2015 Volume 55 Issue 1 Pages 89-102
Rolling theory has made remarkable progress for the last 100 years. The history of rolling theory is described in this report, comparing rolling theory with innovation of strip rolling technology. In Japan, computer control system started to be introduced to iron and steel company in 1960s. Therefore, research of rolling theory became in dispensable. Before 1960, it was published mainly in the Western countries. It is said that two-dimensional rolling theory had been completed. First of all, in Japan flow stress was investigated to calculate rolling load precisely, and approximate three-dimensional analysis for deformation of rolled strip was researched to predict the distribution of rolling pressure in width direction, which made up crown and shape of rolled strip. After that, FEM (finite element analysis method) replaced the approximate three-dimensional analysis, by which three-dimensional deformation of rolled strip could be calculated precisely. The results of these researches supported the innovation of crown and flatness control technology and the invention of many rolling mills with high functional ability for crown and flatness control. Next, the continuous strip rolling theory was completed chiefly in Japan, by which the static and dynamic characteristics of tandem strip mills could be understood. It is said that the continuous rolling technology for cold and hot strip tandem mills would not be realized without the continuous strip rolling theory.
The definition is vague even if a rolling theory is said, and how to understand is various by a person. I decide to push forward when numerical analysis is defined that can explain a rolling phenomenon as a rolling theory in a wide meaning in this report. The numerical analysis becomes one of the important tools to explain various kinds of unusual phenomena in the rolling or to predict it. I am certain that the role of the rolling theory served as for the development of the rolling technology is very large.
Amount of crude steel production increased suddenly for approximately 100 years since 1880 when Japan began steel production in earnest. In 1940 before entering into the Pacific War, and in 1945 of the end of it, the amount of steel production was very small in Japan, but it increased suddenly after the Korea War broke out in June of 1950. It reached 120 million tons in 1973, but it becomes roughly flat with more than 100 million tons afterwards. At all events, the amount of steel production increased suddenly in comparison with other developed countries. Movement of computer control began in the 1960s in the Western countries. It was systematized on a base of the past experiences accumulated in the Western countries, but it was necessary to form the computer control system on a base of the rolling theory because there were not the accumulated data on rolling operation in our country where the overseas technique and facilities were introduced. Therefore, it is not exaggeration even if it is said that the quality became stable and pushed up market competitiveness to the first place in the world, because the system was well able to follow new steel grade or totally new rolling condition, which became a flexible computer control system. A rolling technology is not only a rolling technology, and it goes without saying that it consists as synthesis technology such as hardware techniques of rolling mills or rolling rolls, measurement techniques to observe the rolling state, metallurgy-based software techniques to elaborate materials, control techniques to get highly precise thickness and shape of rolled strips, and lubrication techniques to realize extension of roll life and reduce rolling load. The best rolling technology in the world was not realized only with the rolling theory, but it was stimulated with advancement of the neighboring techniques such as described above, and it was made up technically. For example, the role of the rolling theory is introduced as follows. It is necessary to decide a pass schedule (including a draft schedule and the pass number) to get the aimed thickness from a certain thickness of a strip. There are two methods to do so. The one is a method to decide by looking for the pass schedules from the past data and another one is a method to decide by calculating a pass schedule with the rolling theory. The former is a Western method, and the latter is the method that our country adopted. In other words, a pass schedule is calculated near the capacity limit of a rolling mill by using rolling load and torque, and it is decided to adjust the calculated pass schedule so that the rolled strip does not worsen the flatness degree when it becomes thin near the last pass. The former shows a strength for the rolling condition in the range where it had a past experience at all, but it is not helpful in the case that a totally new steel grade and strip thickness are considerably different from the past experiences. However, it is a strength by the latter method that it can be done so without a problem in this case.
I want to survey it while comparing the rolling theory that supported the rolling technology with the progress of the rolling technology in this report as much as possible. As I want to describe it boldly in spite of my little knowledge for it since I understood writing of this report. I am grateful if I have the opinion of gentlemen. However, I exclude the rolling theory for wire & rod, shape steel, and steel pipe from an object on account of the space, and I want you to forgive that you limited only to the strip rolling.
At first I survey the rolling-related research and development activity in Japan from the activities of academic society and institute before surveying the rolling theory. The main rolling technologies developed in Japan and the amount of crude steel production since 1950 is shown in Fig. 1.1) In addition, the installation of hot strip mills and their capacities are shown together with the situation of the times and the social condition to deepen your understanding. It is found in Fig. 1 that high ability of mill power of the hot strip mills is well correspond to the increase in the amount of crude steel production. The mill powers at the time of their new establishment are described with cross marks, and the ability reinforcement of the hot strip mills of steel companies was carried out with the increase of production such as high strength steel sheets after 1980, whose mill power is described with circle marks. The rolling theory committee which consisted of rolling engineers and researchers started in 1955 as one of the subcommittees of the steel material sectional meeting in the steel technology combination meeting for co-research of steel technology, which consisted of the ISIJ, the heavy industry station of the Ministry of International Trade and Industry, and the Japan Iron & Steel Federation. Thereafter, it was promoted in 1972 to one sectional meeting of the production engineering section of the ISIJ, that is the rolling theory committee. Its main events and combination meetings for the study of rolling theory were written jointly in the graph of the amount of crude steel production. It is necessary how rolling load is predicted precisely to show the effect of the computer control system. A joint society for the study of plastic flow stress of rolled materials was started in 1955, and efforts to get the model of it with high precision were made. As the result, the books of “rolling theory and resistant to deformation” were published in 1960, and the practical models for plastic flow stress were announced in 1967 and in 1968, one of which was Misaka & Yoshimoto’s model145) and another one is Shida’s model.146) The thickness control technology progressed drastically thereafter. It is not exaggeration even if it is said that it was almost completed concerning the thickness control technology in the stable rolling state by a newly developed rolling mill with hydraulic screw down device in 1970s.
History of Japanese crude steel production and construction of hot strip mills, and main events in Rolling Theory Committee and trends of rolling technology.1)
An object of the interest moved to the control technology of strip crown and shape, that is the control technology of strip thickness distribution in the width direction, and new type rolling mills were developed consecutively to actualize it. I will describe in detail in the later paragraph, but it may be said that the role of the rolling theory carried out for progress and development of the control technology of strip crown and shape is very large. In addition, a full-continuous cold strip rolling technology was developed in 1971, and a series of new cold processes coupled with upper stream processes or downer stream processes than cold strip rolling process would be developed in succession afterward. In the full-continuous cold strip rolling process it is necessary to change the aimed gauge on the fly, but the technique could not be realized without the progress of the continuous rolling theory. The rules for thickness control could not be found if it could not be predicted what kind of phenomenon happened in the tandem cold strip mills when the aimed gauge was changed on the fly.
It is showed in Fig. 2 the change of number of the research and development themes announced in the Rolling Theory Committee of the ISIJ. It is proper to think that there was the peak of research and development such as crown, shape and edge drop control technology at the beginning in the 1970s, because there was the gap of several years from the time of starting it to the time of announcement in the case of the companies. It is thought that the research and development of this field were carried out flourishingly from the early days of the 1970s when the amount of crude steel production increased suddenly in looking Fig. 2 from such a viewpoint. Publication about width control and width reduction became popular from the late in the 1970s, but there were many problems in the comprehensive width control technique including a rough rolling mill to a cold tandem mill. In addition, the frequent width change was difficult in a continuous casting process. At first an edge rolling mill of a rough rolling mill train reduced the width of a slab widely, but the width spread widely after the slab was rolled by the rough rolling mill. Therefore, the effect of the width reduction by the edge rolling mill was reduced by more than half. It was the bigger problem than it that large crops caused at the front part and the tail part of the slab rolled by the rough rolling mill, which reduced the yield rate. A sizing press came to be developed with this, which was able to reduce the width of a slab widely without large spread after flat rough rolling. Figure 2 shows that there were many publication of lubrication technology at the late of 1970s. For the reason, it is thought to be a big cause that the research and development of hot rolling lubrication began, which aimed at energy saving under the influence of the oil crisis that occurred in 1973 and 1979. From the late of 1980s, the publication of lubrication technology became popular, because it is thought that the appearance of a high speed steel roll and the development of lubricant which was suitable for it were carried out. It is understood even that the publication about the roll became popular immediately at this time, as shown in the lower column of Fig. 2. As a lubrication theory, mechanism of the emulsion lubrication, extension of the roll life and advancement of the strip surface property were considered for, there are many publication of the rolling lubrication techniques after 1990. As for the study on numerical analysis of rolling phenomenon, there were general characteristics analysis of tandem strip rolling and an associate 3 dimensional analysis of rolled strip deformation at the late in the 1970s, but 3 full-scale dimensional analysis that made full use of finite element method (FEM) came to be performed afterwards. The study on quality control of materials came to be conducted flourishingly from 1990, and the study on the cooling technology which was the means for materials quality control, came to be gradually performed.
History of number of papers reported in Rolling Theory Committee conventions according of fields (1976 to 2011).1)
When steel production in Japan began in earnest, it was desperate to make full use of the rolling facilities which were introduced from the Western countries. Therefore, it is thought that in our country the research and development of the rolling theory or the rolling technology began in earnest since the late in the 1960s, when the introduction of the computer control system began. In the following, I will try to show the history of the development of rolling theory while comparing the relation between the rolling theories and the rolling technologies which was used practically in rolling process.
In the case of strip rolling, strip is rolled in the same condition in the width direction, so it may be thought that rolling state is plane strain state approximately by neglecting deformation of the strip in the width direction. It is true that the deformation in the width direction cause near the edge of the strip during rolling, but it does not generally have an influence on the rolling load, as it is the local deformation which is limited in the strip edge neighborhood. Therefore, two-dimensional rolling theory was popular at the early stage. After Siebel showed a friction hill for the first time for the object of strip rolling,3) Karman introduced an influence of stress in the rolling direction by satisfying an equilibrium equation of forces.4) In other words, Karman assumed that horizontal stress q was uniform in the thickness direction and a coefficient of friction was constant along the roll gap. It is thought that an application for cold rolling is possible, because this supposition is enough when a coefficient of friction is relatively small in the case of cold rolling. However, it is not applicable when a coefficient of friction is large and adhesion is easy to cause like hot rolling. Therefore, Orowan or Siebel considered shear stress τ equivalent to friction stress to work on the materials surface that the rule which the coefficient of friction influenced was unclear, and thought the equilibrium equation about horizontal force Q to work in a section of rolled strip because the horizontal stress q was not necessarily uniform in the thickness direction.5,6) It was reasonable to calculate the rolling load imposed from rolled strip by integrating rolling pressure distribution closely, but a practical formula for rolling load to help industrially was necessary as there was not the electric computer in this time. Therefore, charts were published for the convenience of spot engineers or relatively simple calculating formulas. They are a diagram of Trinks for hot rolling,7) and a nomograph of Sims8) or Lianis & Ford9) for cold rolling. Furthermore, there are Ekelund’s equation10) and Orowan & Pascoe’s one11) which have been used famously for a long time. As a mood of strip thickness control in the rolling direction increased, calculating formulas with high precision for estimating rolling load and rolling torque came to be demanded. An effort to solve the above-mentioned differential equation closely was made afterwards. The main equations are one of Sims12) for hot rolling and another one of Hill or Bland & Ford13,14) for cold rolling. This effort leads to continuous rolling theory for tandem strip rolling, and it is needless to say that it becomes the big result.
In addition, when flattening deformation causes at the contact region of rolls with rolled strip in the case of cold strip rolling, the real length of contact arc becomes longer than that calculated from its geometric shape. Hitchcock suggested the expression for the roll radius after flattening deformation of rolls.15) In this case, it was introduced under the assumption that a rolling roll became a single arc after flattening deformation and the pressure distribution became into a parabolic form. It was the valuable result of research to calculate rolling load in that time, but it was published in the recent study that the contact arc was not a single arc but in a complicated shape after flattening deformation of rolls in the case of light reduction. The assumption of Hitchcock begins to be contradicted in those days.
In any case, it may be said that two-dimensional rolling theory was almost completed in this time. It must be said to be an astonishment that the potential of technical development of Japan absorbs and digests their research results, and creates the original technologies from them. Economy of Japan had a hard time for securing of the amount of steel production by correspondence with the superannuated facilities before the Korean War broke out in June of 1950 as described above, but the amount of steel production with the active state of the economy would increase rapidly. The first steel rationalization plan including update of facilities was devised and was carried out since 1956, and promising rolling facilities were installed one after another. Therefore, the steel companies in Japan did not become inferior to the Western countries from a viewpoint of the rolling equipment. However, the product quality was insufficient. In such situation rolling engineers and researchers paid their attention to make a formula for resistance flow stress to give more precise prediction of rolling load. The Rolling Theory Subcommittee which is a forerunner of the Rolling Theory Committee started in 1955, and a joint society for the study of resistance flow stress of materials was run by industry-university co-operation combination. As a result of the society, the book whose title was ‘Rolling Theory and Resistance to Deformation’16) was published in 1960. It may be thought that much respect must be paid to the foresight of peoples of these days.
In addition, there are two theories published in this period that had an influence on research and development of next generations. One is the load cell AGC developed by BISRA,17) that is to say automatic gauge control. A gauge meter formula was suggested, which would develop and progress a gauge control technology drastically afterwards. In the head end of the strip, the strip thickness at the exit of roll gap is calculated by the gauge meter formula and is memorized, that is to say lock-on. The unevenness of the strip thickness in the rolling direction can be lost by adjusting a roll gap so that the thickness in the remaining part of the strip agrees with the value memorized. Another one is the tandem rolling theory. When continuous cold rolling is in a steady state, the volume speed is constant at any part of the roll gap which is width x thickness x speed of the strip. When the roll gap or the roll revolutions changes from the steady state and the equilibrium state collapses, the tension between rolling stands and the strip thickness changes according to their variation. Then, the steady state shifts to a new steady state. By expressing the relations between those two rolling steady states in the form of a influence coefficient, the mutual relations of rolling variables can be found and it can explain a continuous rolling phenomenon theoretically in the tandem rolling mill. It can be obtained the guidance of design such as the strip thickness control system and the tension control system for tandem rolling mills by clarifying the mutual relations of the rolling variables. The pioneering studies were carried out about such a continuous rolling theory by Hessenberg & Jenkinns and the others.18,19,20) Research and development for tandem rolling mills had come to be performed flourishingly in Japan since the 1960s under the environment that computer control system had come to be introduced positively and performance of computers improved, by which numerical analysis had become easy to be carried out. Afterwards, the splendid results were obtained one after another in Japan.
It is found from Fig. 1 that high economic growth era began and steel production went into mass production age. The steel companies in Japan began to stray from the technology introduced from the Western countries, and started to research and develop for Japanese original technologies in this time. Then, full-scale application times of the rolling theory was invited, and the book, whose title was ’Theory and Application of Rolling’, was published in 1969 by the Rolling Theory Committee.21) An effort to improve strip thickness precision at the stable region in tandem rolling was made in this time. As a result, the phenomena such as thickness distribution in the width direction which is called strip crown, and 3-dimensional shapes which is called flatness degree came to attract much attention. Therefore, 3-dimensional deformation analysis was necessary to explain the phenomena. However, it was not strict 3-dimensional deformation analysis, and approximate 3-dimensional analysis based on 2-dimensional analysis. On the other hand, the examinations that paid much attention to mill modulus were carried out to improve the accuracy of strip thickness, which led to the beginning of development to the absolute mode AGC that is Automatic Gauge Control. Furthermore, a rolling mill with hydraulic screw down device was developed at the end of the 1960s and became able to change the mill modulus, which came to be introduced into tandem rolling mills in the 1970s. General characteristics analysis of tandem rolling mills became necessary to improve the accuracy of strip thickness in tandem strip rolling. As the performance of computers came to improve suddenly in the same time, it was welcome that characteristics analysis of the complex system such as tandem strip rolling mills became easy to be carried out, in which very many factors influenced each other. The circumstances would be described in detail in the following.
4.1. Approximate 3-dimensional Rolling TheoryFor 3-dimensional analysis of strip rolling, there were the majority of reports in which it was assumed that stress and strain were uniform in the strip thickness direction like the analysis of Karman in 2-dimensional rolling theory. However, when deformation to the width direction is considered into the strip rolling theory, stress and strain in the thickness and width directions are not uniform in the cross section of rolled strip, and the direction of frictional force to work between the roll and strip is different at each position in the roll contact arc.
Yanagimoto solved at first the 3-dimensional stress problem in the sticking friction state for the object of plate rolling under the assumption that the direction of friction force was constant at the entry site and at the exit site from the neutral point of the roll contact arc.22) Troost formed the equilibrium equation under the assumption that the direction of friction force was uniform only in the width direction, but he did not come to solve the stress state without mentioning friction force about the rolling direction.23) Geleji obtained the direction of friction force at each position in the roll contact arc by supposing the relation between the increment of strip deformation in the width direction and that of strip thickness reduction only at the specific domain near the edge of rolled strip, where 3-dimensional deformation of strip was caused.24) In the same way as the theory of Orowan in 2-dimensional rolling theory, Rudisill & Zorowski formed rolling theory by taking into consideration the non-uniform deformation in the thickness direction.25) However, this was not a problem to be able easily to solve as a matter of course. In the case of sticking friction, this was solved by using some suppositions and approximations, but it was a rolling theory far from practicality because the material flow in the width direction was ignored. In the other hand, Stone & Gray took into consideration only bending of work rolls for a 4 high rolling mill which was most common, under the assumption that the work rolls were the beams placed on the elastic base.26) Beside, Shiozaki took into consideration the bending of back-up rolls too with the above.27) Shohet & Tousend took into consideration the bending of rolls caused by shearing force besides bending moment.28) Shiozaki expressed a spring model for elastic deformation of the rolling mill and plastic deformation of the rolled strip, which divided the rolls and the strip into many pieces in the width direction. The distribution of rolling pressure and that of strip thickness could be solved by the spring model, so that the former was consistent with the later. It was epoch-making for those days that the effect of roll bending force could be estimated qualitatively by using the spring model.
4.2. Mill ModulusA housing of rolling mills finally supports the rolling load through rolls, bearings, roll positioning screws and hydraulic cylinders. The mill modulus is composed with them all. Every parts of rolling mills are deformed elastically, on which rolling load is imposed, but unexpected deformation has a serious influence on rolling operation because rolling load is very great. It is difficult to avoid the fact that the factors of some rolling condition change in the practical rolling operation. When there is a change in outside factors such as thickness at the entry of roll gap, flow stress of rolled strip, tension between rolling stands and friction coefficient between work roll and strip, the rolling load changes necessarily and it is thought that thickness at the exit of roll gap changes in proportion to it. From this fact, it may be said that the sensitivity of the thickness at the exit of roll gap for the change of rolling load is small in the case of a rolling mill with large mill modulus. On the other hand, rolling rolls are finished by cutting and grinding processing, but they are not able to be accomplished without eccentricity between the barrel and the neck of rolls. When the rolling rolls with eccentricity rotate and swing, by which the thickness at the exit of roll gap changes such as the roll gap is controlled. If mill modulus is small, the change of roll gap seems really small, which is caused by swinging of the roll during rotating. Therefore, it is found that small mill modulus is effective for the change of roll gap caused by inside factors of rolling mills. In addition, in the case of controlling the thickness of rolled strip, it has very much effect for the thickness control by a screw-down device with large mill modulus, but it is very effective for the thickness control by tension between the rolling stands with small mill modulus. As there was close relation between mill modulus and rolling properties in this way, the studies on the characteristic of rolling mills in which mill modulus was considered and the studies on the optimum mill modulus were performed.29,30,31,32,33,34,35,36,37,38) As mentioned above, the optimum mill modulus is different in the stages of rolling operation, or in the properties of disturbance caused by outside factors. The screw down device with hydraulic pressure system was developed for the purpose of high speed and high response, and the mill modulus control came to be performed for a choice of the optimum mill modulus according to a rolling purpose by using its high responsiveness.39,40,41) The results of these researches and developments will lead to absolute mode AGC technology later and will improve strip thickness control technology drastically.
4.3. Static Continuous Rolling Theory for Tandem Rolling MillsIn the case of strip rolling, it is general that there are 6 to 7 rolling mill stands in the finishing train of the hot strip tandem rolling mills, and there are 4 to 5 rolling mill stands in the cold strip tandem rolling mills. Explaining the case of cold strip mills for example, there are many rolling factors such as strip thickness at the entry and the exit of roll gap, tension between rolling stands, coefficient of friction, roll gap, roll speed, roll diameter and flow stress to deformation. As these factors lie for all stands, dozens of rolling factors for the whole rolling mills will have an influence each other by mediating tension between rolling stands. It is generally a wiser policy to consider all stands as one system than to examine the connection of each rolling factor individually because very many rolling factors change with connection mutually in this way. As for a concrete technique, the simultaneous equations for the whole rolling stands are formed on a basis of some equations of constant volume speed and agreement of thickness and tension, and are solved to get general characteristics of tandem strip mills. It is called continuous rolling theory that the characteristics of tandem rolling mill can be calculated by such a technique. When continuous rolling theory is classified, it is classified into two of the dynamic continuous rolling theory with a factor of time and the static continuous rolling theory without a factor of time. About such a static continuous rolling theory, the extremely initial studies were performed in the 1950s as already described, but it was mainly researchers and engineers in Japan who developed and compiled them, and applied them to practical rolling process, which gave concrete results.42,43,44,45,46) It is the feature of this static continuous rolling theory that the mutual influence degree of each rolling factors between the two steady state can be grasped by ignoring the changes of the rolling factors in the transitional state, when the tandem rolling mills shift from one steady state to another steady state through an transitional state. In the steady state, the volume speed of rolled strip is constant at each stand of tandem rolling mills. The equation for this condition expresses the relations between each stand of tandem rolling mills. For example, as an example described here, the influence which roll gap change (ΔSr/h)i at each stand gives on the change of the aimed thickness for the product ((Δh/h)5) is largely different between with and without controlling the tension between rolling stands. In other words, the influence of the 1st stand is the largest when a roll gap is changed without tension control between rolling stands, but the influence of the down-stream stand (the 4th or 5th stand) is large with tension control between rolling stands not to change. It is found that the static continuous rolling theory is necessary to construct the strip thickness controlling system with high precision by understanding the characteristics of tandem rolling mills and finding the optimum controlling method in this way. In addition, as the relations of changes of each variable between the two steady states become clear, the relations of each variable can be found by judging from the difference between the current rolling condition and the next rolling condition. Therefore, the next rolling draft schedule can be predicted on the basis of the current rolling draft schedule. There were many examples that the static continuous rolling theory was applied to the decision of draft schedule in this way. Furthermore, many attentions were paid for the above-mentioned rolling mills with the hydraulic screw-down device to be enacted in variableness with mill modulus. It was shown the concept for the optimum mill modulus distribution that the controllability of tandem cold rolling mills could be raised by changing the mill modulus of every rolling stands in tandem cold rolling mills.46)
It may be said that the seed of the development of dynamic continuous rolling theory was already sprinkled in this time in response to the performance enhancement of electric computers, which was large capacity and speed up of computers.
The high economic growth of 1960s ended under the influence of oil crises caused in 1973 and 1979 in this period, and a demand to the full-scale innovation of rolling process technologies increased including energy saving. It was made the effort to reduce the off-gauge of the non-constant region near the top and bottom end of strip coil as much as possible for the purpose of improvement of rolling yield rate and dimensions precision of rolled strip, by which controlling technology for strip crown and shape came to attract much attention. Therefore, the main innovation technologies in this period are a full continuous cold rolling mill, and a new rolling mill with the shape controlling device, which is called HC mill.
5.1. Development to 3-dimensional Rolling TheoryThe subject of concern at this time was to improve the controlling system for the distribution of thickness in the width direction which was called strip crown control or shape control, as gauge controlling system of strip in the steady state reached the level of completion, anyway. In other words, the demand became higher to produce the strips which had the thickness distribution as little as possible in the width direction and the superior flatness. Generally strips have the crown with thick gauge distribution around the center of strip width and the edge-drop with gauge falling sharply near the both edges of strip width. The non-unifomity of strips gauge is based on elastic deformation of rolls caused by rolling pressure. The poor flatness causes in the case that longitudinal strain distribution of strips in the rolling direction is not uniform in the width direction, which is caused for the reason that reduction of strips thickness is not uniform in the width direction and metal flow in the width direction is large near the width edge of strips. Therefore, it is necessary to take the difference of deformation of rolls and strips between positions along the width direction into account to analyze these problems theoretically. 3-dimensional analysis for plastic deformation of strips must be carried out with elastic deformation analysis of rolls. The rolling theory for 3-dimensional deformation of strips developed after the 1980s, which contributed greatly to development of the strip rolling technologies.
It is the 1970s that the base was made. At first, the direction of friction force is decided by the flow of materials, and the material flow changes according to the stress state. Therefore, stress must be calculated with strip deformation to demand it without assuming the direction of friction force. Suzuki & others are first to try such an analysis.47) However, in their study the relative displacement of material to rolls and tension distribution at the entry and the exit of the roll gap were expressed as a special formula. Tozawa & others took shear stress in the width direction caused by width spread into account and solved this problem sincerrely.48) Sugiyama & others analyzed strip deformation three-dimensionally for a domain of strip edge neighborhood using the relation of friction force introduced by Gelegi under the assumption that material deformed two-dimensionally around the width center of strips.49) However, it was supposed that the stress in the rolling direction did not have the distribution at the exit of the roll gap. Furthermore, there were also research reports in which width spread of strips was analyzed using the energy method.50,51) The energy method is effective in analysis of the problem that it is hard to handle by the elementary analytical method. If the field of velocity of material flow is assumed which expresses well the practical deformation and has appropriate freedom in it, the energy method is effective and simple analytical method. As for the elastic deformation of rolls, Tozawa & Ueda handled flattening deformation of the surface of work rolls caused by rolling pressure as the partial compressing deformation imposed on the surface of a half infinite body with bending deformation of rolls obtained separately to it.52) In addition, as flattening deformation might be estimated excessively according to this way, some modifications to this were supposed by Nakajima & Matsumoto, Kohno & others and Mizuno & Kanamori.53,54,55) Bending deformation of rolls causes the change in the sectional profile of rolls in accordance with the effect of Poisson’s ratio. Therefore, displacement of the surface at the top and bottom of rolls caused by elastic deformation is different from displacement of the central axis of rolls. Kuhn & Weinstein examined this.56) The profile of the strip surface became able to be predicted with considerable precision, so the lack of control ability of present tandem rolling mills for strip crown and shape became clear. A new rolling mill with higher ability to control strip crown-shape than conventional 4Hi mills was developed in 1974, which was called HC mill.57) As this rolling mill with 6Hi structure could made work-rolls to be small, the control characteristic of deformation shape of rolls was improved by shifting a middle roll in the width direction. This rolling mill was put to practical use for cold strip rolling. The development rush of rolling mills with high control ability for strip crown-shape began with appearance of this rolling mill. The rolling theory to improve the precision of strip crown-shape control progressed remarkably for the development and practical use of such rolling mills with high control ability of strip crown-shape.
5.2. Dynamic Continuous Rolling Theory for Tandem Rolling MillsDynamic continuous rolling theory means a technique to obtain transitional characteristic that a stable rolling state is destroyed by various kinds of rolling disturbances or change of rolling condition and the next stable rolling state is revived. For example, the rolling disturbances are the change in friction coefficient of roll gap and oil film thickness of roll bearings during acceleration and deceleration of rolling mills, and the change in strip thickness at the entry of the roll gap. The analysis of dynamic characteristic becomes to be an essential technique for analysis of the change of rolling state and evaluation of rolling behavior with various control systems used together when some disturbance occurs. Most of the theoretical constitution is the same as the static continuous rolling theory, but the two rolling theories are different from the following viewpoints. One is that the dynamic continuous rolling theory has the time factor, and other one is that the condition of volume speed uniformity does not hold up in the dynamic continuous rolling theory, which is assumed in the static continuous rolling theory. In other words, it is necessary to consider the change with time of tension between each stand in cold strip rolling, and to consider the change with time of loop between each stand and the change with time of strip temperature at each stand in hot strip rolling.
The analysis of dynamic characteristic began formerly for analysis of cold tandem strip rolling. R. A. Phillips, and Sekulic & Alexander carried out the analog simulation of AGC system of cold tandem strip rolling, but various kinds of abbreviations were adopted from the reason that number of factors was confined for an analog computer used.58,59) When number of variables increases in the case of tandem strip rolling mills, it is very difficult to put the change domain of all variables in the dynamic range of analog computers.
It was impossible in this way to design a real dynamic control system and examine facilities of a new form of tandem rolling mills by approximate handling with analog computers. The mood which was going to use the digital computer in the rolling field increased rapidly in those days in our country, which came to attract the spotlight as means of numerical analysis in the various field of engineering. Just at that time, new capital investment was carried out lively in our steel companies. The strong need for improvement of productivity and quality and the eager request of the rolling engineers and researchers in our country to surpass the conventional techniques imported from foreign countries became a driving force of technique development in this field. Under such a background, the dynamic continuous rolling theory for strip tandem rolling was compiled since then mainly in our country. The calculation methods of numerical analysis for dynamic characteristic of cold strip tandem rolling mills have a linear numeration method and a non-linear numeration method. The latter is a method to calculate a non-linear simultaneous equation in the same form63) whereas the former is a method to solve a linear simultaneous equation obtained by Taylor expansion.60,61,62) In addition, many papers were published about analysis of the dynamic characteristic for hot strip tandem rolling mills.64,65,66,67,68) As these analyses of the dynamic characteristic for strip tandem rolling mills were enabled, the following innovative technologies were enabled in the gauge control technology for strip tandem rolling process. They are (1) the gauge control technology during accelerating and decelerating of strip tandem rolling mills, (2) the technology to change the aimed gauge through threading of strip, and (3) the gauge control technology at the top and bottom region of the strip coil. Particularly, the technology to change the aimed gauge freely on the fly and the full continuous cold strip tandem rolling technology69,70) based on it became the first step of the trend of continuation of various processes in cold strip rolling afterwards. The development of this technology improved drastically production capacity, product quality, product yield and reduction of number of labors, which came to raise the competiveness of steel products of our country remarkably. As mentioned above, the analysis of the dynamic characteristic for strip tandem rolling mills is an indispensable technique to design new rolling methods and control systems. It is not exaggeration even if it is said that such rolling technologies could not be developed without this tool or the dynamic continuous rolling theory for tandem strip rolling.
5.3. Mill ModulusElastic deformation of rolling mills came to be predicted precisely, by which the absolute-value AGC came to be introduced. The details of elastic deformation are shown as follows: the deformation of rolls is 40–70%, that of mill housing is 10–16%, that of screw-down device is 4–20%. Deformation of rolls is overwhelmingly large. As for deformation of rolls, they are the bending deformation of the central axis, flattening deformation of the contact parts between roll and strip, and that between each roll. In the case of 2-hi rolling mills, bending deformation of rolls appears directly in the roll gap, but in the case of multi-hi rolling mills, bending deformation of work-roll is smaller than that of back-up roll under the influence of contact part. Therefore, flattening deformation increases with number of the roll contact points. These findings are the results of calculation methods that were developed to improve precision for predicting strip crown. Furthermore, topic in this time is that a rolling mill with a hydraulic screw-down device was introduced into tandem strip rolling mills to improve precision of gauge control system. The control method of the hydraulic screw-down device was a mechanical servo method71) at first, but it came to be an electric hydraulic servo method39) developed afterwards, by which screw-down speed was faster 8 times than the conventional one. The hydraulic screw-down device was a powerful control technique to realize a highly precise thickness, which improved precision of thickness remarkably in a high–speed rolling state. However, on the occasion of applying the hydraulic screw-down rolling mill to tandem strip rolling mills, a new issue was raised to have to avoid the mutual interference caused by responsive imbalance of the roll gap control system and the tension control system, which made a way to the non-interference control technology. As described above, simulation of the continuous rolling by combining a control model with models of the rolling theory was carried out under the trend of continuation of various processes, and optimization of the whole control system came to be realized.
The real low economic growth era began, and the development of technologies for great variety and small quantity of products was carried out to deal with high quality of the steel products and demand of the steel market for diversification of consumers’ tastes, namely the rolling technology which could custom make the various products freely in the rolling process. At the time when the past basic research and development flowered, development of many new type rolling mills with the crown-shape control function were reported.72,73,74,75,76,77,78) A pair cross rolling mill with a big effect of profile control for hot rolling mills was put to practical use,79) which became a standard rolling mill for the profile control of hot strip rolling afterward. In the latter half of the 1980s, Japanese steel companies advanced abroad one after another by joint venture establishment including the United State where investment of the raw material industry decreased, and the new rolling technologies developed in Japan came to be exported.
6.1. Application of the Finite Element Method to 3-dimensional Rolling TheoryThe finite element method which is called FEM came to be used very much according to improvement and progress of calculation technology in response to large facility and high performance of electric computers. However, for 3-dimensional problems, element division had to be performed in the three directions, by which number of the elements increased, so calculation time or memory capacity became a subject of discussion. Therefore, shortening calculation time including reducing number of the elements is one problem for application of this analysis. Li & Kobayashi analyzed the rolling state of a slab by 3-dimensional rigid-plastic FEM, and demanded width spread under the assumption that the velocity of strip deformation was distributed linearly in the width direction.80) Mori & Osakada solved this problem by accepting compressibility of materials, but it was an approximate 3-dimensional analysis in which the element division was two layers in the thickness direction, so their calculation time was at the same level as that of 2-dimensional problem.81) Afterwards, Toyoshima & Ikeda analyzed strip rolling by the penalty method,82) and Yanagimoto & others did so by the Lagrange multiplier method.83) By the method of Yanagimoto & others, calculation time becomes longer than other methods, but the analysis close to real phenomenon is possible. Komori & others suggested a new analytical method to shorten calculation time without cutting down analysis precision.84) This is the method that an energy function about the whole deformation domain is not minimized at a time and it is divided into a lot of sub-regions, and the energy function about a large domain which is a set of some sub-regions is minimized, whose action is repeated by moving the medium size domain sequentially. It is shown that calculation time is drastically shortened. In addition, the method was suggested which combined the 3-dimentional analysis of materials by using the conventional slab method and that of rolls deformation to demand the strip profile with high precision.85,86) Furthermore, the systems for predicting the strip profile by combining the analysis of rolls deformation and the rigid–plastic FEM of the compressible materials used to analyze strip deformation were performed.87,88,89,90) Therefore, as calculation of strip crown and shape with high precision came to be possible at this time and new rolling mills with the strong function for crown-shape control were already developed as mentioned above, it may be said that strip crown-shape control technologies progressed drastically. The rolling analysis methods came to be applied to the more complicated phenomena with large-capacity and speed-up of electrical computers. The research for analysis of the poor flatness91,92) and the rolling theory for the thin and hard strips93) were announced.
6.2. Development of the Width Rolling TheoryA casting process almost became a continuous casting machine, and a width changing technique was examined at a time in the continuous casting process, but it was found to be difficult technically. It became necessary to change the width of a slab widely by a rough rolling train in the hot strip rolling mill and put together the range of slab width casted. The researches were performed for the formation of wide width reduction of a slab, the characteristic of the dog-bone shape in reducing the width, the analysis of edge rolling by the rigid-plastic FEM, and the width control method.94,95,96,97) An edge rolling mill is consists of rolling mills of vertical type (V type) and horizontal type (H type) which is called a rough rolling mill. As large diameter rolls cannot be applied by the structural limitation, plastic deformation causes only near the width edge of a slab by width reducing with the V-rolling mill. And large dog-bone shape forms. At next H-rolling the formed dog-bone shape is flattened, and width spreads more than that of normal rolling. Therefore, the effect of width reducing decreases half in the next H-rolling. In addition, the production yield worsens because a crop occurs at the head and tail end of a slab. These phenomena came to be explained by numerical analysis, and it was found that these could not be improved by a rough rolling mill of the conventional V-H type, which led to practical use of a pressing machine for width sizing.98) The development of the width press sizing machine promoted efficiency of the width control technology, and the range of gathering up the width variation of the casted slabs came to be extended to around 400 mm. The automatic width control technology (AWC) was developed which was consist of the technology for setting the width reduction by using the model to predict the width change in the V-H rolling, the technology for the width reduction pattern control used in the unsteady state of the top and end region of a slab, and the technology for the feed-forward control by using the actual width measured at the entry of a rough rolling mill and the feed-back control by using the actual width measured at the exit of a rough rolling mill in the middle region of a slab.99) These new technologies improved precision of the width and reduction of crop-loss at the head and tail end of a slab.
As for the problem of crop-loss at the head and tail end of a slab, the development of the control technologies for crop-shape was carried out earlier in a plate rolling process. The model was developed to express the influence of free deformation at the width edge of plates and width spread on the distribution of metal flow in the rolling direction, by which the plate thickness could be distributed in the rolling direction by changing the roll gap while rolling a plate. The new rolling technologies were put to practical use, which controlled the thickness distribution in the rolling direction on the way to the final pass or reduced plate width by an edge rolling mill such that the plane shape of plates after the finish rolling became rectangular. Their control effects were published.100,101,102)
6.3. Technology of the Full Continuous Hot Strip RollingThe connecting of the continuous cold strip rolling process had been intended early in the 1970s, but that of the continuous hot strip rolling process was late. The connecting of the continuous casting process and the continuous hot strip rolling process aimed at the energy saving to utilize the heat of a slab produced in the continuous casting process. The connecting technology is the synthesis technology of every engineering field such as the heat technology, the lubrication and friction technology like the roll abrasion, the process managing technology, the computer utilization technology and others as well as the gauge control technology and the crown-shape control technology. The continuous hot strip rolling mills were put to practical use which realized the highly precise and flexible production technology by combining the innovative technologies of many engineering field.103,104) As for the main technique, an example of the hot strip factory at Yawata steelworks of Nippon Steel Company is explained easily in the following. As the roll surface which came in contact with the edge part of the strip was worn partially in the hot rolling, the coffin schedule had to be taken before to roll gradually the strips with the narrow width to the wide width. However, the schedule-free rolling was realized in which the surface of the work-rolls became smooth by letting the work-rolls shift in the width direction and scattering the roll abrasion. In addition, the width change of the casting slab was necessary in the hot strip rolling process, the H-V rough rolling mill enabled the width reduction of up to 350 mm which had a large width reduction device coupling H-V rolling mills closely. Furthermore, the above-mentioned HC rolling mill was applied to the continuous hot strip rolling mills at first in the world and came to be able to control the crown–shape of the strip freely. Afterwards, a lot of the continuation technologies came to be put to practical use in the hot strip rolling process.
The research and development related to the new materials ended which steel companies started for the low economic growth in the 1980s. It is said that the remarkable environment change surrounded the Japanese society or steel industry in Japan in the middle of the 1990s and the international competitiveness was being lost so that the continuation of the company was asked which was not experienced conventionally. The technological innovation to have a production technology with cost competitiveness was required, and besides, the appropriate response as the manufacturing industry came to be demanded for the environment change to surround the steel industry including the social request to the issues of earth environment, energy, and resources recycling.
Following the fully continuous cold strip tandem mills developed 25 years ago, the endless hot strip tandem mills was realized for the first time in the world,105) and the cold strip tandem mills for a thin gauge with the fastest speed in the world was constructed at this time.106) In addition, the above-mentioned pair cross mill was applied to the cold strip rolling mills and the effect for the edge drop of strips was confirmed, which opened the way of application to the cold strip rolling mills.107)
7.1. Crown-shape Control Technology to Edge Drop Control TechnologyIt may be said that the crown-shape control technology was almost completed in the 1980s. The concept for the crown-shape control is briefly explained next. The ways to control crown-shape are to make a strip crown into the target crown without strip shape disturbance simultaneously by predicting the strip shape with formulas to express the strip crown change and the shape change. As for the strip crown, the way to introduce the transcription rate and the heredity coefficient are well used in the hot strip rolling.108) The transcription rate means how much the strip crown formed under the uniform rolling load is transcribed into the strip crown after rolling, and the heredity coefficient means a constant to express how much the strip crown at the entry of the roll gap influences that after rolling. In the cold strip rolling, the strip crown at the entry of the roll gap is inherited approximately 100% except the edge-drop region of strip width. However, when there is non-uniformity in the width direction such that the length at some region of strips comes to be larger than that at other region after rolling, the longitudinal tensile stress of the former becomes smaller, and the rolling load per unit width grows bigger, and the roll deformation grows bigger too. As a result, the length at the same region does not become so large. This phenomenon is the shape stabilization mechanism caused by tension feed-back effect. The theoretical examination about the strip shape is performed partly, but an empirical formula is often used practically. The edge-drop is controllable without disturbing the strip shape even in the cold strip rolling unlike the strip crown, which is caused by the roll flattening and the 3-dimensional deformation at the width edge of strips. Two methods are now suggested for the actuator of the edge-drop control. One is the method to reduce the edge drop such that the work-rolls are shifted in the width direction by a rolling mill with the work-roll shift device, and the strip edge in the width direction is rolled into the form to be thicker.109,110,111) The other is the method to apply a pair cross rolling mill with the high controllable function for the strip crown and shape. It is found that it is applied to the upper stream stands of the cold strip tandem mills, which is able to reduce the edge drop. It was put to practical use in the cold tandem strip rolling mills with the function for changing the cross angle through a strip threading.112) In the cold strip rolling with the pair cross rolling mill, it is checked by the theoretical analysis that the thickness at the strip edge becomes thicker as the cross angle increases.113) The logics for controlling the edge drop are just announced recently, and it is difficult to judge their superiority or inferiority. However, it is important that the heredity coefficient and the transcription rate are quantified like the crown-shape control system. In such a meaning, it is thought that attention is paid to the method suggested by Ikeda & others, in which the behavior of edge-drop is formulated by the concept of the heredity and transcription similar to the crown-shape control, and the control logic displays a rolling phenomenon precisely, and the control quantity is easily demanded.114)
7.2. Expansion of Application of the Finite Element MethodThe residual stress remains in strips after rolling, but if the compressive stress is large, the strip performs buckling, and it is thought that the poor flatness occurs in the strip. Ishikawa & others demanded the stress distribution at the exit of the roll gap to the lower stream side, and judged the outbreak of the poor flatness such as center buckling and wavy edge by the buckling eigenvalue analysis.115) And then they obtained the shape after buckling by the large deformation analysis using the FEM. Ishikawa & others116) and Yamashita & others117) examined the occurrence of cross buckling by using the FEM under the assumption that it was caused by the shear stress. Komori and others analyzed too the occurrence of cross buckling by the energy method under the assumption that the elastic buckling occurred continuously at the micro domain by the residual stress.118) They explained the outbreak mechanism of herring-bone as described next.119) It is thought that the heat scratch occurs when the thickness of the oil film in roll gap becomes less than a certain value by the increase of the roll bite angle at the entry of roll gap. If it occurs once, the thickness of the oil film becomes thick by decreasing of roll bite angle with increase of the roll flattening caused by increase of the rolling pressure and the heat scratch disappears. Furthermore, the roll flattening decreases by decreasing of rolling pressure caused in advancement of rolling, and the roll bite angle comes to increase, which causes the heat scratch again. It is explained that the periodic repetition of this phenomenon becomes herring-bone. The analysis for the slight reduction rolling appeared here and there in the past. The analysis in which the material was assumed to be elastic-plastic and the roll flattening deformation was taken into account by modification of Orowan’s and Karman’s researches,120,121) and the analysis to use the dislocation theory of the continuation distribution122) were announced. These researches for the slight reduction rolling were performed as the 2-dimensional problem, but it may be still said that there was considerable progress in handling the materials as elastic-plasticity from rigid-plasticity. A considerably complicated phenomenon became able to be clarified by application of the FEM because of the technology advancement of a computer with high performance and speed-up.
For the purpose of the low alloy high strength steel which was called HSLA, the research to predict the material quality in the hot strip rolling was carried out. When the thermo-mechanical control process, which was called TMCP and had been developed for plate rolling, begun to be applied to the field of the strip rolling, the studies on the predictive control of material quality was started. The metallurgical formulas for the change of material structure caused by hot processing such as work hardening, dynamic recovery, dynamic recrystallization, static recovery and static recrystallization were announced formerly by Yada & others.123) As for change of the micro structure in hot processing, these were arranged as appropriate regression equations by the quantitative approach of the change of internal micro structure before and after many compression tests from the results observed by a microscope. These metallurgical formulas are the data of materials measured at the constant strain velocity and the constant temperature, but it is impossible to calculate the internal micro structure during and after hot rolling because the strain velocity and the rolling temperature change by the moment during hot rolling. Therefore, the technique to calculate the change of the internal micro structure depending on the history of stain velocity and rolling temperature was necessary and some techniques were suggested in the 1990s.124,125,126) In addition, the internal micro structure of material after hot rolling changes while cooling down. The model to analyze the incremental phase transformation for the purpose of the nucleation mechanism in the grain boundary was formulated by Yanagimoto and others, based on the models127,128) targeted at the plain carbon steel for ferrite, pearlite, and bainite transformation.129) It can be said that the formation process of the structure corresponds to the material genome to make the product property in the rolling process, and the mechanical property of strips corresponds to the material genome to clarify the material property after rolling. The role of rolling process and rolling theory is to make the products from a slab. It is thought to be essential that the engineers and researchers for rolling collaborate with those for materials to improve the technology for prediction and control of quality.
7.3. Technology of the Full Continuous Hot Strip RollingAs described above, in 1996 the endless hot strip mill was operated ahead of the world in the third hot rolling factory at Chiba steelworks of Kawasaki steel company.105) In this facility a rough bar is joined in front of a finishing mill train, in which it is rolled consecutively without a break. Then it is cut to a coil right in front of the down-coiler. Of course, it is the essential technique to change the target gauge on the fly. It was published that the unevenness of thickness near the head and tail end of the strip was large conventionally, but the equalization of material quality was realized along the whole length of a coil owing to this process. It was published too that the production of thinner strips became easy by improvement of threading stabilization and the productivity increased up to 20% drastically. Furthermore, the request to develop the roll material with a little abrasion became strong by demand such as a schedule-free technology of the hot strip rolling, and the roll of high speed steel for hot strip rolling came to be adopted to the hot strip rolling mills.130,131,132)
There were few reports of research and development of rolling because of the economic slump after the 21st century started, but the development of a manufacturing process of steel with supper fine grain begun as a national project for the purpose of development of high strength steel to save non-ferrous components of steel such as the rare metals which jump up in price of products. As the result, the production technologies of the high strength steel with supper fine grain by the ultra-speed multi-passes rolling were announced.133,134) In addition, the endless hot strip rolling mills were operated newly, and as for joining technology of a rough bar which was a key technology, the friction welding technology using strong shear deformation was developed.135) There are an induction welding technology and a laser welding technology except this technology for the joining technology. These three joining technologies became ones developed in Japan. Furthermore, the study on the rolling theory came to challenge more complicated and more difficult matters. A new type intelligent rolling mill was developed and was put to practical use for the purpose of in-line leveling of high performance steel plates which are mainly composed of high strength steel plates for shipbuilding.136,137,138) It may be said that this is the facility to make full use of the rolling theory.
8.1. Technology of the Material Quality ControlAs for a numerical analysis technique to control the internal structure by the processing process,139,140,141,142,143) Yanagimoto and others showed an acquisition method of material genome based on the results of compression tests. It is the method to identify the material genome which is necessary to analyze the internal structure by obtaining the followings from ① to ⑤: ① a load-displacement curve by one step compression tests, ② one axis compression flow stress curve (at constant strain velocity and temperature) by the reverse analysis of the load-displacement curve, ③ a load-displacement curve by two steps compression tests, ④ one axis compression flow stress curve (at constant strain velocity and temperature) by the reverse analysis and the softening rate, ⑤ the grain size by the quenching structure freeze tests. In addition, it was shown by calculating the rolling load in the actual hot strip tandem rolling144) that analysis precision of rolling load was good according to the internal structure analysis assuming the dislocation density to be a parameter because of considering the residual dislocation caused between the stands. However, the rolling load was underestimated so as to go to the latter stand of high speed as strain accumulation between the stands was not considered in the equation of Misaka & others145) to be used frequently. Application of these analytical techniques to an actual rolling mill is going ahead.147,148) In this case, the relation between rolling conditions and mechanical characteristics is formulated by equations of regression through the crystal grain size to be provided by the internal structure analysis. It is thought that the material qualities of products will be able to be predicted and the manufacturing processes to elaborate materials will be able to be designed in the future by the full-scale application of such a calculation science.
8.2. Development of the Rolling Theory2)It may be said that the researches of the strip rolling theory began to challenge to the considerably difficult phenomena. Therefore, when the rolling theoretical studies published from the late in the 1990s are surveyed, there are the rolling theories including the region of minus forward slip,149) the 3-dimensinal deformation analysis of the cold strip in a cross rolling by the rigid-plastic FEM,150) the combination analysis of the strip rolling by the rigid-plastic FEM and the flattening deformation of rolls,151) the minimum thickness in the cold strip rolling,152) the vertical buckling and the cross buckling in the light reduction rolling of a very thin strip,153,154) and the study on the roughness transcription in the light reduction rolling as the basic examination result.155) The investigation of the elastic-plastic analysis is necessary to clarify the phenomenon of the light reduction rolling. There were the studies that applied the elastic-plastic FEM for a long time,156,157) but the light reduction rolling theory by the non-arc roll flattening shape,158) the analysis of stress and strain of the strip in the light reduction rolling,159) the study on the non-uniform deformation of the strip and the removing process of the yield point elongation in the light reduction rolling160) and others were published recently. The calculation of the elastic-plastic FEM progresses remarkably in comparison with that of old days, and as for the commercial program, the elastic-plastic FEM becomes main current. About the light reduction rolling, there are still unexplained phenomena and the results of the future researches are looked forward to. After 2000, the number of publication of paper related to rolling decreases sharply in our country. On the other hand, that has a considerable number in the Western countries and Southeast Asia. Many matters investigated in Japan in the past are surely published, but it is a fact that new knowledge is found those contributions to technological advancement of a measuring instrument or an analytical instrument. It is thought that it is necessary to continue research and development because our country has to maintain the international competitiveness of the material industry in predominance. I want to expect that it is over for the unnecessary concern whether it is only me who worry that it is not so far when the material industry of our country lose the international competitiveness in the remaining situation.
The studies on the rolling theory intended for the extensive rolling such as a shape, a wire, a rod, and a pipe as well as a strip, but I limited to a strip rolling to make this reports. In addition, a very large number of papers are published, but the papers picked up in this report are only a part. I feel that I am sorry for their authors whom I was not able to pick up, but I want you to forgive me. In addition, I left out the control theory, the lubrication theory and others which supported the rolling technology innovation except for the rolling theory. In the future, the calculation science with rapid advancement and high precision will come to be necessary, and the high durability of the rolling rolls and the quantification and theorization of lubrication in rolling process will be expected. Furthermore, the research and development of the innovative rolling technology will be expected, which is different from a conventional conception.
