# The theory and method of determining the drum lini

2022-07-23
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The theory and method of determining the cylinder lining (IV)

II. The theory of determining the cylinder lining

the so-called determining the cylinder lining is to wrap a certain thickness of liner material on the cylinder of the printing plate cylinder and the rubber cylinder as required, so as to adjust the gap between the cylinders and make the cylinder gear mesh at the position where the gear pitch circle is tangent, so as to generate the contact pressure required by the printing process between the cylinders

the method of determining the cylinder lining depends on the configuration of cylinder diameter of lithographic press, that is, in a group of plate cylinder, rubber cylinder and impression cylinder, the diameter of each of the three cylinders should be taken (here the diameter of the cylinder is the diameter of the cylinder including the lining), so as to obtain the ideal rolling state. Therefore, through practice, people have put forward various theories on the allocation of the cylinder of the lithographic press, which can be divided into equal diameter theory and different diameter theory

1. Equal diameter lining theory. According to the theory of equal diameter lining, if the three rollers of an offset press have the same diameter, there will be no sliding between the rollers during rolling, and an ideal rolling state can be obtained. In order to make the diameters of the rubber cylinder and the imprint cylinder equal, considering the extrusion amount of the rubber cylinder, the following treatment should be carried out:

the first treatment method is to assume that the extrusion amount (i.e. the compression amount) is 0.1mm, and make both the rubber cylinder and the imprint cylinder 0.05mm higher than the cylinder surface to obtain the extrusion amount of 0.1mm. However, due to the effect of the extrusion amount, the deformation is mainly the rubber blanket, and the printing plate cylinder is almost not deformed. Although the cylinder diameter is equal, the middle part of the embossing area is the rubber blanket is -0.05mm, and the printing plate cylinder is + 0.05mm. The diameters of the two cylinders are still different

the second treatment method is to increase the lining amount of the rubber drum so that it is 0.1mm higher than the surface of the pitch cylinder, which is the only tool pressure that can process qualified Charpy impact specimen notches except the optical curve grinder in China. On the surface, the cylinder diameters of the two rollers on the contact line of the impression are equal, but the excess of the lined rubber roller is 0.1mm, and the printing plate roller is zero

the experimental results of the above two methods on the printing press are quite different from the expected results

2. Reducing lining theory. The typical theories of reducing lining are geometric velocity difference theory and setz reducing theory

① geometric velocity difference theory. This theory is the enveloping theory advocated in the textbooks of the former Soviet Union, also known as λ Distribution theory, which holds that when a rigid plate cylinder contacts with an elastic rubber cylinder, the radii of only one or two points are equal, and the radii of the other points cannot be equal. Therefore, when the two rollers are in contact, only one or two points have the same linear velocity, and the other points are not equal, resulting in the surface slip of the plate cylinder and the rubber cylinder

people have used the geometric velocity difference theory to carry out complex mathematical derivation, trying to find an ideal extrusion amount distribution to minimize the slip. However, the mathematical model based on this theory is quite different from the actual rolling state of rubber cylinder and plate cylinder. It believes that as long as the radius is inconsistent, it will inevitably lead to the continuation of the weak and stable market of the fast-speed steel pig iron market, and there will be slippage. It ignores the fact that the rubber layer will be squeezed like water to make up for it by increasing speed, thus producing or not producing slippage. This theory discusses only a few cases in the rubber blanket, which has little practical significance

figure circumference of rubber elastic roll

② sites reducing theory. What led to the emergence of this theory was an experimental study carried out by setz of Miller Company in the United States on a smooth table. This experiment is to apply ink to the rubber roller with radius r, so that the rubber roller can rotate on the smooth test table without pressure, and the rubber roller can rotate once. The length of the ink mark on the test table is 2 π R, as shown in figure (a). Then apply a certain pressure to the rubber roller and repeat the above test process. The length of the ink mark on the test table is 2 π R ', as shown in figure (b). The experiment shows that R ′> R, that is to say, the pressure applied to the cot is greater than that applied to the cot, and the radius has an increment △ r = R ′ - R. The reason why the rubber roller radius increases due to pressure is that the rubber belongs to an incompressible elastomer (the so-called "incompressible" refers to that the volume of the object remains the same under the action of external force). When the rubber roller is extruded, there will be a bulge near the extrusion position. The distance from the top of the bulge to the center of the rubber roller circle is roughly equal to the radius r 'of the rubber roller, which is naturally greater than the rotation radius r of the rubber roller without pressure

in 1960, Penrose Yearbook published another experimental study by British Miller, which further confirmed the above results. Miller uses two equal diameter cylinders, one is rigid, and the other is covered with rubber blanket, which is elastic. Make the two upper cylinders drive the elastic cylinder and the rigid cylinder under different contact pressures, and measure their rotational speed. The results show that the rotating speed of the follower cylinder is faster with the increase of the contact pressure. Therefore, on the premise of keeping the driving cylinder speed constant, the actual rotation radius of the driving cylinder must increase with the increase of contact pressure, which is consistent with the experimental results of setz. If the thickness of the blanket covered by the driving cylinder is changed and 0.19mm and 0.17mm blanket are used respectively, it can be found that the thicker the blanket of the driving cylinder is, the higher the speed change rate of the follow-up cylinder is, that is, the larger the actual rotation radius of the driving cylinder is. If the blanket covered by the driving cylinder were replaced by cardboard, the situation would be very different. After the pressurised paperboard, the cutter, dryer, printing device, etc. soon lose elasticity, resulting in the paperboard itself being compressed, the actual rotation radius of the driving cylinder is correspondingly reduced, and the rotation speed change rate of the following cylinder is also becoming smaller and smaller, as shown in the curve below. In Miller experiment, the driven elastic cylinder is equivalent to the rubber cylinder of offset press, and the followed rigid cylinder is equivalent to the plate cylinder or impression cylinder of offset press

based on the fact that the diameter of the rubber elastic cylinder increases after pressure is applied, setz's reducing diameter theory believes that the radius of the rubber cylinder must be smaller than the other two cylinder radii, that is, the radius of the printing plate cylinder is the largest, the radius of the impression cylinder is in the middle, the radius of the rubber cylinder is the smallest, or the radius of the rubber cylinder is the smallest, and the radius of the printing plate cylinder and the impression cylinder are the same

The setz reducing diameter theory is based on experiments, which defines the rolling state of blanket in the embossing area. The drum lining method set up under the guidance of this theory is relatively correct after the test of production practice. The drum diameter dimensions listed in the table are set according to this theory

note: the paper thickness is 0.1mm

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