Rolling

# Load analysis and driven power calculation

Sheet rolling device rolls plate metals in cylinder, arch or other work piece forms. It has a wide application in boilers, ship building, oil and chemical industries, metal structures, mechanic manufactury. Four-roll bend device is characterized with a suitable centeral adjustment, little extra direct edges, precise circle corrective, great effectiveness and ability to finish pre bend process, formation of a work piece in a single roll operation. It plays a considerably significant role in plate metal formation. Rolling bend strength position is somewhat intricate in four roll sheet bend process, it is capable of bearing large weight. This means that bear pieces should have proper power as well as firmness. So, sheet roll designing must be highly accurate and dependable. Confirmation of rolling bend device strength parameters is required, like pressure upon rolls, bend torque, moto driven energy. Load analyse of roll device will provide guiding facts on sheet roll design pieces. Calculating the device major power will be the main information to choose the proper motor. In case the engine power is less than necessary, motor will get overloaded and damaged by the produced heat. In case it is too big the produced energy will not be consumed causing power waste. This article will deliver information on  four-roller sheet bending device operational principles and its essencial frame as well as analysis of strength abilities and how to gain calculating formulas for four-roll bend device power.

## For-roll Bend Device Structure and Its Operation Principles

In accordance with three-point formation principles this machine applies the relational position changes and the rotating movemennt of work rolls torealize elasto-plastic bend to make a work piece with predefined shapes and accuracy.

Four-roll sheet bend rollers are depicted in fig. 1. It consists of a down frame, overturning appliance, top and bottom rollers, two-side roll, a tall frame, a linking beam, a stand, a balance appliance, transmitting appliance, electric and hydraulic systems and others. Operating roller has four rollers: a top roller, a bottom one and two side-rollers. Top roller is the major driving roll. It is inset in the tall and bottom frames through bear frame, it is static and makes just rotating movement.

Bottom roll is inset into the bear base. It does a direct motion in slide guiding frame channel for density compensation while the sheet gets bent. Two side-rollers are inset in bear base. It moves upwards and downwards at an angle with upright course to gain a particular semidiameter of cylinderic curve.

1. Leftside frame
2. Overturning appliance
3. Top roll
4. Bottom roll
5. Side-roll
6. Balance appliance
8. Rightside frame
9. Stand

Generally, rolling plate metals in a cylinder work piece through four-roller bend device implies these four operations: centeral adjustment, pre bending, rolling, circle correcting.

While operating the device, put the roll sheet end in the midst of top and bottom rollers, adjust the center, raise one side-roll, align sheet end and side-roller, raise bottom roll to push the sheet firmly, then raise the next side-roll to produce strength and force the sheet end to bend.

During pre bend of the other end, there is no necessity to move the plate away off the roll device. Push it to another side of device, then pre bend applying the method described above.

Continue rolling to gain the specified cylinder curve radius through a single or multiple feed. Correct the round shape to aquire proper roundness or cylindrical form. For achieving the required result just putting the sheet in the roll machine once is enough.

### 2.1 Calculating the utmost bend moment of sheet.

Figure 2 shows that the sheet area pressure is distributed alongside steel sheet highness while line bending is realized.

Dynamic relations of proper stress may be the following.

In this formula:

σ is the work piece stress.

σ s is the sheet yielding border

ε  is the work piece strain

ε is the line reinforce module of sheet, it appears on apropriate manuals.

y is the space between neutral axle and a specific spot.

Ｒ′ is the curve semidiameter prior to the bounce of neutral coat. Its calculation is the following:

Here:

R is the roll semidiameter.

δ shows how thick the rolling steel sheet is.

E is the sheet elastic module.

Ko is the sheet relational force module. It appears in appropriate manuals.

K1 is the form ratio, cross-section of a rectangle K1 equals 1.5.

The bend point over cross-section M is as the following:

If 1 and 2 formulas are put in 4, the result will be:

b is the utmost breadth of rolling steel. The primary deformitybend point M0 is.

### 2.2 Calculating roller strength.

Four functioning rollers have two types of arrangements: symetric and assymetric. This requires separate strength analyse of four-roller device.

Symmetric arrangement

Figure 3 shows the steel sheet strength.

In accordance with strength balancing, it is possible to obtain every roller strength on the sheet steel.

In the above formula:

FH is hydraulic otlet strength of bottom the roll.

Fc is the side-roll strength.

Fa is the top roll sheet deformity strength.

Fa is the top roller overall strength.

a0 is the bevel in the midst of side-roll and top roll strength lines.

The formula given below determines its value:

Da is the top roller diameter.

Dc is side-roller diameter.

y is the lean bevel of side-roller. This is the bevel in the midst of side-roller adjusting and upright directions.

A is the space between rolling angle intersected spot and the centeral part of top roll.

#### Asymmetric arrangement.

Figure 4 shows the sheet strength under asymmetric arrangement.

In accordance with strength balancing it is possible to obtain every functioning roller strength:

Fb is the bottom roller strength

a is the bevel in the midst of top roll and bottom roll strength lines.

β is the bevel between top roll and side-roll strength lines.

This formula determines a, β value:

In this formula:

Db is the bottom roller diameter.

B is the space between top roll acting line and the centeral part of bottom roll.

B＝ [1+Db /(2R’+δ]B’;

B`shows how long the remained direct ridge is. B’＝2δ

### 3. Calculating Driven Powers.

#### 3.1 Top roll driving torque

Top roll of four-roller bend device is referred to as driven roll. Overall driving torques upon top roll adds torques spent on deformity overcoming frictions. Torques spent in deformity are specified through bend inner strength as well as the strength which equals the top toll outer strength.

In this formula:

Wn is the operation realized through bend inner strength.

Ww is the operation upon top roll through outer strength.

L is the bend angle corresponding to sheet lengths.

It is possible to obtain torque consumption during deformation.

Formulas 19 and 20 determine torque frictional overcome. Frictional torque of shaft-roller under symmetric position.

Assymetric position:

In above formula:

f is roll frictional ratio, which equals 0.8 mm.

μ is roll neck slide frictional ratio, which equals 0.05-0.1.

da, db, dc are roll-neck diameter of top, bottom and side rolls respectively.

Overall drive torque upon top roll is:

### 3.2 Top roll driven powers.

#### Calculating drive powers:

v is the roll rate.

r is drive roll semidiameter.

η is transmitting performance, which equals 0.9.

Drive powers of driven roll is estimated while pre bending and rolling. Major driving framework drive power appears the great estimate for calculating results.

Pq is the drive power of major driving framework.

Py is the drive roll power in pre bending.

Pj is the drive roll driven power during roll process. Pq estimate of drive powers serves like a base in major engine power selection.

Conclusion.

In accordance with four-roll sheet bend device operational principles roll strength has to be analysed, then gain the proper formulas of functioning rolls under various positions.

Depending on the analyse of utmost deformity bend point and roller bearing strength deternmine relations of strength, bend point and driven powers, then decide on the system of calculating drive powers of major driving framework.

Drive powers of pre bend and roll process are estimated separately. The major engine power selection depends on the great estimate of calculation result.