Finite Element Analysis and Design Optimization of Deep Cold Rolling of Titanium Alloy at Room and Elevated Temperatures

High strength-to-density ratio, high corrosion resistance and superior biocompatibility are the main advantages of Ti-6Al-4V (Ti64), making it a long been favored titanium alloy for aerospace and biomedical applications. Designing titanium components to last longer and refurbishing of aged ones using surface treatments have become a desirable endeavor considering high environmental damage, difficulty in casting, scarcity and high cost associated with this metal. Among mechanical surface treatments, Deep Cold Rolling (DCR) has been shown to be a very promising process to improve fatigue life by introducing a deep compressive residual stress and work-hardening in the surface layer of components. This process has shown to be superior compared with other surface treatment methods as it yields a better surface quality and induces a deeper residual stress profile which can effectively be controlled through the process parameters (i.e. ball diameter, rolling pressure and feed). However, residual stresses induced through this process at room temperature are generally relaxed upon exposure of the components to elevated operating temperatures. In this work, high-fidelity Finite Element (FE) models have been developed to simulate the DCR process in order to predict the induced residual stresses at room temperature and their subsequent relaxation following exposure to temperature increase. Accuracy of the developed models has been validated using experimental measurements available in the literature. A design optimization strategy has also been proposed to identify the optimal process parameters to maximize the induced beneficial compressive residual stress on and under the surface layer and thus prolong the fatigue life. Conducting optimization directly on the developed high-fidelity FE model is not practical due to high computational cost associated with nonlinear dynamic models. Moreover, responses from the FE models are typically noisy and thus cannot be utilized in gradient based optimization algorithms. In this research study, well-established machine learning principles are employed to develop and validate surrogate analytical models based on the response variables obtained from FE simulations. The developed analytical functions are smooth and can efficiently approximate the residual stress profiles with respect to the process parameters. Moreover the developed surrogate models can be effectively and efficiently utilized as explicit functions for the optimization process. Using the developed surrogate models, conventional (one-sided) DCR process is optimized for a thin Ti64 plate considering the material fatigue properties, operating temperature and external load. It is shown that the DCR process can lead to a tensile balancing residual stress on the untreated side of the component which can have a detrimental effect on the fatigue life. Additionally, application of conventional DCR on thin geometries such as compressor blades can cause manufacturing defects due to unilateral application of the rolling force and can also lead to thermal distortion of the part due to asymmetric profile of the induced residual stresses. Double-sided deep rolling has been shown as a viable alternative to address those issues since both sides of the component are treated simultaneously. The process induces a symmetric residual stress which can be further optimized to achieve a compressive residual stress on both sides of the component. For this case, a design optimization problem is formulated to improve fatigue life in high stress locations on a generic compressor blade. All the optimization problems are formulated for multi-objective functions to achieve most optimal residual stress profiles both at room temperature as well as elevated temperature of 450℃. A hybrid optimization algorithm based on combination of sequential quadratic programming (SQP) technique with stochastic based genetic algorithm (GA) has been developed to accurately catch the global optimum solutions. It has been shown that the optimal solution depends on the stress distribution in the component due to the external load as well as the operating temperature

Optimal Design of Magnetorheological Dampers Constrained in a Specific Volume Using Response Surface Method

In recent years, semi-active magnetorheological (MR) and electrorheological (ER) fluid technology based devices and systems have been developed and successfully utilized in many applications as valves, shock absorbers, dampers and clutch/brake systems. These promising devices have the adaptivity of the fully active systems to accommodate varying external excitations while maintaining the reliability and fail-safe features of the passive systems. Compared with ER based devices or systems, MR based devices have recently received special attention due to their high performance with minimal power requirements. Moreover MR fluids have significantly higher yield strength and are less sensitive to contaminants and temperature compared with the ER fluids. The geometric optimal design of MR valves/dampers is an important issue to improve the damper performance, such as damping force, valve ratio and inductive time constant. Considering this, the primary purpose of this study is to establish a general design optimization methodology to optimally design single–coil annular MR valves constrained in a specific volume in MR damper. To accomplish this, first the damping force of MR damper has been modeled using Bingham plastic model. The magnetic circuit of MR damper has been analyzed using finite element method in ANSYS environment to obtain magnetic field intensity which can be subsequently used to obtain the yield stress of the MR fluid in the active volume where the magnetic flux crosses. Then the developed finite element model of the MR valve is effectively used to construct an approximate response function relating the magnetic field intensity to the identified design parameters in the selected design space using response surface method and design of experiment methodology. Using the derived approximate relation for the magnetic field intensity in the MR damper model, the design optimization problem has been formulated using gradient based nonlinear mathematical programming technique based on the Sequential Quadratic Programming (SQP) technique and also stochastic optimization technique based on the Genetic Algorithm (GA) to find optimal geometrical parameters of the MR valve in order to maximize the damping performance under given constrained volume. Finally a PID controller has been designed to evaluate the close-loop performance of the optimally designed MR damper in a quarter-car suspension model