A Simplified Model for the Estimation of Forces in Flow Forming and Its Comparison with Ideal Deformation and FEM Models
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ORIGINAL CONTRIBUTION
A Simplified Model for the Estimation of Forces in Flow Forming and Its Comparison with Ideal Deformation and FEM Models Prabas Banerjee1 • Nirmal Hui1
Received: 18 April 2020 / Accepted: 2 October 2020 Ó The Institution of Engineers (India) 2020
Abstract In this work, an approximate analytical model is developed for determining the components of forces as a function of various forming parameters of backward metal flow forming process. The developed model is compared with an ideal deformation model to get an idea about deformation efficiency. It is also compared with a threedimensional finite element (FE)-based model. The proposed model is also compared with the experimental results, available in the literature. It is observed that the developed model gives reasonable qualitative prediction and can be used for quantitative prediction by multiplying the results with a suitable correction factor. The proposed method takes less computational time compared to the FEM model. Keywords Flow forming Finite element method Ideal deformation technique Forming forces List of Symbols Dpi Diamter of the preform DR Diameter of the roller E Total energy Ev Energy per unit volume Fa Axial roll force Fr Radial roll force Ft Tangential roll force f Feed speed ratio havg Average thickness of the preform L Length of the roller arc in contact with preform & Prabas Banerjee [email protected] 1
l1, l2 l0 l00 m N n P pavg pmax pmin Rp RR R T ti, tf V vf W
Initial and final length of the preform, respectively Length of roller contact considering roller deformation Length of roller contact during axial deformation Gradient of a line RPM of the mandrel Material constant Hydrostatic stress Average pressure Maximum pressure Minimum pressure Radius of the preform Radius of the roller Roller nose radius Torque of the flow forming process Inlet and exit thickness of the preform, respectively Volume of the preform Axial feed of the roller Width of the roller
Greek Symbols a Entry angle of the roller b Exit angle of the roller D Reduction in thickness eeq Equivalent strain el, et Logarithmic strain in the axial and transverse directions, respectively ev Volumetric strain g Deformation efficiency h Angle of bite r Flow stress of the material ry Yield stress of the material x Rotational velocity of the preform
Department of Mechanical Engineering, National Institute of Technology, Durgapur 713 209, India
123
J. Inst. Eng. India Ser. C
Introduction Flow forming is one of the popular methods among advanced metal forming processes for the manufacturing of axisymmetric products [1]. The flow formed tube elongates in the axial direction with reduction in the outside diameter of the preform. The inside diameter, which is same as the diameter of the mandrel, remains unchanged [2]. The flow forming process is categorized into two types, viz., forward and backward flow forming. When the material elongates in the same axial direction as that of the movement of the roller, the process is known as a forward flow formi
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