Plate rolling machine is a kind of universal forming equipment to roll sheet metal into cylindrical, arc and other general shapes of the workpiece.

It has been widely used in boiler, shipbuilding, petroleum, chemical industry, metal structure and mechanical manufacturing industry.

Four roll plate bending machine is featured convenient center alignment, small surplus straight edge, high accuracy roundness correction, high efficiency as well as able to complete pre-bending and workpiece forming in one-time rolling without switching the plate end.

It occupies an increasingly important position in sheet metal forming.

The roll bending force condition is relatively complex during the working process of four roller plate bending machine, and it bears a great load which requires the bearing parts has enough strength and rigidity.

Therefore, precise and reliable design of plate rolls is necessary.

First, the force parameters of the roll bending machine need to be confirmed, such as pressure on the roller, bending torque, and motor-driven power.

The load analysis of the rolling machine can be reference data for designing parts of plate rolls.

The calculation of the main driven power of the plate roll bending machine is the key reference data for choosing the main motor.

The motor power should be chosen properly.

If too small, the motor will be overloaded for a long time which will damage the motor because of heat caused by insulation.

If too large, the output power cannot be fully utilized which will waste the electricity.

Therefore, doing load analysis and improving the driven power calculation of the four-roll plate bending machine has important practical value for choosing a proper motor.

In this post, we not only introduce the basic structure and working principle of the four-roll plate bending machine but also analyze the force capabilities based on that and finally get the calculation formula for the main driven power of four rolls bending machine.

Table of Contents

**Four Roll Bending Machine Structure and Working Principle**

According to the principle of three-point forming, the rolling machine makes use of the relative position change and rotation motion of the working roll, so that the sheet can produce continuous elastoplastic bending to obtain the workpiece with predetermined shape and precision.

The structure of four roller plate bending rolls as shown in figure 1, it is mainly composed of low frame, overturn device, upper roller, lower roller, two side roller, high frame, connecting beam, base, balancing device, transmission device, electrical system, hydraulic system, etc.

The working roll of the four roller plate rolls consists of four rolls: upper, lower and two side rolls.

The upper roller is the main drive roller, which is embedded in the high and low frame through the bearing body, and its position is fixed, so it can only do the rotary motion.

The lower roller is fixed in the bearing pedestal. In order to compensate for the thickness of the bent plate, the bearing pedestal can do the straight-line movement in the sliding guide groove of the frame.

The two side rollers are installed in the bearing pedestal. In order to obtain the specified radius of cylinder curvature, the side roller bearing pedestal can move up and down in the direction of a certain angle with the vertical direction.

Fig.1 Structure of four-roll plate bending machine

１. left frame

２. overturn the device

３. upper roller

４. lower roller

５. side roller

６. balancing device

７. connecting beam

８. right frame

９. base

In general, rolling a metal sheet into a cylindrical workpiece on a four-roll bending machine consists of four processes, namely:

- Center alignment
- Pre-bending
- Rolling
- Roundness correction

During rolling machine operation, first place the front end of the bending roll plate between the upper and lower roller, and align the center (lift one side roller, aligning plate end and side roller), then lift lower roller to press the plate tightly and lift the other side roller to apply force which makes the end of the metal plate bending.

When pre-bending the other end of the plate, the metal sheet does not need to take out from the rolling machine. Move the plate to the other end of the machine and pre-bending with the same method.

Then use one-time feeding or multi-time feeding to roll continuously until reaching the required cylinder curvature radius

Finally, do the roundness corrections in order to get the required roundness and cylindricity.

Thus it can be seen that when bending the plate with four rolls, it is necessary to put the plate into the rolling machine only once to achieve the purpose of all the bending rolls.

## Load Analysis

### 2.1 Calculation of the maximum bending moment of the plate

As shown in FIG. 2, the stress distribution of the plate section along the direction of steel plate height during the linear pure plastic bending is shown in FIG. 2.

Fig.2 Stress distribution of plate

The functional relation of true stress can be expressed as follows:

In the above formula:

σ – the stress of the workpiece;

σ_{s}– the yield limit of the material;

ε – the strain of the workpiece;

ε – The linear reinforcement modulus of the material, can be found on the relevant manual.

ｙ- The distance from the neutral axis to any point;

Ｒ′ – The radius of curvature before the neutral layer rebound, can be calculated as follows:

In the above formula:

Ｒ – Rolling radius;

δ – Thickness of rolled steel plate;

Ｅ- Elastic modulus of the steel plate;

K0 – The relative strength modulus of the material, can be found in the relevant manual.

K1 – Shape coefficient, rectangular cross sectionＫ１＝1.5

The bending moment on the cross-section Ｍ is:

Put formula （１）and（２）into（４）, we get:

In the above formula:*ｂ*– The maximum width of rolled sheet steel plate.

Initial deformation bending moment Ｍ_{０} is:

**2.2** **Working roll force calculation**

According to the structural characteristics of the four rolls, it is easy to know that the four working rolls can be arranged in two different ways:

Rollers are arranged in a symmetrical arrangement and asymmetrical manner.

Therefore, it is necessary to do the force analysis of the four-roll machine separately.

**2.2.1** **The rollers are arranged in a symmetrical manner**

The force of the steel plate is shown in FIG. 3.

Fig.3 Effect of force under roller arranged symmetrically

According to the force balance, the force of each working roll on the steel plate can be obtained:

In the above formula:

F_{H} – Hydraulic output force of lower roller;

F_{c} – Side roll force;

F_{a} – Upper roller plate rolling deformation force.

F_{a} – Upper roll total force;

α_{0} – The angle between the force action line of the side roller and the force line of the upper roller.

The value of α_{0} can be determined by the following formula according to the geometric relationship:

In the above formula:

D_{a} – Upper roll diameter;

D_{c} – Side roll diameter;

γ – Tilt Angle of the side roll, which is the angle between the adjustment direction of the side roller and the vertical direction;

A – The distance from the intersection point of the roll angle to the center of the upper roller.

**2.2.2 ** **The rollers are arranged in an asymmetrical manner**

The force of the steel plate is shown in FIG. 4 when the roller is arranged in an asymmetric manner.

According to the force balance, the force of each working roll on the steel plate can be obtained:

In the above formula:

F_{b}– Lower roll force;

α – The angle between the force action line of the upper roller and the force line of the lower roller;

β – The angle between the force action line of the upper roller and the force line of the side roller.

The value of α, β can be determined by the following formula according to the geometric relationship:

In the above formula:

D_{b} – Lower roll diameter;

B – The distance between the action line of the upper roller and the center of the lower roller,

B＝ [1+D_{b} /(2R’+δ]B’;

B’ – The length of the remaining straight edge, B’＝2δ

In the formula: A_{1} = Asinγ/sin(γ – φ)

**Driven Power Calculation**

### 3.1 Upper roller drive torque

The upper roller of 4 rolls bending machine is a driven roller.

The total drive torque acting on the upper roller is adding up the torque consumed on the deformation and overcomes the friction.

Friction torque includes frictional resistance consumption to overcome shaft roller rolling on the bending plate and torque consumption in the roller bearing friction.

The torque that is consumed in the deformation can be determined by the work done by the bending internal force and by the force equal to the external force on the upper roller.

In the formula:

W_{n }– The work done by bending internal forces;

W_{w }– The work on the upper roller by external forces;

L – The bending Angle corresponds to the length of the plate.

Make formula (17) equal to formula (18), we get the torque consumed in deforming:

The torque for overcoming friction can be determined by formulas (19) and (20).

Friction torque of shaft roller in the symmetrical arrangement:

Friction torque of shaft roller in the asymmetrical arrangement:

In the above formula:

*f* – Coefficient of rolling friction, *f* ＝0.8mm

μ – Sliding friction coefficient of the roller neck, μ＝0.05-0.1；

d_{a,} d_{b,} d_{c }are the roller neck diameter of the upper roller, lower roller and side roller separately.

The total driving torque on the upper roller is:

**3.2 Upper roller drive power**

The calculation formula for driving power is:

In the formula:

ν – Rolling speed;

r – Driven roller radius, r=D_{a} /2

η – Transmission efficiency, η＝0.9

According to the actual application condition of the four-roll plate bending machine, the driving power of the driving roller is calculated during the pre-bending and rolling process, and the driving power of the main drive system is the larger value in the calculation result:

In the above formula:

P_{q }– Driving power of the main drive system;

P_{Y } – The driving power of the driving roller when pre-bending;

P_{J } – The driving power of the driving roller when rolling circle.

The calculated value P_{q }of the driving power can be used as the basis for selecting the main motor power.

## Conclusion

(1) According to the structural characteristics and working principle of the four rolls plate bending machine, the force of the working roller is analyzed, and the calculating formula of the working roll under the different arrangements is obtained.

(2) On the basis of analyzing maximum deformation bending moment and the bear force of working roller, combining function transformation principle, to establish the relationship between the force, bending moment and device driver power, and put forward a method to calculate the driving power of main drive system.

According to the actual application conditions, the driving power of the pre-bending and rolling is calculated respectively, and the main motor power is selected based on the larger value of the calculated results.

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RAJAN PATELi did not found relative strength modulus anywhere can you please write something about its value for mild steel. it would be great to have this value because i can compare our existing design with theory.

russell djcould you display with units in imperial. I’m a bit unfamiliar to do conversions and such

MachineMfgsorry for the inconvenience, however, you can use google to do the conversions. Anyway, thanks for your comments.

harshad sonawaneSir, how to calculate relative strength modulus (K0) for any material ???

manieswarBy using 4 roll bending machine , what range of angles can be obtained better than 3 roll bending machine

Tuncay KamasCould you please provide K0 for any steel so that we can also calculate the springback. Without it, all the mathematical model means nothing.