Question

Derive the expression for power required in rolling operation

Answer 1

Abstract

Equations are derived for the normal roll pressure, specific roll load and torque in hot rolling mills, using the condition for plastic deformation in rolling derived by Orowan, together with von Kármán's equation of equilibrium. Although applying strictly to the rolling of ideal plastic-rigid materials, these equations may be applied to the rolling of materials which strain-harden by using a mean value of the yield stress in the




... In this study, Sims model shows an acceptable performance (7.5% error); however, it is higher than other predictions. This model consider sticking friction, and do not consider coefficient of friction for calculations 7 , which has been shown to be a good assumption for hot rolling of big pieces (using bigger rollers) 1 . Although the high rolling temperatures, sticking friction could not have been reached in this work due to the use of small diameter rolls, and probably this is the reason why this model did not make better predictions.

... during normal running, the operating point of the mill is based on a fully threaded condition at the operat- ing speed, with a strip tension of 0.01 kn/mm 2 between adjacent stands, and each looper at an angle of 15°. the operating point strip thickness , hout the average strip temperature T at the mill entry and at the exit of each stand, the peripheral speed V0 of the work rolls, and the undeformed work roll radius R of each stand are listed in table 2. the equivalent carbon content of the workpiece is 0.3% by weight. sims's model [9] is used to predict the roll force in the roll bite (i.e., the area between the work rolls where the strip thickness is reduced). the model is enhanced by using shida's empirical results [10] to better estimate the resistance to deformation of the material being rolled. ...

... where Q p is a factor [9] that compensates for friction and any inhomogeneities of deformation, and R p is estimated using the hitchcock approximation [11]. the exit thick- ness hout is estimated using the linearized relation for the output thickness as



... In Schleifprozessen dient die Prozesskraft als Grundlage für die Ermittlung des thermischen Energieeintrags und damit des Schleifbrandrisikos [7,17]. Für die Modellierung der Prozesskraft beim Walzen gibt es in der Literatur unterschiedliche Ansätze [5,19,21,24]. Die bestehenden Modelle beziehen sich dabei maßgeblich auf den Blechwalzprozess. Die örtlich und zeitlich veränderlichen Kontaktbedingungen des Zahnradwalzprozesses werden nicht abgebildet. ...

... Zusammenfassend lässt sich feststellen, dass mittels des Stands der Technik die Walzkräfte beim Nachverdichten von PM Zahnrädern nicht örtlich und zeitlich aufgelöst beschrieben werden können. Die Kenntnis der Walzkraft ermöglicht jedoch eine wissensbasierte Prozessauslegung und Rückschlüsse auf die resultierende Oberflächenqualität, das Dichteprofil und die Verzahnungsqualität. Bereits bestehende Walzkraftmodelle konventioneller Prozesse können aufgrund der Porosität nicht auf das Walzen pulvermetallurgischer Werkstoffe übertragen werden [5,19,21,24]. Die durch die Porosität bestimmten Werkstoffeigenschaften sind unbekannt und können mittels des Standes der Technik nicht berechnet werden. Basierend auf den Untersuchungen von Kauffmann kann zwar die Tiefe td,98 des vollverdichteten Bereichs eines einzelnen Kontakts bestimmt werden, jedoch erlaubt dieser Ansatz nicht die zeitlich aufgelöste Ermittlung der Prozesskraft im Walzprozess [11]. ...





... During past decades, various methods had been proposed to describe the roll-strip contact stress [1][2][3][4][5][6][7][8][9][10]. In early period, the slab method proposed by Karman [1], Orowan [2], Sims [3], Bland and Ford [4] had been widely used in rolling process. ...

... During past decades, various methods had been proposed to describe the roll-strip contact stress [1][2][3][4][5][6][7][8][9][10]. In early period, the slab method proposed by Karman [1], Orowan [2], Sims [3], Bland and Ford [4] had been widely used in rolling process. These methods used to calculate strength parameters (rolling force and torque) might be suitable, but the contact stress pre- dicted by them were very poor because the roll-strip contact was usually described by Coulomb friction (or Constant friction) which was over-simplified to explain the complex condition at interface. ...