Theoretical And Experimental Study On The Deformation Of The Machined Parts From Initial Residual Stress

Residual stresses commonly exist in manufactured parts because these stresses are inevitably generated during all forming processes that involve thermo-elastic-plastic deformation,such as casting,welding and cutting.The generation of residual stress creates a nonzero stress state within manufactured products,which is different from the stress-free theory of elasticity.Moreover,these residual stresses evolve into the initial stress over time or applied loads,which persistently affects the performance of machined products including chemical resistance,fatigue life and distortion.Hence,the varied impact of initial stresses on the components enable it to be a critical factor in determining the product quality.However,the dimensional instability induced by initial stresses will limit the performance of the component,potentially depriving the capability of the component to be used after a product has been manufactured because the manufacture accuracy is required.The origin of the initial stress from the residual stress has been discussed in this paper.The internal stresses in a prestressed body are called residual stresses or initial stresses depending on whether the prestressed body is subjected to external forces.When no external load is applied to a prestressed body,the body contains residual stresses and follows the given assumptions that it is self-equilibrating in the absence of external forces,whereas they are referred to as initial stresses after external forces are applied to the body.In other word,initial stress derives from the self-equilibrating residual stress.When the material is subjected to external force in application,the residual stress evolves into initial stress.Firstly,the undeformed frame is selected as the referential configuration and the Kirchhoff stress is expanded into Taylor series under the referential configuration.It is proved that the stress can be decomposed into the residual stress and the current stress from by the applied load in no consider of the high-order small quantity.Then,the Kirchhoff stress under the reference frame is transformed into the Euler stress under the current configuration by means of the stress transformation.Based on the principle of virtual work,a general model is established to predict the deformation induced by initial stress.In the consideration of the symmetry of Euler stress and strain,the stress equilibrium equation and boundary conditions with initial stress under the current configuration are derived by using Gauss divergence theorem.It can be seen from the general model that when the residual stress in the ideal state is zero,the initial stress in the current configuration is also zero,and the stress equilibrium equation and boundary conditions in accordance with traditional theory of elasticity,respectively.This also indirectly means that the correctness of the general model in theory.In comparison with with the traditional elastic theory,when the initial stress in the body is affected by external force,the deformation of the body in the equilibrium equation and stress boundary is not only related to the initial stress,the initial stress gradient,but also to the external force.The proposed model was used to predict the deformation of a thin aluminium plate found in a previous study,in which a finite difference method-based model was developed and validated with experimental results.A comparison showed that the proposed model had 10% higher predictive accuracy than the plate theory.In addition,the general model is derived from the virtual work principle,and is not limited to the size of the object as the material bending model.Therefore,from the physical perspective,the general model proposed in this paper is more universal.The variation of the distortion induced by the initial stress necessarily cause the error change of the machined surface for the component,which may lead to the geometric parameters exceeding the allowable tolerance range.In this work,based on the least square method,the form and position tolerance of aviation thin-walled parts is comprehensively evaluated,and the influence of deformation on the machining surface parallelism is discussed.In order to investigate the effect of initial stress on the dynamic accuracy,we take the thick walled cylinder subjected to the uniformly distributed pressure on the inner radius for an example.according to the incompressible condition of material and the assumption of plane strain,the differential equation for displacement accompanied with residual stress is derived in combination with the generalized Hooke’s law.The displacement formula can be obtained by separating variables.The expression indicates that the displacement of the cylinder will remain concentric when the residual stress is uniformly distributed during unloading.According to the elastic-plastic theory,the theoretical formula of residual stress for thick walled cylinder under the uniform pressure is introduced,and the residual stress is substituted into the equilibrium equation and boundary conditions with initial stress derived from the above section.It is proved that the eccentricity for the rotor can be caused by the initial stress in combination with the centroid formula of material mechanics.Finally,the irregular deformation of the cylinder with uniformly distributed residual stress under external force is analyzed by numerical model.When the object is in motion,the inertia force can be introduced by Alembert principle,and the influence of the initial stress on the dynamic performance of the object can also be obtained theoretically.On the basis of the robust design in quality engineering,the orthogonal design and signal-to-noise ratio of Taguchi method are adopted to optimize the process parameters in the feasible region of ductile iron plane milling—cutting speed,feed per tooth and cutting depth for the optimization of the resulting machining stress by using the experiment.The orthogonal experiment is applied to perform the statistical analysis on the main effect of the mean residual stress and the main effect of the signal-to-noise ratio,then obtained minimum value of the mean value of the residual stress and the maximum value of the signal-to-noise ratio at the corresponding level of each factor,and then the statistics is used to test and analyze the significance of each process parameter.On this basis,the effectiveness of the selected process parameters within the range is verified for the low residual stress.