Como calcular a potência do motor para máquinas laminadoras de placas

How to calculate engine power for plate rolling machines

1 . Preface

Construction and installation company Laiwu Iron and Steel Co., Ltd. decided to select an engine for the heavy plate rolling mill in support of the tender for reconstruction and expansion of the 750 m3 blast furnace at Laiwu Iron and Steel General Plant ( Lai Steel). The thick plate rolling mill, which has been inactive for many years, will be used in preparation for the production of the blast furnace body and has the capacity to roll steel sheets 40 mm thick.

Referring to the working principle of a multi-roll straightening machine and considering the force and energy parameters, the working principle and calculation formulas of force and energy parameters for the plate rolling machine were logically deduced.

The test results indicate that the selected motor has sufficient drive power to meet the design capacity requirements of the plate rolling mill.

2. Steel plate bending process on roll type plate rolling machine

Bending deformation of a steel sheet in a sheet rolling mill is a transverse bending process. As illustrated in Figure 1, under the influence of the bending moment M under an external load, the longitudinal fibers above the neutral layer undergo compression, while the longitudinal fibers below the neutral layer undergo tensile deformation.

Fig. 1 Bending deformation diagram of steel plate

Fig. 1 Bending deformation diagram of steel plate

According to the magnitude of the external load torque, when the maximum stress in the surface layer of the steel sheet is below the yield strength of the steel sheet material, the longitudinal fibers in each layer are in a state of elastic deformation. As the bending moment under the external load increases, the deformation of each layer of steel fibers continues.

When the external load reaches a certain point, the tension in the longitudinal fibers on the surface of the steel sheet exceeds the yield limit of the material and the fibers undergo plastic deformation. The greater the load, the deeper the zone of plastic deformation extends from the surface layer to the neutral layer.

When the stress in all longitudinal fibers in the cross section of the steel plate exceeds the yield strength of the material, all fibers enter a state of plastic deformation and the bending process is completed.

3. Working principle of plate bending machine

The plate rolling machine has two working parameters:

  1. The reverse bending ratio 1/ρ, which refers to the curvature of the steel plate after bending in one direction due to the action of the bending moment M.
  2. The residual curvature 1/r, which refers to the curvature of the steel plate after elastic recovery under the influence of the internal elastic moment after the external load is removed (r is the diameter of the rolled steel tube).

Selection of the reverse bending ratio is critical in determining whether the steel plate can achieve the desired bending result. In a three-roll sheet metal roller, the reverse bending rate is obtained by pressing the reduction roller.

Different residual curvatures can be obtained by adjusting the reduction to produce different diameters of rolled tubes.

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) exerted on the roll, the bending torque and the driving power of the plate rolling machine motor.

4.1 Pressure (bending force) acting on the plate bending roller

The pressure on the roller can be calculated based on the moment required to bend the steel plate. In this case, the steel plate is considered a beam under concentrated load. The load is the pressure exerted by each roller on the steel plate, as illustrated in Figure 2.

Fig. 2 Pressure acting on the roller

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
  • t : Scroll step

In the calculation, the bending moment of the steel plate under the second roller is assumed as pure plastic bending moment M is that is, M 2 =M is ​​(the pure plastic bending moment M is the maximum bending moment that can be achieved in elastic bending -plastic).

f1

In the formula:

  • σ is — yield strength of the steel plate material, 250Mpa;
  • s — plastic section coefficient, which is bh 2 /4t b for steel plate;
  • b – width of the steel plate, m;
  • h — thickness of the steel plate, mm.

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

f2

Total pressure:

f3

4.2 Bending torque acting on the plate calender roll

The bending torque M K acting on the roller can be determined according to the principle of equality of function.

The bending work AK produced by the bending torque on the roller must be equal to the work AP for plastic deformation of the steel sheet, that is, A p = A k (shown in Fig. 3).

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

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

The plastic deformation work A p2 of the steel plate under the second roller is:

f4

In the formula:

  • M 2 – bending moment of the steel plate under the second roller;
  • l 2 — the length of the steel sheet under the second roller;
  • 1/r p 2 — plastic deformation curvature of the steel sheet under the second roller.

Bending work acting on the second roller:

f5

Where d 2 is the diameter of the working roll.

To do:

f6

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 roller is equal to the pure plastic bending moment M k2 .

So the formula is as follows:

f7

5. Calculation of plate rolling machine motor drive power

Engine power can be calculated according to the following formula:

f8

In the formula:

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

According to the above calculation formula, the motor drive power of the 40mm thick steel sheet rolling mill is selected as follows:

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

That's why:

f9

According to the above calculation, the motor drive power of the 40mm steel sheet rolling mill is selected as 25kW.

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