Analytical Calculation Of Deformation And Stress Field In Upsetting Of Large Steel Ingots

As the foundation of manufacturing the core parts of major equipment,large forgings play an important role in the construction of national basic economy,national defense industry and modern advanced science and technology.Its production capacity,product level and performance quality are symbols of a country's manufacturing level and comprehensive strength.Large forgings are forged from steel ingots.Upsetting is an indispensable sequence in forging process.The internal strain state and stress state of steel ingot play a decisive role in forging quality during upsetting.There are mainly analytical and numerical methods to study the mechanical properties of ingot upsetting.For complex deformation problems,only discrete numerical solutions can be obtained by computer technology,and the results are often quite different from the actual situation.At this time,the value of analytical method is highlighted.The analytical results can not only clearly analyze the relationship between various parameters,but also test the numerical solution.According to the current research situation of ingot upsetting,the internal strain state and stress state of steel ingot during upsetting are studied by analytical calculation method.The main work and research results are as follows:?1?A friction model with continuous distribution on the end face is established and parameterized.In the new friction model,the end frictional shear stress?_r is a function of radius r,maximum frictional shear stress?_max and its position r₀.The new friction model provides convenience for analytical study of upsetting large steel ingot.?2?A new method to prove the first variational principle of rigid-plastic materials is proposed.The first variational principle of rigid-plastic materials is proved by functional variation.The new method not only shows the rigorous mathematical proof process,but also shows the idea of applying theorem to solve.The new method provides convenience for plastic forming theory research and beginners'learning.?3?According to the deformation characteristics of upsetting large steel ingot,the velocity field permitted by the movement has been initially set.With the aid of rigid plastic first variational principle and the new friction model,the analytic solution of the real velocity field of ingot upsetting is obtained.The shape of steel ingot under different reduction,the influence of different friction conditions on the shape and the distribution of dynamic recrystallization critical line are studied.Using this analytical solution,the expression of displacement increment is obtained.The shape of ingot upsetting after deformation can be quantitatively obtained through displacement increment expression.The results of analytical calculation are consistent with those of numerical calculation.The research on upsetting velocity field and blank shape has important theoretical guiding significance for closing the cavity inside the ingot,compacting the porosity inside the ingot and eliminating the porosity in the ingot.?4?According to the instantaneous size and shape of upsetting large ingot and the force boundary condition,on the basis of preset stress field shear stress,the analytical solution of stress field inside the drum blank during upsetting is obtained by using the simultaneous solution method of equilibrium differential equation,stress boundary condition and plastic condition.Based on the analytical results,the distribution law of stress field is analyzed.The comparison between analytical results and numerical results shows that the two are relatively close.The establishment of analytical solution of internal stress field of steel ingot has important reference value for formulating upsetting process of large steel ingot,predicting defects of upsetting deformation and determining the size of forming load.