Finite Formulation Based Multi-physics Coupled Method And Its Application In Cooling System Design Of Permanent Magnet Machines

Finite formulation method(FFM),also known as the cell method(CM),is a new numerical method based on the algebraic formed control equations.Since its resulting schemes can always obey the local conservation law,and are with definite physical meanings,FFM has its particular advantages in approximating the solutions of multi-physics coupled problems.This dissertation focuses on the calculation techniques of the coupled fields of permanent magnet synchronous machines(PMSMs)based on the basic principles of FFM,and the main research contents are as follows:(1)The thermal analysis techniques of PMSMs based on FFM are analyzed and illustrated in this dissertation.The doubly circulatory procedure with the two-way coupling of physical parameters and the temperature distribution is established since the copper loss,the iron loss,the eddy-current loss of the permanent magnets,the heat conductivity coefficients,and the heat convectional coefficients are temperature-related parameters.The inner loop of the procedure is employed to guarantee the energy conservation of the air enclosed in the end-caps and modify the temperature-dependent heat convection coefficients,while the outer loop is used to correct the heat conductivity coefficients and the electromagnetic losses that change with temperatures.The main purpose of the proposed circulatory procedure is to implement the mutual adaptation between the physical parameters input and the output results,and to obtain a higher precision.To simplify the computational procedure and reduce significantly the computational burden introduced by the rewind process of the heat conductivity coefficients,the product of temperature rise and conductivity coefficient instead of the temperature rise alone is chosen as the solution quantity.(2)This dissertation demonstrates the fluid field calculation techniques based on FFM.A second-order schemed discrete form is exhibited to diagonally dominate the stiffness matrix of the convective term.The newly established second-order scheme is absolutely stable and share the same computational accuracy with the second-order upwind scheme in calculating the fluid field under low Mach numbers.For unstructured grids,external long-distance upwind points are not indispensable with the new second-order scheme.However,for most discrete schemes,the stiffness matrices are kept asymmetric,and thus making the calculation process adifficult mission.A first-order scheme starts from the centered difference scheme is established to enhance the symmetric characteristics of the convective-term global stiffness matrix.The computational accuracy of the new first-order scheme is higher than the first-order upwind scheme in low-Mach-number regions.In order to heighten the computational efficiency with decent accuracy,the first-order scheme is firstly employed to obtain a initial solution,and the second-order scheme is then used to improve the convergence results.(3)The coupled relationships between the fluid flow field,the temperature field,the electromagnetic field of electrical machines are analyzed in this dissertation.The thermally mathematical model of the fluids is derived based on area coupling.The fluid-structure interaction relations are numerically realized by the boundary coupling and the source coupling.The equations of the viscosity,the remanent flux density,the coercive force,the electrical conductivity coefficients are modified based on the temperatures.The mathematical model of the coupled fluid-thermal-electromagnetic field is thus established based on the multiphysics calculation techniques of FFM.The coupled fields of a water-cooled PM traction motor are analyzed with the computation techniques,and the solutions are validated by experimental results.(4)In order to maintain the temperature rise and balance the temperature distribution of a totally enclosed PMSM,a mixed axial-radial ventilation system with the clapboards as the centrifugal fan is established.The sensibility of the temperature rise is analyzed with the changes in the numbers and sizes of the axial vents in the stator core and the diameters of the vents slotted in the rotor core.