KR101164538B1 - Optimum design method for ring rolling schedule - Google Patents

Abstract

The present invention relates to an optimal design method of a ring rolling schedule using a finite element analysis method of a ring rolling process.
According to an embodiment of the present invention, a method of optimally designing a ring rolling schedule may include: a spatial mesh system for calculating a velocity field of a ring material and a ring according to the calculated velocity field in a ring rolling process; Ring rolling that repeats the finite element analysis while updating the velocity field and the information about the deformation and rotation with time increments by interlocking an actual mesh system to reflect the deformation and rotation of the material. Optimal design method of ring rolling schedule using finite element analysis of the process.Optimized ring rolling schedule in which the minimum load and torque are imposed on the roll of the ring rolling machine by linking the feed rate of the pressure roll and the feed rate of the conical roll. Design it.
According to the present invention, by performing the finite element analysis of the ring rolling process by interworking the spatial mesh system and the axial mesh system, the calculation amount and the calculation time can be greatly reduced, thereby improving efficiency. In addition, the finite element analysis method of the ring rolling process is designed to link the feed rate of the pressure roll and the feed rate of the conical roll to propose an optimized ring rolling schedule that minimizes the load and torque imposed on the roll of the ring rolling machine. can do.

Description

Optimal design method for ring rolling schedule

The present invention relates to an optimal design method of a ring rolling schedule using a finite element analysis method of a ring rolling process.

The ring rolling process is a special forming process for producing seamless rings. As shown in FIG. 1A, the driving roll 110 is placed in a state where a donut-shaped ring blank 200 is positioned between the main roll 110 and the pressure roll 120. Rotate and the pressure roll 120 enters the drive roll (110) direction. According to this driving, the ring material is increased in diameter as the thickness decreases, and finally, the final ring product 300 is completed as a seamless high strength ring. At present, it is critically used in many industries, such as rotating engine parts of jet engines, bearing races, ring parts of nuclear reactors, and rims of bicycles.

The most problem in the ring rolling process is a phenomenon in which high loads and torques are applied to rolls such as the driving roll 110 and the pressure roll 120. The lesser load and torque act on the rolls in producing the same ring, which is advantageous in terms of cost.

To date, much research has been conducted on loads and torques applied to rolls in a ring rolling process. In 1968, Johnson first obtained the torque of the driving roll and the rolling load of the pressure roll by basic analysis and experiment. However, there was a limitation in that it is a rolling process that presses a pressure roll to a ring material at a predetermined depth and molds it to the end in one rotation. In 1973, Hawkard et al. Applied the slip line field method using Hill's indentation to find the load and torque of the roll. In 1980 and 1986, Yang Dong-Yeul calculated the torque of the driving roll by applying the offset method and analyzed the process variables affecting the load and torque. In 1991, S.G XU9 et al. Calculated the load of rolling rolls and the torque of driving rolls by using three-dimensional rigid plastic finite element method.

In other words, in the previous studies, the focus was on simply obtaining loads and torques, and in many cases, comparisons were made after finding loads and torques, and there was no research on minimizing loads and torques. Therefore, it is necessary to establish an optimal design methodology of a ring rolling schedule that can minimize the load and torque acting on the roll by adjusting the approach speed of the pressure roll 120 and the cone roll 130. It is becoming.

In recent years, in the analysis of a ring rolling process, the analysis by the finite element method is performed a lot. The finite element method has been interpreted by several researchers, beginning with the study of eight-node elements, in which the expansion of the rigid plastic finite element formula from two to three dimensions is simplified. As a result, a three-dimensional finite element method has been published by Huisman et al., And Kim et al. Have conducted an abnormal three-dimensional ring rolling analysis based on the rigid plastic finite element method. In recent years, ring rolling has been designed using a commercial finite element analysis tool.

However, if the existing three-dimensional finite element method is used as it is, in order to obtain accurate results, the number of elements and nodes required for modeling is greatly increased, thereby greatly increasing the amount of calculation and calculation time. Accordingly, the rolling rolling schedule Building an optimal design methodology did not help.

The present invention has been made to solve the problems as described above, the problem to be solved by the present invention is to provide a finite element analysis method of the ring rolling process improved efficiency by greatly reducing the amount of calculation and calculation time.

In addition, another problem to be solved by the present invention is to provide an optimal design method of the ring rolling schedule to minimize the load and torque imposed on the roll of the ring rolling machine, by using the finite element analysis method of the ring rolling process.

Optimal design method of the ring rolling schedule according to an embodiment of the present invention for achieving the above object is calculated in the ring rolling process, the Spatial Mesh System (Spacial Mesh System) for calculating the velocity field of the ring material Finite element while interlocking an actual mesh system to reflect the deformation and rotation of the ring material according to the velocity field and updating the information about the velocity field and the deformation and rotation with respect to time increments. Optimal design method of ring rolling schedule using finite element analysis method of ring rolling process that repeats the analysis.The minimum load and torque is applied to the roll of the ring rolling machine by linking the feed speed of the pressure roll and the feed speed of the cone roll. Design an optimized ring rolling schedule that is imposed.

The feed rate of the pressure roll is expressed as a linear straight line that is bent as a function of time at each node of the model that shapes the pressure roll, and the feed rate of the cone roll is applied to each node of the model that shapes the cone roll. In this case, the first linear straight line, which is a function of the time, and the first linear straight line about the feed rate of the pressure roll, and the first linear straight line about the feed rate of the cone roll, is continuous. Conditions and the distance the roll is conveyed is subject to a constant feed distance condition, the feed rate of the pressure roll and the feed rate of the cone roll may be limited by a predetermined minimum and maximum feed speed, respectively.

The first linear straight line with respect to the feed rate of the pressure roll and the first linear straight line with respect to the feed rate of the conical roll may be as follows.

[expression]

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t <T / 2 pressure roll feed rate of _from, y _{m, 2} is T / 2 pressure at <t ≤ T Roll feed rate, y _{a, 1} is the cone roll feed rate at 0≤ t < T / 2, y _{a, 2} is the cone roll feed rate at T / 2 < t ≤ T , and a _m , b _m , c _m , d _m , a _a , b _a , c _a , d _a are constants)

The continuous condition and the conveying distance condition in the first linear straight line about the feed rate of the pressure roll and the first linear straight line about the feed rate of the cone roll may be as follows.

[Continuous Condition Expression]

[Travel distance condition formula]

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t <T / 2 pressure roll feed rate of _from, y _{m, 2} is T / 2 pressure at <t ≤ T Roll feed rate, y _{a, 1} is the cone roll feed rate at 0≤ t < T / 2, y _{a, 2} is the cone roll feed rate at T / 2 < t ≤ T , a _m , b _m , c _m , d _m , a _a , b _a , c _a , d _a are constants, D _m is the distance of the pressure roll, D _a is the distance of the cone roll)

The range of the feed rate limited by the minimum and maximum feed rate in the pressure roll and the range of the feed rate limited by the minimum and maximum feed rate in the conical roll may be as follows.

[expression]

Where y _m is the pressure roll feed and y _a is the cone roll feed

The optimal design method of the ring rolling schedule according to an embodiment of the present invention is the continuous condition, the conveying distance in the first linear straight line for the feed rate of the pressure roll and the first linear straight line for the feed rate of the cone roll By the conditions and the limitation of the minimum and maximum feed speeds, the possible ranges of the constants constituting the bent straight line relating to the feed speed of the pressure roll and the bent linear straight line relating to the feed speed of the cone roll are determined. Constructing a plurality of sets of constants according to a predetermined method within a possible range of each constant, to obtain a plurality of objective functions statistically; finite element analysis of the ring rolling process using the plurality of sets of constants The objective function is constructed by using the finite element analysis step by the method and the result of the multiple finite element analysis method. It may include the step.

Optimal design method of the ring rolling schedule according to an embodiment of the present invention is the plurality of through the result of the finite element analysis performed by inputting the feed rate of the pressure roll and the feed rate of the cone roll to a predetermined constant value The method may further include normalizing a result value of the meeting finite element analysis.

The spatial mesh system configures the shape of the ring material as a dense mesh of only the anticipated portion of deformation, and fixes the space in the ring material. The physical mesh system constitutes the volume of the ring material as a uniform and dense mesh in its entirety. It may be characterized in that the deformation and rotation in the space to be constant.

The finite element analysis method of the ring rolling process includes a first step of calculating a velocity field at each node of the spatial mesh system with respect to the time increment Δt, and a velocity field at each node of the spatial mesh system. A second step of interpolating to calculate the velocity field at each node of the physical mesh system, the liquid for a small time increment (ddt) relative to the time increment according to the velocity field calculated at each node of the physical mesh system. A third step of updating each of the nodes of the virtual mesh system to update the physical mesh system so that the center of the ring material is moved or the radius thereof is increased, and the ring material deformed according to each node moved in the physical mesh system. A fourth step of updating the spatial mesh system by moving each node of the spatial mesh system to conform to the shape of; If the cumulative value Σddt of the minutes is smaller than the time increment, the fifth step of repeating the third and fourth steps for the further progress by the small time increment, and the cumulative value of the small time increment If greater than or equal to the time increment, a sixth step of updating the physical mesh system with respect to the time increment.

The finite element analysis method of the ring rolling process may be characterized in that the velocity field at each node of the spatial mesh system is applied constant during the time increment.

The fourth step may further include checking boundary conditions of the spatial mesh system.

The sixth step may further include updating the spatial mesh system with respect to the time increment in accordance with the updated physical mesh system.

The finite element analysis method of the ring rolling process may repeat the first to sixth steps for the next time increment when the first to sixth steps of the time increment are completed. have.

According to the present invention, by performing the finite element analysis of the ring rolling process by interworking the Spatial Mesh System and the Actual Mesh System, the calculation amount and the calculation time are greatly reduced, thereby improving efficiency. You can.

In addition, the finite element analysis method of the ring rolling process is designed to link the feed rate of the pressure roll and the feed rate of the conical roll to propose an optimized ring rolling schedule that minimizes the load and torque imposed on the roll of the ring rolling machine. can do.

It is a perspective view which shows an example of the ring rolling process by a ring rolling machine.
It is a front view which shows an example of the ring rolling process by a ring rolling machine.
It is a top view which shows an example of the ring rolling process by a ring rolling machine.
Figure 2a is a perspective view showing a spatial mesh system applied to the finite element analysis method according to an embodiment of the present invention.
Figure 2b is a perspective view showing an axial mesh system applied to the finite element analysis method according to an embodiment of the present invention.
Figure 3 is a flow chart showing a step by step finite element analysis method of the ring rolling process (S100) according to an embodiment of the present invention.
4 is a schematic diagram illustrating finite element modeling for ring rolling.
Figure 5 is a graph comparing the load applied to the pressure roll in the actual experiment and the load applied to the pressure roll in the finite element analysis simulation by the finite element analysis method of the ring rolling process according to an embodiment of the present invention.
Fig. 6 is a graph showing the travel distance with respect to time at one node of numerical modeling of rolls.
7 is a flowchart illustrating a method of optimally designing a ring rolling schedule according to an embodiment of the present invention.
8 is a graph showing the objective function of the load applied to the pressure roll according to the feeding distance.
9 is a graph showing the objective function of the load applied to the cone roll according to the feeding distance.
10 is a graph showing the objective function of the torque applied to the pressure roll according to the feeding distance.
11 is a graph showing the objective function of the torque applied to the cone roll according to the feeding distance.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1A is a perspective view illustrating an example of a ring rolling process by a ring rolling machine, FIG. 1B is a front view illustrating an example of a ring rolling process by a ring rolling machine, and FIG. 1C illustrates an example of a ring rolling process by a ring rolling machine. It is the top view shown.

Figure 2a is a perspective view showing a spatial mesh system applied to the finite element analysis method according to an embodiment of the present invention, Figure 2b is a physical mesh system applied to the finite element analysis method according to an embodiment of the present invention It is a perspective view shown.

Finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention uses a three-dimensional rigid plastic finite element method, and as shown in Figures 2a and 2b, to reduce the amount of computation, Two mesh systems are used: SMS, Spacial Mesh System (510) and Actual Mesh System (AMS) (520).

In addition, each node of the spatial mesh system 510 is attached to the space in the circumferential direction of the ring material 200 with respect to the velocity field, and the shape of the cross section is formed by the rigid plastic finite element method in the spatial mesh system 510. It deforms based on the velocity field obtained. The velocity field is assumed to be constant for a given time increment, and the axial mesh system 520 will deform and rotate according to this velocity field.

As shown in FIG. 1C, as the process proceeds, the overall thickness of the ring material 200 continuously decreases and the radius of the ring material 200 increases. Due to the limited density of the spatial mesh system 510, the velocity field obtained by the finite element method and the shape of the ring material 200 deformed based on the finite element method are subject to an error, so that the volume of the ring material 200 is incremented every hour. By recalculating, the position of the rotation center axis of the ring material 200 is correctly corrected.

That is, the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention is a spatial mesh system (Spacial Mesh System) for calculating the velocity field of the ring material 200 in the ring rolling process ( 510 and an actual mesh system 520 for reflecting the deformation and rotation of the ring material 200 according to the calculated velocity field are inter-worked to increase the information on the velocity field, deformation and rotation. It is a finite element analysis method of the ring rolling process that repeats the finite element analysis while updating the.

Also, as shown in FIG. 2A, the spatial mesh system 510 fixes the shape of the ring material 200 to a space composed of a dense mesh of only the anticipated portion of deformation, and as shown in FIG. Mesh system 520 is characterized in that the shape of the ring material 200 is composed of a uniform and dense mesh as a whole to deform and rotate in space so that the volume is constant.

On the other hand, step by step the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention, 1) through a finite element method at time t to a given geometry (Geometry) in the spatial mesh system 510 Calculate the velocity field for 2) Obtain the velocity field at the node of the axial mesh system 520 by interpolating the velocity field in the spatial mesh system 510. 3) Move the nodes of the axial mesh system 520 according to the interpolated velocity field during small time increments (ddt). 4) to move the center of the ring material 200 or to increase the radius. 5) Adjust the nodes in the spatial mesh system 510 according to the shape in the updated physical mesh system 520. 6) Check the boundary conditions of the spatial mesh system 510. 7) If the cumulative value of the small time increment (Σddt) is smaller than the time increment (Δt) (Σddt <Δt), the same procedure is repeated again, and the cumulative value of the small time increment (Σddt) is larger than the time increment (Δt). Equal to (? Ddt ≧ Δt), update the shape of the axial mesh system 520 for a given time increment Δt.

The shape of the spatial mesh system 510 is updated again and again according to the shape of the improved axial mesh system 520, and the same process is performed in the analysis of the next time increment Δt.

Figure 3 is a flow chart showing a step by step finite element analysis method of the ring rolling process (S100) according to an embodiment of the present invention.

That is, as shown in Figure 3, the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention is the velocity at each node of the spatial mesh system 510 with respect to the time increment (Δt) First step (S110) of calculating the field, second step (S120) of calculating the velocity field at each node of the physical mesh system 520 by interpolating the velocity field at each node of the spatial mesh system 510. , The center of the ring material 200 by moving each node of the axial mesh system 520 during a small time increment (ddt) with respect to the time increment according to the velocity field calculated at each node of the axial mesh system 520. The third step (S130) of updating the physical mesh system 520 so that the moved or radius is increased, so as to fit the shape of the ring material 200 deformed according to each node moved in the physical mesh system 520. Move each node of the spatial mesh system 510 to move it If the cumulative value Σddt of the small time increment is smaller than the time increment, the third step S130 and the fourth step S140 for the further progress by the small time increment are updated. A fifth step (S150) of repeatedly performing the operation and a sixth step (S160) of updating the physical mesh system 520 with respect to the time increment when the cumulative value of the small time increment is greater than or equal to the time increment. Can be.

Also, as noted earlier, the velocity field at each node of the spatial mesh system 510 may be applied constant during time increments.

The fourth step S140 may further include a step S141 of checking a boundary condition of the spatial mesh system 510, and a sixth step S160 may be performed according to the updated physical mesh system 520. The method may further include updating the spatial mesh system 510 with respect to time increment (S161).

Finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention is the first step for the next time increment when the process of the first step (S110) to the sixth step (S160) for the time increment is completed It may be characterized by repeating (S110) to sixth step (S160).

4 is a schematic diagram illustrating finite element modeling for ring rolling.

On the other hand, by way of example, look at the numerical modeling in the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention. Finite element modeling for ring rolling was modeled as shown in FIG. 4 according to the geometry shown in FIG. Referring to FIG. 1A, finite element modeling for ring rolling includes a main roll 110, a Mandrel 120, an upper and lower axial roll 130 and a ring. It consists of a ring blank (200). Conical roll 130 is a device provided to prevent the fishtail (Fishtail) phenomenon is deformed by the upper portion of the ring material 200. The driving roll 110 transmits torque to the material and transfers it in the circumferential direction, while the pressure roll 120 idles. In addition, the pressure roll 120 enters the radial direction, so that the cross section of the ring material 200 is deformed according to the shape of the driving roll 110.

The driving roll 110, the pressure roll 120, and the cone roll 130 used in the analysis can be assumed to be rigid bodies, and the ring material 200 is set to a rigid body to perform finite element analysis. The geometrical specifications of the rolls constituting are shown in Table 1. The friction factor was assumed to be 0.7 overall. The size of the ring material 200, the shape of the final molded product, and the like are different for each analysis and will be described later. The ring material 200 used SCM440. The flow stress equation for the ring material 200 has a relationship as in Equation 1 in hot forming.

Where K ₀ is the strength factor, n is the work hardening index, m is the strain rate sensitivity factor, and a ₀ , a ₁ , b ₀ , and b ₁ are the material constants. These material constants depend on the temperature. The material constants with temperature derived from the flow stress obtained from the high temperature compression test results provided by DEFORM are shown in Table 2. In addition, the heat transfer coefficient was applied to 20 kW / m ² ℃. For the temperature analysis, hot forming was interpolated by polynomial approximation based on the data, and was calculated by adding it to the finite element analysis.

Figure 5 is a graph comparing the load applied to the pressure roll in the actual experiment and the load applied to the pressure roll in the finite element analysis simulation by the finite element analysis method of the ring rolling process according to an embodiment of the present invention.

The finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention was verified by comparing loads applied to the pressure rolls using the numerical modeling.

Process conditions are as follows. A process of forming a ring material 200 having an outer diameter of 302 mm, an inner diameter of 120 mm, and a height of 158 mm into a final ring product 300 having an outer diameter of 450 mm, an inner diameter of 350 mm, and a height of 180 mm. One uses the shape and condition of numerical modeling. The feed rate of the pressure rolls averages 1 mm / s.

Actual experiments were also performed on the above process under the same conditions to obtain the load applied to the pressure roll. As shown in Figure 5, the load applied to the pressure roll in the finite element analysis simulation by the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention and the pressure roll in the actual experiment The distribution is almost similar. The results obtained by the finite element analysis simulation show a slightly higher load distribution than the actual experimental values, but the results show almost identical results.

Therefore, the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention can be seen to produce a reliable result in the ring rolling.

As described above, the finite element analysis of the ring rolling process is performed by interworking the Spatial Mesh System and the Actual Mesh System to improve efficiency by greatly reducing the amount of calculation and the calculation time. .

Next, look at the optimal design method of the ring rolling schedule using the finite element analysis method (S100) of the ring rolling process according to an embodiment of the present invention.

According to an embodiment of the present invention, a method of optimally designing a ring rolling schedule (S200) includes a spatial mesh system 510 for calculating a velocity field of a ring material 200 and a calculated velocity field in a ring rolling process. Ring that repeats the finite element analysis while updating information about the velocity field, deformation, and rotation with respect to time increments by interlocking the axial mesh system 520 to reflect the deformation and rotation of the ring material 200 according to the present invention. An optimal design method of the ring rolling schedule using the finite element analysis method (S100) of the rolling process, by linking the feed speed of the pressure roll 120 and the feed speed of the cone roll 130 to the roll of the ring rolling machine 100 Design an optimized ring rolling schedule with minimal load and torque.

In conjunction with the feed rate of the pressure roll 120 and the feed rate of the cone roll 130, the optimized ring rolling schedule to apply a minimum load and torque to the roll of the ring rolling machine 100 is mathematically approached.

Fig. 6 is a graph showing the travel distance with respect to time at one node of numerical modeling of rolls.

The feed rate of the pressure roll 120 or the cone roll 130 may be represented as shown in FIG. 6 to be limited to the case for one node, which is an example in which the horizontal axis represents the time and the total rolling time is 20 seconds. It's about the case. Determining the feed rate of the pressure roll 120 or the cone roll 130 with respect to time in the form of connecting two straight lines with respect to the center line among the total 20 seconds can represent all the feed speeds expressed only by the first linear straight line. .

In the first linear straight line, each straight line may be represented by two constants as shown in Equation 2. In other words, a total of four constants in two straight lines are needed to determine the feed rate of a particular roll. In this case, if the continuous conditions where two straight lines meet at 10 seconds, which is 1/2 of the total rolling time of 20 seconds, and the feeding distance condition that the distance that the rolls are fed in the actual process are applied, they can be expressed as Equations 3 and 4, respectively. In this way, the feed rate of the pressure roll 120 or the cone roll 130 can be obtained with only two constants.

Where t is a variable relating to rolling time, 20 seconds is an exemplary total rolling time, y ₁ is a roll feed rate at 0 ≦ t ≦ 10, y ₂ is a roll feed rate at 10 < t ≦ 20, and a , b , c and d are constants.

Where t is a variable relating to rolling time, 20 seconds is an exemplary total rolling time, y ₁ is a roll feed rate at 0 ≦ t ≦ 10, y ₂ is a roll feed rate at 10 < t ≦ 20, a , b , c and d are constants and D is the roll travel distance.

By way of example, since the feed distance D of the roll under the feed distance condition is 41 mm for the pressure roll 120 and 8 mm for the conical roll 130, this is expressed in the case of the pressure roll 120 and the conical roll 130. When the equations 3 and 4 are combined, the constants c and d may be represented by the equations a and b as shown in Equation 5.

Where c _m and d _m are constants related to the feed speed of the pressure roll 120, and c _a and d _a are constants related to the feed speed of the cone roll 130.

In designing the ring rolling schedule, it is necessary to determine the extreme value (maximum value, minimum value) of the feed speed of the pressure roll 120. In the optimal design method (S200) of the ring rolling schedule according to an embodiment of the present invention, Hua follows the minimum and maximum values of the feed speed of the pressure roll 120 proposed by Equation 6.

Where ν _{f , min} is the minimum value of the feed speed of the pressure roll 120, ν _R1 is the linear velocity at the drive roll 110, D is the diameter of the current ring, R is the outer radius of the current ring, r is the inner radius, R ₁ is the radius of the driving roll 110, R ₂ is the radius of the pressure roll 120, ν _{f , max} is the maximum feed speed of the pressure roll 120, and β is the friction angle ( β = tan ^-1 μ ).

In addition, in the case of the extreme value (maximum value, minimum value) of the feed speed of the conical roll 130, since there is no clearly proposed equation, the equation (7), which is a thickness reduction equation of the ring material 200 established under a constant feed rate condition, is used. In order to use Equation 7, it is necessary to assume that the ring must maintain a constant shape throughout the rolling process, and that the upper cone roll 130 must always be in contact with the upper portion of the ring material 200.

Here, Δh is the thickness of the ring material 200 is changed per ring material 200, D is the diameter of the drive roll, ΔH is the feed distance per wheel of the drive roll (110). Equation for the calculation of the maximum value ΔH and Δh is the maximum per one revolution when no idling occurs between the ring material 200 and the driving roll 110 at the point of maximum feed speed of the compression roll 120 as shown in Equation 8 Consider the thickness reduction rate.

When the volume reduction of the ring material 200 is made in this time interval, the maximum value of the feed rate of the cone roll 130 represents 3.426 mm / s. However, as in the case of the pressure roll 120, this boundary condition is 0.8mm / s when n is 2 when applied from the time point n is 8.

On the contrary, the minimum value of the feed rate of the conical roll 130 is when ΔH represents the minimum value, and thus, as the minimum value of the feed rate of the pressure roll 120 represents a number very close to 0, it is regarded as 0 mm / s.

In the pressure roll 120 and the cone roll 130, the minimum and maximum transfer speeds limit the transfer distance. By the determination of the extreme value (maximum value, minimum value) in the feed speed of the salping pressure roll 120 and the cone roll 130, the feed roll 120 has a minimum feed rate of at least 0 mm / s and a maximum of 4.1 mm / s. In the case of the cone roll 130, there may be a limit of a feed rate of at least 0 mm / s, a maximum of 3.426 mm / s.

That is, the conveying speed of the pressure roll 120 is expressed as a first straight line that is bent as a function of time at each node of the model in which the pressure roll 150 is shaped, and the conveying speed of the conical roll 130 is a conical roll ( 130, which is expressed as a first straight line that is bent as a function of time at each node of the model, and a first straight line about the feed rate of the pressure roll 120 and a bend about the feed rate of the cone roll 130. The first straight line is subject to the continuous condition in which the two straight lines are continuous at the bent portion, and the feeding distance condition in which the distance the roll is fed is constant, and the feed rate of the pressure roll 120 and the feed rate of the cone roll 130 are respectively It may be limited by predetermined minimum and maximum feed rates.

The first linear straight line with respect to the feed rate of the pressure roll 120 and the first linear straight line with respect to the feed rate of the conical roll 130 may be the same as Equation (9).

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t ≤ T / 2 pressure roll feed rate of _from, y _{m, 2} is the pressure at the T / 2≤ t ≤ T roll feed _rate, y _{a, 1} is 0≤ t ≤ T / 2-roll cone-feed rate of from, _{a y, 2} are conical feed roll speed of from T / 2≤ t ≤ T, and a _m, b _m, c _m , d _m , a _a , b _a , c _a , d _a are constants)

The continuous condition and the feed distance condition in the first linear straight line regarding the feed rate of the pressure roll 120 and the first linear straight line regarding the feed rate of the conical roll 130 may be as shown in Equations 10 and 11, respectively. have.

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t ≤ T / 2 pressure roll feed rate of _from, y _{m, 2} is the pressure at the T / 2≤ t ≤ T roll feed _rate, y _{a, 1} is 0≤ t ≤ T / 2-roll cone-feed rate of _from, y _{a, 2} is the feed rate of the conical roll at T / 2≤ t ≤ T, a m, b m, c m , d _m , a _a , b _a , c _a , d _a are constants, D _m is the distance of the pressure roll, D _a is the distance of the cone roll)

The range of the feed rate limited by the minimum and maximum feed rate in the pressure roll 120 and the range of the feed rate limited by the minimum and maximum feed rate in the cone roll 130 may be as shown in Equation 12, respectively. .

(Where y _m is the pressure roll feed rate, y _a is the cone roll feed rate)

When the determined range (threshold) of the conveying speed of each roll as shown in Equation 12, to create the orthogonal array for 0≤ t ≤10 intervals as shown in Table 3. Next, 10 <t ≤20 section proceeds in finite element analysis by a Stroke 10 = a _m a _a +10 right of orthogonal array by using a relationship, such orthogonal array (Table 3).

In addition, in order to be able to directly compare the results when the ring rolling schedule is designed according to the optimal design method (S200) of the ring rolling schedule according to an embodiment of the present invention and the process is performed only at a constant feed rate, Results indicators for finite element analysis were standardized. In other words, f ^* _{load, torque} represents the load and torque applied to each roll at a constant feedrate of pressure roll 120 4 mm / s and cone roll 130 1.77 mm / s, which is the result of finite element analysis. Standardize and use indicators.

7 is a flowchart illustrating a method of optimally designing a ring rolling schedule according to an embodiment of the present invention.

That is, as shown in Figure 7, the optimal design method of the ring rolling schedule (S200) according to an embodiment of the present invention is the transfer of the curved primary straight line and the cone roll 130 with respect to the feed rate of the pressure roll 120 Feeding speed of the bending primary straight line and the cone roll 130 regarding the feeding speed of the pressure roll 120 by the continuous conditions, the feeding distance conditions, and the limit of the minimum and maximum feeding speed in the bending primary straight line regarding the speed. Step (S210) in which the possible range of each constant constituting the first linear straight line with respect to each other is determined, in order to obtain a plurality of objective functions statistically, a plurality of constant sets are constructed according to a predetermined method within the possible range of each constant. In step S220, a plurality of finite element analyzes are performed by the finite element analysis method S100 of the ring rolling process using a plurality of constant sets (S230), and the result of the plurality of finite element analyzes is used. Purpose A may include the step (S240) that make up.

In addition, the optimal design method of the ring rolling schedule (S200) according to an embodiment of the present invention is a finite element analysis performed by inputting the feed rate of the pressure roll 120 and the feed rate of the cone roll 130 to a predetermined value The method may further include normalizing the resultant values of the plurality of finite element analyzes through the resultant values (S240).

The predetermined constant value is as described above.

Standardized outcome indicators are: Equation 13 is a standardized load result indicator of the pressure roll 120, Equation 14 is a standardized torque result indicator of the pressure roll 120, Equation 15 is a standardized load result indicator of the cone roll 130, 16 is a standardized torque result indicator of the cone roll 130, and equation (17) is a standardized result indicator for the maximum load and torque imposed on the pressure roll 120 and the cone roll (130).

Table 4 shows the results of finite element analysis according to the constants a _m , b _m , a _a , and b _a .

Deriving the objective function for each result indicator through the regression analysis of Table 4 is the same as Equation 18 to Equation 25, which are shown in Figs. To simplify the symbols that represent constants, the constants a _m , b _m , a _a , and b _a are represented by a , b , c , and d , respectively.

8 is a graph showing the objective function of the load applied to the pressure roll according to the conveying distance, Figure 9 is a graph showing the objective function of the load imposed on the cone roll according to the conveying distance. 10 is a graph showing the objective function of the torque imposed on the pressure roll according to the conveying distance, Figure 11 is a graph showing the objective function of the torque imposed on the cone roll according to the conveying distance.

As shown in Table 4, the analysis of the ring rolling schedule through the optimal design method (S200) of the ring rolling schedule according to an embodiment of the present invention as a result of the load and torque of each than the molding process at a constant feed rate It can be confirmed by the numerical value that the reduction rate appears.

In this way, the finite element analysis method of the ring rolling process is designed to link the feed rate of the pressure roll and the feed rate of the cone roll to propose an optimized ring rolling schedule that minimizes the load and torque imposed on the roll of the ring rolling machine. can do.

While the present invention has been particularly shown and described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, And all changes and modifications to the scope of the invention.

Claims (13)

delete In a ring rolling process, a spatial mesh system for calculating a velocity field of a ring material and an actual mesh system for reflecting deformation and rotation of the ring material according to the calculated velocity field As an optimal design method of the ring rolling schedule using the finite element analysis method of the ring rolling process that repeats the finite element analysis while updating the velocity field and the information on the deformation and rotation with time increments by interworking with each other. ,
Designing an optimized ring rolling schedule in which the minimum load and torque are imposed on the roll of the ring rolling machine by linking the feed rate of the pressure roll and the feed rate of the cone roll,
The conveying speed of the pressure roll is represented by a first straight line that is bent as a function of time at each node of the model in which the pressure roll is shaped,
The feed rate of the cone roll is represented by a first straight line that is bent as a function of time at each node of the model in which the cone roll is shaped.
The first linear straight line regarding the feed rate of the pressure roll and the first linear straight line about the feed rate of the cone roll are applied to the continuous condition in which the two straight lines are continuous at the bent portion and the feed distance condition in which the roll is fed at a constant distance. Receiving,
The feed rate of the pressure roll and the feed rate of the cone roll are each optimal design method of the ring rolling schedule is limited by a predetermined minimum and maximum feed rate. In claim 2,
Optimum design method of the ring rolling schedule as shown in the following equation, respectively, the first linear straight line about the feed rate of the pressure roll and the first linear straight line about the feed rate of the cone roll.
[expression]

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t <T / 2 pressure roll feed rate of _from, y _{m, 2} is T / 2 pressure at <t ≤ T Roll feed rate, y _{a, 1} is the cone roll feed rate at 0≤ t < T / 2, y _{a, 2} is the cone roll feed rate at T / 2 < t ≤ T , and a _m , b _m , c _m , d _m , a _a , b _a , c _a , d _a are constants) In claim 2,
The continuous design and the conveying distance conditions in the curved primary straight line relating to the feed rate of the pressure roll and the curved primary straight line relating to the conveying speed of the cone roll are the optimum design method of the ring rolling schedule as follows:
[Continuous Condition Expression]

[Travel distance condition formula]

(Where t is a variable of the rolling time, T is the total rolling _time, y _{m, 1} is 0≤ t <T / 2 pressure roll feed rate of _from, y _{m, 2} is T / 2 pressure at <t ≤ T Roll feed rate, y _{a, 1} is the cone roll feed rate at 0≤ t < T / 2, y _{a, 2} is the cone roll feed rate at T / 2 < t ≤ T , a _m , b _m , c _m , d _m , a _a , b _a , c _a , d _a are constants, D _m is the distance of the pressure roll, D _a is the distance of the cone roll) In claim 2,
The range of the feed rate limited by the minimum and maximum feed rate in the pressure roll and the range of the feed rate limited by the minimum and maximum feed rate in the conical roll, respectively, according to the following formula.
[expression]

Where y _m is the pressure roll feed and y _a is the cone roll feed In claim 2,
The first linear straight line relating to the feed rate of the pressure roll and the first linear straight line relating to the feed rate of the conical roll by the continuous condition, the feeding distance condition, and the restriction of the minimum and maximum feeding speed, Determining a possible range of each constant constituting a curved primary straight line relating to a feed speed of a roll and a curved primary straight line relating to a feed speed of the conical roll;
Constructing a plurality of sets of constants according to a predetermined method within a possible range of each constant, so as to obtain a plurality of objective functions statistically,
A plurality of finite element analyzes are performed by the finite element analysis method of the ring rolling process using the plurality of constant sets, and
Constructing an objective function using the results of the multiple finite element analyzes
Optimal design method of the ring rolling schedule comprising a. The method of claim 6,
And standardizing the resultant values of the finite element analysis through the results of the finite element analysis performed by inputting the feed rate of the pressure roll and the feed rate of the cone roll to a predetermined constant value. Optimal design method of rolling schedule. The method according to any one of claims 2 to 7,
The spatial mesh system is configured to fix the shape of the ring material to a space by forming a dense mesh of only the anticipated deformation area,
The axial mesh system deforms and rotates the space of the ring material by forming a uniform and dense mesh as a whole to maintain a constant volume.
Optimal design method of the ring rolling schedule, characterized in that. 9. The method of claim 8,
The finite element analysis method of the ring rolling process
Calculating a velocity field at each node of the spatial mesh system with respect to the time increment Δt,
A second step of calculating a velocity field at each node of the physical mesh system by interpolating the velocity fields at each node of the spatial mesh system,
According to the velocity field calculated at each node of the axial mesh system, the nodes of the axial mesh system are moved during the small time increment (ddt) with respect to the time increment so that the center of the ring material is moved or the radius is increased. A third step of updating the physical mesh system,
A fourth step of updating the spatial mesh system by moving each node of the spatial mesh system to match the shape of the ring material deformed according to each node moved in the physical mesh system;
A fifth step of repeating the third step and the fourth step for the further progress by the small time increment if the cumulative value Σddt of the small time increment is smaller than the time increment, and
A sixth step of updating the virtual mesh system with respect to the time increment if the cumulative value of the small time increment is greater than or equal to the time increment.
Optimal design method of the ring rolling schedule comprising a. In claim 9,
The finite element analysis method of the ring rolling process
During the time increment, the velocity field at each node of the spatial mesh system is applied constant. In claim 9,
The fourth step further comprises the step of checking the boundary conditions of the spatial mesh system. In claim 9,
The sixth step further comprises updating the spatial mesh system with respect to the time increment in accordance with the updated axial mesh system. In claim 9,
The finite element analysis method of the ring rolling process
If the process of the first step to the sixth step for the time increment is completed, the first step to the sixth step for the next time increment repeat design method of the ring rolling schedule.

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