**Table of Contents**show

**1. ****Introduction**

**1.**

**Introduction**

In the production of boilers and pressure vessels, roll bending technology has been widely used,

It not only has cylindrical and conical roll bending, but also has a variety of section steel roll bending, especially cylindrical tube section roll bending as the most typical.

They are made of sheet metal and can be formed by pressing method or rolling bending method, which is also called rolling plate.

The pressing method usually uses the universal die to press the plate.

The roll bending machine is used to conduct continuous three-point bending of the plate to make the plate produce plastic deformation and reach the required bending radius.

**2. Roll bending**

**2. Roll bending**

Roll bending is to bend forming in the roll bending machine by the use of sheet metal or profile as a blank.

The shape of sheet metal roll bending parts is cylindrical, conical and variable curvature;

Generally, the three-roll plate bending machine is used to bend the parts with equal thickness and variable thickness in the thickness direction.

There are two kinds of profile roll bending parts: equal curvature and variable curvature.

There are many kinds of profiles, such as angle, T-shaped profile.

There are two kinds of blank: extrusion and plate bending.

Four-roll plate bending machine is generally used for bending such parts.

**2.1 ****R****oll**** bend****ing characteristics**

**2.1**

**R**

**oll**

**bend**

**ing characteristics**

When rolling, the sheet material is placed between the upper and lower (side) roller shafts of the roller bed. When the upper roller shaft drops, the plate material will be bent and deformed by the bending moment.

Because of the rotation of the upper and lower roller shafts, the friction between the roller shaft and the steel plate drives the plate to move, which makes the pressure position of the sheet metal change continuously, thus forming a smooth bending surface and completing the roll forming.

In the process of roll bending, the deformation mode of sheet metal is equivalent to that of free bending.

The curvature of the roll bending part depends on the relative position between the rollers, the thickness of the sheet metal and the mechanical properties.

By adjusting the relative position between the rollers, the blank can be bent into any curvature smaller than the curvature of the upper roller.

Due to the existence of bending elastic recovery, the curvature of the roll bending part cannot be equal to that of the upper roller.

The most important characteristic of roll forming method is its strong versatility.

Generally, there is no need to add process equipment to the plate rolling machine, and only rollers suitable for different section shapes and sizes are needed for rolling bending of profiles.

The disadvantages of roll bending are low productivity and low precision.

**2.2 ****P****late roll****er**

**2.2**

**P**

**late roll**

**er**

Roll bending machine includes plate roller and section steel roll bending machine.

Since most of the materials processed in roll-bending process are plate blanks, and the plate roller can also perform general section steel rolling with some process equipment, the roll bending machine is mainly the plate roller.

There are three basic types of plate rolling machines:

- symmetrical three roll plate roller
- asymmetric three roll plate roller
- four roll plate roller

**2.3 ****R****oll bending process**

**2.3**

**R**

**oll bending process**

The main method of rolling and bending on plate roller is to roll cylindrical surface with plate blank.

If proper technological measures and necessary equipment are adopted, conical surface and roll bending section steel can also be rolled.

*Fig.1 Common pre-bending methods*

Steel plate rolling consists of three steps: pre-bending (pressing head), centring and rolll bending.

**1) Pre-bending**

It can be seen from Figure 1 that only the part of the steel plate in contact with the upper roller shaft can be bent.

Therefore, there is a length at both ends of the steel plate, which can not be bent.

This length is called the remaining straight edge.

The size of the remaining straight edge is related to the bending form of the equipment.

The theoretical value of the remaining straight edge is shown in Table 1.

The actual residual straight edge is usually larger than the theoretical value, which is 6-20t for symmetric bending and 1/10-1/6 for asymmetric bending.

Table 1 Theoretical residual straight boundary value of steel plate bending

Equipment type | Plate rolling machine | Press | |||

Bending form | Symmetrical bending | Asymmetric bending | Die bending | ||

Three-roll | Four-roll | ||||

Remaining straight edge | Cold bending | L/2 | (1.5~2 )t | (1~2) t | 1.0 t |

Hot bending | L/2 | (1.3~1.5) t | (0.75~1) t | 0.5 t |

Note: in the table, L is the center distance of side roll of plate bending machine, and t is thickness of steel plate.

- The general die is used for multiple bending on the press.

It is shown in Fig. 1 (a).

This method is suitable for pre-bending of various thickness steel plates.

- Pre-bending with formwork on three roll bending machine.

It is shown in Fig. 1 (b).

This method is suitable for t≤t0/2, t≤24mm, which does not exceed 60% of the equipment capacity.

- Pre-bending shall be carried out on the three roll bending machine with backing plate and cushion block.

As shown in Fig. 1 (c).

This method is suitable for t≤t0/2, t≤24 mm, which does not exceed 60% of the equipment capacity.

- Pre-bending with cushion block on three roll bending machine.

It is shown in Fig. 1 (d).

This method is suitable for thin steel plate, but its operation is more complicated and is rarely used.

**2) Centering**

The purpose of centering is to make the plain line of the workpiece parallel to the roll axis, prevent the occurrence of torsion, and ensure the geometric shape of the workpiece after roll bending is accurate.

The centering methods include side roll centering, special baffle centering, inclined feed centering and side roll slotting centering, as shown in Fig. 2.

*Fig. 2 Centring methods*

**3) Roll bending**

Rolling bending of steel plate is usually carried out on a rolling machine.

The typical rolling parts are cylindrical and conical.

*a. Roll bending for cylindrical parts*

When bending the cylinder on a symmetrical three roll bending machine, the position of the upper roll shaft during final bending can be determined according to the known bending radius, as shown in Fig. 3 (a).

Where:

- h – vertical center distance between upper roll and side roll, mm
- R – bending radius of workpiece, mm
- t – steel plate thickness, mm
- r
_{1}– radius of upper roller shaft, mm - r
_{2}– radius of side roll shaft, mm - L
^{2}– side roll center distance, mm

*Fig. 3 Calculation of the position of the rolling machine’s axis*

The final bending position of the side roll shaft is shown in Fig. 3 (b) when the cylindrical surface is rolled on a four-roll plate bending machine, which can be obtained by the following formula:

Where:

- h – vertical center distance between side roll and lower roll, mm
- R – bending radius of the workpiece, mm
- t – steel plate thickness, mm
- r
_{1}– radius of upper and lower roller shafts, mm - R’- R+t, mm
- L
^{2}– side roll center distance, mm

Due to the springback of sheet metal, the value of H obtained in the above formula needs to be corrected properly in practical application.

*b. Roll bending of conical surface:*

The common methods of cone roll bending are small mouth deceleration method, double speed four roll bending method, rotary feeding method and zone rolling bending method.

Because the surface prime lines of the cone are not parallel to each other, and the curvature of each point on the prime line is not the same.

The following measures should be taken to make the upper roller press on the plain line of the cone at every moment of the bending process and form different curvature radii along the plain line.

Firstly, the position of the upper roller can be adjusted to make it incline to a certain angle with the lower roller.

Secondly, in order to keep the upper roller close to the cone surface line, the feed rate at both ends of the cone should be unequal.

For conical parts with large taper, the values of vertical center distance Ya and Yb at both ends of upper and lower rollers can be obtained according to the geometric figure shown in Fig. 4.

Firstly, the center distance Ya and Yb of the upper and lower rollers are obtained according to the calculation method of circular simple parts, that is, according to formula (1).

From the geometric figures shown in Fig. 4 (b) and Fig. 4 (c), the following values are obtained:

The position of the blank from the right end of the roller is determined by l_{b}+c, where

For conical parts with small taper, equation (2) can be simplified as follows:

When the conical part is rolled, it is easy to produce distortion.

The reliable method to eliminate the distortion is that the upper roll is inclined reasonably and the lower roller is parallel.

In the process of rolling and bending, the blank is formed by sectional overlapping roll bending.

**2.4 ****P****rocess classification of roll bending**

**2.4**

**P**

**rocess classification of roll bending**

According to the different temperatures of the rolling plate, it can be divided into cold rolling, hot rolling and medium rolling.

**1) Cold rolling**

When the plate is rolled at the normal temperature (room temperature), known as cold rolling.

Cold rolling is suitable for thin and medium plate rolling.

Due to a certain amount of spring back when applied, as shown in Fig. 5.

After the required bending amount is reached, it should be rolled back several times at this curvature.

The springback of high strength steel is large.

In order to reduce springback, it is better to conduct annealing treatment before the final forming.

The minimum diameter of the cylinder that can be bent on the bending machine depends on the diameter of the upper roll.

Considering the springback of the cylinder after bending, the minimum diameter of the cylinder that can be bent is about 1.1 ~ 1.2 times the diameter of the upper roll.

The operation of cold rolling is convenient, the curvature is easy to control and the production cost is low.

But for thicker plates, equipment power is required.

And it is easy to produce cold work hardening phenomenon.

*Fig. 4 Calculation of the position of the roller in the roll bending machine*

**2) Hot rolling**

It is generally considered that when the thickness (t) of carbon steel plate is greater than or equal to one-fortieth of inner diameter (D) (t≥1 / 40 D), hot rolling should be carried out.

(Note: according to this simple formula and the calculation method of fiber elongation, the difference between cold and hot thickness is large.)

During heat bending, the sheet metal should be heated to 950 ~ 1100 ℃.

At the same time, the heating should be uniform, the operation should be rapid, and the final temperature should not be lower than 700 ℃.

It is unnecessary to consider the springback when hot coiling. For a closed cylinder, roll bending can be done until the longitudinal seam is just closed.

In order to prevent the deformation of the workpiece from being removed from the plate too early during hot coiling, the workpiece should be rolled continuously at the final bending rate until the surface color of the workpiece turns dark.

When the workpiece is in the cold state, it should be placed according to the state shown in Figure 6, or it can be placed vertically.

Hot rolling can prevent the cold work hardening of materials and reduce the power required by the bending machine.

At the same time, there are many shortcomings:

If the hot rolling operation is difficult, the steel plate will produce a serious oxidation phenomenon when heated to a higher temperature.

**3) Warm rolling**

When the plate is heated to 500 ~ 600 ^{o}C for rolling, which is called warm rolling.

Compared with cold rolling, warm rolling has better plasticity, which can reduce the possibility of brittle fracture of cold rolling and reduce the load of the bending machine.

Compared with hot rolling, it can reduce the surface defects caused by oxide scale and improve the operating conditions.

The disadvantage of warm rolling is that there is internal stress caused by rolling after forming.

According to the requirements of products, heat treatment for stress relief is needed.

Since the heating temperature of the warm rolling is usually below the recrystallization temperature of the metal, it still belongs to the scope of cold working.

Roll bending can not be formed at one time, but cold roll bending many times will cause cold work hardening of materials.

When the deformation of bending parts is very large, the cold work hardening phenomenon will be very obvious, so that the service performance of roll bending parts will seriously deteriorate.

Therefore, the allowable bending radius r of cold rolling forming should be larger than the minimum bending radius of sheet metal, and R = 20 t (t is the plate thickness).

When R < 20 t, hot roll bending should be carried out.

For parts with a small bending radius, it is necessary to do a small amount of manual sizing after roll bending.

Reasonable sizing allowance should be reserved for the parts after roll bending, that is, each side is slightly smaller than the template (or card plate), δ = 2 ~ 4mm (shown in Fig. 7).

For roll bending parts with relatively large bending radius, the curvature after rolling must be inspected according to the shape inspection standard, that is to say, such parts can fit the card plate under certain external force (P).

**3. Capacity conversion of bending machine equipment**

**3. Capacity conversion of bending machine equipment**

The capacity of the bending machine can be converted to expand its scope of use.

As shown in Figure 8, the conversion formula is as follows:

*Fig. 8 Capacity conversion of plate rolling machine*

**3.1 ****T****he plate width required by the rolling material is the same as that required by the rolling machine specification, ****but**** the bending radius is different****.**

Where:

- D
_{1}– designed outer diameter of the cylinder for veneer reeling machine, mm - D
_{2}– outer diameter of the cylinder to be rolled by veneer reeling machine, mm - d – diameter of lower roll shaft of veneer reeling machine, mm
- t
_{1}– maximum plate thickness of cylinder designed for veneer reeling machine, mm - t
_{2}– allowable plate thickness of cylinder to be rolled by veneer reeling machine, mm

3.2 The rolling material is the same as the diameter required by the specification of the plate bending machine, but the plate width is different, and the rolling is symmetrical, that is, a1=c1，a2=c2

Where:

- b
_{1}– maximum plate width of cylinder designed for plate rolling machine, mm - b
_{2}width of Cylinder plate to be rolled by plate rolling machine, mm - L-supporting distance of roll and shaft of plate rolling machine, mm
- t
_{1}– designed maximum plate thickness of cylinder for plate rolling machine, mm - t
_{2}– allowable plate thickness of cylinder to be rolled by plate rolling machine, mm

**3.3 ****T****he roll bending diameter is the same as the plate width required by the specification of the bending machine, ****but**** the material is different****.**

Where

- σ
_{s}_{1 }– yield strength of cylinder sheet rolled by plate rolling machine, MPa - σ
_{s2}– yield strength of cylinder sheet to be rolled by plate rolling machine, MPa - t
_{1}– maximum plate thickness of circular strip designed and rolled by plate rolling machine, mm - t
_{2}– thickness of cylinder plate to be rolled by plate rolling machine, mm

**3.4 ****T****he rolling diameter, plate width and material are the same, and the rolling temperature is different****.**

Where

- σ
_{s}_{1}– yield strength of cylinder sheet rolled by plate rolling machine, MPa - σ
_{s}_{2 }– tensile strength of cylinder sheet designed and rolled by plate rolling machine, MPa - t
_{1}– maximum plate thickness of cylinder designed for plate rolling machine, mm - t
_{2}– thickness of cylinder plate to be rolled by plate rolling machine, mm - R
_{x}– is a constant, generally taken as 10-20. - In hot rolling, σ
_{s}= σ_{b} - K
_{0}– relative strengthening coefficient of steel, K_{0}= n/r_{0}. - R
_{0}is the radius of the cylinder designed by the rolling machine, r_{0}≥20 t_{1}. - N is generally 5-10.

## 4. Application

Roll bending technology is widely used in production.

With the application of stainless steel, aluminum, composite steel plate and other materials, higher requirements are put forward for the surface quality of roll bending parts.

Annealing treatment before roll bending has become inevitable for steel grades sensitive to hardenability.

Therefore, reasonable calculation and selection of roll bending equipment, analysis of the measures taken to ensure that the quality of roll bending meets the requirements.

Through the above analysis, calculation and application of the roll bending process, different specifications of curved surface bending can be completed on the bending machine, which improves the utilization rate of the equipment.

omerThank you for research. I want to citetion of figure and special information.

ShaneOkay, I’m glad that our post can be helpful for you.

JoaoVery informative, many thanks!

Could you please share the titles of the books/references you have referenced?

Shanewhat we refer to are non English academic papers, and should be paid, so it will not be helpful for you.