Finite Element Solution Of Contact Problem&Its Application In The Deformation Of Rolls Of 4-High Mill

The lateral thickness distribution in transverse direction of strip is one of the most important facts that affect the shape of cold rolling strip,and it’s determined by roll gap of rolls.The accurate solution of rollers can derive the lateral thickness distribution in transverse direction of strip,thus it’s the emphasis of the research on the shape of cold rolling strip.Nowadays,finite element method is one of the most efficient ways to solve the deformation of rollers,and the difficulty of solving the deformation of rollers is to dispose the contact of work roll and back-up roll reasonably.This thesis explained the general strategy and the main steps of processing contact problem using direct contact technic.The general strategy is deleting the normal degree of freedom of contact nodes on contact faces,and merging contact elements.The main steps contain the search of pairs of contact nodes,the judging of contact condition,the implement of contact constraint,the establishment and solution of control equation,the update of contact condition and contact iteration.According to the basic theory,this thesis developed the elastic contact procedure using FORTRAN programming language.This job extended the rigid-plastic finite element program.Using the developed program,this thesis simulated the rolling process of strip in A and B situation The roll force of A and B was 278.5kN and 319.5kN,while the valued roll force was 266.6kN and 308.9kN.The relative error of roll force was 4.5%and 3.4%,respectively.Meanwhile,comparing the simulated value and valued value of lateral thickness distribution in transverse direction of strip in A and B situation,the simulated value of the thickness distribution of strip conform to the valued value.The maximum relative error of thickness in A and B situation was 1.4%and 1.6%.From the above comparison,we can gain the program can afford the requirement of precision,and can be used to simulate the rolling process of strip.In order to research the influence of different rolling process parameter on the elastic flattening of roll and the thickness distribution of strip,this thesis simulated the elastic flattening of roll in different reduction rate,half width of strip and the diameter of work roll.Form the result,we can know that the elastic flattening of work roll is bigger when the reduction rate,half width of strip and the diameter of work roll are bigger.And this thesis simulated the thickness distribution of strip in different reduction rate,half width of strip,the diameter of work roll and the tension force.Form the result,we can know that the thickness distribution of strip is more uniform when the half width of strip,the diameter of work roll and the tension force are bigger,or when the reduction rate is smaller.