CN111266500B - Method for determining the feed rate of a core roll driven by the feed rate in a ring rolling process - Google Patents

Method for determining the feed rate of a core roll driven by the feed rate in a ring rolling process Download PDF

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CN111266500B
CN111266500B CN202010115186.0A CN202010115186A CN111266500B CN 111266500 B CN111266500 B CN 111266500B CN 202010115186 A CN202010115186 A CN 202010115186A CN 111266500 B CN111266500 B CN 111266500B
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ring
outer diameter
stage
amount
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CN111266500A (en
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郭良刚
李晓月
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Northwestern Polytechnical University
Taicang Yangtze River Delta Research Institute of Northwestern Polytechnical University
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Taicang Yangtze River Delta Research 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
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    • B21H1/06—Making articles shaped as bodies of revolution rings of restricted axial length

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Abstract

A method for confirming the core roller feed speed driven by feed amount in the ring rolling process, firstly considering the biting condition and the rolling-through condition in the ring rolling process, confirming the curve of the feed amount changing with the ring outer diameter in real time in the four stages of starting rolling, stable rolling, reducing and rounding in the ring rolling process; secondly, determining an equation of the feeding amount at each stage; and finally, reversely solving the core roller feeding speed according to the mathematical relation between the core roller feeding speed and the feeding amount, and determining the core roller feeding speed driven by the feeding amount in the ring rolling process. According to the method, the core roller feeding speed suitable for the control requirement of the ring rolling equipment is obtained through the feeding amount in the ring rolling process according to the four-stage change of starting rolling, stable rolling, reducing and rounding, so that the problems of stability and forming quality in the ring rolling process are solved, the control requirement of the ring rolling equipment in the actual ring rolling process is met, the efficiency is high, the method is scientific and reliable, and important technical support is provided for realizing the optimal design and the stable control of the ring rolling process.

Description

Method for determining the feed rate of a core roll driven by the feed rate in a ring rolling process
Technical Field
The invention belongs to the field of ring rolling forming processing, and particularly relates to a method for determining the feeding speed of a core roller driven by the feeding amount in the ring rolling process.
Background
In the ring rolling forming process, the feeding speed of the core roller is an important parameter influencing the feeding amount, and has important influence on the stability of the ring rolling process and the quality of the formed ring piece. The larger the core roller feeding speed is, the larger the feeding amount per revolution is, and conversely, the smaller the feeding amount per revolution is. When the core roll feeding speed is too high, the feeding amount per revolution is too large and does not meet the gripping condition in the ring rolling process, so that the ring cannot be smoothly gripped into the rolling pass, and when the core roll feeding speed is too low, the feeding amount per revolution is too small and does not meet the rolling-through condition in the ring rolling process, so that the ring cannot be rolled through. Therefore, the reasonable design of the core roll feeding speed is the core technical problem to be solved by the ring rolling process. Conventionally, the feeding speed of a core roller is determined by experience, and the method needs a plurality of trial and error to obtain the feeding speed of the core roller meeting the requirement of the feeding amount, so that a ring can be smoothly meshed into a rolling pass (meeting the meshing condition) and can also be subjected to plastic deformation to penetrate through the whole wall thickness of the ring (meeting the rolling-through condition), but the method has the defects of low efficiency and lack of scientificity. Hualin et al (Hualin, Zhaojian, Lanjian, et al. Cold rolling of rings core roller feed speed Standard design [ J ] China mechanical engineering, 2006,17(9): 953-.
Disclosure of Invention
In order to solve the problems that the design of the core roller feeding speed in the existing ring rolling process technology is often dependent on experience and trial and error methods, the efficiency is low, the scientificity is lacked, the control requirement of actual ring rolling equipment is difficult to meet and the like, the invention provides a method for determining the core roller feeding speed driven by the feeding amount in the ring rolling process.
The method comprises the following specific steps:
step one, determining the outer diameter size of the ring piece at the feed amount change stage and the end of different stages in the ring rolling process.
The feeding amount is the wall thickness reduction amount of the ring in the ring rolling process; the feed amount varies with the real-time outer diameter of the ring.
The determined feed amount is changed into four stages, namely a rolling starting stage, a stable rolling stage, a reduction stage and a rounding stage.
Setting the whole ring rolling process as 100%, and setting the ratio K of the initial rolling stage with given feed amount in the whole ring rolling process110-30 percent, and the proportion K of the feed in the whole ring rolling process in the stable rolling stage250-80 percent, and the proportion K of the feed quantity reduction stage in the whole ring rolling process35-15 percent, and the proportion K of the feed in the whole ring rolling process in the feed rounding stage42 to 5 percent, and four accounts need to satisfy K1+K2+K3+K4＝100％。
The proportion is the proportion of the feed amount change in each stage in the whole ring rolling process.
1. The feeding amount starts the rolling stage.
In the feeding amount starting rolling stage, the real-time outer diameter D of the ring piece can be adjusted from the outer diameter D of the ring blank0Increasing the outer diameter D of the ring part until the end of the rolling stage of the feeding amount1When the ring is transited from the static state to the rotating state, the feeding amount H1From the initial value H of the feed0Increasing to a maximum value H of the feed in the form of a variation of a cubic polynomial functionmax。
The proportion K of the feed amount in the whole ring rolling process in the starting rolling stage1Comprises the following steps:
Figure GDA0003002817920000021
the outer diameter D of the ring at the end of the feed start-rolling stage1Determined by equation (2):
D1＝D0+K1×(Df-D0) (2)
in formulas (1) and (2): d0Indicates the outer diameter D of the ring blank1Indicating the outer diameter of the ring at the end of the feed start-rolling phase, DfShowing the outer diameter of the final formed ring.
2. And a stable rolling stage of the feeding amount.
In the feeding amount stable rolling stage, the real-time outer diameter D of the ring piece is the outer diameter D of the ring piece at the end of the feeding amount starting rolling stage1Increasing the outer diameter D of the ring piece until the end of the steady rolling stage of the feeding amount2Feed amount H2Maintaining maximum feed HmaxAnd is not changed.
The proportion K of the feed quantity stable rolling stage in the whole ring rolling process2Comprises the following steps:
Figure GDA0003002817920000031
the outer diameter D of the ring piece at the end of the steady rolling stage of the feed amount2Determined by equation (4):
D2＝D1+K2×(Df-D0) (4)
in equations (3) and (4): d2Is the outer diameter of the ring at the end of the steady rolling stage of the feeding amount.
3. A feed amount reducing stage.
In the stage of reducing the feeding amount, the real-time outer diameter D of the ring piece is equal to the outer diameter D of the ring piece at the end of the stage of stably rolling the feeding amount2Increase to the outer diameter D of the ring at the end of the feed reduction phase3Feed amount H3From the maximum value H of the feed quantitymaxReduced to the minimum value H of the feed in the form of a variation of a cubic polynomial functionmin。
The proportion K of the feed amount reduction stage in the whole ring rolling process3Comprises the following steps:
Figure GDA0003002817920000032
the outer diameter D of the ring at the end of the feed reduction phase3Determined by equation (6):
D3＝D2+K3×(Df-D0) (6)
in equations (5) and (6): d3Is the outer diameter of the ring at the end of the feed reduction phase.
4. And a feed rounding stage.
In the feed amount rounding stage, the real-time outer diameter D of the ring is determined by the outer diameter D of the ring at the end of the feed amount reduction stage3Increasing to the outer diameter D of the finally formed ring partfFeed amount H4Maintaining a minimum feed HminAnd is not changed.
The proportion K of the feed amount rounding stage in the whole ring rolling process4Comprises the following steps:
Figure GDA0003002817920000033
the target ring size, namely the outer diameter D of the finally formed ring, is reached at the end of the feed rounding stagef。
And step two, establishing a feed quantity equation of the whole ring rolling process.
The feed equation of the whole ring rolling process means that the real-time outer diameter D of the ring piece is from D to D from the beginning to the end of the ring rolling process0To DfThe feed H is a function of the change in the real-time outer diameter D of the ring during the whole process.
According to the feeding amount change stage in the ring rolling process and the outer diameter size of the ring piece at the end of different stages determined in the step one, establishing a feeding amount equation of the whole ring rolling process:
H＝H1+H2+H3+H4(D0≤D≤Df) (18)
wherein:
H1＝a1D3+b1D2+c1D+d1(D0≤D＜D1)
H2＝Hmax(D1≤D＜D2)
H3＝a2D3+b2D2+c2D+d2(D2≤D＜D3)
H4＝Hmin(D3≤D≤Df)
H1the feed quantity equation of the feed quantity starting rolling stage is a cubic polynomial function, wherein a1、b1、c1、d1Four coefficients, respectively, of a cubic polynomial function, respectively:
Figure GDA0003002817920000041
in the formula (11), s is the non-negative initial slope of the curve.
H2The feed quantity equation of the feed quantity steady rolling stage is that the feed quantity is kept at HmaxA constant function that is invariant.
H3For feed quantity reduction stage feed quantity equationThe equation for the feed is a cubic polynomial function, where a2、b2、c2、d2Four coefficients, respectively, of a cubic polynomial function, respectively:
Figure GDA0003002817920000042
H4feed equation for feed rounding stage for keeping feed at HminA constant function that is invariant.
And step three, determining the feeding speed v of the core roller under the driving of the feeding amount.
Let H and Δ t be the feeding amount of the whole ring rolling process and the rolling time used by the feeding amount, respectively, then the core roll feeding speed v is:
Figure GDA0003002817920000051
assuming no slip between the contact surfaces of the rings and the main roll, there are:
πD＝Δtω1R1 (21)
Figure GDA0003002817920000052
wherein D is the real-time outer diameter of the ring piece, omega1Is the main roll speed, R1Is the main roll radius.
By substituting formula (22) into formula (20):
Figure GDA0003002817920000053
the calculation formula of the core roller feed speed v obtained from the equation (23) is:
Figure GDA0003002817920000054
in the formula (24), D represents the real-time outer diameter of the ring, v represents the core roller feed speed, and R1Representing the radius of the main roll, omega1The main roller rotation speed is expressed, and the feed amount is expressed by equation (18).
At this point, the change curve of the core roll feeding speed is determined by reverse solution through the pre-designed feeding amount, and the determination of the core roll feeding speed driven by the feeding amount in the ring rolling process is completed.
The method considers the actual ring rolling process, and firstly, determines the stage of the change of the feed amount along with the real-time outer diameter of the ring in the ring rolling process and the outer diameter size of the ring at the end of each stage; secondly, establishing a feed quantity equation of the whole ring rolling process; and finally, reversely solving to obtain the core roller feeding speed according to the mathematical relationship between the core roller feeding speed and the feeding amount, and determining the core roller feeding speed driven by the feeding amount in the ring rolling process.
The method comprises the steps of designing the feeding speed of the core roller under the condition of the ring rolling process in a reverse mode from the result feeding amount of the ring rolling process, and determining the change curve of the feeding speed of the core roller along with the real-time outer diameter of the ring piece in a reverse mode through the preset four change stages of the feeding amount meeting the ring rolling biting condition and the rolling through condition along with the real-time outer diameter change of the ring piece. The method does not need trial and error for many times, can directly obtain the core roller feeding speed which meets the ring rolling biting condition and the rolling penetration condition and changes along with the real-time outer diameter of the ring piece, meets 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. FIG. 1 is a schematic diagram of deformation of a ring rolling process at different times, which is obtained by performing a finite element simulation virtual rolling test under the condition of the core roll feeding speed determined by the method of the present invention. As can be seen from the figure, the ring rolling process realizes stable forming, and the ring piece with good roundness is obtained, thereby proving the applicability of the method.
Drawings
FIG. 1 is a schematic diagram of finite element simulated virtual rolling deformation in a ring rolling process under the condition of the core roller feeding speed determined by the method. Fig. 1(a) to 1(f) show deformation results at different times in the ring rolling process 50s, 100s, 150s, 200s, 250s, and 290 s.
FIG. 2 is a schematic diagram showing the feed variation curve of the whole ring rolling process.
FIG. 3 shows the feed variation profile of the entire ring rolling process.
FIG. 4 is a graph showing the variation of the feed rate of the core rolls in the whole ring rolling process.
FIG. 5 is a flow chart of the present invention.
Detailed Description
The embodiment is a method for determining the feeding speed of a core roller driven by the feeding amount in the ring rolling process, and the method comprises the following specific steps:
step one, determining the outer diameter size of the ring piece at the feed amount change stage and the end of different stages in the ring rolling process.
The feeding amount in the ring rolling process is the wall thickness reduction amount of the ring piece in the ring rolling process; the feed amount varies with the real-time outer diameter of the ring. The feeding amount is a decisive factor influencing the metal flow in the ring rolling process, and plays an important role in influencing the stable forming and the forming quality in the ring rolling process. Considering the stability, the gripping condition and the rolling-through condition of the ring rolling process and the control mode of ring rolling equipment, dividing the change of the feed amount in the ring rolling process into a starting rolling stage, a stable rolling stage, a reducing stage and a rounding stage; the schematic diagram of the variation curve of the feed amount along with the real-time outer diameter of the ring piece in the starting rolling stage, the stable rolling stage, the reducing stage and the rounding stage of the ring rolling process is shown in fig. 2.
In fig. 2, the horizontal axis of the coordinate system represents the real-time outer diameter D of the ring, and the vertical axis represents the feed H during ring rolling. HmaxMaximum value of curve representing feed amount, H0Initial value, H, representing feed amount curveminMinimum value of curve representing feed amount, D0Indicates the outer diameter D of the ring blank1Indicating the outer diameter of the ring at the end of the start-up phase, D2Indicating the outer diameter of the ring at the end of the steady rolling phase, D3Indicating the outer diameter of the ring at the end of the reduction phase, DfShowing the outer diameter of the final formed ring.
As shown in the feeding amount curve of fig. 2, the feeding amount is divided into four stages, namely, a rolling start stage, a rolling stabilizing stage, a reduction stage and a rounding stage. All stages are completely passed through in the ring rollingThe proportion of the process is the proportion of the stage. Setting the whole ring rolling process as 100%, and setting the percentage K of the starting rolling stage in the whole ring rolling process 110 to 30 percent, and the proportion K of the stable rolling stage in the whole ring rolling process250-80% of the ratio K of the reduction stage in the whole ring rolling process 35 to 15 percent, and the proportion K of the whole ring rolling process in the rounding stage42-5%, and four accounts need to satisfy K1+K2+K3+K4＝100％。
The specific change process of the feed amount curve is as follows:
1. the feeding amount starts the rolling stage.
In the feeding amount starting rolling stage, the real-time outer diameter D of the ring piece can be adjusted from the outer diameter D of the ring blank0Increasing the outer diameter D of the ring part until the end of the rolling stage of the feeding amount1When the ring is transited from the static state to the rotating state, the feeding amount H1From the initial value H of the feed0Increasing to a maximum value H of the feed in the form of a variation of a cubic polynomial functionmax。
The proportion K of the feed amount in the whole ring rolling process in the starting rolling stage1Comprises the following steps:
Figure GDA0003002817920000071
the outer diameter D of the ring at the end of the feed start-rolling stage1Determined by equation (2):
D1＝D0+K1×(Df-D0) (2)
in formulas (1) and (2): d0Indicates the outer diameter D of the ring blank1Indicating the outer diameter of the ring at the end of the feed start-rolling phase, DfShowing the outer diameter of the final formed ring.
2. And a stable rolling stage of the feeding amount.
In the feeding amount stable rolling stage, the real-time outer diameter D of the ring piece is the outer diameter D of the ring piece at the end of the feeding amount starting rolling stage1Increasing the outer diameter D of the ring piece until the end of the steady rolling stage of the feeding amount2Feed amount H2Keep the feed amount to the maximumLarge value of HmaxAnd is not changed.
The proportion K of the feed quantity stable rolling stage in the whole ring rolling process2Comprises the following steps:
Figure GDA0003002817920000081
the outer diameter D of the ring piece at the end of the steady rolling stage of the feed amount2Determined by equation (4):
D2＝D1+K2×(Df-D0) (4)
in formulas (3) and (4): d2Is the outer diameter of the ring at the end of the steady rolling stage of the feeding amount.
3. A feed amount reducing stage.
In the stage of reducing the feeding amount, the real-time outer diameter D of the ring piece is equal to the outer diameter D of the ring piece at the end of the stage of stably rolling the feeding amount2Increase to the outer diameter D of the ring at the end of the feed reduction phase3Feed amount H3From the maximum value H of the feed quantitymaxReduced to the minimum value H of the feed in the form of a variation of a cubic polynomial functionmin。
The proportion K of the feed amount reduction stage in the whole ring rolling process3Comprises the following steps:
Figure GDA0003002817920000082
the outer diameter D of the ring at the end of the feed reduction phase3Determined by equation (6):
D3＝D2+K3×(Df-D0) (6)
in the formulae (5) and (6), D3Is the outer diameter of the ring at the end of the feed reduction phase.
4. And a feed rounding stage.
In the feed amount rounding stage, the real-time outer diameter D of the ring is determined by the outer diameter D of the ring at the end of the feed amount reduction stage3Growing to the final formed ringOuter diameter DfFeed amount H4Maintaining a minimum feed HminAnd is not changed.
The proportion K of the feed amount rounding stage in the whole ring rolling process4Comprises the following steps:
Figure GDA0003002817920000083
the target ring size, namely the outer diameter D of the finally formed ring, is reached at the end of the feed rounding stagef。
In the embodiment, the proportion K of the starting rolling stage with the given feed amount in the whole ring rolling process130 percent of the ratio K of the feed amount stable rolling stage in the whole process of ring rolling250 percent of the ratio K of the feed amount reduction stage in the whole ring rolling process315 percent of feed amount rounding stage and the proportion K of the whole ring rolling process 45%, setting the external diameter D of the ring blank02212.9mm, outer diameter D of final-formed ringf5040mm, the above parameters are substituted into formulas (2), (4) and (6), respectively, to obtain the outer diameter D of the ring at the end of the feed start rolling stage13061mm, and the outer diameter D of the ring piece at the end of the feed steady rolling stage24474.6mm and the outer diameter D of the ring at the end of the feed reduction phase3＝4898.6mm。
And step two, establishing a feed quantity equation of the whole ring rolling process.
The feed equation of the whole ring rolling process refers to that the ring rolling process is from beginning to end, namely the real-time outer diameter D of the ring piece is from D0To DfThe feed H is a function of the real-time outer diameter D of the ring during the whole process.
And (4) respectively establishing a feed equation of each different stage according to the feed variation stage determined in the step one and the outer diameter size of the ring piece at the end of each stage, and finally establishing a feed equation of the whole ring rolling process. Wherein:
I. feed quantity equation in starting rolling stage of feed quantity
The function of the rolling starting stage is a cubic polynomial function, namely the real-time outer diameter D of the ring piece is determined by the outer diameter D of the ring blank0Increase to rolling start stepRing outside diameter D at end of segment1While, the feed amount H1And the real-time outer diameter D of the ring is in a cubic polynomial function relation. The feed amount equation is determined by equation (8):
H1＝a1D3+b1D2+c1D+d1 (D0≤D＜D1) (8)
in the formula (8), a1、b1、c1、d1The four coefficients, each of a cubic polynomial, are determined by equation (11).
Determining the boundary condition of the feeding amount at the rolling starting stage by the curve of the feeding amount at the rolling starting stage and the formula (8) as follows:
Figure GDA0003002817920000091
in the formula (9), s is the slope of the rolling initial curve with a non-negative value.
The equation system for solving the feed quantity equation coefficient in the rolling stage is established by combining the formula (8) and the formula (9) as follows:
Figure GDA0003002817920000101
solving equation (10) yields:
Figure GDA0003002817920000102
in the present embodiment, the initial slope s of the curve is set to 0 and the initial value H of the feed amount is set06mm, maximum value of feed amount Hmax9mm and comparing the above parameters with D determined in step one0＝2212.9mm、D1The formula (11) is replaced by 3061mm, and the feed quantity equation coefficients of the feed quantity acceleration stage are calculated as follows: a is1＝-7.87×10-8、b1＝3.11×10-4、c1＝-0.3997、d1＝173.84。
II. Equation of feed amount in stable rolling stage of feed amount
The function of the feeding amount steady rolling stage is a constant function, namely the outer diameter D of the ring at the end of the feeding amount starting rolling stage1Increasing the outer diameter D of the ring piece until the end of the steady rolling stage of the feeding amount2While, the feed amount H2The feeding amount is in constant function relation with the real-time outer diameter D of the ring piece, and the maximum value H is keptmaxAnd is not changed. The feed equation is determined by equation (12):
H2＝Hmax(D1≤D＜D2) (12)
III feed amount equation in feed amount reduction stage
The function of the feed amount reducing stage is a cubic polynomial function, namely the outer diameter D of the ring piece when the real-time outer diameter D of the ring piece is finished by the feed amount steady rolling stage2Increase to the outer diameter D of the ring at the end of the feed reduction phase3While, the feed amount H3And the real-time outer diameter D of the ring is in a cubic polynomial function relation. The feed amount equation is determined by equation (13):
H3＝a2D3+b2D2+c2D+d2(D2≤D＜D3) (13)
in the formula (13), a2、b2、c2、d2The four coefficients of the cubic polynomial are determined by equation (16).
The boundary condition of the equation of the feed amount in the reduction stage is determined by the curve combination formula (13) of the feed amount reduction stage:
Figure GDA0003002817920000111
the equation coefficient of the feed amount in the reduction stage is established by the above equation (13) and equation (14) and the system of equations is solved as follows:
Figure GDA0003002817920000112
solving equation (15) yields:
Figure GDA0003002817920000113
in the present embodiment, the minimum value H of the feed amount is givenmin5mm, and mixing it with HmaxD determined in step one, 9mm2＝4474.6mm、D3When the formula (16) is replaced by 4898.6mm, the feed equation coefficients of the feed deceleration stage are calculated as follows: a is2＝8.39×10-7、b2＝-0.0059、c2＝13.7966、d2＝-10725。
IV, feed quantity equation in feed quantity rounding stage
The feed amount equation of the feed amount rounding stage is a constant function, namely the outer diameter D of the ring at the end of the feed amount reduction stage of the real-time outer diameter D of the ring3Increasing to the outer diameter D of the finally formed ring partfWhile, the feed amount H4The feeding amount H is kept at a minimum value H in a constant function relation with the real-time outer diameter D of the ring pieceminAnd is not changed. The feed amount equation is determined by equation (17):
H4＝Hmin(D3≤D≤Df) (17)
to sum up, the feed curve equation of the whole ring rolling process is as follows:
H＝H1+H2+H3+H4(D0≤D≤Df) (18)
wherein:
H1＝a1D3+b1D2+c1D+d1(D0≤D＜D1)
H2＝Hmax(D1≤D＜D2)
H3＝a2D3+b2D2+c2D+d2(D2≤D＜D3)
H4＝Hmin(D3≤D≤Df)
this implementationIn the examples, a1＝-7.87×10-8、b1＝3.11×10-4、c1＝-0.3997、d1＝173.84、a2＝8.39×10-7、b2＝-0.0059、c2＝13.7966、d2＝-10725、Hmin＝5mm、Hmax＝9mm、D0＝2212.9mm、D1＝3061mm、D2＝4474.6mm、D34898.6mm and Df5040mm is respectively substituted into the formula (18), and the feed quantity equation of the whole ring rolling process is obtained as follows:
Figure GDA0003002817920000121
the feed amount in the whole ring rolling process can be plotted with the change curve of the real-time outer diameter D of the ring member according to the feed amount equation in the formula (19), as shown in FIG. 3.
And step three, determining the core roller feeding speed under the driving of the feeding amount.
Let H and Δ t be the ring rolling feed amount and the rolling time for the feed amount, respectively, the core roll feed speed v is:
Figure GDA0003002817920000122
assuming no slip between the contact surfaces of the rings and the main roll, there are:
πD＝Δtω1R1 (21)
Figure GDA0003002817920000123
in the formulas (21) and (22), D is the real-time outer diameter of the ring part, omega1Is the main roll speed, R1Is the main roll radius.
By substituting formula (22) into formula (20):
Figure GDA0003002817920000124
the calculation formula of the core roller feed speed v obtained from the equation (23) is:
Figure GDA0003002817920000125
in the formula (24), D represents the real-time outer diameter of the ring member, v represents the core roller feed speed, and R1Representing the radius of the main roll, omega1Indicates the main roller rotation speed, and H indicates the feed amount and is determined by equation (18).
In this example, R is given1800mm and omega1Combining the formula (19) with the formula (1.2 rad/s), the change curve of the core roll feeding speed along with the real-time outer diameter D of the ring member in the whole ring rolling process can be drawn by the formula (24), and is shown in figure 4.
And then, reversely solving and determining a change curve of the core roller feeding speed along with the real-time outer diameter of the ring piece through a preset feeding amount curve. The curve can meet the control requirement of the ring rolling equipment, and a new method is provided for determining the process curve in the actual ring rolling process.

Claims (8)

1. A method of determining the feed rate of a core roll driven by the feed rate in a ring rolling process, comprising the steps of:
step one, determining the outer diameter size of the ring piece at the feed amount change stage and the end of different stages in the ring rolling process;
the feeding amount is the wall thickness reduction amount of the ring in the ring rolling process; the feeding amount changes along with the outer diameter of the ring piece in real time;
the determined feed amount is changed into four stages, namely a rolling starting stage, a stable rolling stage, a reduction stage and a rounding stage;
setting the whole ring rolling process as 100%, and setting the ratio K of the initial rolling stage with given feed amount in the whole ring rolling process110-30 percent, and the proportion K of the feed in the whole ring rolling process in the stable rolling stage250-80 percent, and the proportion K of the feed quantity reduction stage in the whole ring rolling process35-15 percent of the feed rate in the whole ring rolling processK42 to 5 percent, and four accounts need to satisfy K1+K2+K3+K4＝100％；
Step two, establishing a feed quantity equation of the whole ring rolling process;
the feed equation of the whole ring rolling process means that the real-time outer diameter D of the ring piece is from D to D from the beginning to the end of the ring rolling process0To DfIn the whole process, the feeding amount H is in a function relation with the change of the real-time outer diameter D of the ring piece;
according to the feeding amount change stage of the ring rolling process and the outer diameter size of the ring piece at the end of different stages determined in the step one, establishing a feeding amount equation of the whole ring rolling process:
H＝H1+H2+H3+H4 (18)
in formula (18): h is the rolling feed of the ring piece; h1Starting a feeding quantity equation of a rolling stage for the feeding quantity; h2A feed quantity equation in the feed quantity steady rolling stage; h3A feed amount equation for the feed amount reduction stage; h4A feed quantity equation in the feed quantity rounding stage;
step three, determining the core roller feeding speed v under the driving of the feeding amount:
the formula for calculating the core roller feed speed v is:
Figure FDA0003002817910000011
in formula (24): d represents the real-time outer diameter of the ring piece; v represents the core roller feed speed; r1Represents the main roll radius; omega1Indicates the main roll speed; h represents the ring rolling feed amount determination;
and finally, determining the change curve of the core roller feeding speed by reversely solving the pre-designed feeding amount, and finishing the determination of the core roller feeding speed in the ring rolling process.
2. The method of determining the feed rate of a core roll driven by a feed rate in a ring rolling process of claim 1 wherein the feed rate is determined by the feed rateIn the rolling starting stage, the real-time outer diameter D of the ring piece can be determined by the outer diameter D of the ring blank0Increasing the outer diameter D of the ring part until the end of the rolling stage of the feeding amount1When the ring is transited from the static state to the rotating state, the feeding amount H1From the initial value H of the feed0Increasing to a maximum value H of the feed in the form of a variation of a cubic polynomial functionmax；
The proportion K of the feed amount in the whole ring rolling process in the starting rolling stage1Comprises the following steps:
Figure FDA0003002817910000021
the outer diameter D of the ring at the end of the feed start-rolling stage1Determined by equation (2):
D1＝D0+K1×(Df-D0) (2)
in formulas (1) and (2): d0Indicates the outer diameter D of the ring blank1Indicating the outer diameter of the ring at the end of the feed start-rolling phase, DfShowing the outer diameter of the final formed ring.
3. The method for determining the feed rate of a core roll driven by a feed during ring rolling according to claim 2, wherein the real-time outer diameter D of the ring is determined by the outer diameter D of the ring at the end of the rolling period from the feed during the steady-state feeding period1Increasing the outer diameter D of the ring piece until the end of the steady rolling stage of the feeding amount2Feed amount H2Maintaining maximum feed HmaxThe change is not changed;
the proportion K of the feed quantity stable rolling stage in the whole ring rolling process2Comprises the following steps:
Figure FDA0003002817910000022
the outer diameter D of the ring piece at the end of the steady rolling stage of the feed amount2Determined by equation (4):
D2＝D1+K2×(Df-D0) (4)
in equation (4): d2Is the outer diameter of the ring at the end of the steady rolling stage of the feeding amount.
4. Method for determining the feed speed of a core roll driven by the feed during ring rolling according to claim 3, characterized in that the real-time outer diameter D of the ring in the feed reduction phase is determined by the outer diameter D of the ring at the end of the feed stabilization phase2Increase to the outer diameter D of the ring at the end of the feed reduction phase3Feed amount H3From the maximum value H of the feed quantitymaxReduced to the minimum value H of the feed in the form of a variation of a cubic polynomial functionmin；
The proportion K of the feed amount reduction stage in the whole ring rolling process3Comprises the following steps:
Figure FDA0003002817910000023
the outer diameter D of the ring at the end of the feed reduction phase3Determined by equation (6):
D3＝D2+K3×(Df-D0) (6)
in equation (6): d3Is the outer diameter of the ring at the end of the feed reduction phase.
5. Method for determining the feed speed of a core roller driven by the feed in a ring rolling process according to claim 4, characterized in that the real outer diameter D of the ring at the end of the feed reduction phase is determined by the outer diameter D of the ring at the end of the feed rounding phase3Increasing to the outer diameter D of the finally formed ring partfFeed amount H4Maintaining a minimum feed HminThe change is not changed;
the proportion K of the feed amount rounding stage in the whole ring rolling process4Comprises the following steps:
Figure FDA0003002817910000031
the target ring size, namely the outer diameter D of the finally formed ring, is reached at the end of the feed rounding stagef。
6. The method of determining the feed rate of a core roll driven by a feed in a ring rolling process of claim 5 wherein said established feed start-up phase feed equation H1Is a function of a cubic polynomial in which1、b1、c1、d1Four coefficients, respectively, of a cubic polynomial function, respectively:
Figure FDA0003002817910000032
in the formula (11), s is the non-negative initial slope of the curve;
the stable rolling stage of the feed amount is to keep the feed amount to be HmaxA constant function that is invariant;
the feed amount decreasing stage feed amount equation H3Is a function of a cubic polynomial in which2、b2、c2、d2Four coefficients, respectively, of a cubic polynomial function, respectively:
Figure FDA0003002817910000033
the feed amount rounding stage is to keep the feed amount at HminA constant function that is invariant.
7. The method of determining the feed rate of a core roll driven by the feed rate in a ring rolling process of claim 6, wherein:
feed quantity equation H of the feed quantity starting rolling stage1＝a1D3+b1D2+c1D+d1，(D0≤D＜D1)；
The feed quantity equation H of the feed quantity steady rolling stage2＝Hmax，(D1≤D＜D2)；
The feed amount decreasing stage feed amount equation H3＝a2D3+b2D2+c2D+d2，(D2≤D＜D3)；
Feed quantity equation H of feed quantity rounding stage4＝Hmin，(D3≤D≤Df)。
8. A method of determining the feed rate of a core roll driven by the feed rate in a ring rolling process as set forth in claim 1, wherein: when the calculation formula of the core roller feeding speed v in the three steps is determined, H and delta t are respectively the feeding amount of the whole ring rolling process and the rolling time used by the feeding amount, and the core roller feeding speed v is as follows:
Figure FDA0003002817910000041
assuming no slip between the contact surfaces of the rings and the main roll, there are:
πD＝Δtω1R1 (21)
Figure FDA0003002817910000042
wherein D is the real-time outer diameter of the ring piece, omega1Is the main roll speed, R1Is the radius of the main roll;
by substituting formula (22) into formula (20):
Figure FDA0003002817910000043
obtaining a core roller feed speed v from the formula (23);
wherein D represents the real-time outer diameter of the ring, v represents the feeding speed of the core roller, and R1Representing the radius of the main roll, omega1The main roller rotation speed is expressed, and the feed amount is expressed by equation (18).
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