تجزیه و تحلیل حساسیت از مدل المان محدود برای شبیه سازی اکستروژن لوله از جنس استنلس استیل

In this work, a sensitivity analysis has been performed on a finite element model of glass-lubricated extrusion of stainless steel tubes. Fifteen model parameters, including ram speed, billet and tool temperatures, friction coefficients and heat transfer coefficients, were considered. The aim of the study was to determine the parameters that are most important for the response of the extrusion force. The relationship between the model parameters and the responses was analyzed by a calculation of two different regression models: one linear polynomial model and one model that includes interaction terms. Additional simulations were then carried out to validate the regression models. The results show that the initial billet temperature is the factor that has the strongest impact on the extrusion force within the parameter ranges studied in this work. The goodness of prediction and goodness of fit are very good for both regression models.

Seamless stainless steel tubes can be manufactured by extrusion using glass as lubrication. The process is performed at high temperature and is associated with large deformations and high strain rates. Finite element (FE) simulation has become an important tool in the design and development of extrusion and other manufacturing processes. Most of the simulation work involves aluminum extrusion, but some work on steel and titanium extrusion has also been reported, for example, by Damodaran and Shivpuri (2004) and Hansson (2006). A large number of input parameters are used in a FE analysis of extrusion. These parameters include boundary conditions, initial conditions and parameters that describe the mechanical and thermal properties of the material. The accuracy of the extrusion simulation depends, to a large extent, on the accuracy of these parameters. In addition, many of these are often impossible to measure during the extrusion process itself or in tests under similar conditions. Among the simulation work that is reported on extrusion, only few authors include investigations on how changes in input parameters affect the computed results. Flitta and Sheppard (2005) studied the effect of the variation of initial billet temperature and ram speed on FEM predictions of temperature evolution during aluminum extrusion. The simulation was compared with data obtained from experiments. Sivaprasad et al. (2004) studied the effect of ram speed on the distribution of strains, strain rates and temperature in glass-lubricated extrusion of 304 L stainless steel rods. The results were compared with processing maps by Venugopal et al. (1992) and used to identify the best ram speed for obtaining the desired microstructure. A more systematic approach to sensitivity analysis was performed by Snape et al. (2002), who investigated the sensitivity to variations in different input parameters of three axisymmetric FE models: compression, impression-die forging and backward extrusion. A full factorial design of experiments (DOE) was used. The analysis was restricted to the parameters that define the flow stress of the material and heat transfer and friction at the die–workpiece interface. The maximum strain, maximum load, forging work and final die fill were considered as response variables. In this paper, no physical forging trials were used for comparison. Compared to aluminum extrusion, steel extrusion is carried out at higher speed, at higher temperature and with larger temperature gradients between the billet and the tools. The billet–container, billet–mandrel and billet–die contact areas in glass-lubricated steel extrusion are all lubricated in different ways. It could, therefore, be expected that the friction and heat transfer conditions are somewhat different, and it is of interest to investigate the effects of changes in friction, temperature and heat transfer on each one of these contact areas separately.In the present study, a sensitivity analysis is carried out on an axisymmetric FE model of the extrusion of tubes. The material that is extruded is Sandvik Sanicro 28 (UNS: N08028), an austenitic stainless steel designed for service in highly corrosive conditions. The extrusion model is similar to a model developed in Hansson (2010). In Hansson (2010), the initial billet temperature was calculated using simulations of the process steps preceding extrusion. Forces from the extrusion model are compared with data obtained from an experimental extrusion press for validation. The aim of the sensitivity analysis is to study the influence of certain process parameters on the resulting extrusion force. The parameters that affect the force and ones that do not have any significant impact will be determined. This knowledge will be valuable for further work on extrusion simulation, where more effort can be put into giving accurate values to the parameters that have a greater effect. Another important objective is to evaluate whether it is possible to find empirical models for the extrusion force that show the importance of the process parameters and their interactions. Such models could have a practical use in the process development of extrusion. Fifteen different process parameters, such as initial temperature, ram speed, friction and heat transfer coefficients between the billet and the tools, are included in the sensitivity study. The initial peak force and the extrusion forces at 300, 475 and 650 mm ram displacement are considered as responses. The relationship between the parameters and the responses is established according to two different regression models; one linear polynomial model and one model that includes interactions. Additional simulations are then carried out to verify the regression models. The DOEs for the numerical experiments are created by fractional factorial design using MODDE, a commercial software for DOE and optimization. In total, 107 extrusion simulations are carried out within this study. All simulations are performed in the commercial FE software MSC.Marc 2008r1.

A sensitivity study has been performed on a FE model of glass-lubricated extrusion of stainless steel tubes. The result from the study uncovers which of the included boundary and initial conditions are most important for the response of the extrusion force. This is a valuable contribution for increasing the understanding of this process. The initial billet temperature is the factor that has the strongest impact on the extrusion force. Special effort should be put into giving accurate initial condition for the billet temperature when modeling extrusion. In industrial extrusion, it is important to control the heating before extrusion in order to achieve the desired temperature in the billet. The parameters that are significant for predicting the initial peak force in this case are the initial billet temperature together with the coefficients of friction at the contact areas between billet–container, billet–mandrel and billet–glass-pad. Process parameters, such as ram speed, container and mandrel temperature, and contact heat transfer coefficient between billet–container and billet–mandrel, are important for predicting the extrusion force later on in the process. Analyses have been performed using both a linear and an interaction polynomial regression model. The goodness of prediction and goodness of fit are excellent for both models. The interaction model is, however, much more complicated than the linear model and requires more simulations. The conclusion is that a linear model is sufficient for the prediction of the extrusion force in this case. The force response upon changes in the simulation parameters, within the ranges studied in this work, is almost linear. Using the simplified models from regression analysis, it is easy to get a quick response of how changes in initial and boundary conditions affect the extrusion force. To run one of the FE simulations takes several hours in computational time. An interesting approach for further work would be to include geometrical changes, i.e. billet and tube dimensions, among the factors in a new parametric FE study.