CENTERING MECHANISMS FOR CONTINUOUS STRIP-FINISHING EQUIPMENT N. P. Belozerov
UDC 621.771.23.09:65.011.54
The manufacture of quality products and stabilization of the production process in continuous finishing (slitting) equipment requires a minimum deviation of strip movement in the machinery. The factors affecting strip displacement can be classified as design and process factors. Among the design factors are nonperpendicularity of the axes of the rollers and machine; differences in the speeds of the traction-mechanism drives; nonparallelism or eccentricity of the rollers (which transport the strip); nonuniform distribution of the downward force of the traction-mechanism roller over the strip width. Among the process factors are: telescoping of the coils about to be processed; strip waviness; strip width variation; strip camber. Experience in operating finishing equipment shows that quality strip is usually obtained and normal finishing assured if the strip does not deviate more than 10-15 mm from the machine axis. An accuracy of i mm is required only in equipment which trims the strip. The strip is generally kept within the 10-15 mm limit by centering mechanisms. These mechanisms either redistribute the tension over the strip width or move the strip to the required position~ However, the presence of centering mechanisms equipped with automatic systems does not guarantee stabilization of the axial position of the strip. To achieve this, the following must also be ensured: efficient location of the various pieces of equipment in the finishing unit; efficient location of the centering mechanisms; proper selection of type of centering mechanism; proper selection of the structures of the stabilizing systems, i.e., the location and number of transducers. It should be kept in mind that stabilization of the strip axis with automatic systems is effective only if the force exerted by the centering mechanism on the strip is greater than the maximum perturbation. It is therefore necessary to eliminate as many as possible design factors which might effect strip displacement during assembly and adjustment of the unit, and to eliminate those factors associated with the quality of the strip itself by means of the stabilizing system. Analysis of the object (the strip being transported together with the centering mechanism) as one component of an automatic control system shows that the object may be regarded as a proportional or integral component if the displacement or angle of rotation of the Centering mechanism is taken as the input and the displacement of the strip as it comes off the centering mechanism is taken as the output. Among those centering mechanisms for which the control object can be represented in the form of a proportional component are mechanisms which directly move the strip. Such mecha= nisms either have rollers with a strip-contact angle of 1800 and a rotation axis located in the plane of the leading side of the strip or floating uncoilers with a long path equal to or greater than the strip width. Among those centering mechanisms for which the control object can be represented in the form of an integral component are: mechanisms having rollers with a strip-contact angle from 0 to 180 ~ and a rotation axis which coincides with the roller-body symmetry axis and which is either located on an extension of the rotation axis of the leading side of the strip or brought out into a plane perpendicular to the leading side; traction-providing transport rollers with elastic coatings and gripping devices. To verify the possibility of representing the control object in the form of simple components and to determine its quantitative characteristics, a study was made of two types of centering mechanisms which are widely used and can be most easily incorporated into the transport scheme of a strip-finishing unit. As a mechanism of the proportional type, we used two 150-mm-diameter rollers with a common strip-contact angle of 180 ~ and a rotation axis Slavyansk Branch of the All-Union Scientific-Research, Planning, and Design Institute of Metallurgical Machinery (VNllmetmash). Translated from Metallurg, No. 9, pp. 30-32, September, 1981.
0026-0894/81/0910-0353507.50
9 1982 Plenum Publishing Corporation
353
/\ Fig. i. Oscillograms of displacement of strip (i) and mechanisms (2) of integrating (a) and proportional (b) types. located in theplane of the lead side of the strip along the symmetry axis. The integratingtype mechanism used was a 400-mm-diameter roller with a strip-contact angle of 90 ~ and a rotation axis located along the symmetry axis in the plane of the bisector of the angle formed by the leading and trailing sides of the strip. The strip width was 180 mm, strip thickness 0.i m~n, and yield and ultimate strengths 0.2 and 0.3 GPa, respectively. The reaction of the control object to the control action was determined from the phase shift between the input (angle of rotation of the mechanism) and output (strip displacement) with a harmonicvariation in the input. It is apparent from the oscillograms in Fig. i that phase shifts of 95-100 and 15 ~ occur between the strip displacement and the amplitudes of the rotation angles of the two types of mechanisms. Such values are typical of integral and proportional types of components. The deviation in the phase shifts from 90 and 0 ~ can be attributed to the fact that the transducers measuring the position of the strip were placed a certain distance from the beginning of the trailing side of the strip. The quantitative characteristics of the control object were evaluated according to the control capacity of the centering mechanisms, i.e., according to the magnitude of their effect on the strip relative to design and process parameters. The design parameters of the centering mechanisms were: the angle of rotation; the lengths of the inlet and outlet spans of the strip; the material of the surface of the rollers. The process parameters were: strip tension; strip speed; condition of strip surface~ It is understood that the mechanism retains it control capacity only within certain ranges of values of these parameters. The amount of lateral strip displacement for the control object with an integrating-type mechanism was determined from the formula: AB = ] / ~ / 2 . Vstr .sin oz. At,
where Vst r is the linear velocity of the strip; ~, angle of rotation of the centering roller; ~ / time of action of the centering roller on the strip at a constant angle of rotation; 2, a coefficient characterizing the decrease in the effect of the roller on the strip due to the presence of the vertical component of the angle of rotation. During the control process, the centering mechanism rotates and redistributes the forces applied to it from the side of the strip. The effect of the mechanism on the strip will change in relation to the design and process parameters. We have therefore introduced the control coefficient K c into the equation. Now the equation takes the form: AB = - ~ / 2 . Ke" Vstr 9sin ~. At, AB 1 =
9
The value of this coefficient determines the magnitude of the effect of the mechanism on the strip, i.e., the controllability of the control object. It is apparent from the curves (FIE. 2a, b, c) plotted from the results of analysis of the oscillograms that K c varies within the range 0.48-0.92, i.e., the mechanism retains its control capacity at a fairly high level. The coefficient values shown were obtained with a control (inlet) span length of no less than 5 strip widths and an outlet span width of no more than 3 strip widths. A
354
Kc
I
~c b
a
0,8
o--c
0,6 :Y
0
60
0
Y20 V,rn/min
~cc
2,8
5,6
8,~~kg f/mm2
d
~
0,6 0
~ ~5
~
~ ~o
0,
~'---o 0
2
..1.. ~
c~~
Dependence of control coefficient on Fig, 2. strip speed at a constant tension of 2.8.107 Pa (2.8 kgf/mm 2) and a constant sway angle of • 1 ~ (a), onltension at a constant strip speed of 60 m/min and a sway angle of • ~ (b), and on sway angle (of the mechanism) at the above constant values of strip speed and tension (c); dependence of relative displacement of strip and mechanism on mechanism sway angle at a constant tension of 4.5.107 Pa (4.5 kgf/ mm 2) (d): i) steel roller; 2) rubberized roller; 3) steel roller, strip lubricated with ~SS lubricant at a concentration of 5 mg/cm2; 4) steel roller, strip lubricated with "Industrial 20" oil; 5) ratio of span length to strip width equal to 4; 6) same, 2.2. decrease span to 3 strip widths and an increase in the outlet span to 5 strip widths leads to a 37-40% reduction in the value of the coefficient. The lateral strip displacement for the control object with a mechanism in the form of a proportional-type component was determined from the formula Bst r = R sin a, where R is the distance from the mechanism rotation axis to the trailing branch of the strip; a is the angle of rotation of the mechanism. It is apparent from Fig. 2d, which shows the mean relative displacements of the strip and mechanism for two values of span length, that the amplitude of the strip displacement is roughly 60% of the mechanism displacement when the ratio of the span length to strip width is 2.2 and the rotation angle changes within • 2 ~ . A further increase in rotation angle is accompanied by tearing of the strip edges. An increase in the length of the span to 4 strip widths produces a lateral strip displacement which is about 90% of the displacement of the mechanism (Fig~ 2, d-2). Given the same value of span length and a mechanism rotation angle of • 5 ~ , a change in tension within the range (2-7).107 Pa (2-7 kgf/mm 2) is accompanied by a • 1% change in relative strip displacement. Thus, the control capacity of a centering mechanism consisting of a roller with a stripcontact angle of 90 ~ and a rotation axis located in the plane of the bisector of the contact angle is maximal when the rotation angle varies within the range • 1.5 ~ Here, the lengths of the inlet and outlet spans must be equal to no less than 3 strip widths, and their ratio must be no less than 1.5. The control capacity of a centering mechanism consisting of two rollers with a common strip-contact angle of 180 ~ and a rotation axis located along the symmetry axis in the plane of the leading branch of the strip is maximal within a range of span lengths having an upper limit of 4 strip widths and a range of rotation angles of • 5 ~ .
355
