Patent Publication Number: US-2023149995-A1

Title: Hot rolling mills and hot rolling methods

Description:
TECHNICAL FIELD 
     The present invention relates to hot rolling mills and hot rolling methods. 
     BACKGROUND ART 
     Patent Document 1 discloses a rolling mill that includes an upper work roll, an upper backup roll, a lower work roll, a lower backup roll, and cross angle adjustment mechanisms each of which is provided in association with a corresponding one of the rolls, and each cross angle adjustment mechanism moves a roll chock by relatively moving pistons. 
     Prior Art Document 
     Patent Document 
     Patent Document 1: JP h9-220608-A 
     SUMMARY OF THE INVENTION 
     Problems to Be Solved by the Invention 
      Roll-cross four-high rolling mills that control the strip crown and the strip shape by causing upper and lower rolls to cross each other are generally classified into pair cross mills that change the cross angle of work rolls along with backup rolls, and work roll mills that form a cross angle only between work rolls. These two types have been developed, and it is known that these types allow wide control ranges. 
     Among them, pair cross mills have a problem that shape control cannot be performed with high responses because the cross angle of backup rolls also is changed. 
     In contrast, in work-roll crossing, inclination-subjects have a weight which is by far smaller than that in pair crossing, and thus can be inclined quickly (with high responsiveness). In terms only of responsiveness, preferably, only work-roll crossing is used to increase the cross angle to enable crown control. 
     However, there is a problem about work-roll crossing that thrust forces (forces acting in the axial direction) between backup rolls and work rolls increase as the cross angle increases, thus it is hard to adopt work-roll crossing for small-diameter work rolls. 
     On the other hand, there is a demand for a technology that enables rolling of a hard steel strip (e.g. an ultrahigh strength steel) or the like that is hard to be rolled as compared with conventional technologies, and also enables reduction of a work-roll diameter to lower the rolling load in order to avoid a size increase (manufacturing-cost increase) of rolling mills. 
     Here, in Patent Document 1 mentioned above, a description is made that a combination of a work-roll crossing method and a pair roll crossing method allows complicated shape control in the strip-width direction. In Patent Document 1, further, a description is made that complicated shape control can be achieved by generating high-order components by a pair crossing method, and then by combining a simple crossing method therewith, in which a second-order component is the main component. 
     However, as a result of vigorous examination by the present inventors, it has become clear that it is not possible to specifically solve a problem of enabling rolling of a hard steel strip while making it easy to adopt small-diameter work rolls, widening control ranges, and ensuring also responsiveness. 
     More specifically, the description of Patent Document 1 does not solve a problem of excessive thrust forces being generated in work-roll crossing, and it is hard to adopt small-diameter work rolls. In addition, despite the description of Patent Document 1, it has become clear that not only control by work-roll cross mills but control by pair cross mills also is close to shape control of a second-order component, and a problem has become clear that controllability of so-called quarter buckles in which buckles are generated at widthwise ¼-positions is not sufficient. 
     That is, through examination by the present inventors, it has become clear that adopting small-diameter work rolls is difficult due to excessive thrust forces, and that the fourth-order component shape control capability is low. 
     The present invention provides hot rolling mills and hot rolling methods that can ensure wide control ranges and responsiveness as compared with conventional technologies. 
     Means for Solving the Problems 
     The present invention includes plurality of means for solving the problems described above, and an example thereof is a hot rolling mill in which angles of an upper-side pair of an upper work roll and an upper backup roll, and a lower-side pair of a lower work roll and a lower backup roll are adjusted in a state where the upper-side pair is kept parallel and in a state where the lower-side pair is kept parallel, and thereafter work-roll horizontal actuators and backup-roll horizontal actuators are controlled such that the angles of the upper work roll and the lower work roll are adjusted in a state where the angles of the upper backup roll and the lower backup roll are maintained. 
     Advantages of the Invention 
     According to the present invention, it is possible to ensure wide control ranges and responsiveness as compared with conventional technologies. Problems, configurations, and advantages other than those described above are made clear by the following explanation of embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a side view depicting the apparatus configuration of a rolling mill according to a first embodiment of the present invention. 
         FIG.  2    is a top view depicting an overview of the configuration of equipment around an upper work roll in the rolling mill depicted in  FIG.  1   . 
         FIG.  3    is a schematic view of a change in the work-roll cross angle during rolling in the rolling mill according to the first embodiment. 
         FIG.  4    is a figure depicting strip crown change amounts that are observed when work rolls in a pair-cross state are caused to slight-cross in the rolling mill according to the first embodiment. 
         FIG.  5    is a schematic view depicting how thrust forces are generated before work-roll slight crossing in a rolling mill according to a second embodiment of the present invention. 
         FIG.  6    is a schematic view depicting how the work-roll thrust forces are cancelled out by the work-roll slight crossing in the rolling mill according to the second embodiment. 
         FIG.  7    is a side view depicting the apparatus configuration of a rolling mill according to a third embodiment of the present invention. 
         FIG.  8    is a side view depicting the apparatus configuration of a rolling mill according to a fourth embodiment of the present invention. 
         FIG.  9    is a figure depicting how a work-roll diameter influences the order of control by bending in a rolling mill according to a fifth embodiment of the present invention. 
         FIG.  10    is a figure depicting a distribution, in the strip-width direction, of strip crown change amounts in a case where bending is performed in a rolling mill with D w /L b  = 0.32. 
         FIG.  11    is a figure depicting a distribution, in the strip-width direction, of strip crown change amounts in a case where bending is performed in a rolling mill with D w /L b  = 0.21. 
         FIG.  12    is a figure depicting how a work-roll diameter influences the order of control by work-roll crossing in the rolling mill according to the fifth embodiment. 
         FIG.  13    is a figure depicting how a work-roll diameter influences strip crown change amounts generated by work-roll crossing. 
         FIG.  14    is a figure depicting crown control ranges in a rolling mill with D w /L b  = 0.32. 
         FIG.  15    is a figure depicting shape control ranges in the rolling mill with D w /L b  = 0.32. 
         FIG.  16    is a figure depicting crown control ranges in a rolling mill with D w /L b  = 0.24. 
         FIG.  17    is a figure depicting shape control ranges in the rolling mill with D w /L b  = 0.24. 
         FIG.  18    is a figure depicting influence of D w /L b  on crown control and shape control ranges in the rolling mill according to the fifth embodiment. 
     
    
    
     MODES FOR CARRYING OUT THE INVENTION 
     Embodiments of hot rolling mills and hot rolling methods according to the present invention are explained below by using the figures. 
     Note that identical or corresponding constituent elements in the figures used in the present specification are given identical or similar reference characters, and repetitive explanations of these constituent elements are omitted in some cases. 
     In addition, in the following embodiments and figures, a drive side (also written as a “DS (Drive Side)”) means a side where electric motors to drive work rolls are installed when a rolling mill is seen from its front side, and a work side (“WS (Work Side)”) means the opposite side. 
     First Embodiment 
     A first embodiment of hot rolling mills and hot rolling methods according to the present invention is explained by using  FIG.  1    to  FIG.  4   . 
     First, the overall configuration of a hot rolling mill is explained by using  FIG.  1    and  FIG.  2   .  FIG.  1    is a side view of the rolling mill according to the present embodiment, and  FIG.  2    is a top view depicting an overview of the configuration of equipment around an upper work roll in the rolling mill depicted in  FIG.  1   . 
     In  FIG.  1   , a hot rolling mill  1  is a Roll-cross four-high rolling mills that rolls a rolled material S, and has a housing  100 , a control apparatus  20 , and a hydraulic apparatus  30 . Note that the rolling mill is not limited to a one-stand rolling mill like the one depicted in  FIG.  1   , and may be a rolling mill including two stands or more. 
     The housing  100  includes a pair of an upper work roll  110 A and a lower work roll  110 B that are provided on the upper side and lower side, a pair of an upper backup roll  120 A and a lower backup roll  120 B that support the work rolls  110 A and  110 B, and are provided on the upper side and lower side. 
     Hydraulic cylinder apparatuses  170  are cylinders that apply rolling forces to the upper backup roll  120 A, the upper work roll  110 A, the lower work roll  110 B, and the lower backup roll  120 B by pressing the upper backup roll  120 A. The hydraulic cylinder apparatuses  170  are provided on the work side and drive side of the housing  100 . 
     A load cell  180  is provided at a lower portion of the housing  100 , as rolling force measurement means for measuring a rolling force on the rolled material S applied by the work rolls  110 A and  110 B, and outputs measurement results to the control apparatus  20 . 
     Upper work-roll bending cylinders  190 A are provided on the entry side and exit side of the housing  100  on each of the work side and the drive side. By being driven as appropriate, the upper work-roll bending cylinders  190 A apply bending forces vertically to bearings of the upper work roll  110 A. 
     Similarly, lower work-roll bending cylinders  190 B are provided on the entry side and exit side of the housing  100  on each of the work side and the drive side, and by being driven as appropriate, the lower work-roll bending cylinders  190 B apply bending forces vertically to bearings of the lower work roll  110 B. 
     A backup-roll sliding apparatus  200 A is provided at a portion vertically above the upper backup roll  120 A, and a backup-roll sliding apparatus  200 B is provided at a portion vertically below the lower backup roll  120 B. 
     The hydraulic apparatus  30  is connected to hydraulic cylinders of work-roll pressing apparatuses  130 A and  130 B and work-roll position control apparatuses  140 A and  140 B, to hydraulic cylinders of backup-roll pressing apparatuses  150 A and  150 B and backup-roll position control apparatuses  160 A and  160 B, and furthermore to the work-roll bending cylinders  190 A and  190 B also. Note that parts of communication lines and hydraulic-fluid supply lines are omitted in  FIG.  1    for convenience of illustration. The same applies also to the following figures. 
     The control apparatus  20  receives input of measurement signals from the load cell  180  and position measuring instruments of the work-roll position control apparatuses  140 A and  140 B and backup-roll position control apparatuses  160 A and  160 B. 
     The control apparatus  20  actuation-controls the hydraulic apparatus  30 , and supplies and discharges a hydraulic fluid to and from the hydraulic cylinders of the work-roll pressing apparatuses  130 A and  130 B and work-roll position control apparatuses  140 A and  140 B to thereby control actuation of the work-roll pressing apparatuses  130 A and  130 B and the work-roll position control apparatuses  140 A and  140 B. 
     Similarly, the control apparatus  20  actuation-controls the hydraulic apparatus  30 , and supplies and discharges a hydraulic fluid to and from the hydraulic cylinders of the backup-roll pressing apparatuses  150 A and  150 B and backup-roll position control apparatuses  160 A and  160 B to thereby control actuation of the backup-roll pressing apparatuses  150 A and  150 B and the backup-roll position control apparatuses  160 A and  160 B. 
     Due to the actuation control, the control apparatus  20  controls angle adjustment by the work-roll pressing apparatuses  130 A and  130 B and work-roll position control apparatuses  140 A and  140 B, and angle adjustment by the backup-roll pressing apparatuses  150 A and  150 B and backup-roll position control apparatuses  160 A and  160 B. Details of the angle adjustment by the control apparatus  20  according to the present embodiment are mentioned later. 
     Furthermore, the control apparatus  20  supplies and discharges a hydraulic fluid to and from the work-roll bending cylinders  190 A and  190 B to thereby control actuation of the work-roll bending cylinders  190 A and  190 B. 
      Next, configuration related to the upper work roll  110 A is explained by using  FIG.  2   . Note that since the upper backup roll  120 A, the lower work roll  110 B, and the lower backup roll  120 B also have configuration equivalent to the configuration of the upper work roll  110 A, and detailed explanations thereof are approximately the same as the explanation about the upper work roll  110 A, the explanations thereof are omitted. 
     As depicted in  FIG.  2   , there is the housing  100  on both end sides of the upper work roll  110 A of the hot rolling mill  1 , and is provided to stand perpendicular to the roll shaft of the upper work roll  110 A. 
     The upper work roll  110 A is rotatably supported by the housing  100  via a work-side roll chock  112 A and a drive-side roll chock  112 B. 
     A work-roll pressing apparatus  130 A, on each of the work side and the drive side, is arranged between the entry side of the housing  100  and the work-side roll chock  112 A or the drive-side roll chock  112 B, and presses the work-side roll chock  112 A or the drive-side roll chock  112 B of the upper work roll  110 A in the rolling direction at a predetermined pressure. 
     A work-roll position control apparatus  140 A, on each of the work side and the drive side, is arranged between the exit side of the housing  100  and the work-side roll chock  112 A or the drive-side roll chock  112 B, and has a hydraulic cylinder (pressing apparatus) that presses the work-side roll chock  112 A or the drive-side roll chock  112 B of the upper work roll  110 A in the direction opposite to the rolling direction. The work-roll position control apparatus  140 A includes a position measuring instrument (illustration omitted) that measures the amount of operation of the hydraulic cylinder, and controls the position of the hydraulic cylinder. 
     Here, a home-position control apparatus means the apparatus that measures the oil column position of a hydraulic cylinder as a pressing apparatus by using a position measuring instrument incorporated in the home-position control apparatus, and controls the oil column position until the oil column reaches a predetermined oil column position. 
     These work-roll pressing apparatuses  130 A and  130 B, backup-roll pressing apparatuses  150 A and  150 B, and home-position control apparatuses  140 A,  140 B,  160 A, and  160 B play a role of an angle adjustor that adjusts the roll cross angle. 
     Note that whereas  FIG.  1    and  FIG.  2    depict an example in which hydraulic apparatuses are used as the work-roll position control apparatuses  140 A and  140 B and the backup-roll position control apparatuses  160 A and  160 B which are actuators of crossing apparatuses, they are not limited to hydraulic apparatuses, and apparatus with electric configuration or the like can be used. 
     In addition, whereas the pressing apparatuses are disposed on the entry side of the rolled material S, and the home-position control apparatuses are disposed on the exit side of the rolled material S in the depicted mode, they may be disposed on the opposite sides in some cases, and the arrangement is not limited to a pattern depicted in  FIG.  1    and the like. 
     Furthermore, whereas  FIG.  1    and  FIG.  2    depict an example in which the pressing apparatuses are provided opposite the home-position control apparatuses, this is not essential, and only the home-position control apparatuses are provided in other possible configuration. It should be noted that installation of the pressing apparatuses makes it possible to eliminate backlashes between the roll chocks  112 A and  112 B and the home-position control apparatuses, and to stabilize the positions of the roll chocks  112 A and  112 B in the rolling direction. 
     Next, a method of cross angle adjustment at a time of rolling in the rolling mill according to the present embodiment is explained with reference to  FIG.  3    and  FIG.  4   .  FIG.  3    is a schematic view of a change in the work-roll cross angle during rolling.  FIG.  4    is a figure depicting strip crown change amounts that are observed when work rolls in a pair-cross state are caused to slight-cross. 
     The control apparatus  20  according to the present embodiment adjusts angles of an upper-side pair of the upper work roll  110 A and the upper backup roll  120 A, and a lower-side pair of the lower work roll  110 B and the lower backup roll  120 B in a state where the upper-side pair is kept parallel and in a state where the lower-side pair is kept parallel. 
     Furthermore, thereafter, the control apparatus  20  adjusts angles of the upper work roll  110 A and the lower work roll  110 B in a state where angles of the upper backup roll  120 A and the lower backup roll  120 B are maintained. 
     As adjustment angles at that time, for example, the cross angle between the upper-side pair and the lower-side pair can be made equal to or greater than 0.2 degrees. 
     This has been found out on the basis of findings like the ones mentioned below. 
     Thrust forces are generated by relative speed differences between the rolled material S and the work rolls  110 A and  110 B, and relative speed differences between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B. 
     Because of this, as the cross angle of the work rolls  110 A and  110 B increases, thrust forces between the rolled material S and the work rolls  110 A and  110 B increase, and similarly, as the relative angles between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B increase, thrust forces between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B increase also. 
     In addition, it has been known that in a case of work-roll crossing, thrust forces acting between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B are greater than thrust forces acting between the rolled material S and the work rolls  110 A and  110 B. 
     In view of this, the present inventors have come up with an idea of causing the work rolls  110 A and  110 B to further slight-cross (e.g. at an angle equal to or smaller than 0.1°) suitably from a pair-cross state as depicted in  FIG.  3   . 
       FIG.  4    depicts results of simulations of change amounts ΔCh25 of strip crown Ch25 in a case where work-roll slight crossing of ±0.05° is performed from predetermined pair cross angles in the hot rolling mill  1  depicted in  FIG.  1    under the rolling condition that a rolled material with hardness of 20 kgf/mm 2  is 20% rolling reduction ratio into a 2-mm strip. The work-roll diameter is 450 mm, and the maximum strip width is 1880 mm. 
     As depicted in  FIG.  4   , it has become clear that, for the same changes of ±0.05° in the work-roll slight cross angle, the control range of the work-roll slight cross angle is wider for a change from a greater pair cross angle. 
     For example, it has become clear that, in  FIG.  4   , in a case where slight-crossing of the work rolls relative to the backup rolls is performed within the range of ±0.05° from a state where the pair cross angle is 0°, ΔCh25 is as small as 1.5 µm; on the contrary, in a case where slight-crossing of the work rolls relative to the backup rolls is performed within the range of ±0.05° from a state where the pair cross angle is 0.2°, ΔCh25 is 20 µm, which is ten times or more greater. 
     In view of this, it has become clear also that it is desirable if a pair cross angle is made equal to or greater than 0.2° because larger crown changes can be made, and wider crown and strip shape control ranges can be attained even with small work-roll cross angle changes in a large pair cross angle range, for example in the range of 0.2° or greater. 
     Next, advantages of the present embodiment are explained. 
      In the hot rolling mill  1  according to the first embodiment of the present invention mentioned above, the work rolls  110 A and  110 B in a pair-cross state are caused to cross further relative to the backup rolls  120 A and  120 B, and thereby even with a micro relative cross angle between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B, for example even for the same cross angle change of 0.05°, higher controllability can be attained, and simultaneously, responsiveness can be ensured also. 
     In addition, because thrust forces between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B can be reduced, it becomes possible to attain advantages that small-diameter work rolls  110 A and  110 B can be applied, and rolling of hard steel strips becomes possible. 
     Furthermore, it has conventionally been required to make large work-roll cross angle changes in terms of ensuring control ranges when work-roll crossing is applied. In view of this, as a measure for reducing thrust forces, oil lubrication between rolls has been adopted. 
     However, in a case of the hot rolling mill  1  and hot rolling method according to the present embodiment, the cross angle between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B can be made a micro angle. 
     Thrust forces acting between rolls significantly influence the rolling load and roll surface conditions. For example, there is data that with water lubrication, the thrust coefficient µ t  is generally 0.2 if the cross angle θ between roll shafts is 0.2°, and the cross angle θ and the thrust coefficient µ t  generally have a proportional relation in the range of 0.2° or smaller. In a case where this relation is used, for example with a slight cross angle of 0.05°, the thrust coefficient described above is estimated as 0.2× (0.05/0.2) = 0.05 [-]. 
     Accordingly, the thrust coefficient can be reduced to a value equivalent to or smaller than the coefficient (equal to or smaller than 0.1) of thrust forces acting between the rolled material S and the work rolls  110 A and  110 B, thus it is possible to attain an advantage that oil lubrication becomes unnecessary even in work-roll crossing in the present embodiment. 
     In addition, the control apparatus  20  adjusts the pair cross angle at which the upper-side pair and the lower-side pair are caused to cross each other such that the pair cross angle is equal to or greater than 0.2 degrees, thus the advantages mentioned above can be particularly made significant by keeping the pair cross angle equal to or greater than 0.2°. 
     Second Embodiment 
     A hot rolling mill and hot rolling method according to a second embodiment of the present invention are explained by using  FIG.  5    and  FIG.  6   .  FIG.  5    is a schematic view depicting how thrust forces are generated before work-roll slight crossing in the rolling mill according to the present second embodiment.  FIG.  6    is a schematic view depicting how the work-roll thrust forces are cancelled out by the work-roll slight crossing in the rolling mill according to the present second embodiment. 
     First, a way of thinking about directions of action of thrust forces is explained. 
     The coefficient of thrust forces acting from the rolled material S on the work rolls is correlated with the cross angle and the reduction ratio of rolling, and an estimation formula like the following Formula (1) has been proposed.  
     
       
         
           
             
               μ 
               
                 T,1 
               
             
             = 
             F 
             
               
                 
                   θ 
                   1 
                 
                 , 
                 r 
               
             
             = 
               
             
               μ 
               1 
             
             
               
                 1 
                 − 
                 exp 
                 
                   
                     − 
                     3 
                     
                       
                         
                           
                             
                               θ 
                               1 
                             
                             
                                 
                               
                                 0.9 
                               
                             
                           
                           / 
                           
                             
                               r 
                               
                                 1.1 
                               
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     In Formula (1), µ T,1  is the coefficient of thrust forces between the rolled material S and the work rolls  110 A and  110 B, µ is the coefficient of friction, θ 1  is the cross angle between the rolled material S and the work rolls  110 A and  110 B, and r is the reduction ratio of rolling. 
     In addition, taking directions of action into consideration, the coefficient of thrust forces between the work rolls  110 A and  110 B and the backup rolls  120 A and  120 B  is defined by the following Formula (2).  
     
       
         
           
             
               μ 
               
                 T 
                 2 
               
             
             = 
             − 
             K 
             
               θ 
               2 
             
           
         
       
     
      where µ T2  is the coefficient of thrust forces between the backup rolls  120 A and  120 B and the work rolls  110 A and  110 B, θ 2  is the cross angle between the backup rolls  120 A and  120 B and the work rolls  110 A and  110 B, and K is the influence coefficient (≈ 1.0° -1 ) . 
     Accordingly, if a pair cross angle θ PC , a slight cross angle θ WRS , and the rolling load are used, thrust forces acting on the work rolls  110 A and  110 B are represented by the relation of Formula (3) like the one mentioned below. 
     
       
         
           
             
               
                 
                   F 
                   T 
                 
                 = 
                 P 
                 
                   
                     
                       μ 
                       
                         T 
                         , 
                         1 
                       
                     
                     + 
                     
                       μ 
                       
                         T 
                         2 
                       
                     
                   
                 
                 = 
                 P 
                 
                   
                     F 
                     
                       
                         
                           θ 
                           1 
                         
                         , 
                         r 
                       
                     
                     − 
                     K 
                     
                       θ 
                       2 
                     
                   
                 
                 = 
               
             
             
               
                 P 
                 
                   
                     F 
                     
                       
                         
                           θ 
                           
                             PC 
                           
                         
                         + 
                         
                           θ 
                           
                             WRS 
                           
                         
                         , 
                         r 
                       
                     
                     − 
                     K 
                     
                       θ 
                       
                         WRS 
                       
                     
                   
                 
               
             
           
         
       
     
     In Formula (3), θ WRS  is very small relative to θ PC , thus F (θ PC +θ WRS , r) assumes a positive value. 
     In view of this, in the hot rolling mill  1  and hot rolling method according to the present embodiment, in a case where work-roll crossing is performed in a state where thrust forces like the ones depicted in  FIG.  5    are acting, θ WRS  is adjusted in such a direction that it becomes a positive value, that is, the angles of the work rolls  110 A and  110 B are adjusted in such directions that they become greater than the angles of the backup rolls  120 A and  120 B. 
      Thereby, as depicted in  FIG.  6   , it is attempted to reduce thrust forces acting on the work rolls by causing thrust forces acting from the rolled material S and thrust forces acting from the backup roll to cancel out each other. 
     In addition, in a case where work-roll shift is performed, it is desirable if thrust forces acting on the work rolls  110 A and  110 B are used. 
     That is, if the slight cross angle of the work rolls  110 A and  110 B is set such that the thrust forces act in such directions that the work rolls are shifted, the thrust forces act to support the work-roll shift, thus the capacities of shifting apparatuses can be reduced. 
     In other respects, the configuration/operation is approximately the same as the configuration/operation of the hot rolling mill and hot rolling method according to the first embodiment mentioned before, and details are omitted. 
     In the hot rolling mill and hot rolling method according to the second embodiment of the present invention also, advantages almost the same as those of the hot rolling mill and hot rolling method according to the first embodiment mentioned before are attained. 
     In addition, when adjusting the angles of the work rolls  110 A and  110 B, the control apparatus  20  adjusts the angles of the work rolls  110 A and  110 B in such directions that they become greater than the angles of the backup rolls  120 A and  120 B. Thereby, it is possible to cause thrust forces from the backup rolls  120 A and  120 B to act in directions opposite to thrust forces from the rolled material S acting on the work rolls  110 A and  110 B, and the total of the thrust forces acting on the work rolls  110 A and  110 B can be reduced. Accordingly, it is possible to attain advantages that the loads on the work rolls  110 A and  110 B in the axial direction can be reduced, it becomes easier to adopt small-diameter work rolls  110 A and  110 B, and bearings of the work rolls  110 A and  110 B are less likely to be damaged. 
     Third Embodiment 
     A hot rolling mill and hot rolling method according to a third embodiment of the present invention are explained by using  FIG.  7   .  FIG.  7    is a side view depicting the apparatus configuration of a rolling mill according to the present third embodiment. 
     A hot rolling mill  1 A according to the present embodiment depicted in  FIG.  7    is the same as the hot rolling mill  1  according to the first embodiment, except that it does not include the backup-roll sliding apparatuses  200 A and  200 B. 
     In addition, a control apparatus  20 A of the hot rolling mill  1 A according to the present embodiment executes adjustment of a pair cross angle at which the upper-side pair and the lower-side pair cross each other before rolling of the rolled material S is started. Furthermore, adjustment of the angles of the work rolls  110 A and  110 B is executed during the rolling of the rolled material S. 
     In other respects, the configuration/operation is approximately the same as the configuration/operation of the hot rolling mill and hot rolling method according to the first embodiment mentioned before, and details are omitted. 
     In the hot rolling mill and hot rolling method according to the third embodiment of the present invention also, advantages almost the same as those of the hot rolling mill and hot rolling method according to the first embodiment mentioned before are attained. 
     As mentioned above, the roll chocks of the backup rolls  120 A and  120 B are supported by the housing  100  through the pressing apparatuses  150 A and  150 B, the home-position control apparatuses  160 A and  160 B, and the load cell  180 . 
     If the cross angle of the backup rolls  120 A and  120 B during rolling is changed in such a state, large sliding resistances are generated between fixation members due to the rolling load, thus actuators to change the cross angle need to have large capacities, and also members such as bearings for making sliding sections movable are required. 
     The movable members have low rigidity, and become a factor to lower the rigidity of the rolling mill itself. In that case, this becomes a factor of disturbance of the shape of the rolled material S, also causes strip movement of the rolled material S along lateral direction and lowers the stability of strip threading. 
     In contrast, by executing the angle adjustment in a pair-cross state before rolling of the rolled material S is started, the change can be made at a time of a low load. Accordingly, it is possible to reduce the capacities of the actuators to change the cross angle of the backup rolls  120 A and  120 B, and also it becomes unnecessary to provide mechanisms such as bearings to make the backup rolls  120 A and  120 B smoothly movable on sliding surfaces of support members. Accordingly, it is possible to attain advantages that it is possible to reduce equipment costs by making the equipment a simple and convenient one with low capacities, and also it becomes possible to avoid reduction of the rigidity of the rolling mill and to more stabilize rolling. 
     Furthermore, by executing the angle adjustment of the work rolls  110 A and  110 B during the rolling of the rolled material S, the control apparatus  20 A can ensure responsiveness while surely attaining wide control ranges. 
      Fourth Embodiment 
     A hot rolling mill and hot rolling method according to a fourth embodiment of the present invention are explained by using  FIG.  8   .  FIG.  8    is a side view depicting the apparatus configuration of a rolling mill according to the present fourth embodiment. 
     A hot rolling mill  1 B according to the present embodiment depicted in  FIG.  8    is the same as the hot rolling mill  1  according to the first embodiment, except that it does not include the backup-roll sliding apparatuses  200 A and  200 B, and is further provided with thrust force measuring apparatuses  300 A and  300 B that measure thrust forces acting on the shafts of the work rolls  110 A and  110 B. 
     In addition, a control apparatus  20 B of the hot rolling mill  1 B according to the present embodiment controls the work-roll pressing apparatuses  130 A and  130 B and the work-roll position control apparatuses  140 A and  140 B such that the angles of the work rolls  110 A and  110 B relative to the backup rolls  120 A and  120 B are changed when the thrust forces measured by the thrust force measuring apparatuses  300 A and  300 B become greater than a predetermined upper limit value. For example, in a case where the direction of thrust forces acting between the rolled material S and the work rolls  110 A and  110 B is a positive direction and the thrust forces become greater than the upper limit value, the cross angle of the work rolls  110 A and  110 B is controlled so as to be increased. 
     Furthermore, the work-roll pressing apparatuses  130 A and  130 B and the work-roll position control apparatuses  140 A and  140 B are controlled such that the angles of the work rolls  110 A and  110 B relative to the backup rolls  120 A and  120 B are changed when the thrust forces measured by the thrust force measuring apparatuses  300 A and  300 B become smaller than a predetermined lower limit value. For example, in a case where the thrust forces become smaller than the lower limit value, the cross angle of the work rolls  110 A and  110 B is controlled so as to be decreased. 
     In other respects, the configuration/operation is approximately the same as the configuration/operation of the hot rolling mill and hot rolling method according to the first embodiment mentioned before, and details are omitted. 
     In the hot rolling mill and hot rolling method according to the fourth embodiment of the present invention also, advantages almost the same as those of the hot rolling mill and hot rolling method according to the first embodiment mentioned before are attained. 
     In addition, the higher the hardness of a rolling-subject steel strip is, the larger the thrust forces on the work rolls are. In view of this, by controlling the work-roll pressing apparatuses  130 A and  130 B and the work-roll position control apparatuses  140 A and  140 B such that the angles of the work rolls  110 A and  110 B relative to the backup rolls  120 A and  120 B are changed when the thrust forces measured by the thrust force measuring apparatuses  300 A and  300 B are greater than the predetermined upper limit value, the control apparatus  20 B can perform control such that thrust forces on the work rolls  110 A and  110 B do not exceed thrust forces that the work rolls  110 A and  110 B can endure, and can prevent damage of members. 
     Furthermore, the control apparatus  20 B can eliminate backlashes between the work rolls  110 A and  110 B and members supporting them by controlling the work-roll pressing apparatuses  130 A and  130 B and the work-roll position control apparatuses  140 A and  140 B such that the angles of the work rolls  110 A and  110 B relative to the backup rolls  120 A and  120 B are changed when the thrust forces measured by the thrust force measuring apparatuses  300 A and  300 B become smaller than the predetermined lower limit value, and can stabilize the positions of the work rolls in the strip-width direction. 
     Fifth Embodiment 
     A hot rolling mill and hot rolling method according to a fifth embodiment of the present invention are explained by using  FIG.  9    to  FIG.  18   . 
       FIG.  9    is a figure depicting how a work-roll diameter influences the order of control by bending.  FIG.  10    is a figure depicting a distribution, in the strip-width direction, of strip crown change amounts in a case where bending is performed in a rolling mill with D w /L b  = 0.32.  FIG.  11    is a figure depicting a distribution, in the strip-width direction, of strip crown change amounts in a case where bending is performed in a rolling mill with D w /L b  = 0.21.  FIG.  12    is a figure depicting how a work-roll diameter influences the order of control by work-roll crossing.  FIG.  13    is a figure depicting how a work-roll diameter influences strip crown change amounts generated by work-roll crossing.  FIG.  14    is a figure depicting crown control ranges in the rolling mill with D w /L b  = 0.32.  FIG.  15    is a figure depicting shape control ranges in the rolling mill with D w /L b  = 0.32.  FIG.  16    is a figure depicting crown control ranges in a rolling mill with D w /L b  = 0.24.  FIG.  17    is a figure depicting shape control ranges in the rolling mill with D w /L b  = 0.24.  FIG.  18    is a figure depicting influence of D w /L b  on crown control and shape control ranges. 
     The hot rolling mill according to the present embodiment is the same as the hot rolling mill  1  according to the first embodiment in terms of basic apparatus configuration. 
     As a further limitation, in the hot rolling mill according to the present embodiment, the work rolls  110 A and  110 B satisfy the condition that D w /L b  is equal to or greater than 0.15 and equal to or smaller than 0.3 where D W  is the diameter of the work rolls  110 A and  110 B, and L b  is the maximum strip width of the rolled material S. 
     The ratio D w /L b  between a work-roll diameter D W  and a maximum strip width L b  is within the range of 0.32 to 0.40 in typical pair cross mills, and, in this range, it is possible to perform second-order shape control by work roll bending, but it is difficult to perform higher-order shape control. In addition, principles similar to those of pair cross mills are applied to work-roll cross mills, and generally the same tendency is observed. 
       FIG.  9    and the figures that follow are figures depicting simulation results of change amounts of the strip crown and strip shape under the condition that a rolled material with hardness of 20 kgf/mm 2  is 20% rolling reduction ratio into a 2-mm strip. Here, not the strip shape control order but the strip crown control order is depicted because the strip crown and the strip shape generally correspond to each other. As depicted in  FIG.  9   , it can be known that the order of strip crown control by bending tends to increase as D w /L b  decreases. 
       FIG.  10    depicts a distribution of strip crown change amounts that are observed when increase bending is applied in a case where D w /L b  is 0.32 (D w : 600 m, L b : 1880 mm), and  FIG.  11    depicts a distribution of strip crown change amounts that are observed when increase bending is applied in a case where D w /L b  is 0.21 (D w : 400 m, L b : 1880 mm). 
     As depicted in  FIG.  10    and  FIG.  11   , it can be known that the crown change amounts near the strip center are small, and there is significant influence on strip ends in a case of a high control order (control order 2.6), that is, in a case where D w /L b  is 0.21. 
     In addition, as depicted in  FIG.  12   , it can be known that the control exponent of work-roll crossing is approximately 1.65, thus by making D w /L b  at least equal to or smaller than 0.3, the difference between the control orders of work-roll crossing and bending can be increased, and it is expected that a complicated shape like quarter buckle can be controlled. 
     In addition, the crown control order is approximately 1.65, and influence of D w /L b  is extremely small. Although it is considered that this order is slightly influenced by rolling conditions due to roll flattening, roll deflection, or the like, the control order is generally 2.0 irrespective of a work-roll diameter. 
       FIG.  13    depicts results of simulations of a changed roll diameter about crown change amounts ΔCh25 when work rolls are caused to cross at -0.05° to 0.05° relative to backup rolls from a state of a pair cross angle 0.5° where crown Ch25 is the difference of the strip thickness between the strip center and a 25-mm position from a strip end. As depicted in  FIG.  13   , it can be known that a geometrically-generated gap increases as the diameter is reduced, thus controllable ranges also widen naturally. 
       FIG.  14    to  FIG.  17    depict results of estimation by simulations of the strip crown control range and the second-order and fourth-order strip shape control ranges. 
       FIG.  14    and  FIG.  15    depict results that are obtained under the condition of: pair cross (0.50°), D W  = 602 mm and D w /L b  = 0.32, and  FIG.  16    and  FIG.  17    depict results that are obtained under the condition of: pair cross (0.50°), D W  = 450 mm and D w /L b  = 0.24. 
     Then,  FIG.  14    and  FIG.  16    depict relations of strip crown change amounts ΔCh¼ at a widthwise ¼-position (quarter position) to strip crown change amounts ΔCh25 of a 25-mm position from an end, and  FIG.  15    and  FIG.  17    depict relations of fourth-order component change amounts ΔC4 to second-order component change amounts ΔC2 of the deviation of longitudinal strain. 
     It can be known that, under the conventional range condition of DW/Lb = 0.32 depicted in  FIG.  14    and  FIG.  15   , the value of ΔCh¼ relative to ΔCh25, and the value of ΔC4 relative to ΔC2 change at generally equal gradients in both a case where the cross angle of work-roll crossing is changed, and a case where work-roll bending is increased and reduced, and the ranges within which ΔCh25 and ΔCh¼ and ΔC2 and ΔC4 can be controlled individually are very narrow. 
     In contrast, as depicted in  FIG.  16    and  FIG.  17   , in a case where a condition of the present invention, D w /L b  = 0.24, is adopted, the value of ΔCh¼ relative to ΔCh25, and the value of ΔC4 relative to ΔC2 change at different gradients in a case where the cross angle of work-roll crossing is changed, and a case where the work-roll bending is increased and reduced. Accordingly, it can be known that the locus that is formed by following an increase in work-roll bending, a change in the work-roll cross angle from 0.45° to 0.55°, a reduction of work-roll bending and a change in the work-roll cross angle from 0.55° to 0.45° in this order gives a parallelogram shape, and the ranges within which ΔCh25 and ΔCh¼, and ΔC2 and ΔC4 can be controlled individually widen significantly. 
     Here, as indicators of the ranges within which ΔCh25 and ΔCh¼, and ΔC2 and ΔC4 can be controlled individually, respectively, the area size in the parallelogram in the graph of ΔCh25 and ΔCh¼ is defined as Sc, and the area size in the parallelogram in the graph of ΔC2 and ΔC4 is defined as Ss. Taking this into consideration,  FIG.  18    depicts results of plotting ratios relative to area sizes S C0.35  and S S0.35  when D w /L b  is 0.35 in relation to D W/ L b . 
     As depicted in  FIG.  18   , it has become clear that, by adopting the condition that D w /L b  = 0.28 or smaller, as compared with D w /L b  = 0.32 under which the work-roll diameter is categorized as a small diameter even in the current situation, a center/edge buckle which is approximately twice or more than twice as long can be realized, and the shape controllability is enhanced significantly. 
     Here, in hot rolling processes, typically, work rolls are connected to motors and rotation-driven. In that case, if the diameter of the work rolls is reduced, the spindle diameter is reduced, thus transmittable torque also decreases. 
     Whereas reduction of the diameter of the work rolls reduces rolling torque also, the influence of the reduction of the diameter of the work rolls is more significant on the limitation of torque transmission of spindles. That is, if the diameter of the work rolls is too small, difficulties in terms of mechanical feasibility arise, and it is considered that disadvantages outweigh advantages. 
     The rolling torque depends on rolling conditions, and it is determined that it is possible to make feasible modes in which advantages outweigh disadvantages by making D w /L b  at least equal to or greater than 0.15 in typical hot rolling plants; therefore, it is desirable if the lower limit of D w /L b  is set to 0.15 or greater. 
     Summarizing what have been described thus far, it is desirable if a suitable range of D w /L b  is 0.15 or greater and 0.30 or smaller, and more suitably 0.15 or greater and 0.28 or smaller. 
     In other respects, the configuration/operation is approximately the same as the configuration/operation of the hot rolling mill and hot rolling method according to the first embodiment mentioned before, and details are omitted. 
     In the hot rolling mill and hot rolling method according to the fifth embodiment of the present invention also, advantages almost the same as those of the hot rolling mill and hot rolling method according to the first embodiment mentioned before are attained. 
     In addition, the work-roll bending cylinders  190 A and  190 B that apply bending forces to the work rolls  110 A and  110 B are further provided, the work rolls  110 A and  110 B satisfy the condition that D w /L b  is equal to or greater than 0.15 and equal to or smaller than 0.3 where D W  is the diameter of the work rolls  110 A and  110 B, and L b  is the maximum strip width of the rolled material S. Thereby, both bending force control and cross angle control are performed, harder steel strips than ones that conventional technologies can cope with can be rolled with a work-roll diameter equal to or smaller than that in the conventional technologies, and also more complicated shape control becomes possible. 
     Others 
     Note that the present invention is not limited to the embodiments described above, and includes various modification examples. The embodiments described above are explained in detail in order to explain the present invention in an easy-to-understand manner, and the present invention is not necessarily limited to those including all the configurations explained. 
     In addition, it is also possible to replace some of the configurations of an embodiment with configurations of another embodiment, and it is also possible to add a configuration of an embodiment to the configurations of another embodiment. In addition, some of the configurations of each embodiment can also have other configurations, be deleted or be replaced with other configurations. 
     Description of Reference Characters 
     
         
         S: Rolled material 
           1 ,  1 A,  1 B: Hot rolling mill 
           20 ,  20 A,  20 B: Control apparatus 
           30 : Hydraulic apparatus 
           100 : Housing 
           110 A: Upper work roll 
           110 B: Lower work roll 
           112 A: Work-side roll chock 
           112 B: Drive-side roll chock 
           120 A: Upper backup roll 
           120 B: Lower backup roll 
           130 A,  130 B: Work-roll pressing apparatus 
           140 A,  140 B: Work-roll position control apparatus 
           150 A,  150 B: Backup-roll pressing apparatus 
           160 A,  160 B: Backup-roll position control apparatus 
           170 : Hydraulic cylinder apparatus 
           180 : Load cell 
           190 A: Upper work-roll bending cylinder 
           190 B: Lower work-roll bending cylinder 
           200 A,  200 B: Backup-roll sliding apparatus 
           300 A,  300 B: Thrust force measuring apparatus