
System of Control over the Kinematic Parameters of Continuous Trains of a Rolling Mill
УДК621.771.251.08 On modern bar and wire mills the rotation of entry guide rollers of the working stands is controlled visually. As there are no devices for automated control over the rotation it is impossible to control the rollers availability during rolling. Thus, if one or both rollers stop, for example, due to the damage of the bearing, the metal pickup by the rollers or due to any other causes, it results in «cobbles». It is especially important to control the guide rollers availability during rolling on wire mills, equipped with finishing blocks. There are no devices for automated control over the guide rollers availability, besides, the visual control over the finishing block is impossible as the stands are covered with a housing, and the rolling speeds are high, up to 80110 m/s. Therefore any «cobbles» at this section of the mill result in severe problems. It is possible to avoid emergency situations provided that the condition of the guide rollers is under continuous control, the speed of their rotation is recorded, its value is displayed on the monitor and the deviation of the rollers speed is estimated.
Periodical press provides some information about the application of automated systems for diagnostics of the condition of guide rollers in the finishing blocks at Belarussian and Moldavian metallurgical works. The systems' application results in complete elimination of any «cobbles» due to the guide rollers jamming. RPC «Donix» has developed a new method of control over the kinematic parameters of the rolling mill. The method includes control over the rotation of guide rollers with the sensors mounted on the guides as well as control over the kinematic parameters of the mill. Kinematic parameters are controlled through the measurement of angular speeds of the rollers which is carried out by magnetic field sensors. After that linear speeds are derived from the known diameters of the rollers and the relations of linear speeds of the stock in the adjacent stands or trains. The obtained relations are compared with the reference values, corresponding to the speed schedule with minimal interstand tensions. The main condition of rolling on a continuous mill is the momentary volume constant, given by the following expression:
C = F_{i}·V_{i},
where С is the rolling constant; F_{i} is the stock crosssection area at the exit from the istand, V_{i} is the stock speed at the exit from the istand. This condition defines the relationship to determine the elongation ratio in the istand:
µ_{i } = F_{i1} / F_{i} = V_{i} / V_{i1}
The values of the new elongation ratios are determined using the expression
µ_{i }' = F'_{i1} / F'_{i} = V'_{i} / V'_{i1}
If the schedule is mismatched the rolling constant in each stand s due to the s in the stock crosssection area and in the stock speed at the exit as a result of pushing or tensioning. Taking into account these s, the new speed V'_{i} and area F'_{i} are expressed as follows: where and are the s in the stock speed and crosssection area at the exit from the istand, respectively. The s in the stock speed and crosssection area are given by the expressions: where and are the s in the stock speed and crosssection area, respectively, under the influence of the front tension; Thus, the expressions for V'_{i} and F'_{i} may be written as follows: where i = 1..n and n is the number of stands in the train. According to Ref. [1] the relative in the stock crosssection area and the in the stock speed at the exit can be expressed through the forces of the front and rear tensions Q_{i} and Q_{i+1} with the corresponding technological coefficients (dimensional coefficients of the front/rear tension influence on the rolling parameters):
V'_{i }= V_{i} · ( 1 + Bn_{i }· Q_{i}  Bз_{i }· Q_{i1} ); (1)
where An_{i}, Bn_{i} are the technological coefficients of the front tension influence, and Aз_{i}, Bз_{i} are the technological coefficients of the rear tension influence on the in the stock crosssection area and forward creep, respectively. Multiplying the right parts of the expressions (1) and (2) we obtain the expression to determine the rolling constant for the mismatched schedule
If we open the brackets and neglect the terms containing squares or products of unknown variables we obtain the equation of kinematic parameters for the iinterval of stands
C'_{ }= C_{i} · [ 1  (Bз_{i} + Aз_{i }) · Q_{i1} + ( Bn_{i}  An_{i }) · Q_{i} ].
At certain values of technological coefficients the set of n equations gives n1 values of the interstand tension force Q_{i }as well as the constant of continuous rolling for various mismatches of the speed schedule. Using the method proposed in Ref. [1] we obtained the following relationships to determine the values of technological coefficients: where k_{1}, k_{2}, k_{3} и k_{4} are the experimentally obtained setup coefficients that between 0 and 1;is the absolute spread in the istand; µ_{i}  the elongation ratio; F_{i}  the stock crosssection area; b1_{i}  the stock width at the exit from the istand; Dk_{i}  the working diameter; s_{i}  the forward creep;  yield strengths of the rolled material at the entrance and at the exit, respectively;  the friction coefficient on the stockroll contact area;  spread index. As an example we solve the set of equations for a threestand train of a continuous mill when the initial set of equations consists of three equations with three unknown variables Q1, Q2 and С' where С_{1}С_{3} are the rolling constants for stands 13; Q_{1}, Q_{2} are the stock tensions in the 1^{st} and the 2^{nd}interstand intervals. If the process is stable the new rolling constant is similar for all the stands of the train, so the left parts of the equations can be equated as follows: Then we divide the equation (3) by С_{1} and the equation (4) by С_{3} and express the relation С_{i+1 }/ С_{i} through j_{i}. As a result we receive the following equations: After the transformation the equations have the following form: where
E_{ }= ( Bn_{1}  An_{1} ) + j_{1 }· ( Aз_{2} + Bз_{2} );
F_{ }= j_{1 }· ( An_{2} + Bn_{2} ); G_{ }= 1  j_{1};
M_{ }= 1  j_{1 }.
The final expressions for Q_{1} and Q_{2} are as follows:
The value of the new constant C' is defined by the following expression
C'_{ }= C_{1 }· ( 1 + (Bn_{1}  An_{1} )_{ }· Q_{1 }) ,
and the values of the new speed and width are defined by the following expressions, respectively,
V'_{i }= V_{1 }· ( 1 + Bn_{i }· Q_{i}  Bз_{i} · Q_{i1 });
or B'_{ }= B_{i }· ( 1  An_{i }· Q_{i}  Aз_{i} · Q_{i1 }). Thus, the relation of the reference µ_{i}_{ }and the measured µ_{i }' elongation ratios represents the mismatch of the speed schedule. For both the common and individual drives the main parameters of comparison are the relations of linear speeds V_{i}/V_{i1} for adjacent stands of each interstand interval. A more precise setup of the rolling mill is possible if the relation of linear speeds is controlled and kept constant. The suggested method makes it possible to control the kinematic parameters on a continuous rolling mill by comparing the measured values with the reference values. Control over the kinematic parameters includes control over the relation of linear speeds which ensures minimal interstand tensions on the continuous mill, and hence the required accuracy of the stock crosssection along the length of the rolled stock. The suggested method was implemented by the experts of RPC «Donix» on the finishing block of wire mill 150 of CJSC «Makeevka Metallurgical Works» («CJSC MMW»). Magnetic field sensors were placed in immediate proximity to the magnetized entry guide rollers. The sensors generated the electric signal which is proportional to the rotation speed of the roller. The signal converter together with the program unit generate the current and archive data about the rollers' speeds and their s on each stand with the further data storage in the computer. Thus the operator can control and correct the rolling process, if necessary. We studied different methods of magnetizing the rollers, conditions of the rollers operation and of their during short scheduled downtimes. As a result we developed and constructed a simple and reliable device for marking the rollers. From August 2005 till October 2005 the system of control over the entry guide rollers of the finishing wire block was tested on wire mill 150 of CJSC «MMW». The system's interface includes two windows for the speed schedule presentation. Virtual speeds of the rollers for each controlled stand and rotations of the main drive of the block are presented in the first window as bar graphs. Virtual linear speeds of each roller are presented in the second window as line diagrams (graphs). During the testing period speed graphs of the rollers' rotation for every rolled billet were saved to the computer. To analyze the accuracy of the rollers' speed measurement we used a mathematical model of the kinematic conditions of rolling in the block developed by RPC «Donix». During the testing period the system ensured the following control functions:
The developed system of control over the rotation of entry guide rollers of the finishing block may be used to avoid «cobbles» due to the roller jamming. That is achieved by means of the visual and program monitoring of speed deviations. To facilitate the operator's work the system is provided with the function of logical analysis and voice signals generation, characterizing the location and the cause of the guide deviation from the normal operation conditions. The system of control over the kinematic parameters will increase the mill efficiency by means of reducing the downtimes, rejects due to the entry guide rollers jamming in the mill blocks, and by means of reducing the bad quality wire rod production. References:

