2020 Volume 60 Issue 11 Pages 2477-2484
Analysis of chatter vibration characteristics is an important factor that determines the quality of the slab in a rolling process. A numerical model is proposed to investigate the vibration characteristics. A hot plate rolling mill that includes the driving system is modeled by multibody dynamics to investigate the cause and characteristics of the chatter vibration. Since the spindle of a thick plate hot rolling mill is inclined within 2 degrees depending on the connection part, it is necessary to take into account the elastic effect of the spindle deflection. Therefore, the rigid body model of the previously studied method and the flexible body model that can consider the elastic effect were compared with the experimental model and the accuracy was verified. The chatter frequency was analyzed according to the rolling process and compared with the theoretical calculation results to investigate what occurred during the rolling process. The chatter frequency was compared with the natural vibration frequency of the spindle connected to the work roll and could be expected to be directly related to the bending vibration.
The hot plate rolling process that is used in the steel industry is a process of reducing the plate thickness using complex heating and cooling conditions. Chatter in the rolling process is a phenomenon caused by vibrations between the workpiece and the manufacturing machine. The chatter vibration of the rolling process has a significant effect on the surface and thickness of the metal slab. Chatter vibration is classified into three types: first octave, third octave and fifth octave. The first octave chatter vibration is usually affected by the stiffness of the mill and the stiffness of the workpiece being rolled. In addition, it can be confirmed by chatter marks and worsened by torsional vibration of the rolling mill. It has a natural frequency between 10–30 Hz for the system.1,2) The third octave chatter, in which the vibration frequency is usually in the range of 100–250 Hz, often occurs in cold rolling of thin strips.3) A common cause in the fifth octave chatter vibration may be forced vibration due to defective gear teeth, roll bearings, drive couplings and poor surfaces of the work roll. The chatter frequency is typically 500–1200 Hz.4)
Several theoretical studies have been performed to model chatter vibrations in rolling, and many mathematical models for rolling processes have been established with varying degrees of simplification.5,6,7,8,9,10) Alternatively, studies using experimental tests have been conducted and the progress of the rolling process has limited data collection and interpretation under various rolling conditions.11,12,13) In the method using multibody dynamics, rigid body modeling was performed for some elements of the rolling mill.14,15) However, in models with constant tilt of the spindle, such as hot plate mills, the accuracy of the analysis can be reduced due to the exaggerated vibration in the universal joint.
In this study, we investigated the dynamic behavior of hot rolling mill in Hyundai Steel Mill to investigate the cause of chatter vibration. In the experimental study, rolling force, roll speed and acceleration were measured from tachometer, load cell and accelerometer respectively. Numerical models of rolling mills including drive systems are built for multibody dynamics analysis. The numerical model represents both the rigid body model from the previous researched method and the flexible in this study model and is compared with the experiments. In order to investigate the cause of chatter vibration, it was compared with the theoretical formula and the vibration characteristics were analyzed according to the rolling process. In addition, it was confirmed that it is generated from bending vibration compared with the mode frequency of the spindle.
A hot plate mill system processes a rolling hot slab with a temperature in the range of 1100 to 1300°C, and consists of a spindle, backup roller, working roller, and main motor, as shown in Fig. 1. Power generated by the motors is transmitted to the working rollers in the rolling mill through the spindles. A spindle not only transmits the power generated by the motor but also controls the gap between the upper and lower roll. Work rolls rotate with friction, directly contacting the slab. The generation of vibration from the work rolls is reduced by the chock of the work rolls. The backup roll reduces the vibration and bending force of the work roll. The backup roller chock reduces the vibration of the backup roller. Lower cylinders play the role of applying the rolling force to the lower backup roll chocks, using hydraulic methods. The upper backup roll chocks are fixed by the screw motor.
Schematic illustration of hot rolling mill.
In order to investigate the properties of chatter vibration in hot plate mill, we used the control system to measure hot plate rolling parameters such as the rolling force, rotational speed of the roll, and the gap of the rolls, as shown Fig. 2. The gap between the work rolls is measured after the calibration operation is performed by the slab thickness measuring device installed on the back of the rolling stand. We also measured the vibration acceleration by attaching the accelerometer to the housing and the chocks of each roll, as shown in Fig. 3(a). We measured each acceleration as shown in Fig. 3(b) and performed fast furrier transform (FFT). Reflective tape was attached on the surface of the spindle and the speed of the work roll was measured by the tachometer as shown in Fig. 3(c). The rolling force was measured as shown in Fig. 3(d) by a load cell attached to the bottom of the backup roll chock.
Block diagram of the experiment.
The vibration experiment and measured data. (Online version in color.)
The kinematic model of a typical rolling mill is analyzed by the method of transmitting the force of the motor directly to the working roll, using vibration or fixed elements generated on the roll itself. However, since the spindle that transmits the power of the rolling mill is actually connected by a universal joint, additional vibration may occur. Therefore, in this study, we have calculated the vibration phenomena occurring in the spindle using the universal joint and bearing element between the spindle elements and confirmed that chatter mark phenomenon can occur from the bending and torsional vibration of the spindle through the rigid and flexible dynamic model.
3.1. Rigid Multibody Dynamics ModelFirst, a numerical model of a rolling mill including a drive system was constructed from the rigid bodies studied above, and multi-body dynamic analysis was performed. Since rolling force has a significant effect on chatter vibration, the values measured in the experiments were applied. In general, in the case of a mill model, the half model is often used because of its vertical symmetry. However, since the rotational speeds of the upper and lower rolls are different in the actual operation process, the full model is constructed in this study. It also includes a spindle that transfers torque to the work roll as shown in Fig. 4. The six spindles are connected with the motor by universal joints. The backup roll is rotated due to the friction of the work roll and the slab is transferred due to the friction with the work roll. The chock supporting each roll and the pinion element supporting the spindle are modeled as spring and damper elements. Gravity was applied to all the components along the negative z-direction. Table 1 shows the conditions for the experiment and numerical simulation.
Schematic illustration of multibody dynamics model. (Online version in color.)
| Parameter | Value |
|---|---|
| Slab thickness at input, hin (mm) | 133 |
| Slab thickness at output, hout (mm) | 121.5 |
| Slab width, w (mm) | 2684 |
| Slab length, l (mm) | 4114 |
| Radius of the work roll, rw (mm) | 590 |
| Radius of the backup roll, rw (mm) | 1100 |
| Mass of the work roll, Mw (kg) | 65350 |
| Mass of the backup roll, Mw (kg) | 226400 |
| Friction coefficient, μ | 0.3 |
| Universal joint |
MotionSolve from HyperWorks16) was used for the analysis. The torque of the motor was applied to the measured data in the experiment and the rolling force measured by the load cell was applied to the backup roll chock. The numerical model was validated by comparing with the experimental results. Figure 5 shows the results of FFT numerical simulations and experiments about vertical acceleration data measured in the upper work chock.17)
FFT of the work roll chock acceleration in the hot plate mill.
The vibration frequency with peak value in the experiment appeared in two types, 17.5 Hz for the first octave and 538 Hz for the fifth octave. Rigid multibody dynamic analysis was calculated at 20 Hz for the first octave and 531 Hz for the fifth octave. However, it can be seen that the magnitude of the peak frequency is about 5 times larger than the experiment.
3.2. Flexible Multibody Dynamics ModelGenerally, a spindle of a rolling mill is a power transmission device that connects roll from an electric motor. In the previous study, the position of the spindle was assumed to be a straight line.14) However, the spindle of the plate mill is mainly located at about 2° or less using a universal spindle. Therefore, in the case of a high speed rolling mill, it can be assumed that the vibration generated in the spindle may affect the shape of the slab.18) Thus, it is necessary to consider the elastic effect of the spindle deflection, and hence the spindle is assumed to be a flexible model. The spindle is made of AISI4140 steel as shown in Table 2. The proposed numerical model was also analyzed by the same analysis method as the rigid body model.
| Density (Kg/m3) | 7850 |
| Young’s modulus (GPa) | 210 |
| Shear Modulus (GPa) | 80 |
| Poisson’s ratio | 0.3 |
| Yield strength (MPa) | 415 |
As a first step, the elastic effect on the spindle was analyzed. In doing so, working force was calculated from the universal joint connected to the work roll and the results are shown in Fig. 6(a). In the case of the rigid body model, the reaction forces generated during the rolling process between the work roll and the slab were unstably calculated. On the other hand, in the flexible body model of the spindle, the reaction forces generated in the rolling process between the work roll and the slab can produce the relatively stable load results due to the elastic effect of the spindle. As a result of calculation of the displacement of the spindle, the flexible model was stably calculated as shown in Fig. 6(b).
Comparison of rigid and flexible multibody dynamics analysis. (Online version in color.)
The peak frequencies of the proposed numerical model were calculated to be 16.5 Hz for the first octave and 536 Hz for the fifth octave as shown in Fig. 7. And it can be seen that the amplitude of the frequency is quite similar to the experimental data. In other words, if the position of the drive motor and the work roller are installed at an inclined angle rather than in a straight line as in the previous study, a flexible multibody dynamic model considering elastic effects is more effective because the working force and deformation applied to the spindle must be sufficiently considered.
Numerical simulation of the proposed method.
From the previous results, it is shown that the spindle elasticity has a significant cause on chatter vibration analysis.
Therefore, we calculated the natural mode of oscillation frequency of the spindle and investigated the element that generates chatter vibration. An eigen mode analysis was performed using the Craig-Bampton method and the calculation results are shown in Fig. 8. The mode frequencies of each spindle are shown in Table 3.
Mode shapes of spindles using Craig-Bampton method. (Online version in color.)
| 1st spindle (upper) | 2nd spindle (upper) | 3rd spindle (upper) | |||
|---|---|---|---|---|---|
| mode | frequency [Hz] | Mode | frequency [Hz] | Mode | frequency [Hz] |
| 1 | 26.8 | 1 | 86.9 | 1 | 87.37 |
| 2 | 76.2 | 2 | 216.9 | 2 | 284.8 |
| 3 | 150.8 | 3 | 393.1 | 3 | 650.6 |
| 4 | 361.7 | 4 | 597.7 | 4 | 1069.0 |
| 5 | 484.1 | 5 | 825.7 | 5 | 1113.6 |
| 1st spindle (lower) | 2nd spindle (lower) | 3rd spindle (lower) | |||
|---|---|---|---|---|---|
| mode | frequency [Hz] | mode | frequency [Hz] | mode | frequency [Hz] |
| 1 | 26.8 | 1 | 86.8 | 1 | 14.0 |
| 2 | 76.2 | 2 | 216.8 | 2 | 37.9 |
| 3 | 150.9 | 3 | 391.6 | 3 | 73.1 |
| 4 | 361.7 | 4 | 597.7 | 4 | 123.3 |
| 5 | 484.1 | 5 | 825.7 | 5 | 183.5 |
In this study, the theoretical equation in the previous study was used to investigate the relationship between spindle natural vibration and chatter frequency. The chatter frequency in this study can be easily confirmed by the chatter mark phenomenon occurring on the slab as shown in Fig. 9.14) The chatter mark is a series of marks made by vibration of the rolls and the plate. If the chatter pitch and line velocity of strip are known, the chatter frequency can be expressed as follows:
| (1) |
Chatter mark caused by chatter vibration.
In the next step, the cause of chatter vibration of first octave from rolling process was analyzed. First, the natural frequency of vibration of rolling mill without rolling process was calculated with the peak frequency of 575 Hz as shown in Fig. 10 from the proposed numerical model. As a result of investigating the vibration data during the rolling process, the peak frequency was found at 538 Hz in the experiment and 536 Hz in the numerical model as shown in Fig. 11. From these two results, we confirmed that the fifth octave chatter vibration is a form of natural frequency of vibration from the rolling mill. Finally, we analyzed this section because it was the largest of the vibration data in the 0.2 second section at which the rolling of the slab began. As a result, the peak vibration frequency converted from the experimental and proposed numerical acceleration data is 14.5 Hz as shown in Fig. 12. In other words, it was confirmed from the two data results that the first octave chatter vibration with chatter marks occurs due to the vibration when rolling starts.
Natural frequency of vibration of rolling mill without rolling process.
Natural frequency of vibration of rolling mill during the rolling process.
Chatter mark caused by chatter vibration.
The dynamic behavior of a hot plate rolling mill including the driving system was investigated by multibody dynamics. In this study, the lower spindle only rotates because the lower working roller rotates with fixed position. On the other hand, because the upper spindle adjusts the rolling thickness according to the operating angle, much deformation of the spindle occurs depending on the rolling conditions. Therefore, the vibration data attached to the upper rolling roll chock was selected as a reference value among the measured vibration acceleration data and verified by comparing with the numerical model. The numerical model consists of the rigid body dynamics model used in the previous research method and the flexible multibody dynamics model proposed in this study. As a result, the peak frequency was calculated similarly to the experiment in the first octave and fifth octave chatter vibration regions for both models. However, the amplitude of the frequency was about five times larger in the rigid model.
This is because the elastic effect on the spindle is not taken into account. Therefore, it is more effective to perform flexible multibody dynamics analysis on models with constant tilt of the spindle, such as hot plate mills.
In addition, the chatter vibration characteristics that generate the chatter mark are derived from the theoretical equations and confirmed in the first octave. In order to investigate the structural cause of the rolling mill generating the chatter mark, the natural mode frequency of the spindle was calculated and it was confirmed that the first mode frequency of the spindle connected to the work roll corresponds to the first octave region. Thus, it can be said that bending deformation, which is the first mode shape of the spindle, is related to chatter vibration. In addition, in order to investigate chatter vibration generated in the rolling process, we analyzed the largest vibration data of some sections in the slab where the rolling starts and it was confirmed that the chatter frequency coincided with the first octave chattering frequency.
