reduction balance is smaller than zero, λ_{w} is larger than λ_{f}. This means that the elongation of the web is larger than that of the flange. As a result, upward curling of the stock after rolling becomes larger. Therefore, in order to avoid damage of the web guide in Fig. 3, an excessively small reduction balance is inappropriate.
It is also known that web buckling defects can occur when web thickness reduction is larger than flange thickness reduction.^{12,16)} The possibility of web buckling increases with a smaller reduction balance. Based on the common knowledge of universal rolling, a minus reduction balance should be avoided.
However, the limit for web buckling is influenced by the web thickness and other dimensions of rolled channels. In the experiment of channel universal rolling presented here, web buckling was not observed under any rolling conditions. As regards upward curling after rolling, the level of the curling can be controlled by securing an appropriate balance of the upper and lower horizontal roll diameters.^{12)}
Therefore, the possibility of a minus reduction balance should be examined to determine the appropriate range of the reduction balance. A smaller reduction balance in the determined range is a favorable condition for reducing bulge height.
In this paper, deformation behavior in channel universal rolling was investigated in detail using a laboratory model experiment and two models of FE simulations.
The experimental results showed a flange spread behavior similar to that in H-beam and T-bar universal rolling. The asymmetric flange deformation of the outside corner bulge and flange depth was also investigated, and the influence of the reduction balance on this asymmetric deformation was clarified.
A three-dimensional non-steady-state FE simulation was carried out, and the simulated deformation showed good agreement with that in the experiment. Based on the simulated friction force between the horizontal roll side surface and flange surface, the influence of the downward friction force on the bulge height was clarified.
A steady-state FE simulation was also applied to channel rolling. Although the simulated values of the flange depth and bulge height showed some offset from the experimental data, the trends of the deformation behavior against the reduction balance were similar to those in the experiment. Based on this result, the influence of thickness reductions was investigated in detail by analyzing nine different rolling conditions. The results clearly demonstrated the importance of the reduction balance for describing the rolling deformation behavior in channel universal rolling.
The results presented in this research quantitatively demonstrate the influence of the reduction balance on the deformation behavior of channels in universal rolling. The new findings of this research will contribute to the better application of universal rolling to channel production through the determination of suitable rolling conditions.