Therefore,  an automated  compensation process  has  been  developed  recently,  in  which hydraulic cylinder pushes back  the  rolls  in proportion to the level of reaction force from the plate.  FIGURE 5.  Wedge Compensation. MATHEMATICAL MODEL During  the  leveling  process,  the  plate  touches  the roll  away  from  the  roll  center,  mainly  due  to  the defection of the plate –  Fig.6. As the contact condition between  the  plate  and  rolls  changes  frequently  any calculation model requires to analyze dynamic contact condition with friction effects. FIGURE 6.  Roll / Plate Geometry. For a given contact condition between the plate and rolls, deflection of  an  arbitrary point on  the plate  can be precisely described by the following equations [2   (6) Due  to  changes  in  contact  conditions,  to  evaluate deflection  of  the  plate  computation  process  has  to follow  three stages of calculations (and need  to repeat for every new contact conditions): a)  Contact reaction force. b)  Bending of the plate due to the reaction. c)  New contact position between the plate and a roll. FEM ANALYSIS Accurate  modeling  of  contact  conditions  between rolls  and  a  plate  requires  to  precisely  describe geometry of a  roll. Typical approach  to  this  task  is  to use 3D  solid  elements.  However,  a  large  number  of solid  elements  used  to  describe  rolls  will  result  in  a time  consuming  calculations.  To  deal  with  this problem authors utilized a simplified approach –  Fig. 7. Rolls  are  described  using  beam  elements,  rigid  links and contact segments [3].
A summary of FEM features of our models is presented below: a)  Beam elements representing geometry of a roll; b)  Contact segments on a surface of each roll; c)  Rigid  links  connecting  beam  elements’   nodes  and contact segments;  d)  Steel  plate  described  by  3/D  solid  u/p  elements with elastic-plastic material properties; e)  Contact between rolls’  contact surface and plate; f)  Frame structure is modeled by a grillage. Model  of  a  roll  can  be  compared  with  human  body with  flexible  back  bone  (beam  elements),  rigid  rib (rigid links), and skin (contact elements).                    FIGURE 12.  Plastic Strain (3/4).   FIGURE 13.  Plastic Strain (4/4).  CONCLUDING REMARKS a) Due to the deflection of rolls, roll leveling process creates a non-uniform plastic strain on the top and the bottom surfaces of the plate. b) The effect of roll deflection is successfully simulated using non-linear FEM code. c) The total load of a leveler frame –  structure shows a very good agreement between numerical results and experimental observations. d) For a given shape distortion - simulation models make possible to effectively calculate technological parameters of a leveling process. e) A very good agreement is observed between plastic strain distribution obtained in numerical simulations and experiments.  f) A unique approach to finite element model of a roll has been presented and successfully used in simulations. REFERENCES 1.  Higo,  T.,  Matsumoto,  H.,  and  Ogawa, S., “ Numerical Simulation  for  Coupled  Analysis  of  Plate  and  Mill Deformation  in  Roller  Leveler,”   CAMP-ISIJ,  Vol.16, 2003, pp. 388-391.  2.  Kadota, K.,  and Maeda,  R., “ A Method  of Analysis  of Curvature  in  Leveling  Process  –   Numerical  Study  of Roller Leveling Process 1,”  Journal of  the JSTP vol.34, No.388 1993, pp.481- 486. 3.  ADINA  R&D,Inc., “ Theory  and  Modeling  Guide Volume I : ADINA, Report ARD 02-7,”   Sept. 2002. 轧钢厂矫直工艺中轧辊柔韧度的影响英文文献和中文翻译(2):http://www.751com.cn/fanyi/lunwen_53601.html