CN111283124A - Method for determining feeding speed of core roller driven by ring acceleration in radial rolling of ring piece - Google Patents

Method for determining feeding speed of core roller driven by ring acceleration in radial rolling of ring piece Download PDF

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CN111283124A
CN111283124A CN202010115187.5A CN202010115187A CN111283124A CN 111283124 A CN111283124 A CN 111283124A CN 202010115187 A CN202010115187 A CN 202010115187A CN 111283124 A CN111283124 A CN 111283124A
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ring
stage
rolling
outer radius
speed
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CN111283124B (en
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郭良刚
李学潮
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Northwestern Polytechnical University
Shenzhen Institute of Northwestern Polytechnical University
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Northwestern Polytechnical University
Shenzhen Institute of Northwestern Polytechnical University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21H—MAKING PARTICULAR METAL OBJECTS BY ROLLING, e.g. SCREWS, WHEELS, RINGS, BARRELS, BALLS
    • B21H1/00—Making articles shaped as bodies of revolution
    • B21H1/06—Making articles shaped as bodies of revolution rings of restricted axial length
    • 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
    • B21B37/46—Roll speed or drive motor control

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Abstract

A method for determining the feeding speed of core roller driven by ring speed-increasing in radial rolling of ring parts features that a reverse thinking is used to preset a four-segment ring speed-increasing curve in accordance with actual ring rolling procedure and to reversely determine the feeding speed curve of core roller for realizing the purpose of smooth growth of ring parts in four stages of start rolling, main rolling, speed-reducing and rounding. Fig. 1 shows a finite element simulation virtual rolling test of a multi-step rolling process of a certain large ring piece under the condition of the core roller feeding speed determined by the method, stable forming is realized in the ring rolling process, and the ring piece with good roundness is obtained.

Description

Method for determining feeding speed of core roller driven by ring acceleration in radial rolling of ring piece
Technical Field
The invention relates to the field of ring rolling forming processing, in particular to a method for determining the feeding speed of a core roller driven by ring acceleration in the radial rolling process of a ring piece.
Background
In the radial rolling process of the ring piece, the feeding speed of the core roller has an important influence on the stability of the ring rolling process and the quality of the ring piece. Under the feeding action of the core roller, the diameter of the ring piece is gradually increased at a certain growing speed (ring increasing speed for short). Under the condition that the rotating speed of the main roller and other conditions are unchanged, the change process of the ring acceleration and the stability of the ring rolling process mainly depend on the change characteristics and rules of the feeding speed of the core roller. In the main rolling stage of the ring rolling process, if the ring acceleration can be kept to be constant, the large and large acceleration of the diameter of the ring piece is zero, so that the dynamic contact collision between the ring piece and the roller can be effectively reduced, and the stability of the ring rolling process is improved. Guo Liangggang et al (Guo L G, Yang H. Towards a steady forming of radial-axial rolling [ J ]. International Journal of Mechanical Sciences,2011,53(4):286-299.) establish stable forming conditions in the ring radial and axial rolling process by taking ring acceleration as a constant; hualin et al (Hualin, Zuozhijiang, Lanjian, et al. Cold ring-rolling core-expanding roller feed speed Standard design [ J ]. Chinese mechanical engineering, 2006,17(9):953-957.) combine the cold ring-rolling characteristics of rings, with the feed speed as constant, the feed amount per revolution as constant, the ring acceleration as constant and the rotation speed of the center of the follow-up guide roller as constant in the whole ring rolling process as control conditions, four core roller feed speed design methods are provided. However, the actual ring rolling process is generally divided into four stages of rolling start, main rolling, deceleration and rounding, wherein the rolling start stage realizes stable start of the rolling process and finishes the regulation of irregular ring blanks, the main rolling stage finishes most of the diameter increase of the ring, the ring enters the deceleration rolling stage when the size of the ring is about to reach the target size, the stable deceleration of the rolling process is realized, and the rounding stage is used for realizing the correction of the roundness and the uniformity of the wall thickness of the ring. However, the related research of the above documents does not consider the four stages of the ring rolling process, and it is difficult to meet the control requirements of the ring rolling equipment in the actual ring rolling process, so that it is difficult to realize the optimal design of the ring rolling process. In view of the above, the invention provides a method for determining the feeding speed of a core roller driven by ring acceleration in the radial rolling process of a ring piece, which comprises the steps of designing and considering a ring acceleration curve which changes along with the real-time outer radius of the ring piece in four stages of the ring rolling process in advance, and further reversely determining the change curve of the feeding speed of the core roller along with the real-time outer radius of the ring piece according to the function relationship between the ring acceleration and the feeding speed of the core roller. The method can ensure that the ring rolling process is stably carried out due to the consideration of four necessary stages of rolling start, main rolling, speed reduction and circle finishing in the actual ring rolling process, is identical with the control requirement of actual ring rolling equipment, has high efficiency, is scientific and reliable, and provides important technical support for realizing the optimal design and the stable control of the ring rolling process.
Disclosure of Invention
In order to solve the problems that the forming process is unstable, the formed ring piece quality is poor, the control requirement of a ring rolling device in the actual ring rolling process is difficult to meet and the like caused by the fact that four necessary stages of the actual ring rolling process are not considered in the core roller feeding speed design in the prior art, the invention provides a method for determining the core roller feeding speed driven by the ring speed increase in the ring radial rolling process.
The method comprises the following specific steps:
step one, determining the change form of a ring acceleration curve.
The ring acceleration curve is a curve of which the diameter growth speed of the ring piece changes along with the real-time outer radius of the ring piece in the ring rolling process, and is divided into a starting rolling stage, a main rolling stage, a deceleration stage and a rounding stage according to the actual ring rolling process.
Setting the whole ring rolling process as 100%, and setting the percentage K of the starting rolling stage in the whole ring rolling process110 to 30 percent, and the ratio K of the main rolling stage in the whole ring rolling process250-80 percent, and the percentage K of the reduction stage in the whole process of ring rolling35 to 15 percent, and the proportion K of the whole ring rolling process in the rounding stage 42 to 5 percent, and four accounts need to satisfy K1+K2+K3+K4＝100％。
In the rolling starting stage, the real-time outer radius R of the ring piece is determined by the outer radius R of the ring blank0Increasing the outer radius R of the ring to the end of the start-up phase1Ring speed increase v at the start-up stageD1The real-time outer radius R of the ring piece is changed from an initial value v in the form of a curve of a cubic polynomialD0Increase to a maximum value vDmax。
A main rolling stage, wherein the real-time outer radius R of the ring piece is from the outer radius R of the ring piece at the end of the starting rolling stage1Increasing the outer radius R of the ring to the end of the main rolling stage2Ring speed increase v in main rolling stageD2Real-time outer radius R maintenance v with ringDmaxAnd is not changed.
In the deceleration stage, the real-time outer radius R of the ring is equal to the outer radius R of the ring at the end of the main rolling stage2Increasing the outer radius R of the ring to the end of the deceleration phase3Ring speed increase v at speed reduction stageD3The real-time outer radius R of the ring part is represented by a maximum value v in the form of a curve of a cubic polynomialDmaxIs reduced to a minimum value vDmin。
In the rounding stage, the real-time outer radius R of the ring part is determined from the outer radius R of the ring part at the end of the deceleration stage3Increase to the target ring outer radius RfI.e. the outer radius of the finally formed ring. Speed increasing v of circle-shaping stage ringD4Maintaining a minimum value v with real time outer radius R of the ringDminAnd unchanged, reducing the nonuniformity of the wall thickness of the ring piece by rounding until the ring piece reaches the target size.
Step two, determining the outer radius R of the ring piece at the end of the starting rolling stage, the main rolling stage and the deceleration stage1、R2、R3。
The finishing time of the starting rolling stage, the main rolling stage and the deceleration stage is the outer radius R of the ring piece1、R2、R3Are determined by equations (2), (4), (6), respectively:
R1＝R0+K1×(Rf-R0)(2)
R2＝R1+K2×(Rf-R0)(4)
R3＝R2+K3×(Rf-R0)(6)
in the formulae (2), (4) and (6), R0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece; k1、K2、K3The starting rolling stage, the main rolling stage and the deceleration stage are respectively in proportion to the whole process of the ring rolling.
And step three, establishing a ring acceleration curve equation of the whole ring rolling process.
The ring speed increasing curve equation of the whole ring rolling process comprises ring speed increasing curve equations of a rolling starting stage, a main rolling stage and a decelerating and rounding stage, and is respectively determined as follows:
I. the ring acceleration curve equation in the start-up stage is determined by equation (7):
vD1＝a1R3+b1R2+c1R+d1(RO≤R＜R1)(7)
in the formula (7), vD1The ring is accelerated in the rolling starting stage; r is the real-time outer radius of the ring piece; a is1、b1、c1、d1Respectively, the coefficients of a cubic polynomial.
a1、b1、c1、d1Is determined by solving equation set (9):
Figure BDA0002391271770000041
in the equation (9), k is the slope of the non-negative ring acceleration curve at the start time of the rolling start phase.
II, determining a ring speed increasing curve equation of the main rolling stage by the formula (10):
vD2＝vDmax(R1≤R＜R2)(10)
in the formula (10), vD2Ring acceleration is performed in the main rolling stage;
the ring acceleration rate curve equation for the deceleration phase is determined by equation (11):
vD3＝a2R3+b2R2+c2R+d2(R2≤R＜R3)(11)
in the formula (11), vD3The speed is increased in a speed reduction stage; r is the real-time outer radius of the ring piece; a is2、b2、c2、d2Respectively coefficients of cubic polynomials。
A is a2、b2、c2、d2Is determined by solving equation set (13):
Figure BDA0002391271770000042
the full circle step ring acceleration curve equation is determined by equation (14):
vD4＝vDmin(R3≤R≤Rf)(14)
in the formula (14), vD4The speed is increased in a circle finishing stage;
at this point, the ring acceleration v of the whole ring rolling process is determined by the equations (7), (10), (11) and (14)DThe curve equation of (a):
vD＝vD1+vD2+vD3+vD4(15)
wherein:
vD1＝a1R3+b1R2+c1R+d1(R0≤R＜R1)
vD2＝vDmax(R1≤R＜R2)
vD3＝a2R3+b2R2+c2R+d2(R2≤R＜R3)
vD4＝vDmin(R3≤R≤Rf)
in the formula (15), vDRing acceleration in the whole ring rolling process; v. ofDmin、vDmaxRespectively is the minimum value and the maximum value of the ring speed increasing in the ring rolling process. R0、RfRespectively the outer radius of the ring blank and the outer radius of the target ring piece. R1、R2、R3Respectively setting the outer radius of the ring at the finishing time of a starting rolling stage, a main rolling stage and a deceleration stage in the ring rolling process; the R is1、R2、R3Are respectively determined by the formulas (2), (4) and (6). a is1、b1、c1、d1And a2、b2、c2、d2Are respectively determined by the formulas (9) and (13).
And step four, determining a core roller feeding speed curve in the radial rolling process of the ring piece.
And in the radial rolling process of the ring, the height of the ring is kept constant under the constraint of the conical rollers. Core roller feed speed vfDetermined by equation (19):
Figure BDA0002391271770000051
in the formula (19), vfIs the core roll feed speed; v. ofDRing acceleration in the whole ring rolling process; d0、d0、b0Respectively the outer diameter, the inner diameter and the wall thickness of the ring blank; b is the real-time wall thickness of the ring. According to the volume-invariant principle, the real-time wall thickness b of the ring is determined by equation (20):
Figure BDA0002391271770000052
wherein R is the real-time outer radius of the ring member, R0Is the radius of the ring blank.
And determining the feeding speed of the core roller driven by the ring speed increasing in the radial rolling process of the ring.
The invention provides a method for determining the feeding speed of a core roller driven by ring acceleration in the radial rolling process of a ring piece. Firstly, in order to enable the ring acceleration change in the ring rolling process to meet the actual production condition, the invention provides a four-section type change curve of the ring acceleration along with the real-time outer radius change of a ring piece, and the four-section type change curve comprises four stages of rolling starting, main rolling, deceleration and rounding; secondly, determining the outer radius R of the ring at the finishing time of the starting rolling stage, the main rolling stage and the deceleration stage according to the occupation ratio of each stage in the whole ring rolling process1、R2、R3(ii) a Secondly, establishing a ring acceleration curve equation of the whole ring rolling process; and finally, determining a curve of the change of the core roller feeding speed along with the real-time outer radius of the ring piece in the radial rolling process of the ring piece according to a pre-planned ring acceleration curve.
The invention adopts reverse thinking, presets a four-section ring acceleration curve which accords with the actual ring rolling process in advance, and reversely determines the core roller feeding speed curve, so as to realize the purpose that the diameter of the ring piece is gradually increased according to four stages of starting rolling, main rolling, deceleration and rounding, is favorable for improving the stability of the ring rolling process, is suitable for the control requirement of the existing ring rolling equipment, and provides important technical support for the optimal design and the steady control of the radial ring rolling process. Fig. 1 is a schematic diagram of deformation results of different steps in a ring rolling process obtained by performing a finite element simulation virtual rolling test on a large ring in a multi-step rolling process under the condition of the core roller feeding speed determined by the method, and it can be seen from the diagram that stable forming is realized in each step in the ring rolling process, and finally a ring with good roundness is obtained. This shows that the core roll feed speed determination method proposed by the present invention is applicable.
Drawings
FIG. 1 is a schematic diagram of deformation results of different steps of finite element simulation virtual rolling in a rolling process of a large ring under the condition of the core roller feeding speed determined by the invention. FIG. 1(a) shows the deformation result at the end of the first step of the rolling process; FIG. 1(b) shows the deformation result at the end of the second step of the rolling process; fig. 1(c) shows the deformation result at the end of the third step of the rolling process.
FIG. 2 shows a variation of a ring acceleration curve in the ring rolling process;
FIG. 3 is a graph of ring acceleration determined in accordance with the present invention;
FIG. 4 is a graph of core roll feed speed determined in accordance with the present invention;
FIG. 5 is a block flow diagram of the present invention.
Detailed Description
The embodiment is a method for determining the feeding speed of a core roller driven by ring acceleration in the radial rolling process of a ring piece. Firstly, determining the curve forms of the change of a ring speed increasing and dividing rolling stage, a main rolling stage, a speed reducing stage and a rounding stage according to the actual ring rolling process; secondly, determining the outer radius R of the ring piece at the finishing moment of the starting rolling stage, the main rolling stage and the deceleration stage of the ring rolling process1、R2、R3(ii) a Secondly, establishing a ring acceleration curve equation of the whole ring rolling process; most preferablyAnd then determining the feeding speed of the core roller driven by the ring speed increasing in the radial rolling process of the ring piece.
The specific process of this embodiment is as follows:
step one, determining the change form of a ring acceleration curve.
The ring acceleration curve is a curve in which the diameter and the growing speed of the ring piece change along with the real-time outer radius of the ring piece in the ring rolling process, and is divided into a starting rolling stage, a main rolling stage, a deceleration stage and a rounding stage according to the actual ring rolling process, as shown in fig. 2.
In fig. 2, the horizontal axis of the coordinate system represents the real-time outer radius R of the ring member during ring rolling, and the vertical axis represents the ring speed increase v during ring rollingD。vD0、vDmin、vDmaxRespectively representing the initial value, the minimum value and the maximum value of the ring speed increasing curve in the rolling process; r0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece; r1、R2、R3And respectively showing the outer radius of the ring at the finishing time of a starting rolling stage, a main rolling stage and a deceleration stage in the ring rolling process.
Setting the whole ring rolling process as 100%, and setting the percentage K of the starting rolling stage in the whole ring rolling process110 to 30 percent, and the ratio K of the main rolling stage in the whole ring rolling process250-80 percent, and the percentage K of the reduction stage in the whole process of ring rolling35 to 15 percent, and the proportion K of the whole ring rolling process in the rounding stage 42 to 5 percent, and four accounts need to satisfy K1+K2+K3+K4＝100％。
In the rolling starting stage, the real-time outer radius R of the ring piece is determined by the outer radius R of the ring blank0Increasing the outer radius R of the ring to the end of the start-up phase1Ring speed increase v at the start-up stageD1The real-time outer radius R of the ring piece is changed from an initial value v in the form of a curve of a cubic polynomialD0Increase to a maximum value vDmax。
A main rolling stage, wherein the real-time outer radius R of the ring piece is from the outer radius R of the ring piece at the end of the starting rolling stage1Increasing the outer radius R of the ring to the end of the main rolling stage2Ring speed increase v in main rolling stageD2Real time with ringOuter radius R holds vDmaxThe ring piece growth acceleration under the condition is zero, so that the impact collision between the ring piece and each roller can be effectively reduced, and the stability of the ring rolling process is improved.
In the deceleration stage, the real-time outer radius R of the ring is equal to the outer radius R of the ring at the end of the main rolling stage2Increasing the outer radius R of the ring to the end of the deceleration phase3Ring speed increase v at speed reduction stageD3The real-time outer radius R of the ring part is represented by a maximum value v in the form of a curve of a cubic polynomialDmaxIs reduced to a minimum value vDmin。
In the rounding stage, the real-time outer radius R of the ring part is determined from the outer radius R of the ring part at the end of the deceleration stage3Increase to the target ring outer radius RfI.e. the outer radius of the finally formed ring. Speed increasing v of circle-shaping stage ringD4Maintaining a minimum value v with real time outer radius R of the ringDminAnd unchanged, reducing the nonuniformity of the wall thickness of the ring piece by rounding until the ring piece reaches the target size.
In this embodiment, the initial value v of the ring acceleration rateD0Minimum value vDminAnd maximum value vDmaxTaken as 3mm/s, 2mm/s and 5mm/s, respectively. Outer radius R of ring blank0And target ring outer radius Rf500mm and 900mm respectively. Taking up the ratio K of the rolling stage130 percent, the main rolling stage ratio K250% of deceleration stage K315% in the rounding stage4＝5％。
Step two, determining the outer radius R of the ring at the finishing moment of the starting rolling stage, the main rolling stage and the deceleration stage1、R2、R3。
Setting the proportion of the initial rolling stage to the whole process of ring rolling as K1Determined by formula (1):
Figure BDA0002391271770000081
in the formula (1), R1The outer radius of the ring piece is the finishing moment of the starting rolling stage in the ring rolling process; r0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece.
The outer radius R of the ring at the end of the rolling stage can be determined by the formula (1)1：
R1＝R0+K1×(Rf-R0) (2)
The proportion of the main rolling stage to the whole process of ring rolling is K2Determined by equation (3):
Figure BDA0002391271770000082
in the formula (3), R2The outer radius of the ring piece is the finishing moment of the main rolling stage in the ring rolling process; r0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece.
The outer radius R of the ring at the end of the main rolling phase can be determined from the formula (3)2：
R2＝R1+K2×(Rf-R0)(4)
The proportion of the deceleration stage to the whole ring rolling process is K3Determined by equation (5):
Figure BDA0002391271770000091
in the formula (5), R3The outer radius of the ring piece is the end moment of the deceleration stage in the ring rolling process; r0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece.
The outer radius R of the ring at the end of the deceleration phase can be determined from equation (5)3：
R3＝R2+K3×(Rf-R0)(6)
In this embodiment, the ratio K of the rolling start stage obtained in the step one130 percent, the main rolling stage ratio K250% of deceleration stage K315% in the rounding stage 45%, and R0500mm and RfReplacing the diameter of the ring piece into the formulas (2), (4) and (6) respectively when the diameter of the ring piece is 900mm, and calculating to obtain the outer radius of the ring piece at the end of the starting rolling stage, the main rolling stage and the deceleration stage as R respectively1＝540mm、R2＝740mm、R3＝840mm。
And step three, establishing a ring acceleration curve equation of the whole ring rolling process.
And respectively establishing ring acceleration curve equations of different stages according to the four-stage ring acceleration change curve form determined in the step one.
I, rolling starting stage
In the rolling starting stage, the real-time outer radius R of the ring piece is determined by the outer radius R of the ring blank0Increasing the outer radius R of the ring to the end of the start-up phase1Ring speed increase v at the start-up stageD1The real-time outer radius R of the ring piece is changed from an initial value v in the form of a curve of a cubic polynomialD0Increase to a maximum value vDmax. The loop acceleration curve equation is determined by equation (7):
vD1＝a1R3+b1R2+c1R+d1(R0≤R＜R1)(7)
in the formula (7), vD1The ring speed is increased in the starting rolling stage, namely the diameter of the ring piece is increased; r is the real-time outer radius of the ring piece; a is1、b1、c1、d1Respectively, the coefficients of a cubic polynomial.
The boundary conditions for the change in the ring acceleration curve can be determined from fig. 1 and equation (7):
Figure BDA0002391271770000101
in equation (8), k is the slope of the non-negative ring acceleration curve at the initial time of the initial rolling stage.
The combined type (7) and the formula (8) are as follows:
Figure BDA0002391271770000102
by solving the formula (9), a is obtained1、b1、c1、d1The value of (c).
In this embodiment, the non-negative slope k of the ring acceleration curve at the start-up rolling initial time is taken to be 0, and the initial ring acceleration obtained in step 1 is set to beValue vD03mm/s, maximum value vDmax＝5mm/s、R0500mm and R calculated in step two1The coefficients of each item of the ring acceleration curve equation at the rolling starting stage are calculated to be a respectively in a mode of 540mm substituting into a formula (9)1＝-6.25×10-5、b1＝9.75×10-2、c1＝-50.63、d1When 8753 is substituted into formula (7), the ring acceleration rate curve equation of the initial rolling stage is obtained.
II, main rolling stage
In the main rolling stage, the real-time outer radius R of the ring is equal to the outer radius R of the ring at the end of the initial rolling stage1Increasing the outer radius R of the ring to the end of the main rolling stage2Ring speed increase v in main rolling stageD2Real-time outer radius R maintenance v with ringDmaxThe ring piece growth acceleration under the condition is zero, so that the impact collision between the ring piece and each roller can be effectively reduced, and the stability of the ring rolling process is improved. The ring acceleration curve equation can be determined by a constant function expressed by equation (10):
vD2＝vDmax(R1≤R≤R2)(10)
in the formula (10), vD2The ring speed is increased in the main rolling stage.
In this embodiment, the maximum value v of the ring acceleration obtained in step 1 is setDmaxWhen the formula (10) is substituted with 5mm/s, the loop speed increasing curve equation of the main rolling stage is obtained.
III. deceleration phase
In the deceleration stage, the real-time outer radius R of the ring is equal to the outer radius R of the ring at the end of the main rolling stage2Increasing the outer radius R of the ring to the end of the deceleration phase3Ring speed increase v at speed reduction stageD3The real-time outer radius R of the ring part is represented by a maximum value v in the form of a curve of a cubic polynomialDmaxIs reduced to a minimum value vDmin. The loop acceleration curve equation can be determined by equation (11):
vD3＝a2R3+b2R2+c2R+d2(R2≤R≤R3)(11)
in the formula (11), vD3For increasing the reduction stageSpeed; r is the real-time outer radius of the ring piece; a is2、b2、c2、d2Respectively, the coefficients of a cubic polynomial.
The boundary conditions for the ring acceleration curve are determined from fig. 1 and equation (11) as:
Figure BDA0002391271770000111
the combined type (11) and the formula (12) are as follows:
Figure BDA0002391271770000112
by solving the formula (13), a is obtained2、b2、c2、d2The value of (c).
In this embodiment, the minimum value v of the ring acceleration rate obtained in step 1 is setDmin2mm/s, maximum value vDmax5mm/s, and R calculated in step two2＝740mm、R3The formula (13) is substituted by 840mm, and coefficients of each item of the obtained ring speed-up curve equation at the speed-down stage are respectively a2＝6×10-6、b2＝-1.42×10-2、c2＝11.19、d2By substituting it into equation (11) — 2919.18, the loop acceleration curve equation of the deceleration phase is obtained.
IV, rounding stage
In the rounding stage, the real-time outer radius R of the ring is determined from the outer radius R of the ring at the end of the deceleration stage3Increase to the target ring outer radius RfI.e. the outer radius of the finally formed ring. Speed increasing v of circle-shaping stage ringD4Maintaining a minimum value v with real time outer radius R of the ringDminAnd unchanged, reducing the nonuniformity of the wall thickness of the ring piece by rounding until the ring piece reaches the target size. The loop acceleration curve equation can be determined by equation (14):
vD4＝vDmax(R3≤R≤Rf)(14)
in the formula (14), vD4The speed is increased in a whole circle stage.
In this embodiment, the minimum value v of the ring acceleration obtained in step 1 is setDminThe equation of the ring speed increasing curve of the whole circle stage is obtained by substituting formula (14) for 3 mm/s.
At this point, the ring acceleration v of the whole ring rolling process is determined by the equations (7), (10), (11) and (14)DThe curve equation of (a):
vD＝vD1+vD2+vD3+vD4(15)
wherein:
vD1＝a1R3+b1R2+c1R+d1(R0≤R≤R1)
vD2＝vDmax(R1≤R＜R2)
vD3＝a2R3+b2R2+c2R+d2(R2≤R＜R3)
vD4＝vDmin(R3≤R≤Rf)
in the formula (15), vDRing acceleration in the whole ring rolling process; v. ofDmin、vDmaxRespectively is the minimum value and the maximum value of the ring speed increasing in the ring rolling process. R0、RfRespectively the outer radius of the ring blank and the outer radius of the target ring piece. R1、R2、R3Respectively setting the outer radius of the ring at the finishing time of a starting rolling stage, a main rolling stage and a deceleration stage in the ring rolling process; the R is1、R2、R3Are respectively determined by the formulas (2), (4) and (6). a is1、b1、c1、d1And a2、b2、c2、d2Are respectively determined by the formulas (9) and (13).
In this example, a1＝-6.25×10-5、b1＝9.75×10-2、c1＝-50.63、d1＝8753、a2＝6×10-6、b2＝-1.42×10-2、c2＝11.19、d2＝-2919.18、vDmin＝2mm/s、vDmax＝5mm/s、R0＝500mm、R1＝540mm、R2＝740mm、R3＝840mm、RfWhen the formula (15) is replaced by 900mm, a ring speed increasing curve equation of the whole ring rolling process is obtained:
Figure BDA0002391271770000131
the curve of the ring speed increasing along with the real-time outer radius of the ring in the whole ring rolling process can be drawn by the formula (16), as shown in fig. 3.
And step four, determining the feeding speed of the core roller in the radial rolling process of the ring piece.
In the radial rolling process of the ring piece, the height of the ring piece is kept unchanged under the constraint action of the conical rollers, and according to the principle that the plastic deformation volume is unchanged, the real-time outer diameter D of the ring piece can be determined by the formula (17):
Figure BDA0002391271770000132
in the formula (17), D0、d0、b0The outer diameter, the inner diameter and the wall thickness of the ring blank are respectively; d and b are respectively the real-time outer diameter and the real-time wall thickness of the ring.
The left side and the right side of the formula (17) respectively derive the time to obtain the ring speed increasing v of the whole ring rolling processDThe expression of (a) is:
Figure BDA0002391271770000133
in the formula (18), vDRing acceleration in the whole ring rolling process; v. offIs the core roll feed speed.
Then further from equation (18) the expression core roll feed speed can be found:
Figure BDA0002391271770000134
in the formula (19), b is the real-time wall thickness of the ring. According to the volume invariant principle, the value of b can be determined by equation (20):
Figure BDA0002391271770000135
wherein R is the real-time outer radius of the ring member, R0Is the outer radius of the ring blank, b0The wall thickness of the ring blank.
From the equations (15), (19) and (20), it can be seen that the feeding speed of the core roll during the radial rolling of the ring is only related to the real-time outer radius R of the ring. The real-time outer radius R of the ring piece is set at the outer radius R of the ring blank0And target ring outer radius RfA series of points are taken between, namely, the change curve of the feeding speed of the core roller along with the real-time outer radius of the ring member can be determined.
In this embodiment, the outer diameter D of the ring blank01000mm, ring blank inner diameter d0600mm, ring blank wall thickness b0200mm, outer radius R of ring blank0500mm, target ring outer radius R f900 mm. Making the real-time outer radius R of the ring part be R0500mm to RfTaking a series of points between 900mm and then combining the ring acceleration v of formula (16)DThe curve equation of (a) and the real-time wall thickness b of the ring member of the formula (20) can determine the variation curve of the core roller feeding speed along with the real-time outer radius of the ring member in the whole ring rolling process, as shown in fig. 4. Thus, the determination of the feeding speed of the core roller driven by the ring speed increasing in the radial rolling process of the ring member is completed.

Claims (5)

1. A method for determining the feeding speed of a core roller driven by ring acceleration in the radial rolling of a ring piece is characterized by comprising the following specific steps:
step one, determining a change form of a ring acceleration curve:
the ring speed increasing curve is a curve of the diameter and the growing speed of the ring piece along with the real-time outer radius change of the ring piece in the ring rolling process, and is divided into a starting rolling stage, a main rolling stage, a decelerating stage and a rounding stage according to the actual ring rolling process;
in the rolling starting stage, the real-time outer radius R of the ring piece is determined by the outer radius R of the ring blank0Increasing the outer radius R of the ring to the end of the start-up phase1Ring speed increase v at the start-up stageD1The real-time outer radius R of the ring piece is changed from an initial value v in the form of a curve of a cubic polynomialD0Increase to a maximum value vDmax；
In the main rolling stage, the real-time outer radius R of the ring piece is equal to the outer radius R of the ring piece at the end of the starting rolling stage1Increasing the outer radius R of the ring to the end of the main rolling stage2(ii) a Ring speed increase v in main rolling stageD2Real-time outer radius R maintenance v with ringDmaxThe change is not changed;
in the deceleration stage, the real-time outer radius R of the ring piece is equal to the outer radius R of the ring piece at the end of the main rolling stage2Increasing the outer radius R of the ring to the end of the deceleration phase3(ii) a Speed reduction stage ring acceleration vD3The real-time outer radius R of the ring part is represented by a maximum value v in the form of a curve of a cubic polynomialDmaxIs reduced to vDmin；
In the rounding stage, the real-time outer radius R of the ring piece is equal to the outer radius R of the ring piece at the end of the deceleration stage3Increase to the target ring outer radius RfR is a hydrogen atomfAn outer radius for a final formed ring; the rounding stage ring speed increase vD4Maintaining a minimum value v with real time outer radius R of the ringDminThe wall thickness unevenness of the ring piece is reduced through rounding until the ring piece reaches the target size;
step two, determining the ring radius R at the end of the rolling starting stage, the main rolling stage and the deceleration stage1、R2、R3：
The ring radius R at the finishing moment of the starting rolling stage, the main rolling stage and the deceleration stage1、R2、R3Are determined by equations (2), (4), (6), respectively:
R1＝R0+K1×(Rf-R0) (2)
R2＝R1+K2×(Rf-R0) (4)
R3＝R2+K3×(Rf-R0) (6)
in the formulae (2), (4) and (6), R0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece; k1、K2、K3The rolling starting stage, the main rolling stage and the deceleration stage are respectively in proportion to the whole ring rolling process;
step three, establishing a ring acceleration curve equation of the whole ring rolling process:
the ring speed increasing curve equation of the whole ring rolling process comprises ring speed increasing curve equations of a rolling starting stage, a main rolling stage, a deceleration stage and a rounding stage, and is respectively determined as follows:
the ring acceleration curve equation of the rolling starting stage is determined by the formula (7):
vD1＝a1R3+b1R2+c1R+d1(R0≤R＜R1) (7)
in the formula (7), vD1The ring is accelerated in the rolling starting stage; r is the real-time outer radius of the ring piece; a is1、b1、c1、d1Coefficients of cubic polynomials respectively;
II, determining a ring speed increasing curve in the main rolling stage by an ensured formula (10):
vD2＝vDmax(R1≤R＜R2) (10)
in the formula (10), vD2Ring acceleration is performed in the main rolling stage;
the ring acceleration rate curve equation for the deceleration phase is determined by equation (11):
vD3＝a2R3+b2R2+c2R+d2(R2≤R＜R3) (11)
in the formula (11), vD3The speed is increased in a speed reduction stage; r is the real-time outer radius of the ring piece; a is2、b2、c2、d2Coefficients of cubic polynomials respectively;
the full circle step ring acceleration curve equation is determined by equation (14):
vD4＝vDmin(R3≤R≤Rf) (14)
determining a ring acceleration curve equation of the whole ring rolling process according to the formulas (7), (10), (11) and (14):
vD＝vD1+vD2+vD3+vD4(15)
in the formula (15), vDRing acceleration in the whole ring rolling process;
step four, determining a core roller feeding speed curve in the radial rolling process of the ring piece:
in the radial rolling process of the ring piece, the height of the ring piece is kept unchanged under the constraint of the conical rollers; core roller feed speed vfDetermined by equation (19):
Figure FDA0002391271760000031
in the formula (19), vfIs the core roll feed speed; v. ofDRing acceleration in the whole ring rolling process; d0、d0、b0Respectively the outer diameter, the inner diameter and the wall thickness of the ring blank; b is the real-time wall thickness of the ring; according to the volume-invariant principle, the real-time wall thickness b of the ring is determined by equation (20):
Figure FDA0002391271760000032
in the formula (20), R is the real-time outer radius of the ring piece, R0Is the radius of the ring blank;
and determining the feeding speed of the core roller in the radial rolling process of the ring.
2. The method for determining the feeding speed of the core roller driven by the ring speed increasing in the radial rolling of the ring member as claimed in claim 1, wherein the ratio K of the starting rolling stage in the whole ring rolling process is given by setting the whole ring rolling process to 100%110 to 30 percent, and the ratio K of the main rolling stage in the whole ring rolling process250-80 percent, and the percentage K of the reduction stage in the whole process of ring rolling35 to 15 percent, and the proportion K of the whole ring rolling process in the rounding stage42 to 5 percent, and four accounts need to satisfy K1+K2+K3+K4＝100％。
3. The method for determining the feeding speed of the core roller driven by the ring speed increasing in the radial rolling of the ring member as claimed in claim 1, wherein: a is a1、b1、c1、d1Is determined by solving equation set (9):
Figure FDA0002391271760000033
in the equation (9), k is the slope of the non-negative ring acceleration curve at the start time of the rolling start phase.
4. The method for determining the feeding speed of the core roller driven by ring speed increasing in the radial rolling of the ring member as claimed in claim 1, wherein a is2、b2、c2、d2Is determined by solving equation set (13):
Figure FDA0002391271760000041
5. the method for determining the feeding speed of the core roller driven by the ring speed increasing in the radial rolling of the ring member as claimed in claim 1, wherein the step 3 is to determine the ring speed increasing curve equation of the whole process of the ring member rolling:
vD1＝a1R3+b1R2+c1R+d1(R0≤R＜R1)
vD2＝vDmax(R1≤R＜R2)
vD3＝a2R3+b2R2+c2R+d2(R2≤R＜R3)
vD4＝vDmin(R3≤R≤Rf)
wherein v isDminAnd vDmaxRespectively is the minimum value and the maximum value of the ring acceleration in the ring rolling process; r0、RfRespectively representing the outer radius of the ring blank and the outer radius of the target ring piece; r1、R2、R3The outer radii of the ring piece at the finishing time of the starting rolling stage, the main rolling stage and the deceleration stage in the ring rolling process are respectively.
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