Theoretical Analysis For Cold Radial Forging Process Of Rod Based On Upper Bound Approach

Radial forging a special forging process with several hammers arranged radially around the workpiece and it is widely used in the production of gun barrels,hollow axles,oilfield equipment and Zirconium-based alloy in nuclear industry.At the process design phase,it is necessary to search for the optimum condition rapidly over a whole combination of various process parameters.However,compared with the analytical method,it is inefficient to design the process condition by physical experiment or numerical simulation since radial forging is quite a complex process.Besides,according to the literature,the existing theoretical models based on slab method or upper bound opproach are only available for simple and uniform deformation modes in radial forging process.The former is essentially based on the basic assumption that the deformation is homogeneous within a slab and the latter is based on parallel velocity fields,in which the deformation along the radial direction is homogeneous.Since the slip-line method is generally conducted in the transverse direction of the workpiece,the effects of axial feed and inlet angle of hammer on the forging penetration cannot be considered.Therefore,the aim of this study is to design velocity fields considered inhomogeneous deformation mode and develop upper bound axisymmetric models for radial forging of rods.Then,the effects of process conditions such as radial reduction,axial feed,inlet angle of hammer and front-pull/back-push forces on the evaluation indexes such as forging load,deforming inhomogeneity and forging penetration are investigated,which could contribute to the process design for radial forging process and development for radial forging machine with independent intellectual property rights.The main contents of this dissertation are described as follows.General velocity fields and dissipated work in forging zone are deduced base on volume constancy and velocity boundary conditions.A partial differential equation on the stream function is derived,which reflects the deformation characteristics of radial forging process.General expression of the velocity field is accordingly solved and it determins the predicted metal flow characteristics.Upper bound model with parallel velocity field is developed by uniform deforming mode,while upper bound model with non-uniform velocity field is proposed by inhomogeneous deforming mode.The former can predict forging load efficiently and the latter can study the inhomogeneity of axial deformation.It is concluded that the decrease of inlet angle of hammer or the increases of radial reduction and back-push force is conducive to reduce the inhomogeneity of axial deformation.Therefore,within equipment capacity,large radial reduction is desired to reduce the number of passes and finally reduce the axial deformation inhomogeneity.Based on the parallel velocity field and weight function,a general method for constructing velocity fields without velocity discontinuities is proposed.It is difficult to postulate a single mathematical expression for the velocity fields over the whole deformation domain.Instead,the workpiece domain is considered as a number of separate fields divided by velocity discontinuity boundaries.The velocity discontinuity is introduced based on the assumption of rigid plastic mechanics,which corresponds to a severe deformation region in reality.In order to model the metal flow characteristics reasonably,the velocity discontinuity boundary is replaced as a transition region and its velocity field is constructed by a weight function.As a result,the velocity discontinuities are vanished and an upper bound model with continuous velocity field is developed to study the effects of radial reduction and axial feed on the strain inhomogeneity along the axial direction.It is concluded that the radial reduction and the axial feed contribute to the strain magnitude and the degree of strain inhomogeneity respectively.Based on the transformations for both the geometric coordinate system and the velocity field,a theoretical model for radial forging process is proposed.The rigid-block upper bound analysis is a classical approach for plane strain problems.By simplifying the velocity fields to be constant in each single block and meanwhile reinforce the constraints for the geometry and distribution of the rigid blocks,the solving of kinematically admissible velocity fields is accordingly converted to the design of geometries and distributions of the rigid-blocks.To overcome the limitation that this method cannot be applied to axisymmetric problems,the transformations for both the geometric coordinate system and the velocity field proposed by Wilson is introduced.As a result,the implementation of rigid-block upper bound approach is also available for the construction of the transformed hodograph from the transformed discontinuity field in axisymmetric problems.The predictions of forging penetration depth show that the radial reduction and the inlet angle of hammer are the most important parameters for forging penetration depth and the increase of radial reduction rate or the decrease of hammer angle improves the forging penetration efficiency.Finally,a program named RFDESIGN is developed for process design of radial forging process of rods.Experimental studies on the forging quality such as forging penetration efficiency and deformation inhomogeneity were carried out.It is verified that RFDESIGN is capable of designing and evaluating process conditions properly.