**Table of Contents**show

**1.**** Introduction**

**1.**

**Introduction**

According to the principle of three-point rounding, the plate bending machine makes use of the rotary motion and relative position change of the work roll to produce continuous elastic-plastic bending.

Metal sheets can be bent into cylinder shape, arc shape and other predetermined shapes and precision workpieces.

They are widely used in boiler, shipbuilding, petrochemical, metal structure and sheet metal forming machinery manufacturing industry.

According to the number of rolls, the plate bending machine can be divided into two-roll type, three-roll type and four-roll type, and different plate bending machine has different characteristics.

Compared with the former two-roll type, the four-roll bending machine has many advantages, such as convenient centering, small residual straight edge, high precision of circle straightening, high production efficiency.

In addition, it can complete plate end preplex and workpiece rolling without turning around, which plays a more and more important role in sheet metal forming.

The four-roll plate bending machine is composed of upper roll, lower roll and front and rear two side rolls.

The upper roll rotates at a fixed position, and the steel plate is driven by friction to realize feeding movement.

The clamping, preflex and rolling process of steel plate are realized by controlling the feeding position of the lower roll and two side rolls.

Therefore, in order to improve the rolling accuracy of steel plate, it is necessary to study the accurate position of the lower roll and the two side rolls.

At present, the position control of the lower roll and both sides of the four-roll plate bending machine is still determined by the operator through repeated adjustments based on experience, and the rolling accuracy is controlled by continuous comparison and model checking, which leads to low rolling accuracy and low production efficiency.

Based on the analysis of the technological process of rolling steel plate with four-roll rolling machine, this article puts forward the calculation formula of springback curvature radius according to the elastic recovery theory, and studies the technological position requirements of lower roll and two side rolls in the process of rolling steel plate.

A mathematical model for calculating the position of the lower roll and two side rolls in the process of aligning, preflex and bending is established.

The displacement of the lower roll and the front and rear side rolls in the process of steel plate rolling is accurately determined, which can provide accurate feed data for digital control.

The production practice shows that the calculation results of this method are consistent with the practical application, and higher rolling accuracy and production efficiency can be obtained.

## 1. Process flow of four roll plate bending machine

### 1.1 Structure and working principle of four roll plate bending machine

The mechanical structure of four-roll plate bending machine is mainly composed of the following parts: upper roll device, lower roll device, side roll device, overturning device, low rack, base, high rack, hydraulic pump station, etc.

The upper roll is the driving roll, which is rotated by the servo motor through the transmission device, and its position is fixed;

The lower roll and the side roll are driven rolls.

The rotation of the lower roll and the side roll is driven by the friction between the steel plate and each roll.

The lower roller is fixed in the bearing seat.

In order to adapt to the different thicknesses of the bent plate, the bearing seat can make a vertical linear movement in the sliding guide groove of the frame;

Two side rolls are installed in the side roll bearing seat.

In order to curl to the specified curvature radius of the cylinder, the side roll bearing seat moves up and down in the inclined direction in the sliding guide groove with a certain angle to the vertical direction.

The overturning and reset of lower roll, side roll and upper roll are controlled by hydraulic cylinder.

The main structure of the equipment is shown in Figure 1.

Fig. 1 Structure of four-roll plate bending machine

**1****.2 Process flow of four-roll plate bending machine**

**1**

**.2 Process flow of four-roll plate bending machine**

The technological process of rolling steel plate is generally composed of six steps, such as preparation, feeding, prebending, prebending on the other side, rolling forming and arc correction, as shown in Figure 2.

Fig. 2 Technological process of four-roll plate bending machine

**1.2.1 Preparation and feeding**

The lower roll is raised to the position where the distance between the upper generating line and the lower generating line of the upper roll is slightly greater than the thickness of the workpiece.

The rear side roll is raised to the position where the upper generatrix and the upper generatrix of the lower roll are in the same horizontal plane, and then the front side roll is raised to the position where the center line is between the upper and lower rolls (Fig. 2a);

The workpiece is horizontally fed between the upper and lower rolls, the front end is against the front roll, and the lower roll is raised to clamp the steel plate (Fig. 2b);

Finally, the preparation and feeding process is completed.

**1.2.2 Prebending**

The front side roll is returned to its original position, and the rear side roll is raised to the process height of the curvature of the prebending steel plate (Fig. 2c).

The upper roll rotates anticlockwise to drive the steel plate forward.

When the end of the steel plate is 1/2 of the distance between the two rollers, it should measure the end to make it reach the required curvature.

The process of the other end prebending is similar to that mentioned above.

**1.2.3 Roll bending**

The front side roll is raised, so that it is at the process height of the required curvature.

The rear side roll is lowered, so that the front and rear side rolls are on the same level.

The upper roll rotates counterclockwise to drive the steel plate to move forward to curl the steel plate.

At the same time, the curvature of the protruding steel plate is measured with the template, and the process height is adjusted at any time to make it reach the required radian (Fig. 2d).

The arc calibration process is the same as the roll bending process.

**3****. Calculation of springback radius during steel plate bending**

**3**

**. Calculation of springback radius during steel plate bending**

At present, the vast majority of coils are cold rolled.

The springback phenomenon is very obvious in the cold rolling process, so there should be a certain amount of overwinding to offset the springback.

Generally, the spring back radius should be less than the required radius of the parts (pre-bending radius).

According to the elastic-plastic mechanics, the springback in sheet metal processing depends on the elastic modulus, strengthened elastic modulus, yield limit, pre-coiling radius and sheet thickness.

After theoretical derivation, the calculation formula of the radius of curvature before recovery can be determined as follows:

In the formula:

- R – Pre-coiling radius, mm;
- E – Elastic modulus of the material, MPa;
- t – Thickness of steel plate, mm;
- σ
_{s}– Yield limit of the plate, MPa; - S – Static moment of the section, mm;
- W – Modulus of bending section, mm;
- E
_{1}– Strengthened elastic modulus of steel plate material, MPa; - k
_{0}– Relative strengthening coefficient of material; - k
_{1}– Section coefficient, 1.5 is taken for the rectangular section.

**4. Calculation of working displacement of side roll**

**4. Calculation of working displacement of side roll**

From the analysis of the steel plate rolling process, the position of the upper roll does not move during steel plate rolling, and the rolling is mainly completed by the vertical movement of the lower roll and the oblique feed of the two side rolls.

Therefore, the accurate rolling of steel plate can be completed by precisely controlling the position of each roller in the process.

The following is the mathematical modeling and calculation of the process position of the lower roll and side roll in the main processes such as forward, prebending and coiling.

The geometric parameters of the rolling machine, the material and thickness of the rolled steel plate and the rolling radius are considered.

The following parameter symbols are usually used to derive the displacement formula of the back roll and both sides of the plate bending machine:

- R is the radius of curvature before springback (i.e. the radius to be curled), mm;
- A is the center of the bending machine, which is located at the intersection of the inclination angles of the rollers on both sides;
- α is the inclination angle of the rollers on both sides, °;
- L
_{1}is the distance from point a to the center of upper roll, mm; - L
_{2}is the distance from point a to the center of lower roll, mm; - L
_{3}is the distance from point a to the center of side roll, mm; - D
_{1}is the diameter of upper roll, mm; - D
_{2}is the diameter of the lower roll, mm; - D
_{3}is the diameter of side roll, mm; - Y
_{1}is the lower roll displacement, mm; - Y
_{2}is the displacement of rear side roll, mm; - Y
_{3}is the displacement of front side roll, mm.

**4.1. Calculation of the displacement of the side roll and the lower roll of the plate bending machine**

**4.1. Calculation of the displacement of the side roll and the lower roll of the plate bending machine**

In the alignment process of the plate bending machine shown in Figure 2, the lower roll and two side rolls have the corresponding displacement.

The process position of each roller during alignment is shown in Fig. 3.

Fig. 3 Process position of aligning rolls

According to the geometric relationship, the displacement of the two side rolls and the lower roll can be obtained as follows:

**4.2 Calculation of side roll displacement during pre****bending**

**4.2 Calculation of side roll displacement during pre**

**bending**

In the prebending process of the bending machine shown in Fig. 2, the lower roller and the front and rear rollers have the corresponding displacement.

According to the prebending process requirements, the process position of each roll in the left prebending is shown in Figure 4.

During the right prebending, the positions of the front and rear rollers are just interchanged, and the position of the lower roller is unchanged.

The value of geometric parameter B can be calculated according to the calculation formula of the asymmetric three-roll plate bending machine.

In this article, B = 2t is taken.

Fig. 4 Process position of each roll during prebending

Suppose O is the center of curvature before springback, y is the angle between the upper roll center and bending center line OO_{1} and the lower roll center and bending center line OO_{2};

φ is the angle between the line O_{1}O_{2} between the upper roll center and the lower roll center and the line between the upper roll center and the bending center;

θ is the angle between the line AO_{3} between the center of the bending machine and the center of the side roll and the line OO_{3} between the center of the side roll and the bending center.

According to the geometric relationship, it can be concluded that:

In the formula, the geometric parameter B is the value from the center of lower roll O_{2} to OO_{1}, which can be calculated according to the formula of the asymmetric three-roll plate bending machine.

In this article, B = 2t, and other parameters are the same as the above.

Suppose that * F* is the intersection of OO

_{2}and AO

_{3}, and β is the angle between

*and the middle line of upper and lower rolls.*

*F*In △ AFO_{2}, according to the sine theorem:

Thus:

Similarly, in △ AFO_{2}:

Thus:

In △ AFO_{2}:

Thus:

That is:

Therefore, the displacement between the two side rolls and the lower roll is:

When the right side is prebending, Y_{1} remains unchanged, Y_{2} and Y_{3} can be interchanged.

**4.3 Calculation of side roll displacement during continuous bending**

**4.3 Calculation of side roll displacement during continuous bending**

In the continuous bending process of the plate bending machine shown in Figure 2, the two side rolls are in a symmetrical position, and the lower roll and the front and rear side rolls have the corresponding displacement.

According to the requirements of the continuous bending process, the position of each roller process is shown in Figure 5.

Fig. 5 Process position of each roll during continuous bending

According to the geometric relation, in △OAO_{3}, from the sine theorem:

Thus:

Suppose that O is the center of curvature before springback, λ is the angle between OO_{2} and OO_{3}, then:

In △OAO_{3}：

Thus:

If Y_{1} remains unchanged, Y_{2}=Y_{3}=L_{3}-AO_{3}, so the displacement of the rollers on both sides and the lower roller is:

**5. Actual verification results**

**5. Actual verification results**

Taking the W1220×2500 plate rolling machine as the experimental object, the thickness of rolled plate is 10 mm, the material is Q235, and the rolling radius is 700 mm.

According to the experimental verification, the absolute error between the actual circle radius and the required circle radius is 4.8mm, and the relative error is 0.68%.

On this basis, the correction can meet the accuracy requirements.

Through the analysis of the test data of adjusting the springback radius many times, it can be seen that the main reason for the error is that the plate is analyzed as pure bending when calculating the springback bending radius, and the influence of extrusion force and friction on the springback radius is not considered.

Through technical analysis, the displacement calculation is basically accurate, and can meet the process requirements.

**6. Conclusion**

**6. Conclusion**

In this article, based on the analysis of the rolling process of four-roll plate rolling machine, combined with the calculation formula of the springback radius, using mathematical and mechanical methods, the process position of each roller in the working process of the rolling machine is analyzed.

According to the calculation results, the test is carried out on a four-roll plate bending machine.

The practice shows that this method can effectively reduce the number of tests and improve the accuracy and efficiency of rolling.