Table of Contents

**1****.**** Preface**

**1**

**.**

**Preface**

In order to cooperate with the bidding of the reconstruction and expansion of the 750 m^{3} blast furnace in Laiwu Iron and Steel General Plant (Lai Steel), the construction and installation company of Laiwu Iron and Steel Co., Ltd. decided to select the motor for the plate rolling machine which has been idle for many years and can roll 40mm thick steel plate to prepare for the production of the blast furnace body.

Therefore, referring to the working principle of the multi-roll straightening machine and the calculation of force and energy parameters, the working principle and calculation formula of force and energy parameters of the plate rolling machine are reasonably deduced.

The test run proves that the selected motor driving power can meet the requirements of the plate rolling machine design capacity.

**2. Bending process of steel plate on roller type plate rolling machine**

**2. Bending process of steel plate on roller type plate rolling machine**

The bending deformation of the steel plate on the plate rolling machine is a transverse bending process.

As shown in Figure 1, under the action of bending moment M under external load, the longitudinal fiber above the neutral layer is compressed and the longitudinal fiber below the neutral layer is subject to tensile deformation.

*Fig. 1 Bending deformation diagram of steel plate*

According to the magnitude of external load torque, when the maximum stress of the steel plate surface layer is less than the yield limit of steel plate material, the longitudinal fiber of each layer is in an elastic deformation state;

With the increase of bending moment under external load, the deformation of each layer of steel fiber continues.

When the external load increases to a certain value, the longitudinal fiber stress on the surface of the steel plate exceeds the yield limit of the material, and the fiber produces plastic deformation.

The greater the load, the greater the depth of the plastic deformation zone from the surface layer to the neutral layer.

When the longitudinal fiber stress of the whole section of the steel plate exceeds the yield limit of the material, all the longitudinal fibers are in a plastic deformation state and the bending process is completed.

**3. Working principle of plate bending machine**

**3. Working principle of plate bending machine**

There are two working parameters of the plate rolling machine:

1) The reverse bending ratio 1/ρ refers to the curvature of the steel plate after bending to one side under the action of bending moment M.

2) Residual curvature 1/r refers to the curvature of the steel plate after elastic recovery under the action of the elastic internal moment after removing external load (r is the diameter of rolled steel pipe).

The selection of reverse bending rate is the key to determining whether the steel plate can achieve the bending purpose.

In a three-roller plate roll, the reverse bending rate is obtained by pressing down the reduction roll.

Different residual curvatures can be obtained by adjusting different reductions to obtain different diameters of rolled pipes.

**4. ****Calculation of force and energy parameters of the plate rolling machine**

**4.**

**Calculation of force and energy parameters of the plate rolling machine**

The force and energy parameters of the plate rolling machine refer to the pressure (bending force) acting on the roller, bending torque and driving power of the motor of the plate rolling machine.

**4.1 Pressure (bending force) acting on the roller of the plate bending machine**

The pressure acting on the roller can be calculated according to the moment required for bending the steel plate.

In this case, the steel plate is regarded as a beam under a concentrated load.

The load is the pressure of each roller on the steel plate, as shown in Fig. 2.

*Fig. 2 Pressure (bending force) acting on the roller*

- P
_{1}: Pressure of the first roller on the steel plate - P
_{2}: Pressure of the second roller on the steel plate - P
_{3}: Pressure of the third roller on the steel plate : Roll pitch*t*

In the calculation, the bending moment of the steel plate under the second roll is assumed to be pure plastic bending moment M_{s}, that is, M_{2} = M_{s} (pure plastic bending moment M is the maximum bending moment that may be reached in elastic-plastic bending).

In the formula:

- σ
_{s}— yield limit of steel plate material, 250Mpa; - s — plastic section coefficient, which is bh
^{2}/ 4t_{b}for steel plate; - b – width of steel plate, m;
- h — steel plate thickness, mm.

In this way, P_{1}, P_{2}, P_{3} can be calculated according to the balance condition of external force on the steel plate under the second roller:

Total pressure:

**4.2 Bending torque acting on the roller of plate bending machine**

The bending torque M_{K} acting on the roller can be determined according to the principle of equal function.

The bending work AK produced by bending torque on the roller shall be equal to the work AP for plastic deformation of steel plate, i.e. A_{p} = A_{k} (shown in Fig. 3).

*Fig. 3 Variation of bending moment along plate length*

The plastic deformation work A_{p2} of the steel plate under the second roll is:

In the formula:

- M
_{2}– bending moment of steel plate under the second roller; - L
_{2}— the length of steel plate under the second roller; - 1 / r
_{p}_{2}— plastic deformation curvature of steel plate under the second roller.

Bending work acting on the second roller:

Where D_{2} is the diameter of the work roll.

To make:

For the convenience of calculation, the following assumptions are made:

- r
_{p}_{2}can be approximately equal to the diameter of the rolled tube; - The bending moment M
_{2}of the steel plate under the second roll is equal to pure plastic bending moment M_{k2}.

Then the formula is as follows:

**5. Calculation of motor driving power of plate rolling machine**

**5. Calculation of motor driving power of plate rolling machine**

The motor power can be calculated according to the following formula:

In the formula:

- M
_{k}— bending torque, kN.m; - P – the total pressure acting on the roller, kN;
- d – rolling friction coefficient of roller and steel plate, the steel plate is 0.0008 m;
- μ – friction coefficient of roller bearing, the sliding bearing is 0.05 ～ 0.07;
- D – diameter of roller body, m;
- v – Speed of roll body, V/S;
- t – transmission efficiency, 0.65-0.80.

According to the above calculation formula, the motor driving power of 40 mm thick steel plate rolling machine is selected as follows:

It is known that: h = 40 mm, D = 420 mm, t = 900 mm, the maximum width of rolled steel plate b = 2500 mm, the minimum rolling diameter r = 1000 mm, d = 400 mm, v = 2 m/min.

Thus:

According to the above calculation, the motor driving power of the 40 mm steel plate rolling machine is selected as 25 kW.