Predictions of roll force and torque in flat hot rolling are commonly made, for practical purposes, by the use of methods which assume that the material sticks to the rolls at all points along the arc of contact. In such cases the coefficient of friction, apart from being high enough to produce sticking, has no further influence on the rolling load. However, in the experiments conducted in the present work, there was a difference between the velocity of the rolls and that of the emerging material, which indicated that slipping occurred
between the rolls and the plate. In addition, lubricants are being introduced in hot rolling practice which reduce the coefficient of
friction to the point where complete sticking conditions are improbable. Therefore, the calculation of rolling loads assuming sticking
3 ^ x a. *i s i .. j _ - "j j _ v» - • - — i-v .
vwnux °-1-J Jt*° ilv/ -*.uugcj. av/uoyi/auxc i no a. xccui u
coefficient of friction becomes an adjustable parameter, whose value must be lower than that where sticking conditions exist.
An increase in the magnitude of the coefficient of friction produced an increase in the calculated roll force. The results plotted in Figs.6.2.1 - 6.2.12 showed that the magnitude of the contribution of the coefficient of friction to the roll force decreased as the state of friction approached complete sticking conditions, at which point the contribution of the frictional stresses to the roll pressures was
limited by the strength of the material, i.e.I =k. It was also found • that, as the rolling temperature was increased the threshold value of
p at which sticking conditions initiated was lowered. Thus, as the temperature was raised and the yield stress of the material decreased, the value of the coefficient of friction above which sticking conditions appeared was reduced. Hence, as the rolling temperature was increased from 9006C to 1200°C the upper value of p which might significantly influence the roll force fell from 0.6 to 0.4 (Fig. 6.2.1 - 6.2.4).
Fig.2.4,3 ). Thus,the slope of the friction hill - ds/d§ - at those segments of the contact arc where conditions close to sticking friction existed, was smaller than the corresponding slope under conditions of homogeneous deformation! Consequently the introduction of inhomogeneity of stress distribution into the calculation, by means of the inhomo geneity factor, w(a), led to a, reduction in the magnitude of the effect j of p on the roll force, particularly when the value of p exceeded 0.4 (Fig.6.2.7 - 6.2.10), It can also be seen that the level of roll pressure decreased when inhomogeneous deformation was considered. This was
mainly associated with the reduction of the effective yield stress given by kw(a).
The coefficient of friction has a more complex effect on the values of roll torque, being expressed as,
the position of the neutral angle. It can be seen in Figs.6,4.5 ana. 6.4,6 that the increase in the coefficient of friction caused an increase in
The condition of plasticity under inhomogeneous deformation was expressed by Orowan^^as, s-p=2kw(a) with the function w(a)
'decreasing rapidly as sticking conditions were approached i.e. a^l(see
the neutral angle up to a maximum value, which remained constant at values of p in excess of 0.4. Thus, as the coefficient of friction was increased the associated increase in both the roll pressure and the negative integrand in Eq.7.2.1 tended to counteract one another.
The majority of the calculated values of roll torque obtained under conditions of inhomogeneous deformation were smaller than the corresponding values obtained under homogeneous conditions. This arose because the effective yield stress was lower in the former case. Only when a high value of the coefficient of friction (LI =0.6) was used did the introduction of inhomogeneity increase the roll torque. Since the values of p most likely to occur in the experimental ‘conditions were lower than 0.6, calculations under inhomogeneous deformation may be considered to reduce the values of roll torque.
The experimental values of roll force at 900° C and 1200°C (Figs. 5.1.1. and 5.1.4) showed a linear increase as the percentage reduction was increased. The corresponding calculated forces obtained at constant values of the coefficient of friction showed a similar relationship wiin the percentage reduction(Figs.6.2.1. and 6.2.4). Likewise, the linear increase in the experimentally determined values of roll torque
Twr +.v>o irmwacD q£- + v>o T'orcer,tagc reductionf compared well with the corresponding relationship between percentage reduction and the calculated roll torque, obtained with the use of a constant U . These results seem to indicate that the va.lue of the coefficient of friction was constant throughout the experiments conducted at 900 G and 1200 C. This was not the case with the experimental results of roll force and torque at 1000°C and 1100°C, which showed a reduction in the rate of increase of both parameters as the percentage reduction was increased. A similar rate of increase could be obtained in the corresponding
calculated results if the value of p was assumed to "be inversely proportional to the percentage reduction. This might indicate that the value of the coefficient of friction decreased as the percentage reduction was increased throughout the experiments conducted at 1000°C and 1100°C.
7.3 Values of the coefficient of friction obtained by experiment.