【正文】 oscillating parameters. This is possibly due to the plexity of liquid–solid and solid–solid frictional behaviour between the mould, powder and shell. Zhu and coworkers10 calculated the flowing behaviour of the liquid slag film between the strand and mould. The putation results showed that the average velocity gradient of liquid slag film is behind themould oscillating velocity in one oscillating cycle. This may be one of the reasons that lead to the delay of MDF to velocity.Relationship between correlative parameters ofoscillation and mould frictionIn order to withdraw the fragile solidified shell near the meniscus during high speed casting, an optimum mould oscillation mode should be built to reduce the tensile stress acting on the solidified shell near the meniscus and apply the pressive force to the solidified shell near Negative strip time tN which has been referred to as heal time is the actual time within one cycle during which the mould oscillates downward faster than the strand shell.In the present work, the time during which the pressive force acts on the strand surface within one oscillation cycle is defined as shell pressed time (tMDF,0). Traditionally, negative strip time gives a rough index of the heal time (tMDF,0) for pressive effects on the solidified shell. However, to the authors’ knowledge there are few publications that have clearly shown the relationship between tN and tMDF,0. As discussed above, the present study shows that tMDF,0 is not strictly equal to tN, as can be seen from Fig. 2, therefore, a parison between them is also studied in the present paper.Figure 3 illustrates tMDF,0 over a spectrum of tN during the stead state casting, where a range of operational data from the casting tests were taken. It is interesting to note that although tMDF,0 tends to be different with the certain values of tN, tMDF,0 fluctuates near tN, and tMDF,0 increases with the increase in tN as a whole. In this case, the overall relationship between tMDF,0 and tN may be expressed by a linear function. Hence, to some extent, it is possible and reasonable to use tN as a reliable indicator to estimate the heal time of MDF in practice.Figure 4 illustrates the relationship between the maximum MDF and the maximum relative velocity during one oscillation cycle. The maximum MDF represents the maximum tensile force acting on the solidified shell. In continuous casting, an increase in the casting speed tends to result in an increase in relative velocity between the mould and strand in positive strip period. As can be seen from Fig. 4, the relative velocity of the mould in the positive strip period increases, and accordingly the tensile force acting on the solidified shell is increased. To some extent, there is a substantially proportional relationship between the maximum friction and relative speed.Variations of correlative parameters duringchanges of casing speedIn industry, the desired situation is a stable operation without obvious variation of parameters because the fluctuation is liable to cause abnormality even breakout. Figure 5 shows the example of decrease in casting speed. The casting speed decreases from 1?42 to 1?15 m min21, but the periodic variations of MDF vary slightly. The movements of the MDF change regularly in the range from 215 to 25 kN.Figure 6 demonstrates the variations of correlative parameters of MDF and negative strip time, including the casting speed changing. In the present study, mould frequencies are proportional to casting speed, as can be seen in Fig. 6a. As oscillating frequencies decrease the paratively lower frequencies tend to have larger tN owing to the longer period of one oscillation cycle. As mentioned above, tMDF,0 is a little less than tN and has a similar evolution trend as tN. Figure6c shows variations of the maximum and minimum relative velocity in each oscillating cycle and Fig. 6d shows variations of the maximum and minimum MDF. For the sake of the maximum velocity of mould and casting speed descend towards inverse directions in positive strip period, the maximum relative velocity between mould and strand decreases gradually. Whereas, the minimum velocity of mould and casting speed vary in the same directions, and the minimum velocity of mould varies steadily. As a result, the maximum friction force decreases gradually and the minimum friction maintains at a stable value during the decrease in casting speed. This indicates that changes of casting speed could not always have a serious impact on the mould friction. It is also suggests that a proper relationship between casting speed and oscillating frequencies could control and alleviate the friction fluctuations during changes of casting speed.ConclusionsIn the present work, the measurements of MDF were performed on a continuous slab caster with hydraulic oscillators. The sampling rate of 1250 Hz was high enough to calculate MDF instantaneously, and a large quantity of MDF data had been collected for subsequent analysis. The following conclusions were drawn.1. Transient MDF is explicitly displayed which variesregularly and periodically following the relative velocity between mould and strand. The tensile and pressive friction forces acting on strand surface caused by MDF appear alternatively, and the waveforms of friction tend to be a rectangular or trapeziform shape at different oscillating frequencies.2. The friction and relative velocity between mould and strand do not vary synchronously. The time is defined, during which the pressive force acts on the strand surface, as shell pressed time. The shell pressed time is less than the negative strip time, and the correlation between them can be expressed as a linear function. In addition, the maximum friction is proportional to the maximum relative velocity between mould and strand.3. In plant trials, the maximum friction decreases gradually and the minimum friction maintains at a stable value during the decreas