US3882709A - Method for controlling the profile of workpieces on rolling mills - Google Patents

Method for controlling the profile of workpieces on rolling mills Download PDF

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Publication number
US3882709A
US3882709A US406352A US40635273A US3882709A US 3882709 A US3882709 A US 3882709A US 406352 A US406352 A US 406352A US 40635273 A US40635273 A US 40635273A US 3882709 A US3882709 A US 3882709A
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United States
Prior art keywords
workpiece
profile
crown
rolling
stands
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Expired - Lifetime
Application number
US406352A
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English (en)
Inventor
Toshiharu Kawamoto
Yoji Itoh
Kouji Hiyoudo
Kenya Fukushima
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Nippon Steel Corp
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Nippon Steel Corp
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B37/00—Control devices or methods specially adapted for metal-rolling mills or the work produced thereby
    • B21B37/28—Control of flatness or profile during rolling of strip, sheets or plates
    • B21B37/38—Control of flatness or profile during rolling of strip, sheets or plates using roll bending
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B1/00—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations
    • B21B1/22—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length
    • B21B1/24—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a continuous or semi-continuous process
    • B21B1/26—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a continuous or semi-continuous process by hot-rolling, e.g. Steckel hot mill
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B1/00—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations
    • B21B1/22—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length
    • B21B1/30—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process
    • B21B1/32—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process in reversing single stand mills, e.g. with intermediate storage reels for accumulating work
    • B21B1/34—Metal-rolling methods or mills for making semi-finished products of solid or profiled cross-section; Sequence of operations in milling trains; Layout of rolling-mill plant, e.g. grouping of stands; Succession of passes or of sectional pass alternations for rolling plates, strips, bands or sheets of indefinite length in a non-continuous process in reversing single stand mills, e.g. with intermediate storage reels for accumulating work by hot-rolling
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21B—ROLLING OF METAL
    • B21B27/00—Rolls, roll alloys or roll fabrication; Lubricating, cooling or heating rolls while in use
    • B21B27/06—Lubricating, cooling or heating rolls
    • B21B27/10—Lubricating, cooling or heating rolls externally
    • B21B2027/103—Lubricating, cooling or heating rolls externally cooling externally

Definitions

  • ABSTRACT There is described a method for controlling the profile of a workpiece on a rolling mill, wherein the workpiece is imparted with a predetermined profile in the roughing stage which is suitable for further control in the following finishing stage.
  • the desired profile of the workpiece is attained by adjustment of one or a combination of factors including modifying the rolling loads of the respective roller stands preceding the last stand, cooling of the rolls, and changing the rolling pitch.
  • the final shape control of the workpiece is carried out on the last stand.
  • the instant invention relates to a method for controlling the profile of a plate being rolled on a rolling mill to a desired shape.
  • a rolled plate actually contains, variations in its thickness both in the transverse and the longitudinal directions.
  • the variations in the transverse direction which is across the width of the plate is expressed in terms of the crown and the wedge which together define the profile of the plate.
  • the Crown is the difference between the thickness along the longitudinal centerline of the plate and the thickness at the longitudinal side edges of the platev
  • the Wedge is the difference in thickness between the front and rear ends of the plate (lzw 12d).
  • the present invention contemplates solving the problem of how to distribute the correction in the crown and wedge values to a number of roll stands in the roughing and finishing stages or mills.
  • the present invention is supported by the findings in these studies and is directed to a method which is capable of providing an optimum profile control.
  • the workpiece is preferably rolled in two stages or mills: the roughing mill and the finishing mill.
  • the workpiece is imparted with a rough profile in the roughing stage to a degree suitable for facilitating final shaping into the desired profile in the following finishing stage.
  • the roughly profiled workpiece is finished into the desired profile with high precision in the finishing stage of the rolling.
  • the rolling load required to obtain the desired profile is then distributed to all of the roll stands in the finishing stage with the exception of the last one which performs only shape control.
  • a large plurality of roll stands there may be employed a system using one or several reciprocating multi-roll stands, while distributing the rolling loads to each pass.
  • the load distribution as mentioned above should preferably be applied also to the roll stands in the roughing stage.
  • the profile control during rolling is performed on the basis of factors such as adjustment of the roll cooling temperature and adjustment of the rolling pitch.
  • the rolling profile can be simulated in terms of an even ordered function whose constants correspond to the control factors in actual rolling. It is therefore possible to control the rolling profile by adjusting of the constants thereby effectively adjusting the control factors.
  • FIG. 1 is a cross-sectional view of a generally used workpiece
  • FIG. 2 is a graphical representation of the relationship between the finishing crown ratio (FCR) and the roughing crown ratio (RCR) as will be obtained in accordance with the workpiece profile control method of the present invention
  • FIG. 3 is a block diagram showing a portion of a rolling system employed in the present invention.
  • FIG. 4 is a graphical representation of profile errors (EX.1 and EX.2) occuring when utilizing a conventional method and profile errors (EX.3) occuring when utilizing present invention;
  • FIG. 5 is a graphical representation of the relationship between the bending force and crown variations of the roll stand in accordance with the present invention.
  • FIG. 6 is a graphical representation of the relationship between correction coefficients n 11 plate width (or workpiece width) and rolling force of a roll stand when utilizing the present invention
  • FIGS. 7 to 10 are graphical representations of characteristics of a rolling system utilizing the present invention.
  • FIG. 11 is a block diagram or a flow chart explaining a workpiece profile control method embodying the present invention.
  • FIG. 1 shows in a somewhat exaggerated manner the cross-section of a plate which has been rolled by an ordinary method.
  • the rolled plate P has a varying thickness which is largest in the middle of the plate, as indicated by lit", and is smaller at the side edges as indicated by hw and hd.
  • the plate thus has a crown of he (hw hd)/2 and a wedge of hw lid.
  • the causes of the crown and wedge are well known and it has been the conventional practice to. control them to within predetermined values using a finishing stand.
  • FIG. 2 This relationship is shown graphically in FIG. 2 where the ordinate represents the rough crown ratio (RCR) and the abscisa represents the finish crown ratio (FCR).
  • the crown ratio (RCR) or (FCR) is expressed RCR or FCR /2 (hd hw)/hc)
  • the straight line 1 is a plot of RCR FCR and the hatched area shows the allowable range of the crown ratio at the end of the finishing stage. A plate having a crown ratio within this range allows finish rolling without causing deterioration in its shape.
  • the workpiece undergoes no crown control from the last stand of the finishing stage and the crown control is performed by a roll stand or stands preceding the last stand, preferably, by the fifth stand or, if necessary, by the fifth and other preceding stands when the finishing stage includes six stands, the last stand performing only the shape control.
  • the crown control is performed by a roll stand or stands preceding the last stand, preferably, by the fifth stand or, if necessary, by the fifth and other preceding stands when the finishing stage includes six stands, the last stand performing only the shape control.
  • the Wedge control By carrying out the crown and wedge control in this manner, it becomes possible to obtain a product with a desired profile and with excellent flatness.
  • FIG. 3 diagrammatically shows an arrangement of a mill carrying out the above-mentioned control under various conditions, while FIG. 4 shows the results of experiments conducted using the mill.
  • Fl to F6 are the first to sixth stands of a tandem finish rolling mill.
  • a profile measuring device 1 a shape measuring device 2, a profile control device 3, and a shape control device 4. Both profile control and shape control were carried out by way of roll bending and reduction adjustments, and the rolling was carried out in the following three different ways.
  • the reduction adjustment is performed in the following: mannenThe gree, as
  • the coefficient a is determined bythe loaddis; I tribution for the respective roll stands, the kind of ⁇ workpiece being rolled and the initial roll curve.
  • the coefficient b is determined by the deviation between i the roll center 0' and the plate center 0, and C is a constant.
  • the crown C andthe wedge W can be expressed as follows (symbols are as in FIG. 1):
  • Equations (3) and (4) the contents of the quadratic equation y a(x b) C can be written as Actually by way of example the coefficients a, b are used by, exponentially smoothing the values obtained from the actually measured values C and W,..
  • the coefficient a should be determined in accordance with a desired crown (1.. There are many factors which influence the coefficient a and they are considered in the present invention as follows.
  • al represents the influence of the initial roll curve
  • a2 represents the roll bending amount due to a rolling reaction force
  • a3 represents the resistance to deformation of the workpiece
  • a4 is a learning term including heat crown and abrasive wear.
  • the coefficient a can be calculated from the Equation (5) while the factors al, a3 and 04 can be accurately obtained by precalculation and as a result of learning.
  • the roll bending amount a2 for the desired profile may be obtained from the following equation.
  • the rolling reaction force F,- required for producing such a roll bending amount can then be obtained as a function of a2, more particularly, as f (a2).
  • the rolling reaction force F,- is introduced during the finishing process, on a roll stand positioned close to the final roll stand for imparting the desired profile to the workpiece. If the finishing stage includes six roll stands and the aforementioned rolling reaction force F is introduced, for example, by the fifth stand or other preceding stands, the reference load distribution among the first six stands becomes unbalanced, causing irregularities in the total rolling amount. This, however, can be corrected by increasing or reducing the rolling load of the fourth and other preceding roll stands. If sufficient correction cannot be attained with such adjustment, it may be effected through rolling pitch adjustment and roll cooling adjustment.
  • the load distribution in the roughing stage can be effected in the same manner as in the finishing stage.
  • the crown desired to be produced during the roughing stage is determined from the relationship shown in FIG. 2. More particularly, the rough crown ratio is first obtained which will produce the allowable range of the finish crown ratio. Then, from the rough crown ratio RCR and the rough finish target thickness hHT, the rough crown C is calculated as follows.
  • the load distribution control is then effected in such a manner that the workpiece attains the desired rough crown ratio at the end of the roughing stage.
  • the roll bender is also effective for controlling the crown ratio in the roughing stage. Since the bending force and variations in the crown resulting from such bending force, have the relationship as shown in FIG. 5, the difference between the rough crown C in the preceding operation and the presently required rough crown C is obtained as A C,., C m C and the required reference bending force AT can be obtained from FIG. 5.
  • the correction coefficients n, and 17 for the plate width and the rolling reaction force are obtained from FIG. 6, from which the required bending force AT of the roll bender is calculated by the following equation.
  • the crown correction effected through load distribution in the roughing stage is mainly performed by the last roughing roll stand with aid of one or two preceding stands which are adapted to compensate for any deficient amounts in the correction.
  • a correction coefficient n for the plate width W1 is obtained from the graph of FIG. 7 showing the relation between the plate W and the width correction coefficient 1 required roll bending amount RCR, can be calculated from the equation.
  • the stretching rate A of the sixth and last stand R6 in the roughing stage having six roll stands is expressed as A6 2 h, x, x hHT This is sequentially repeated to determine the thickness schedule in the roughing stage.
  • the rolling reaction force F,- is normalized based upon the kind, width and temperature of the steel plate being rolled and converted into the required rolling reaction force F, upon determination of the screw value in consideration of the spring back of the rolling mill. That is,
  • This routine learning takes into consideration the learning of the correction coefficient 1 resulting from correction of the curve of FIG. 8 and correction by the operator.
  • the allowable range of the finish crown ratio FCR is defined by the determination of the rough crown ratio RCR.
  • W0 represents the body length of the roll.
  • an initial roll curve K C is employed using the correction coefficient K taking into consideration a particular schedule, or the like.
  • the correction of the wedge can be effected through one or a number of arbitrarily selected roll stands in the roughing stage.
  • the correction is effected by adjustment of the selsyn difference (levelling WS D5) of the fifth stand R5 and the last stand R6 is used for effecting a correction such as of bending.
  • the regressions measures of the extent to which two variables increase together, or one increases while the other decreases) of the wedge amount W,., the levelling amount R'5 by the fifth stand R5, and the plate width Ware expressed as follows.
  • the levelling amount R'5 of the stand R5 should be R'5 0.28W- 109 K (l/lOOm/i m) wherein K is a learning term.
  • the correcting amount is obtained by multiplying the. 5'
  • the profile correction is suitably distributed over the roughing and finishing stages and the correction of theprofile is opti-i mally carried out by way of changing the load distribu-- tion and by means of the roll bender, so that the workpiece can be controlled with a desired profile to a high precision.
  • a method of controlling the crown of a workpiece passing through a rolling mill comprising the steps of roughly adjusting the crown by means of a first roughing stage of the rolling mill to produce a profile on the workpiece which is within an allowable predetermined range for a successive second finishing stage of the rolling mill, and finely adjusting the crown by means of said second, finishing stage ofthe rolling mill to pro' -w cute the desired profile on the workpiece by utilizing all but the final stand within said finishing stage.
US406352A 1972-10-16 1973-10-15 Method for controlling the profile of workpieces on rolling mills Expired - Lifetime US3882709A (en)

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Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3958435A (en) * 1974-06-01 1976-05-25 Nippon Steel Corporation Method for controlling the profile of workpieces on rolling mills
US4199967A (en) * 1977-11-09 1980-04-29 Mitsubishi Denki Kabushiki Kaisha Method of controlling a shape of a rolled sheet
US4245490A (en) * 1978-03-08 1981-01-20 Kobe Steel, Limited Thin rolled steel plate having unequal thickness
EP0028275A1 (en) * 1979-11-01 1981-05-13 Reycan Research Limited Apparatus for controlling the shape of aluminium sheet produced in a rolling mill
EP0145287A1 (en) * 1983-11-14 1985-06-19 MORGAN CONSTRUCTION COMPANY (a Massachusetts corporation) Gauge control system for rod or bar rolling mills
EP0175844A2 (de) * 1984-09-26 1986-04-02 Hoesch Stahl Aktiengesellschaft Verfahren und Vorrichtung zur Korrektur des Dickenprofils des zu walzenden Bandes an einer mehrgerüstigen Warmbandstrasse
US4633692A (en) * 1984-08-17 1987-01-06 Mitsubishi Denki Kabushiki Kaisha Device for determining a setting value of a shape operating amount in a rolling mill
US4711109A (en) * 1983-03-14 1987-12-08 Sms Schloemann-Siemag, A.G. Controlling thickness and planarity of hot rolled strips
US4771622A (en) * 1986-03-12 1988-09-20 International Rolling Mill Consultants Inc. Strip rolling mill apparatus
DE3823767A1 (de) * 1988-02-23 1989-01-26 Escher Wyss Ag Verfahren und vorrichtung zum steuern des profils und der planheit von metallbaendern in mehrgeruestigen walzstrassen
US5493885A (en) * 1994-03-10 1996-02-27 Kawasaki Steel Corporation Method and apparatus for controlling rolling process in hot strip finish rolling mill
US5502992A (en) * 1991-06-28 1996-04-02 Siemens Aktiengesellshaft Regulation system in the manufacture of hot rolled strips by means of a multi-stand hot rolling mill
US5651281A (en) * 1993-03-29 1997-07-29 Sms Schloemann-Siemaq Method and apparatus for rolling rolled strips
US6240757B1 (en) 1997-07-11 2001-06-05 Siemens Aktiengesellschaft Process and installation for rolling a metal strip
KR100425601B1 (ko) * 1999-12-28 2004-04-03 주식회사 포스코 압연기의 형상 제어 특성을 실시간으로 시뮬레이션할 수있는 장치
DE19719994B4 (de) * 1997-05-13 2005-01-05 Bwg Bergwerk- Und Walzwerk-Maschinenbau Gmbh Verfahren zur Beeinflussung der Spannungsverteilung in Metallbändern oder -tafeln aus insbesondere nichtferromagnetischem Material
US20060207305A1 (en) * 2004-07-20 2006-09-21 Toshiba Mitsubishi-Electric Industrial Systems Corporation Method of setting/controlling wedge in plate material rolling
US20120000263A1 (en) * 2009-04-17 2012-01-05 Sms Siemag Aktiengesellschaft Method for providing at least one work roll for rolling rolling stock
CN107983772A (zh) * 2017-11-27 2018-05-04 河北工业大学 一种板材冷轧过程中可靠性有限元模型的建立方法
US10894277B2 (en) * 2017-04-03 2021-01-19 Denso Corporation Rolling bending method and rolling bending apparatus

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5542168A (en) * 1978-09-22 1980-03-25 Nippon Steel Corp Shape control method

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3049950A (en) * 1957-09-17 1962-08-21 British Aluminium Co Ltd Manufacture of metal sheet or strip
US3248916A (en) * 1962-09-21 1966-05-03 Westinghouse Electric Corp Workpiece shape control with a rolling mill
US3387470A (en) * 1965-09-28 1968-06-11 Westinghouse Electric Corp Method for measuring roll crown and improving the operation of a rolling mill
US3475935A (en) * 1965-10-29 1969-11-04 Hitachi Ltd Control apparatus and system for strip rolling
US3570288A (en) * 1967-10-21 1971-03-16 Krupp Gmbh Rolling-mill assembly with improved control system
US3620058A (en) * 1967-12-04 1971-11-16 British Iron Steel Research Hot or cold rolling of strip or plate

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3049950A (en) * 1957-09-17 1962-08-21 British Aluminium Co Ltd Manufacture of metal sheet or strip
US3248916A (en) * 1962-09-21 1966-05-03 Westinghouse Electric Corp Workpiece shape control with a rolling mill
US3387470A (en) * 1965-09-28 1968-06-11 Westinghouse Electric Corp Method for measuring roll crown and improving the operation of a rolling mill
US3475935A (en) * 1965-10-29 1969-11-04 Hitachi Ltd Control apparatus and system for strip rolling
US3570288A (en) * 1967-10-21 1971-03-16 Krupp Gmbh Rolling-mill assembly with improved control system
US3620058A (en) * 1967-12-04 1971-11-16 British Iron Steel Research Hot or cold rolling of strip or plate

Cited By (24)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3958435A (en) * 1974-06-01 1976-05-25 Nippon Steel Corporation Method for controlling the profile of workpieces on rolling mills
US4199967A (en) * 1977-11-09 1980-04-29 Mitsubishi Denki Kabushiki Kaisha Method of controlling a shape of a rolled sheet
US4245490A (en) * 1978-03-08 1981-01-20 Kobe Steel, Limited Thin rolled steel plate having unequal thickness
EP0028275A1 (en) * 1979-11-01 1981-05-13 Reycan Research Limited Apparatus for controlling the shape of aluminium sheet produced in a rolling mill
US4711109A (en) * 1983-03-14 1987-12-08 Sms Schloemann-Siemag, A.G. Controlling thickness and planarity of hot rolled strips
EP0145287A1 (en) * 1983-11-14 1985-06-19 MORGAN CONSTRUCTION COMPANY (a Massachusetts corporation) Gauge control system for rod or bar rolling mills
US4633692A (en) * 1984-08-17 1987-01-06 Mitsubishi Denki Kabushiki Kaisha Device for determining a setting value of a shape operating amount in a rolling mill
EP0175844A2 (de) * 1984-09-26 1986-04-02 Hoesch Stahl Aktiengesellschaft Verfahren und Vorrichtung zur Korrektur des Dickenprofils des zu walzenden Bandes an einer mehrgerüstigen Warmbandstrasse
EP0175844A3 (en) * 1984-09-26 1987-01-14 Hoesch Stahl Aktiengesellschaft Method and device for correcting the thickness profile of a hot rolled strip in a multiple-stand rolling mill
US4771622A (en) * 1986-03-12 1988-09-20 International Rolling Mill Consultants Inc. Strip rolling mill apparatus
DE3823767A1 (de) * 1988-02-23 1989-01-26 Escher Wyss Ag Verfahren und vorrichtung zum steuern des profils und der planheit von metallbaendern in mehrgeruestigen walzstrassen
US5502992A (en) * 1991-06-28 1996-04-02 Siemens Aktiengesellshaft Regulation system in the manufacture of hot rolled strips by means of a multi-stand hot rolling mill
US5651281A (en) * 1993-03-29 1997-07-29 Sms Schloemann-Siemaq Method and apparatus for rolling rolled strips
US5493885A (en) * 1994-03-10 1996-02-27 Kawasaki Steel Corporation Method and apparatus for controlling rolling process in hot strip finish rolling mill
DE19719994B4 (de) * 1997-05-13 2005-01-05 Bwg Bergwerk- Und Walzwerk-Maschinenbau Gmbh Verfahren zur Beeinflussung der Spannungsverteilung in Metallbändern oder -tafeln aus insbesondere nichtferromagnetischem Material
US6240757B1 (en) 1997-07-11 2001-06-05 Siemens Aktiengesellschaft Process and installation for rolling a metal strip
DE19729773C5 (de) * 1997-07-11 2007-05-10 Siemens Ag Verfahren und Einrichtung zum Walzen eines Metallbandes
KR100425601B1 (ko) * 1999-12-28 2004-04-03 주식회사 포스코 압연기의 형상 제어 특성을 실시간으로 시뮬레이션할 수있는 장치
US20060207305A1 (en) * 2004-07-20 2006-09-21 Toshiba Mitsubishi-Electric Industrial Systems Corporation Method of setting/controlling wedge in plate material rolling
US7293440B2 (en) * 2004-07-20 2007-11-13 Toshiba Mitsubishi-Electric Industrial Systems Corporation Method of setting/controlling wedge in plate material rolling
US20120000263A1 (en) * 2009-04-17 2012-01-05 Sms Siemag Aktiengesellschaft Method for providing at least one work roll for rolling rolling stock
US10894277B2 (en) * 2017-04-03 2021-01-19 Denso Corporation Rolling bending method and rolling bending apparatus
CN107983772A (zh) * 2017-11-27 2018-05-04 河北工业大学 一种板材冷轧过程中可靠性有限元模型的建立方法
CN107983772B (zh) * 2017-11-27 2019-06-04 河北工业大学 一种板材冷轧过程中可靠性有限元模型的建立方法

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JPS5225824B2 (ja) 1977-07-09
JPS4959757A (ja) 1974-06-10

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