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No description available.

No description available.

No description available.

No description available.

A mathematical model has been used to calculate the roll force and torque produced under a wide range of flat hot rolling conditions. The technique used is based on the numerical solution to the Von Karman equation developed by Alexander and applied to cold rolling conditions. In the present work, extensions have been made that allow the use of a yield .stress which is dependent upon temperature, rate of deformation and extent of inhomogeneity of the deformation process. Like Alexander, the present model considers also the effect of both: the elastic zone at each end of the deformation region and of roll flattening on force and torque. A prerequisite for these calculations has been the experimental determination of the temperature gradients in the plate during rolling, the coefficient of friction between plate and rolls and the flow stress of the material at relevant temperatures and strain rates; the last named data being supplemented by published data on similar material. The results have been compared with experimentally determined force and torque required to roll mild steel plates at temperatures between 900C and 1200C, under uniubricated conditions. The coefficients of friction associated with percentage reductions of between 30 and were within the range 0.2--0.5. The thickness of the scale, the rolling velocity and the temperatures at the plate surface appeared to control the magnitude of the coefficient of friction. The peripheral layers of the plates underwent a severe quench, caused by rapid heat transfer to the rolls: the associated temperature reduction increased with increasing roll pressures and contact time. The resulting temperature gradient was implied in the calculation using a geometric mean of the individual temperature measurements. At rolling temperatures between 900 °C and 1000°C and reductions up to 35 the degree of agreement between the experimental and calculated roll forces and torques were +/-1 Jfo and +/-1% respectively, although the use of Suzuki's flow stress data reduced these discrepancies to about4 6% and4 11% respectively in most cases. However the use of higher reductions or higher, temperatures led to poorer agreement between calculation and experiment 2% and 4 35- in the case of roll force and torque respectively).

A theoretical model has been developed which relates the build-up of stresses in the thin shell of steel solidifying in a continuously casting mould, to the shape distortion and the formation of an air gap. The work postulates that the behaviour of this shell can be analysed as that of a flexible structure formed by four elasto-perfectly plastic beams linked by rigid comers. This "box" represents the whole section of solidified shell at a given metallurgical height only if the section is totally detached from the mould. In general, it represents the detached corner portions alone. The rest of the shell is assumed to remain clamped against the mould wall by the metallostatic pressure. The thermal contraction of the neutral axis "filament" along the whole shell determines the amount of room which is available for the detached corner portion to distort, and thus also the size of the detached lengths of shell. The mechanical equilibrium of the structure is determined by the combined effect of temperature gradients and metallostatic pressure, by the rigidity condition imposed at the corner and by the flexural characteristics of the shell. The yield stress of the steel is assumed linearly dependent on temperature. The analysis of the shape distortion and air gap formation was initially informed by the observed behaviour of a partial physical analogue constructed from bi-metallic strips linked by rigid corners. Thermal moments were induced by immersing this analogue in a water bath at controlled temperatures, and distributed loads were imposed through a system of pulleys. The elastic behaviour of this physical analogue was predicted using basic beam theory. For the analysis of the deformation of a continuously cast structure, mathematical equations were derived which describe the overall moment and force equilibrium; the elastic and plastic stress distribution across the thickness of the shell; and the force and moment equilibrium within the cross-section of the shell. An equation was derived relating the curvature at any point along the shell to the moment at the corner of the structure. An iterative procedure was developed to determine the moment at the corner and a Runge-Kutta algorithm was incorporated to integrate the curvature equation. Further equations were derived which relate the deflection at the corner and the detached length on one side of the section, to the total length of the other side of the section. Recent high temperature studies of the mechanical behaviour of steels have been analysed in terms of the theoretical model developed. The model is able to predict the extent and thickness of the air gaps forming in the corner regions during the casting of billets and slabs and also provides explanation for the formation of both internal and external off-corner cracks. It also demonstrates the theoretical basis behind the practically observed relationship between casting speed and crack formation.

The design of shape control systems is an area of current interest in the steel industry. Shape is defined as the internal stress distribution resulting from a transverse variation in the reduction of the strip thickness. The object of shape control is to adjust the mill so that the rolled strip is free from internal stresses. Both static and dynamic models of the mill are required for the control system design. The subject of this thesis is the static model of the Sendzimir cold rolling mill, which is a 1-2-3-4 type cluster mill. The static model derived enables shape profiles to be calculated for a given set of actuator positions, and is used to generate the steady state mill gains. The method of calculation of these shape profiles is discussed. The shape profiles obtained for different mill schedules are plotted against the distance across the strip. The corresponding mill gains are calculated and these relate the shape changes to the actuator changes. These mill gains are presented in the form of a square matrix, obtained by measuring shape at eight points across the strip.

A device based on an adaptation of the Christopherson tube is investigated for the lubrication and other effects of employing a polymer melt as the lubricant during the wire drawing process. The device is heated to convert the polymer feed into a viscous melt and the pressure required is generated by a hydrodynamic action produced by the motion of the wire. On the basis of experimental evidence, it is apparent that deformation commences before the wire reaches the die, in the Christopherson tube itself, with the die effectively acting only as a seal. Under these conditions, the die geometry becomes of. secondary importance and the deformation actually takes place as if an effective die of continuously changing die angle is being used. To take this aspect of the process into account, a mathematically described effective die shape is used in the present analysis. The plastic strain hardening properties and the strain rate sensitivity of the wire material are also incorporated into the analysis. The study utilises an empirical expression relating shear stress and rate of shear together with an experimentally derived pressure coefficient of viscosity, in determining the coat thickness possible on the wire. The theory contains the effect of a limiting value to the shear stress, which exhibits itself as slip in the polymer. An alternative theory is also presented which assumes that shear stress is zero at the polymer/tube interface. This much simplified analysis allows the length of the deformation zone to be determined. An extensive series of experimental studies have shown that the coat thickness reduces both as speed increases and as the wire material strength increases. Predictions of coat thickness from the analysis tend to be lower than those obtained experimentally. At low drawing speeds a coat defect was observed which gave the coated wire a "bamboo" shape. It is probable that this defect is caused by the slip-stick nature of the polymer melt in the Christopherson tube. The assumed die shape and predicted pressure distributions are verified by experiment.

Planing and moulding operations carried out within the woodworking industry make extensive use of rotary machining. Cutter-marks are produced on the timber surface which are generally accepted as unavoidable. More noticeable surface defects may be produced by such factors as cutter-head imbalance, and until recently most research has concentrated on removing these defects. When a high quality finish is required, a further machining operation, such as sanding, is often required to remove cutter-marks. What is required, is a modified machining process which combines a surface closer to the ideal fixed knife finish, whilst retaining the flexibility, practicality and cost effectiveness of rotary machining.