Determination of the Reduction in the Thickness of Strip during Its Shaping in the Rolls of a Roll-Forming Machine

Abstract

Results are reported from a study of the dependence of the reduction in the thickness of strip on the main process parameters as the strip is bent in the rolls of a roll-forming machine. The study was performed with the use of the theory of experiment planning. The deformation that strip undergoes during its bending in the rolls of roll-forming machines is comprised its bend- ing and spreading. The spreading of the strip occurs as a result of reductions in its thickness at the locations where it is bent. Determining the amount of spreading that takes place entails not only determination of the initial width of the semifinished product (strip) - which is chosen so as to have the product's geometric dimensions conform as closely as possible to the exist- ing standards and specifications - but also determination of the surface strain. The latter is important for determining the pro- duction schedule based on the conditions that characterize the limiting ductility of the material. The decrease in the thickness of the strip at the bend sites is different for different production conditions. The decrease depends not only on the thickness of the initial semifinished product and the bending radius but other parameters as well: the width of the elements being bent, the diameters of the rolls, the bending angles, the properties of the material, etc. Solving such a complex problem by means of the general theory of plasticity with allowance for the effects of all the given factors is quite difficult without the use of certain assumptions. The problem is complicated even more by the fact that the effects of the above-mentioned factors - most of which are statistical in nature - are different in magnitude and direction. All of this defines reduction in thickness which the strip undergoes as a random variable. A random variable - in the present case, the reduction in strip thickness - can be fully described if its distribution law is known, i.e., if a relation is found to connect the possible values of the random variable with the corresponding proba- bilities. The distribution law can be established based on an analysis of statistical data. With this as our goal, we analyzed 781 values of the relative decrease in thickness Δt/t 0 (where Δt = t 0 − t; t is the thickness of the strip at a bending site after the shaping operation) that were obtained in the roll-forming of angles and channels from strips with a thickness in the range t 0 = 1-5 mm. The strips were made of medium-carbon and low-alloy steels and were subjected to roll-forming by different schedules. The ranges of the bending angle in the schedules were α = 0-15°, 0-30°, 0-45°, 0-60°, 0-75°, and 0-90°. The rel- ative bending radius r/t 0 = 0.5-8 and the relative width of the flanges that were formed b/t 0 = 5-35 (r is the bending radius, mm; b is the width of the flanges, mm). The analysis showed that the experimental data on the relative thickness reduction conform to a log-normal distribution law. This was confirmed by the Kolmogorov and Pearson criteria. To determine the dependence of the relative thickness reduction on several variables simultaneously based on the statistical (as opposed to the functional) character of the dependence of this reduction on the process parameters, it is best to use methods that reflect the actual nature of the process being studied. In the given case, the factorial-experiment method turns out to be the best approach.