Abstract—Conical sections and shells made from metal plates are widely used in various industrial applications. 3-roller conical bending process is preferably used to produce such conical sections and shells. Bending mechanics involved in the process is complex and little work is done in this area. In the present paper an analytical model is developed to predict bending force which will be acting during 3-roller conical bending process. To verify the developed model, conical bending experiments are performed. Analytical results and experimental results were compared. Force predicted by analytical model is in close proximity of the experimental results. The error in the prediction is ±10%. Hence the model gives quite satisfactory results. Present model is also compared with the previously published bending force prediction model and it is found that the present model gives better results. The developed model can be used to estimate the bending force during 3-roller bending process and can be useful to the designers for designing the 3-roller conical bending machine. Keywords—Bending-force, Experimental-verification, Internal- moment, Roll-bending. NOMENCLATURE a = horizontal distance of the bottom roller centers in mm E = Young’s modulus in N/mm2 F, G, H = Anisotropy parameters K = strength coefficient in N/mm2 M = bending moment in N-m n = strain hardening exponent P = Vertical load at the top roller and bending plate interface in N r1 = radius of bottom roller in mm R = radius of curvature of the bent plate in mm t = thickness of the plate in mm t e = thickness of elastic layer in mm U = Vertical distance travelled by the top roller for first stage of static bending in mm w = width of the blank in mm x = half the horizontal distance of the bottom roller centers in mm y = distance of fiber from neutral plane in mm y ep = distance of the fiber upto which elasticity E is constant in mm β = bottom roller inclination, θ = Angle between frictional force and horizontal plane at the roller plate interface in radians µ = coefficient of friction at roller plate interface ε = strain σ = stress in N/mm 2 Mahesh Chudasama is with Government Engineering College, Dahod, Gujarat (India) 389151 (Phone: +91 9979074377; e-mail- mkcgecs@gmail.com). Harit Raval is with S.V. National Institute of Technology, Surat, Gujarat (India) 395007 (e-mail:hkraval1@yahoo.co.in). ઽ ത= effective strain ો ഥൌ effective stress ν = Poisson’s ratio χ = curvature of the bend plate between bottom rollers, mm -1 I. INTRODUCTION OR erecting large towers for wind mills or for chimneys, conical sections or shells made up of thick metal plates are used. Apart from these such conical sections find other structural applications in the industries. These conical sections or shells are usually made by using roll bending process. Roll bending is one of the metal forming processes. Forming is the process of imparting the desired shape to the material by deforming the material beyond its elastic stress and below its fracture stress. The stresses induced in the forming operation are thus plastic stresses. Metal forming can be used to impart desired shape, size and finish to the material without significant loss of the material. Moreover, strength of the product is improved through improved stress flow lines. Continuous bending operation, in which a long strip of metal (typically coiled steel) is passed through consecutive sets of rollers or roller stands, until the desired cross sectional profile is obtained, is called roll bending. The process of roll bending is used for many years for the production of the conical shells and sections. Still there is little research work available on the analysis of the process. The normal practice of plate roller bending still heavily depends upon the experience and the skill of the operator as well as designers. In industry, working to templates, or by trial and error, yet remains a common practice to be followed. In the present paper an attempt is made to give analysis of force requirement during the process. The process of roll bending can be divided in four stages namely (i) static bending, (ii) Forward rolling, (iii) Backward rolling and (iv) unloading. Static bending is performed by loading the blank between top roller and bottom rollers as shown in Fig. 1 and then moving the top roller downwards. This process is similar to air bending process but is performed by the rollers instead of punch & die. In the next operation bottom rollers are given rotation initially in forward direction to perform the rolling. When the required length of the plate is bent the machine is stopped. In the next stage of the process the bottom rollers are driven in backward direction to complete the operation. In the final stage the top roller is pulled up and the rolled plate is unloaded. Development of Analytical Model of Bending Force during 3-Roller Conical Bending Process and Its Experimental Verification Mahesh Chudasama, Harit Raval F World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:7, No:11, 2013 2362 International Scholarly and Scientific Research & Innovation 7(11) 2013 ISNI:0000000091950263 Open Science Index, Mechanical and Mechatronics Engineering Vol:7, No:11, 2013 publications.waset.org/9997447/pdf