Development of Analytical Model for Dynamic Bending Force during Single Pass 3-roller Cone Frustum Bending Technique

roller conical bending process is one which is used for producing conical sections or cone frustums from metal plates for various industrial applications. The plates to be bent are cut for the required size and shape and then rolled between three cylindrical rollers. The plate is kept between one top roller and two bottom rollers. Than the top roller is lowered down and the plate gets bend. The rollers are rotated to get the roll bending of the plate. Final dimension of the cone frustum are achieved through setting appropriate machine setting parameters. An attempt is made in this paper to develop the analytical model for the prediction of the bending force during the stage of dynamic roll bending. During the roll bending of the plate there will be shear stresses along with the normal stresses. The analytical model has been developed considering these shear stresses. The model consists of various parameters like material parameters and geometrical parameters. Based on the analytical models derived, effects of some of the material parameters on dynamic bending force have been studied. In the development process complex mechanics involved in this process has been simplified so it will give insight of the process and will be helpful to the researchers and designers working in the area of metal forming, especially in roll bending process. versatility in satisfying the human needs. If there can be small reduction in cost or the increase in the effectiveness of any of the metal forming processes, it will positively affect the metal forming industry and hence the economy in the larger context. Metal forming process in which straight line of the metal is transformed into a curved length is called bending. Roll bending or Roller forming is a continuous bending operation in which a long strip of metal is passed through consecutive sets of rollers or a roller stand, each performing only an incremental part of the bend, until the desired cross sectional profile is obtained. It is observed that the roller bending process usually produces higher dimensional accuracy of the finished products (1). Conical shells and sections are also widely used in manufacturing of air duct transitions, chimneys, fan inlets, towers for wind mills, hull of ships, structural components of on shore oil and gas platforms etc. These conical shells and sections are widely used in process industries. 3-roller conical bending machines are used for production of such conical shells and sections from the metal plates. Conical bending using 3-roller bending machine can be achieved by either setting the top rollers inclined in vertical plane or setting the bottom rollers inclined in horizontal plane. Conical bending can also achieved by inclining the top roller and bottom rollers simultaneously. Bottom roller inclination significantly affects the bending moment as compared to top roller inclination during 3-roller conical bending (2) and hence, only bottom roller inclination in the horizontal plane is considered in the present analysis. In 3-roller conical bending process, the bottom rollers are inclined as shown in figure 1 and the blank is kept between the top roller and the bottom rollers such that one of the generators of the cone frustum remains parallel to the bending axis. In case of 3-roller bending machine, the bending line lies parallel to the top roller axis. The top roller is than lowered down to get the static bending of the plate. At this stage the plate gets bend locally at the bending line, kept