Thermo-elastic analysis and multi objective optimal design of functionally graded flywheel for energy storage systems

In this study, thermo-elastic analysis and a multi objective optimal design of a functionally graded Flywheel rotor that can be used in a Flywheel Energy Storage System (FESS) has been investigated. Due to the rapid mechanization and technological innovations that have taken place since the industrial revolution, our energy need has been increasing at an unprecedented rate. On the other hand, limited availability of known energy resources makes it necessary to find solutions that enables more efficient use of energy. One of the solutions to enhance energy efficiency is to store excess production for future usage. In this context, Flywheel energy storage applications for storing electrical energy have gained a great interest in recent years. Flywheel energy storage systems are in favorable position among others due to their strengths in high energy capacity, fast response, long life, low maintenance and environmentally friendly characteristics. Recent advancements in lightweight high strength materials, power electronics and magnetic bearings have made high speed FESS applications possible today. Obviously, those high speed applications such as turbo machinery components, high speed compressors, brake disks, gears, pumps, generators are of practical interest in engineering. Therefore, development of FESS systems has become a popular research topic for scientists and engineers nowadays. Flywheel energy systems are based on a rotating mass principle. In a FESS, electrical energy is converted into the mechanical energy and stored in the Flywheel rotor as rotational kinetic energy. Energy conversion is achieved by means of an electric motor and a bi-directional power converter. Flywheel rotor is the key element to determine the overall performance and capacity of the system. Energy capacity of a Flywheel rotor can be increased by using materials that is capable of resisting loads at high rotational speeds. Functionally graded materials which is a special kind of composites can be used for this purpose. For this reason, the subjected Flywheel rotor in this study has been assumed to be made of a functional graded material. For the thermo elastic analysis, a complex nonlinear differential equilibrium equation has been established. The complexity came from several factors such as non uniform thickness Flywheel geometry, non homogenous material content and by taking into account of the thermal effects on material properties. The governing equation of motion solved numerically by using generalized differential quadrature method (GDQM). Results of numerical solution has been validate by comparison with an axisymmetric two dimensional finite element model. A perfect correlation of both approaches has been demonstrated. Flywheel shape optimization task has been carried by using non dominated sorting genetic algorithm (NSGA II). Optimal designs have been searched for 18 design spaces having different speed, thickness and radius limits. Depending on the bearing type, maximum speed of the flywheel can be two types such as low speed and high speed. In 9 of the design spaces it has been assumed that conventional mechanical bearings were used. Hence, these designs had a maximum rotational speed limit of 10000 rpm. The other 9 design spaces assumed to have magnetic bearings. Therefore, those designs had a maximum rotational speed limit of 100000 rpm. The optimization problem is defined to maximize the average kinetic energy that the flywheel can store between an ambient temperature range without failure and without exceeding rotational speeds allowed by the bearings while minimizing the mass. The genotype of individuals have been constructed by a mixed type encoding such that thickness (h) and volume fraction coeffficient (m) has been encoded by 15 bit Gray coding and materials are encoded by value encoding. For generating child populations a multi point crossover has been used. Additionally, bit invertion and value changing mutations has been applied to the chromosomes. Genetic algorithm code have generated 1000 populations each of them having 1000 individuals. Therefore 1 million potential candidates have been evaluated for each design space. For the material content, random combinations of two materials out of three possibles (Ti-6Al-4V, Inconel 718, AISI 4340) have been selected for each designs. Optimization results have been achieved by using the Numerical solver and the Genetic algorithm code simultaneously and iteratively for each solution. Optimization study has presented following results, - At constant speed, size of the outer radius is the most effective design parameter in terms of the energy capacity. For reaching a higher energy capacity a bigger Flywheel size is reqiured. However, as the size gets bigger the stresses induced due to the centrifugal force increases proportional to the square of the radius of the Flywheel. - At high speeds the stress concerns becomes more evident such that, maximum design speed can not be achieved due to the violation of the stress limit. In such cases, algorithm starts another loop to determine the maximum allowable speed before continuing the other steps. In other words at high speed designs maximum rotational speed becomes another design variable. Therefore, computational efforts highly increases for high speed design searches. Consequently the convergence speed substantially decreases. - For low speed designs, maximum design speed (10000rpm) is achievable without violating any optimization criteria. Whereas, for the high speed applications, maximum achievable speed can not be attained due to stress constrains. For high speed designs maximum achievable speed depends on the Flywheel material and geometry considered. - For the optimal shape, the algorithm tries to increase the mass near the outer edge to increase the energy capacity. Whereas, near the inner edge mass has been increased in order to reduce stresses. In middle sections, algorithm has kept as minimum thickness as possible to reduce the weight of the design. - For material composition, algorithm allocates the lighter materials near outer radius. Whereas, the heavier materials are placed as possible as at the inner radius region in order to reduce stresses caused by the centrifugal loads. Additionally, algorithm tends to allocate AISI4340 to increase the stored energy due to its high density and strength. Whereas, for low energy capacity designs Ti-6Al-4V has been used to minimize the mass. Inco 718 has been used together with these materials to fine tune the designs with its medium properties. Some of the designs seem to have only one material content instead of a mixed FGM structure. Therefore, it can be said for some optimal designs homogenous material structure is the best choice to provide the optimal energy storage. - Some of the designs seem unrealistic due to very thin web sections. For such solutions the study may be developed further to take into account of resonance vibration effects.