tailieunhanh - Energy Storage in the Emerging Era of Smart Grids Part 3

Tham khảo tài liệu 'energy storage in the emerging era of smart grids part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 48 Energy Storage in the Emerging Era of Smart Grids Fig. 5. Multi-rim setup of the flywheel rotor Analytical approaches In Figure 5 a multi-rim flywheel rotor is illustrated. Its geometry is typically modeled as axially symmetric. This assumption appears sound since the balancing in terms of achieving axisymmetry is an important objective in the manufacturing of a flywheel rotor. Danfelt et al. 1977 was one of the first to publish an analytical method of analysis for a hybrid composite multi-rim flywheel rotor with rim-by-rim variation of transversely isotropic material properties. The method presented in this subsection generalizes Danfelt s approach in terms of its various extensions. Thorough validation of the method by means of FE analysis and experiments is given in references Ha et al. 2003 Ha Jeong 2005 Ha et al. 2006 . To the authors knowledge all publications regarding analytical solutions to the described problem assume a constant rotational velocity. Hence the transient behavior of charging and discharging operations which might indirectly limit the allowable maximum rotational speed cannot be accounted for. The local equation of equilibrium in the radial direction of the cylindrical coordinate system for purely centrifugal loading due to the rotational velocity w reads as i - 1 arr - 00 QW2r 0. 4 For typical strains in flywheel applications the nonlinearity of the FRPC material behavior can be neglected. Thus a linear relationship between stress Ơ strain e and temperature AT can be stated ơ Q e aAT . 5 Herein a is the vector of thermal expansion coefficients and Q is the global stiffness matrix. The stresses and strains are written as vectors of generally six elements of the symmetric stress tensor in cylindrical coordinates. The stress vector therefore comprises the three normal stresses arr Ữ00 ơzz and the the shear stresses Ơ0z ơzr ơr0. Using the temperature difference AT the effect of residual stresses from the curing process can be studied see