第4章 ANSYS 求解技术.doc

第4章ANSYS 的求解技术4.1 第一类边界条件的处理 以2D恒定磁场矢量位计算为例，在某边界上的矢量磁位值已知。如在电磁铁磁场分析中，求解区的外边界上可认为AZ =0即在L1，L2，L3和L4上所有节点的AZ =0。可用下述指令施加边界条件：LSEL,S,1,4,1,1 !选择L1,L2,L3,L4NSLL,S !选择线上的所有节点 D,ALL,AZ,0 !对边界节点赋值AZ=0NSLL, Type, NKEYSelects those nodes associated with the selected lines.Type Label identifying the type of node select: SSelect a new set (default).RReselect a set from the current set.AAdditionally select a set and extend the current set.UUnselect a set from the current set.NKEY Specifies whether only interior line nodes are to be selected: 0Select only nodes interior to selected lines.1Select all nodes (interior to line and at keypoints) associated with the selected lines对于永磁电机磁场分析，可假定定子铁心外圆上的AZ=0，其指令为CSYS,1 ！选择圆柱坐标系统NSEL,S,LOC,X,0.0849,0.0851 !根据半径选取定子铁心外表面上的节点D,ALL,AZ,0 ！对边界节点赋值AZ=04.2 对称边界条件的处理 对于电磁铁的磁场分析，为了减少计算工作量，根据磁场相对于Y 轴对称关系，求解区可只选一半。xyyx磁力线与边界垂直，为自然边界条件，在2D 矢量位磁场分析中可不作处理。磁力线与边界平行，为第一类边界条件AZ=0对于4极永磁电机的磁场分析，根据对称关系，可以取电机的二分之一进行计算。对称边界施加对称边界条件的指令：DSYM, Lab, Normal, KCNSpecifies symmetry or antisymmetry DOF constraints on nodes.Lab SYMMGenerate symmetry constraints as described below (default).ASYMGenerate antisymmetry constraints as described below.Normal Surface orientation label to determine the constraint set (surface is assumed to be perpendicular to this coordinate direction in coordinate system KCN): XSurface is normal to coordinate X direction (default). Interpreted as R direction for non-Cartesian coordinate systems.YSurface is normal to coordinate Y direction. direction for non-Cartesian coordinate systems.ZSurface is normal to coordinate Z direction. direction for spherical or toroidal coordinate systems.KCN Reference number of global or local coordinate system used to define surface orientation.NotesSpecifies symmetry or antisymmetry degree of freedom constraints on the selected nodes. The nodes are first automatically rotated (any previously defined rotations on these nodes are redefined) into coordinate system KCN, then zero-valued constraints are generated, as described below, on the selected degree of freedom set (limited to displacement, velocity, and magnetic degrees of freedom) DOFSEL. Constraints are defined in the (rotated) nodal coordinate system, as usual. See the D and NROTAT commands for additional details about constraints and nodal rotations.Symmetry and Antisymmetry Constraints:Symmetry or antisymmetry constraint generations are based upon the valid degrees of freedom in the model, i.e., the degrees of freedom associated with the elements attached to the nodes. The degree of freedom labels used in the generation depend on the Normal label.For displacement degrees of freedom, the constraints generated are:SYMMASYMNormal2-D3-D2-D3-DXUX, ROTZUX, ROTZ, ROTYUYUY, UZ, ROTXYUY, ROTZUY, ROTZ, ROTXUXUX, UZ, ROTYZ-UZ, ROTX, ROTY-UX, UY, ROTZFor velocity degrees of freedom, the constraints generated are:SYMMASYMNormal2-D3-D2-D3-DXVXVXVYVY, VZYVYVYVXVX, VZZ-VZ-VX, VYFor magnetic degrees of freedom, the SYMM label generates flux normal conditions (flux flows normal to the surface). Where no constraints are generated, the flux normal condition is naturally satisfied. The ASYM label generates flux parallel conditions (flux flows parallel to the surface). SYMMASYMNormal2-D3-D2-D3-DX-AXAZAY, AZY-AYAZAX, AZZ-AZ-AX, AY4.3 移动边界条件的处理电机是旋转机械，稳态和动态特性仿真涉及到转子的旋转，为磁场分析带来了困难。移动边界问题是有限元电机磁场分析中的一个较困难的技术问题。在此介绍两种处理方法。4.3.1 移动单元法对于求解区为整台电机的磁场分析，可在定转子之间的气隙中取一均匀剖分的气隙带，当转子旋转时，不需要对定转子的单元重新剖分，而今需要对气隙带的单元重新剖分。步骤：1. 分别建立定转子模型并进行剖分；2. 在定转子气隙间建立一个等宽的圆环面，并进行剖分；3. 编制一个旋转子程序l 在旋转前，首先删除气隙带面上的单元，然后删除气隙带面积；l 而后对转子（或定子）进行旋转一步；l 旋转后重新建立气隙带面，赋材料特性后，进行剖分。注意：1 该方法较适合于电机以某一固定速度旋转的稳态特性分析；2 对于永磁转子电机，旋转定子较方便，不需要旋转后对永磁体磁化方向重新赋值。对于4极永磁电机计算例气隙带面（A92）定子旋转子程序：FINISH /PREP7*IF,NSTEP,GT,1,THEN ！初始位置不需要旋转ACLEAR,92 ！删除A92上的单元ADEL,92 ！删除A92*AFUN,DEG CSYS,1 ！圆柱坐标系统AGEN,2,1,73,1,DY,1 ! 定子所有面（包括节点、单元等）旋转DYLSEL,S,LOC,X,0.0329,0.0331 ! 选择定子铁心内表面上的线AL,ALL ! 产生铁心内圆面积A92ASEL,S,74,91,1 ！选择所有转子面AOVLAP,ALL ！获得旋转后的气隙带面A93NUMCMP,ALL ！面积编号压缩后气隙带面仍为A92 ASEL,S,92,1 AATT,1,1 ！A92赋材料特性AMESH,92 ！A92剖分*ENDIF4.3.2 移动节点法 对于根据对称关系求解区为电机的一部分的磁场分析，移动边界可采用下述方法处理。两条线重合L34与定子相连L33与转子相连L33和L34处于同一位置，采用相同的分段。L33与转子外圆构成转子表面气隙带随转子一起旋转；L34与定子内圆构成定子表面气隙带，与定子联在一起。定转子面分别形成，并进行剖分。电机旋转后不需要重新剖分，只需要对定转交界面（L33和L34）上的节点进新购和处理即可。移动边界的处理方法如下：1. 首先将移动边界线的节点编号分别存入数组L33和L34L33（1）= 5083L33（2）= 5084L33（N）= 5082+NL33（181）= 5263L34（1）= 5263L34（2）= 5265L34（N）= 5263+NL34（181）= 52642. 转子（或定子）转动NSTEP步，每步对应于L33和L34上的一个节点距离（角度DY0）；3. 令移动边界线L33和L34上对应节点的AZ 相等。移动边界的相应程序段为/COM在前处理网格剖分后加入*DIM,L33,181 ！定义1维数组L33和L34，各180点*DIM,L34,181L33(1)= 5083L33(2)= 5084L33(N)= 5082+NL33(181)= 5263L34(1)= 5263L34(2)= 5265L34(N)= 5263+NL34(181)= 5264/COM 定子移动NSTEP步，每步移动角度DY0DY0= 45/180 ! 在45范围内L33和L34有180个等分节点DY= NSTEP*DY0 ! 旋转步数NSTEP需预先赋值ASEL,S,1,45,1,1 ! 定子铁心及绕组ASEL,A,57 ! 定子表面气隙带 AGEN,2,ALL,DY,1 ! 定子旋转NSTEP步/COM % 施加移动边界条件 % *DO,I,1,181,1L34NSTEP J = I+NSTEPL33 *IF,J,GT,181,THEN J = J-181 *ENDIF CP,I,AZ,L33(J),L34(I) *ENDDOCP, NSET, Lab, NODE1, NODE2, NODE3, NODE4, NODE5, NODE6, NODE7, NODE8, NODE9, NODE10, NODE11, NODE12, NODE13, NODE14, NODE15, NODE16, NODE17Defines (or modifies) a set of coupled degrees of freedom.PREP7: Coupled DOFNSET Set reference number: nArbitrary set number.HIGHThe highest defined coupled set number will be used (default, unless Lab = ALL). This option is useful when adding nodes to an existing set.NEXTThe highest defined coupled set number plus one will be used (default if Lab = ALL). This option automatically numbers coupled sets so that existing sets are not modified.Lab Degree of freedom label for coupled nodes (in the nodal coordinate system). Defaults to label previously defined with NSET if set NSET already exists. A different label redefines the previous label associated with NSET. Valid labels are: Structural labels: UX, UY, or UZ (displacements); ROTX, ROTY, or ROTZ (rotations) (in radians). Thermal labels: TEMP, TBOT, TE2, TE3, . . ., TTOP (temperature). Fluid labels: PRES (pressure); VX, VY, or VZ (velocities). Electric labels: VOLT (voltage); EMF (electromotive force drop); CURR (current). Magnetic labels: MAG (scalar magnetic potential); AX, AY, or AZ (vector magnetic potentials); CURR (current). Explicit analysis labels: UX, UY, or UZ (displacements). If Lab = ALL, sets will be generated for each active degree of freedom (i.e., one set for the UX degree of freedom, another set for UY etc.), and NSET will be automatically incremented to prevent overwriting existing sets. The ALL option cannot be used to modify existing sets-NSET must be a new set number n or NEXT. The degree of freedom set is determined from all element types defined and the DOF command, if used. ALL is the only label applicable to FLOTRAN.NODE1, NODE2, NODE3, NODE4, NODE5, NODE6, NODE7, NODE8, NODE9, NODE10, NODE11, NODE12, NODE13, NODE14, NODE15, NODE16, NODE17 List of nodes to be included in set. Duplicate nodes are ignored. If a node number is input as negative, the node is deleted from the coupled set. The first node in the list is the primary (retained) node. If NODE1 = ALL, NODE2 through NODE17 are ignored and all selected nodes NSEL are included in the set. If NODE1 = P, graphical picking is enabled and all remaining command fields are ignored (valid only in the GUI). A component name may also be substituted for NODE1.NotesDo not include the same degree of freedom in more than one coupled set. Repeat CP command for additional nodesNSTEP = 20 时的定转子相对位置4.4 加载方法4.4.1 实体模型负载（Solid-Model Loads）实体模型加载是指对点、线、面加载。优点：l 与网格剖分无关，修改单元和节点不影响负载；l 可仅对几个实体加载而不用对较多的单元和节点加载，采用图形加载比较容易。 缺点：l 实体模型和有限元模型可能采用不同的坐标系统和不同的加载方向；l 实体加载不便于用于需要对节点而不是对关键点施加约束的情况；l 需要进行约束扩展时可能有问题（当需要将约束扩展到连接线段的两关键点间的节点时）；l 实体加载无法显示。4.4.2 有限元模型负载（Finite element-Model Loads） 优点：l 可对节点直接加载，不必考虑坐标系统和加载方向问题；l 没有约束扩展问题，可直接对节点加约束。缺点：l 修改网格时需要首先删除负载，单元修改后需要重新加载；l 不便于用图形加载4.4.3 施加自由度约束可采用的自由度DisciplineDegree of FreedomANSYS LabelStructuralTranslationsRotationsUX, UY, UZROTX, ROTY, ROTZThermalTemperatureTEMP, TBOT, TE2, . . . TTOPMagneticVector PotentialsScalar PotentialAX, AY, AZMAGElectricVoltageVOLTFluidVelocities PressureTurbulent Kinetic EnergyTurbulent Dissipation RateVX, VY, VZPRESENKEENDS可采用的指令LocationBasic CommandsAdditional CommandsNodesD, DLIST, DDELEDSYM, DSCALE, DCUMKeypointsDK, DKLIST, DKDELE-LinesDL, DLLIST, DLDELE-AreasDA, DALIST, DADELE-TransferSBCTRANDTRAN4.4.4 施加力（集中负载）可采用的“力”DisciplineForceANSYS LabelStructuralForcesMomentsFX, FY, FZMX, MY, MZThermalHeat Flow RateHEAT, HBOT, HE2, . . . HTOPMagneticCurrent SegmentsMagnetic FluxElectrical ChargeCSGX, CSGY, CSGZFLUXCHRGElectricCurrent ChargeAMPS CHRGFluidFluid Flow RateFLOW可采用的指令LocationBasic Commands Additional CommandsNodesF, FLIST, FDELEFSCALE, FCUMKeypointsFK, FKLIST, FKDELE-TransferSBCTRANFTRAN4.4.5 表面载荷DisciplineSurface LoadANSYS LabelStructuralPressurePRES1ThermalConvectionHeat Flux Infinite SurfaceCONVHFLUXINFMagneticMaxwell SurfaceInfinite SurfaceMXWFINFElectricMaxwell SurfaceSurface Charge DensityInfinite SurfaceMXWFCHRGSINFFluidWall RoughnessFluid-Structure InterfaceImpedanceFSIIMPDAllSuperelement Load VectorSELVLocationBasic CommandsAdditional CommandsNodesSF, SFLIST, SFDELESFSCALE, SFCUM, SFFUN, SFGRADElementsSFE, SFELIST, SFEDELESFBEAM, SFFUN, SFGRADLinesSFL, SFLLIST, SFLDELESFGRADAreasSFA, SFALIST, SFADELESFGRADTransferSFTRAN4.4.6 体载荷DisciplineBody LoadANSYS LabelStructuralTemperatureFluenceTEMP1FLUEThermalHeat Generation RateHGENMagneticTemperatureCurrent Density Virtual DisplacementVoltage DropTEMP1JSMVDIVLTGElectricTemperatureVolume Charge DensityTEMP1CHRGDFluidHeat Generation RateForce Density HGENFORCLocationBasic CommandsAdditional CommandsNodesBF, BFLIST, BFDELEBFSCALE, BFCUM, BFUNIFElementsBFE, BFELIST, BFEDELEBFESCAL, BFECUMKeypointsBFK, BFKLIST, BFKDELE-LinesBFL, BFLLIST, BFLDELE-AreasBFA, BFALIST, BFADELE-VolumesBFV, BFVLIST, BFVDELE-TransferBFTRAN-举例：对绕组加电流A2A1！A1=A2=0.8E-3 （绕组毛面积），N=500 （匝数），I=3 A （电流）JA = 3*500/(0.8E-3) ！电流密度JA= I*N/A1ASEL,S,1,1 ！选择绕组A1ESLA,S ！选择A1中的单元BFE,ALL,JS,JA ！对所有单元施加电流密度JAASEL,S,2,1 ！选择绕组A2ESLA,S ！选择A2中的单元BFE,ALL,JS,-JA ！对所有单元施加电流密度-JA等磁位线磁通密度电流密度4.5 求解方法的选取4.5.1 ANSYS的几种求解方法1. 稀疏矩阵直接求解法Sparse direct solution；2. 预条件共轭梯度法Preconditioned Conjugate Gradient (PCG) solution；3. 雅可比共轭梯度法Jacobi Conjugate Gradient (JCG) solution；4. 不完全乔利斯基共轭梯度法Incomplete Cholesky Conjugate Gradient (ICCG) solution；5. 前直接求解法Frontal direct solution；6. 自动迭代求解法Automatic iterative solver option (ITER).稀疏矩阵直接求解法为隐含解法除非具有CIRCU124单元的电磁场分析（采用前直接解法）.还有采用多处理器具有并行特性的其他解法，如: 分布式求解器Distributed solvers (Distributed Domain Solver - DDS, Distributed PCG - DPCG, and Distributed JCG - DJCG), and 代数多网求解器the Algebraic Multigrid (AMG) solver4.5.2 不同解法的特点SolverTypical ApplicationsIdeal Model SizeMemory UseDisk (I/O) UseSparse Direct Solver (direct elimination, shared-memory parallel solver) When robustness and solution speed are required (nonlinear analysis); for linear analysis where iterative solvers are slow to converge (especially for ill-conditioned matrices, such as poorly shaped elements).10,000 to 500,000 DOFs (works well outside this range).1 GB/MDOF (optimal out-of-core); 10 GB/MDOF (in-core)10 GB/MDOFPCG Solver (iterative solver) Reduces disk I/O requirement relative to sparse solver. Best for large models with solid elements and fine meshes. Most robust iterative solver in ANSYS50,000 to 10,000,000+ DOFs0.3 GB/MDOF w/MSAVE,ON; 1 GB/MDOF without MSAVE0.5 GB/MDOFJCG Solver (iterative solver) Best for single field problems - (thermal, magnetics, acoustics, and multiphysics). Uses a fast but simple preconditioner with minimal memory requirement. Not as robust as PCG solver.50,000 to 10,000,000+ DOFs0.5 GB/MDOF0.5 GB/MDOFICCG Solver (iterative solver) More sophisticated preconditioner than JCG. Best for more difficult problems where JCG fails. 50,000 to 1,000,000+ DOFs1.5 GB/MDOF0.5 GB/MDOFFrontal Solver (direct elimination solver) Direct solver predecessor to the direct sparse solver. Uses less memory than sparse solver, always runs out-of-core and is too slow for all but smaller problems (under 50k DOFs). Very robust solver, good for small model nonlinear analyses.Under 50,000 DOFsLess than 0.5 GB/MDOF10 GB/MDOFDPCG Solver (distributed solver) Same as PCG but runs on distributed parallel systems (PPFA license required)50,000 to 100,000,000+ DOFs1.5-2.0 GB/MDOF in total*0.5 GB/MDOFDJCG Solver (distributed solver)Same as JCG but runs on distributed parallel systems (PPFA license required). Not as robust as DPCG or PCG solver.50,000 to 10,000,000+ DOFs0.5 GB/MDOF0.5 GB/MDOF DDS Solver (distributed solver)Iterative solver for distributed parallel systems (PPFA license required). Highly scalable solver time. Best for large linear analyses on large memory systems.1,000,000 - 10,000,000 DOFs2.0-5.0 GB/MDOF in total*0.5 GB/MDOFAMG Solver (iterative solver) Good shared memory parallel performance. Good preconditioner for ill-conditioned problems where PCG is slow. Requires PPFA license but is not a distributed parallel solver.50,000 to 1,000,000+ DOFs1.5-3.0 GB/MDOF in total*0.5 GB/MDOFDSPARSE Solver (distributed sparse)Same as sparse solver but runs on distributed parallel systems (requires a PPFA license). Scalable up to 16 processors.10,000 to 500,000 DOFs. Works well outside this range.1.5 GB/MDOF on master machine, 1.0 GB/MDOF on slave machines. Uses more total memory than the sparse solver.10 GB/MDOF4.5.3 选择求解方法EQSLV, Lab, TOLER, MULTSpecifies the type of equation solver.SOLUTION: Analysis OptionsLab Equation solver type: FRONTFrontal direct equation solver. In-memory only. SPARSESparse direct equation solver. Applicable to real symmetric and unsymmetric matrices. Available only for STATIC, HARMIC (full method only), TRANS (full method only), SUBSTR, and PSD spectrum analysis types ANTYPE. Can be used for nonlinear and linear analyses, especially nonlinear analysis where indefinite matrices are frequently encountered. Well suited for contact analysis where contact status alters the mesh topology. Other typical well-suited applications are: (a) models consisting of shell/beam or shell/beam and solid elements (b) models with a multi-branch structure, such as an automobile exhaust or a turbine fan. This is an alternative to iterative solvers since it combines both speed and robustness. Generally, it requires more memory than the frontal solver, but it is comparable in memory requirement to the PCG solver. When memory is limited, the solver works partly in and out-of-core memory without much increase in CPU time. JCGJacobi Conjugate Gradient iterative equation solver, in-memory option. Available only for STATIC, MODAL (subspace option only), HARMIC (full method only), and TRANS (full method only) analysis types ANTYPE. Can be used for structural and multiphysics applications. Applicable for symmetric, unsymmetric, complex, definite, and indefinite matrices. Recommended for 3-D harmonic analyses in structural and multiphysics applications. Efficient for heat transfer, electromagnetics, piezoelectrics, and acoustic field problems. ICCGIncomplete Cholesky Conjugate Gradient iterative equation solver. Available for STATIC, HARMIC (full method only), and TRANS (full method only) analysis types ANTYPE. Can be used for structural and multiphysics applications, and for symmetric, unsymmetric, complex, definite, and indefinite matrices. The ICCG solver requires more memory than the JCG solver, but is more robust than the JCG solver for ill-conditioned matrices. PCGPre-conditioned Conjugate Gradient iterative equation solver (licensed from Computational Applications and Systems Integration, Inc.). Requires less disk file space than FRONT and is faster for large models (wavefront about 1000). Much faster than the JCG solver. Useful for plates, shells, 3-D models, large 2-D models, p-method analyses, and other problems having symmetric, sparse, definite or indefinite matrices for nonlinear analysis. Requires twice as much memory as JCG (/RUNST can be used to determine the space needed). Available only for analysis types ANTYPE STATIC, TRANS (full method only), or MODAL (with subspace option only). The PCG solver can r