In this paper is proposed the mathematical description of the temperature distribution resulting from the friction between the two inking rollers (one of which is made off steel and the second one has elastic layer) in the offset printing machine. So-called in printing industry steel vibrator roller perform simultaneously rotary and reciprocating motion. This reciprocating motion is the main source of the heat generation. Using the Laplace transform method for heat conduction equations with boundary conditions taking into account the real processes taking place in the inking unit in contact area we obtained and analyzed the solution that could be useful for determination and regulation of parameters in order to decrease time of process stabilization.
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Presented paper is a continuation of issues undertaken and presented in 2010 at a conference Friction 2010. The previously proposed mathematical description of the temperature distribution caused by friction in contact between two rotating inking rollers, one of which moves also reciprocating along the roller pivot and conditions of stationary solution form the basis for the presented here solutions for the non-stationary conditions. The geometry of the rollers motion was taken into account. The solution in form of the Laplace transformer were obtained and analyzed using the Laplace transform method to a system of two equations of heat conduction with boundary conditions taking into account the real processes taking place in the inking unit in contact zones. The analysis showed that the transform does not have branch points. This feature is of great importance for the solution of the problem.
In this paper a proposition of mathematical formula of the temperature distribution caused by friction phenomena in the cylinder/cylinder contact in the inking unit of the offset printing machine is presented. In the inking unit there are pairs of wheeling inking rollers, one of which is made of steel and the second one has got a rubber layer outside. The steel roller besides the circular motion moves reciprocating along the cylinder pivot. The measurements made during the tests in the various research centres have shown that the inking rollers’ temperature increases during the work of the offset printing machine. Some derivative heat equations are applied to the case study and are solved.
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