TECHNICAL PAPER Forces and coefficient of friction during cylindrical three roller bending Shakil A. Kagzi 1 • H. K. Raval 1 Received: 23 June 2017 / Accepted: 11 October 2017 Ó The Brazilian Society of Mechanical Sciences and Engineering 2018 Abstract Three roller bending process is one of the processes of forming cylindrical shells, for manufacturing drums, pressure vessels, windmill towers, etc. During the bending process, forces on the rollers must not exceed their bending capacity. Along with operational and material parameters, the forces exerted during bending and power consumption are affected by the coefficient of friction at the roller-plate interface. It is difficult to determine the coefficient of friction practically during three roller bending process. An attempt is made to determine the forces and friction coefficient at each roller–plate interface, through derived mathematical model, using experimental results. The variation of coefficient of friction under the higher loading conditions was also determined as a case study. With the present mathematical formulation along with the coefficient of friction, the forces at each roller–plate interface could be determined more precisely. The determination of forces and friction coefficient helps in deciding operational and design parameters of the bending machine, respectively. Keywords Three roller bending Á Coefficient of friction Á Bending forces Á Bending power Á Cylindrical bending Á Rolling friction Á Friction Nomenclatures a Distance between the axis of two bottom rollers a e ,a x Perpendicular distance of the vertical forces on the bottom roller at the entry and the exit side, respectively, from the top roller contact point F tangential Tangential force acting at the interface of the two bodies F normal Normal force acting at the point of contact of the two bodies H t ,H e ,H x Horizontal force on the top roller the bottom roller at the entry and the bottom roller on the exit side, respectively I t ,I b Moment of inertia on the top roller and the bottom rollers, respectively J Normal force at the contact between the plate and the bottom roller at the entry side K Strength coefficient M e , M x Bending moment of the resultant force at the bottom roller on the entry and the exit side, respectively, about the top roller contact point M external External bending moment based on applied forces M internal Internal bending moment based on the geometry of material its properties N t , N b Revolution per minute of the top roller and bottom rollers, respectively n Strain hardening exponent P Normal force at the top roller contact point p t , p e , p x Power consumed during bending at the top roller the bottom roller at the entry and the bottom roller on the exit side, respectively p e-shaft , p x-shaft Power consumed in rotating just the shaft of the bottom roller at the entry and the bottom roller on the exit side, respectively Technical Editor: Ma ´rcio Bacci da Silva. & Shakil A. Kagzi shakil128@gmail.com H. K. Raval hkr@med.svnit.ac.in 1 Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat 395007, India 123 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2018)40:129 https://doi.org/10.1007/s40430-018-1059-y