Simulation of process of hot pilgrim rolling

Simulation of process of hot pilgrim rolling YURY B. CHECHULIN, Doctor of Engineering Science, Professor EVGENY U. RASKATOV, Doctor of Engineering Science, Professor YURY A. POPOV, post-graduate student Institute of Mechanics and Machine Building Ural Federal University named after First President of Russia B.N. Yeltsin 620002, Ekaterinburg, ul. Mira, 19 RUSSIAN FEDERATION evgeny.raskatov@gmail.com http://www.urfu.ru Abstract: A mathematical model of the pilger tube rolling process has been developed with an account for nonstationary character of the process from cycle to cycle. The model enables the determination of the power-andforce, deformational and kinematics parameters and the rolled tube dimensions; choice of rational roll design parameters; carrying out a comprehensive analysis of the tube rolling process simulation results Key-Words: Model-based analysis, cobbing, grooving, computational model, shell, batch, stress 1 Introduction One of the effective methods for thick-walled pipes of large diameter billet is rolling on the hot strip pilger mill. Despite the long life of these mills, their further investigation remains relevant. Complex time-dependent geometry of the deformation zone requires further search of rational external calibration rolling tool. Besides periodic, almost percussive nature of the change in the form of external loads of effort rolling and high dynamic loads caused by the reciprocating motion of a massive piece with internal rolling tool require additional design improvements of feeding apparatus (hereinafter referred to as forgoller) and the definition of rational parameters of the workpiece process control. The most appropriate approach to these problems is based on mathematical modeling of geometric and kinematic characteristics of the process. In this case the pilgrim camp provides a simultaneous hot-rolling of two billets in a form of thick-walled shells in two roll mill stands, arranged in parallel and provided with a total group drive. Forgollers are used as feeders for each of the two threads with the application of brake chamber, and pneumatic drive is used as the engine in each of the two mechanisms. 2 Simulation of forgoller with a brake chamber with a floating piston Forgoller with a hydraulic braking consistently includes an air chamber with an internal piston, the hydraulic chamber filled with oil, and the mechanism of billets rotation (tilting). In currently in use construction designs, both air and hydraulic pistons fixed on a long piston guide connecting to the mandrel head, holding mandrel (internal tool) with a thick-walled sleeve attached to it in the process of rolling. The disadvantages of this device are: great length and weight of the rod, that increases dynamical loads on the length of the working cone (about 1500 mm) during the reciprocative transportation, rise in the oil temperature and the difficulty of its sealing, the longitudinal bending rod deformation causing edge piston contact with the inner surface of the air chamber. Besides the great length of the rod determines the extended portion of the periodic filing device, which includes movable stop, spindle and long-stroke hydraulic cylinders support moving carriage (Fig. 1). Fig. 1. A brake chamber with a floating piston To improve the efficiency a brake chamber with a floating piston was offered [1]. The advanced design will control the braking mode depending on the size of the rolled metal. The brake chamber is provided with running water as operating fluid, which has a lower heat capacity than oil and improves excessiveheat removal. Hydraulic braking is due to the outflow ISBN: 978-1-61804-184-5 202

resistance through the annular slit of a constant area and customizable throttling holes. For the deformed bar rolling of a billet in a form of thick-walled shell, one-time rolling cycle is divided into two stages: 1. deformation of the metal itself in the working roll mill stand, accompanied by the workpiece backward movement to the output side of the roll stand with the mandrel head and the air piston guide; 2. the stage of the feeding of moving masses together with the workpiece into the working roll mill stand on the total length of the working cone comparable in length with the dimensions of the mandrel, and the amount of one-off supply to the rolling cycle, simultaneously accompanied by the billet rotation (tilting) at a given angle (up to 90 ). In the first stage of one-time rolling cycle the workpiece is located in roll-grooves of variable geometry of external rolling tool (working rolls). By the beginning of the second stage the radius of the roll-grooves increases dramatically, releasing the workpiece with the internal tool (mandrel) from the contact with rolled metal. In the process of the first stage of the work cycle as a result of the backward movement the air chamber piston compresses air volume piston cavity, increasing its pressure to a value sufficient to return the workpiece to the working roll mill stand. Decrease of the striking force in the final stage of the masses moving in the direction of the working roll mill stand achieved by their braking with a hydraulic decelerator. In the process of modernization of the existing forgoller it is necessary to determine the kinematic characteristics of the motion of moving parts during acceleration and braking. For this purpose motion equations for each period are made up and solved. Rolling cycle of considered pilgrim rolling mill is 1.5 s. Upon that the rolling time of workpiece working cone (i.e. rollback of moving masses in the rearmost position) is 1 second, and the total time to return to the forward position, including acceleration and braking 0.5 s. Let us consider successive stages of mandrel head backward movement to determine the main characteristics of forgoller. Algorithm for numerical simulation of the process of forgoller includes the following mathematical description of the law of motion of the moving mass. The motion equation during acceleration: k H m mp x p 0 F 1 ( H h x ) + R pf = 0, (1) where m mp the mass of the moving parts of the machine and cartridge cases, F 1 active area of air piston; p 0 initial pressure of the air in the pneumatic chamber; H length of the air space in the full forward position of the piston, reduced to a piston; h piston pullback during rolling (piston-stroke); R pf power friction; k the adiabatic index for air (ratio of specific heats for air). Figures 2, 3 shows a graphical solution of equation (1) with the initial conditions, and the following mass, design and control parameters: m mp = 14 t, R pf = 5 kn, H = 2.0 m, h = 1.55 m, F 1 = 0.388 m 2. The nature of acceleration for a certain mass is actually determined by the initial air pressure in the pneumatic chamber. Figures show solution of equation where p 0 = 0.1(0.15, 0.2, 0.25, 0.3) MPa. Fig. 2. The law of motion of mass during acceleration Fig. 3. The law of velocity of mass during acceleration The initial velocity of the piston of the brake (hydraulic) camera is a finite velocity of the air piston. Let us consider the process of hydraulic braking in a chamber with constant and not changing over the length, gap δ and throttling holes in area f. Braking of forgoller moving masses must be considered in two stages. The first corresponds to the starting moment of a hydraulic piston, characterized by sharp, abrupt increase in pressure in its rod end, and, consequently, the corresponding increase in the resistance movement of the brake piston. The second ISBN: 978-1-61804-184-5 203

stage is characterized by the resistance of the brake fluid through the expiration slot gap and throttling hole while the piston moves along the brake hub. At the starting moment, pressure in the form of a shock wave propagates through the brake chamber. In the initial stage of the strike the fluid contained in the chamber begins to move due to its compression simultaneously with the distribution of applied pressure along the sleeve s length. The value of the shock pressure depends mainly on the final speed acceleration of forgoller moving masses, the characteristics of the fluid and the area of throttling holes. After a sudden increase of pressure the rate of moving masses dramatically decreases in the brake chamber rod region This process can be written as follows: m (V 0 V 0 ) = p y F 2 t d, (2) where V 0 the initial braking velocity (final rate of acceleration); V 0 the braking initial velocity for the period after the events of impact deceleration; p y the value of abrupt pressure; F 2 the butt square of the hydraulic piston in rod end; t d the time of fluid pressure distribution. We can pre-estimate the increase in pressure in front of the brake chamber using the following expression: p y = ρ F 2 2 V 0 2 2b 2 (δ + f b ) 2, (3) where ρ the density of the fluid; b = π D, D hydraulic piston diameter. Time of fluid pressure distribution: t d = 2 l a, (4) where l the length of the brake chamber; a the velocity of the shock wave in the selected working fluid. From the above dependencies we can determine the initial rate of deceleration after the instantaneous pressure increase at the time of initial piston entry into the brake chamber sleeve. In the period of active piston hydraulic brake, running along the brake sleeve, in brake chamber certain sizes the motion equation becomes: k H m mp x + p 0 F 1 ( H h + x ) (5) p h F 2 R pf = 0, where p h the pressure in the hydraulic chamber during braking; 12μ Q l p h = b (δ + f 3 + ρ Q 2 b ) 2b 2 (δ + f 2, b ) (6) where Q = F 2 x the total flow rate through the annular gap and the throttling holes; μ the dynamic viscosity of the liquid; l the length of the annular gap, which is mainly determined by the length of the hydraulic piston. The first term of equation (6) is a loss of pressure on the friction in the fluid, and the second is hydrodynamic losses. With expressions (6), the motion equitation (5) takes the form k H m mp x + p 0 F 1 ( H h + x ) 12μ F 2 2 x l b (δ + f 3 ρ F 3 2 2 x b ) 2b 2 (δ + f 2 (7) b ) R pf = 0. Figure 4 shows a graphical solution of the equation (7) with the initial conditions x = 0, x = V 1, and F h = 0.01 m 2, F 2 = 0.09 m 2. Of greatest interest is the value of the finite rate of deceleration of moving masses. Fig. 4. Diagram of deceleration It is necessary to take into account that braking time t 2 completely depends on the time of acceleration t 1, because the total time of rough tube feeding to rolls is determined by the duration of the disclosure of roll-grooves. Braking process actually depends on the following parameters: the initial velocity of the braking V 1, braking time t 2, area of throttling holes F h, number and area of throttling holes, coordinates of the holes location along the length of the brake sleeve. ISBN: 978-1-61804-184-5 204

3 A theoretical efforts of the metal displacement in the deformation zone during pilger rolling thin-walled tubes An essential factor in improving the quality and accuracy of pipe dimensions obtained by this method is to determine the shape and size of sections of rollgrooves of working rolls. It is known [2] that the calibration of pilgrim rolls determines the performance of the mill, the work load of the roll mill stand and the drive line, the energy and the quality of rolled tubes. To evaluate the calibration of pilgrim rolls it is very important to know the maximum tensile stress distribution patterns along and around the perimeter of deformation, which are the main cause of formation of defects (cracks). It is also necessary to estimate the distribution of pressings (radial displacement of metal) in length and around the perimeter of the instantaneous deformation depending on the size of rough tube feeding in rolls that will identify causes of high tensile stress and take measures to reduce them. Simulation of rolling process of pipes and the calculation was carried out using the finite element method in volume production (Fig. 5). The emphasis is made on identifying the stress-strain state in the initial stage of the process of pilgrim rolling where ram head part of the roll bites and performs intense deformation of rough tube. Pipe material in the roll pass undergoes elastoplastic deformation that reach the final values. In describing the pipe material model in the roll pass is considered not only the physical, but also the geometrical non-linearity. In writing state equations the case of simple loading is used. For pipe material Prandtl-Reis elastoplastic model is used. Resistance depends on the degree and rate of deformation and temperature of rolled metal. Fig. 5. Calculation model to determine the stresses in the roll with a finite element mesh Here are the results of the calculation of the tube rolling equal 325 mm from rough tube equal 500 mm with central ram head equal 110. For an estimation of rolls calibration cobbing calculation and the calculation of intense condition of a rough tube in the instant centers of deformation were made where feed rate is 10 mm. Simulation of the pilgrim rolling was made for rough tube, mandrel and angles of roll-grooves in a Cartesian coordinate system, and the results of the stress analysis are presented in a local cylindrical coordinate system. Position of lines of the center of deformation for which results of calculation are given, are shown in figure 6. The beginning of each line is in a zone of transition of a rough tube in the deformation center, and the end of each line in a zone of transition of the center of deformation in a ready site of a pipe. Such position of lines allows to present visually distribution of tension and cobbings both on length, and on perimeter of the center of deformation. Figure 7 showfeeds graphics of distribution of maximum tensile tangential SY and longitudinal SZ tension, and cobbing (normal move UX) on lines 1 and 17 depending on the rotation angle of calibrated roll for feed of 10 mm. Fig. 6. Position of lines Line 1 characterizes the state of stress of metal near the contact line between the rough tube and the top of the roll pass, and line 17 near the flanges of the roll (Fig. 6). In the analysis of simulation results it was found out [3], that the maximum tensile tangential SY and longitudinal SZ tension arise for feed of 10 mm at the rotation angles of the roll 80 130 degrees (the length of the inclined plot of deformation center 450 680 mm). High longitudinal tensile stresses SZ (200 225 MPa) take place in the zones of the top (line 1, Fig. 8, 9) and tapers (line 17), and between these areas of tensile stresses arise longitudinal compressive stresses (line 9), up to 550 680 MPa. For an assessment of calibration of pilgrim rolls it is important to know regularities of change of cobbing on length and perimeter of the center of deformation. ISBN: 978-1-61804-184-5 205

Fig. 9. Diagrams of reduction in cross-section Figure 10 shows the diagram of cobbing with feeding of 10 mm and an angle of rotation of rolls 110. Fig. 7. Graphics of distribution of maximum tension and cobbing Fig. 10. Diagram of cobbing with feeding of 10 mm SX For these feedings maximum cobbing (moving through the normal UX) is at a distance of 500 mm from the transition to a titling-type part of a tube. This uneven distribution of cobbing and high tensile tangential, especially longitudinal tensions is the main cause of the defects of the "cracks" on the surface of thin-walled tubes made of alloy steel with pilgrim rolling (Fig. 11). SZ Fig. 8. Diagram in cross-section, in which there are the maximum tensile stress Fig. 11. Defects of the "cracks" 4 Conclusion The calculation results have shown a good convergence with the experimentally measured characteristics of pressure changes on the operating equipment. ISBN: 978-1-61804-184-5 206

To reduce the high tensile stresses and, consequently, improve the quality of the calibration tube pilgrim mill rolls should be such as to ensure a more uniform distribution of breakdowns, especially on the perimeter of the sleeve. The proposed modernization of forgoller is aimed at improving the reliability of operation and maintenance technical resource, to strengthen the capacity of a rational mode settings to work with the masses of rolled tubes within the range, provided by the equipment and technical documentation. Favorable combination of initial configuration settings, including the dependence of initial pressure in the air chamber from moving masses and rolling options, as well as pressures control mode in the braking chamber reduces braking loads in the supply unit. References: [1] Chechulin Y.B., Popov Y.A., Filimonov I.E., Verification of forgoller pilgrim mill, Steel, No.12, 2011, pp. 32-34. [2] Raskatov E.Y., Modeling the movement of the metal in the deformation at pilgrim rolling, Steel, No.3, 2012, pp. 37-38. [3] Lehov O.S., Raskatov E.Y., Solovev D.A., Study of stress and displacement of the metal in the instantaneous deformation zone at pilgrim rolling, Proizvodstvo Prokata (Rolled Products Manufacturing), No.8, 2011, pp. 35-37. ISBN: 978-1-61804-184-5 207