Ansoft后处理过程中计算器使用方法(英文版)

ANSOFT MAXWELL 2D/3D FIELD CALCULATOR -Examples- Introduction This manual is intended as an addendum to the on-line documentation regarding Post-processing in general and the Field Calculator in particular. The Field Calculator can be used for a variety of tasks, however its primary use is to extend the post-processing capabilities within Maxwell beyond the calculation / plotting of the main field quantities. The Field Calculator makes it possible to operate with primary vector fields (such as H, B, J, etc) using vector algebra and calculus operations in a way that is both mathematically correct and meaningful from a Maxwell’s equations perspective. The Field Calculator can also operate with geometry quantities for three basic purposes: · plot field quantities (or derived quantities) onto geometric entities; · perform integration (line, surface, volume) of quantities over specified geometric entities; · export field results in a user specified box or at a user specified set of locations (points). Another important feature of the (field) calculator is that it can be fully macro driven. All operations that can be performed in the calculator have a corresponding “image” in one or more lines of macro language code. Post-processing macros are widely used for repetitive post-processing operations, for support purposes and in cases where Optimetrics is used and post-processing macros provide some quantity required in the optimization / parameterization process. This document describes the mechanics of the tools as well as the “softer” side of it as well. So, apart from describing the structure of the interface this document will show examples of how to use the calculator to perform many of the post-processing operations encountered in practical, day to day engineering activity using Maxwell. Examples are grouped according to the type of solution. Keep in mind that most of the examples can be easily transposed into similar operations performed with solutions of different physical nature. Also most of the described examples have easy to find 2D versions. 1. Description of the interface The interface is shown in Fig. I1. It is structured such that it contains a stack which holds the quantity of interest in stack registers. A number of operations are intended to allow the user to manipulate the contents of the stack or change the order of quantities being hold in stack registers. The description of the functionality of the stack manipulation buttons (and of the corresponding stack commands) is presented below: · Push repeats the contents of the top stack register so that after the operation the two top lines contain identical information; · Pop deletes the last entry from the stack (deletes the top of the stack); · RlDn (roll down) is a “circular” move that makes the contents of the stacks slide down one line with the bottom of the stack advancing to the top; · RlUp (roll up) is a “circular” move that makes the contents of the stacks slide up one line with the top of the stack dropping to the bottom; · Exch (exchange) produces an exchange between the contents of the two top stack registers; · Clear clears the entire contents of all stack registers; · Undo reverses the result of the most recent operation. Fig. I1 Field Calculator Interface The user should note that Undo operations could be nested up to the level where a basic quantity is obtained. The calculator buttons are organized in five categories as follows: · Input contains calculator buttons that allow the user to enter data in the stack; sub-categories contain solution vector fields (B, H, J, etc.), geometry(point, line surface, volume), scalar, vector or complex constants (depending on application) or even entire f.e.m. solutions. · General contains general calculator operations that can be performed with “general” data (scalar, vector or complex), if the operation makes sense; for example if the top two entries on the stack are two vectors, one can perform the addition (+) but not multiplication (*);indeed, with vectors one can perform a dot product or a cross product but not a multiplication as it is possible with scalars. · Scalar contains operations that can be performed on scalars; example of scalars are scalar constants, scalar fields, mathematical operations performed on vector which result in a scalar, components of vector fields (such as the X component of a vector field), etc. · Vector contains operations that can be performed on vectors only; example of such operations are cross product (of two vectors), div, curl, etc. · Output contains operations resulting in plots (2D / 3D), graphs, data export, data evaluation, etc. As a rule, calculator operations are allowed if they make sense from a mathematical point of view. There are situations however where the contents of the top stack registers should be in a certain order for the operation to produce the expected result. The examples that follow will indicate the steps to be followed in order to obtain the desired result in a number of frequently encountered operations. The examples are grouped according to the type of solution (solver) used. They are typical medium/higher level post-processing task that can be encountered in current engineering practice. Throughout this manual it is assumed that the user has the basic skills of using the Field Calculator for basic operations as explained in the on-line technical documentation and/or during Ansoft basic training. Note: The f.e.m. solution is always performed in the global (fixed) coordinate system. The plots of vector quantities are therefore related to the global coordinate system and will not change if a local coordinate system is defined with a different orientation from the global coordinate system. The same rule applies with the location of user defined geometry entities for post-processing purposes. For example the field value at a user-specified location (point) doesn’t change if the (local) coordinate system is moved around. The reason for this is that the coordinates of the point are represented in the global coordinate system regardless of the current location of the local coordinate system. Electrostatic Examples Example ES1: Calculate the charge density distribution and total electric charge on the surface of an object Description: Assume an electrostatic (3D) application with separate metallic objects having applied voltages or floating voltages. The task is to calculate the total electric charge on any of the objects. a) Calculate/plot the charge density distribution on the object; the sequence of calculator operations is described below: · Qty -> D (load D vector into the calculator); · Geom -> Surface… (select the surface of interest) -> OK · Unit Vec -> Normal (creates the normal unit vector corresponding to the surface of interest) · Dot (creates the dot product between D and the unit normal vector to the surface of interest, equal to the surface charge density) · Geom -> Surface… (select the surface of interest) -> OK · Plot b) Calculate the total electric charge on the surface of an object · Qty -> D (load D vector into the calculator); · Geom -> Surface… (select the surface of interest) -> OK · Normal · · Eval Example ES2: Calculate the Maxwell stress distribution on the surface of an object Description: Assume an electrostatic application (for ex. a parallel plate capacitor structure). The surface of interest and adjacent region should have a fine finite element mesh since the Maxwell stress method for calculation the force is quite sensitive to mesh. The Maxwell electric stress vector has the following expression for objects without electrostrictive effects: where the unit vector n is the normal vector to the surface of interest. The sequence of calculator commands necessary to implement the above formula is given below. · Qty -> D · Geom -> Surface… (select the surface of interest) -> OK · Unit Vec -> Normal (creates the normal unit vector corresponding to the surface of interest) · Dot · Qty -> E · * (multiply) · Geom -> Surface… (select the surface of interest) -> OK · Unit Vec -> Normal (creates the normal unit vector corresponding to the surface of interest) · Num ->Scalar (0.5) OK · * · Const -> Epsi0 · * · Qty -> E · Push · Dot · * · - (minus) · Geom -> Surface… (select the surface of interest) -> OK · Plot If an integration of the Maxwell stress is to be performed over the surface of interest, then the Plot command above should be replaced with the following sequence: · Normal · · Eval Note: The surface in all the above calculator commands should lie in free space or should coincide with the surface of an object surrounded by free space (vacuum, air). It should also be noted that the above calculations hold true in general for any instance where a volume distribution of force density is equivalent to a surface distribution of stress (tension): where Tn is the local tension force acting along the normal direction to the surface and F is the total force acting on object(s) inside (. The above results for the electrostatic case hold for magnetostatic applications if the electric field quantities are replaced with corresponding magnetic quantities. Current flow Examples Example CF1: Calculate the resistance of a conduction path between two terminals Description: Assume a given conductor geometry that extends between two terminals with applied DC currents. In DC applications (static current flow) one frequent question is related to the calculation of the resistance when one has the field solution to the conduction (current flow) problem. The formula for the analytical calculation of the DC resistance is: where the integral is calculated along curve C (between the terminals) coinciding with the “axis” of the conductor. Note that both conductivity and cross section area are in general function of point (location along C). The above formula is not easily implementable in the general case in the field calculator so that alternative methods to calculate the resistance must be found. One possible way is to calculate the resistance using the power loss in the respective conductor due to a known conduction current passing through the conductor. where power loss is given by The sequence of calculator commands to compute the power loss P is given below: · Qty -> J · Push · Num -> Scalar (1e7) OK (conductivity assumed to be 1e7 S/m) · / (divide) · Dot · Geom -> Volume… (select the volume of interest) -> OK · · Eval The resistance can now be easily calculated from power and the square of the current. There is another way to calculate the resistance which makes use of the well known Ohm’s law. Assuming that the conductor is bounded by two terminals, T1 and T2 (current through T1 and T2 must be the same), the resistance of the conductor (between T1 and T2) is given the ratio of the voltage differential U between T1 and T2 and the respective current, I . So it is necessary to define two points on the respective terminals and then calculate the voltage at the two locations (voltage is called Phi in the field calculator). The rest is simple as described above. Example CF2: Export the field solution to a uniform grid Description: Assume a conduction problem solved. It is desired to export the field solution at locations belonging to a uniform grid to an ASCII file. The field calculator allows the field solutions to be exported regardless of the nature of the solution or the type of solver used to obtain the solution. It is possible to export any quantity that can be evaluated in the field calculator. Depending on the nature of the data being exported (scalar, vector, complex), the structure of each line in the output file is going to be different. However, regardless of what data is being exported, each line in the data section of the output file contains the coordinates of the point (x, y, z) followed by the data being exported (1 value for a scalar quantity, 2 values for a complex quantity, 3 values for a vector in 3D, 6 values for a complex vector in 3D) To export the current density vector to a grid the field calculator steps are: · Qty J · Export -> On Grid (then fill in the data as appropriate, see Fig. CF2) · OK Fig. CF2 Define the size of the export region (box) and spacing within Minimum, maximum & spacing in all 3 directions X, Y, Z define the size of the rectangular export region (box) as well as the spacing between locations. By default the location of the ASCII file containing the export data is in the project directory. Clicking on the browse symbol one can also choose another location for the exported file. Note: One can export the quantity calculated with the field calculator at user specified locations by using the Export/To File command. In that case the ASCII file containing on each line the x, y and z coordinates of the locations must exist prior to initiating the export-to-file command. Example CF3: Calculate the conduction current in a branch of a complex conduction path Description: There are situations where the current splits along the conduction path. If the nature of the problem is such that symmetry considerations cannot be applied, it may be necessary to evaluate total current in 2 or more parallel branches after the split point. To be able to perform the calculation described above, it is necessary to have each parallel branch (where the current is to be calculated) modeled as a separate solid. Before the calculation process is started, make sure that the (local) coordinate system is placed somewhere along the branch where the current is calculated, preferably in a median location along that branch. In more general terms, that location is where the integration is performed and it is advisable to choose it far from areas where the current splits or changes direction, if possible. Here is the process to be followed to perform the calculation using the field calculator. · Qty -> J · Geom -> Volume… (choose the volume of the branch of interest) OK · Domain (this is to limit the subsequent calculations to the branch of interest only) · Geom -> Surface… yz (choose axis plane that cuts perpendicular to the branch) OK · Normal · · Eval The result of the evaluation is positive or negative depending on the general orientation of the J vector versus the normal of the integration surface (S). In mathematical terms the operation performed above can be expressed as: Note: The integration surface (yz, in the example above) extends through the whole region, however because of the “domain” command used previously, the calculation is restricted only to the specified solid (that is the S surface is the intersection between the specified solid and the integration plane). Magnetostatic examples Example MS1: Calculate (check) the current in a conductor using Ampere’s theorem Description: Assume a magnetostatic problem where the magnetic field is produced by a given distribution of currents in conductors. To calculate the current in the conductor using Ampere’s theorem, a closed polyline (of arbitrary shape) should be drawn around the respective conductor. In a mathematical form the Ampere’s theorem is given by: where ( is the closed contour (polyline) and S( is an open surface bounded by ( but otherwise of arbitrary shape. IS( is the total current intercepting the surface S(. To calculate the (closed) line integral of H, the sequence of field calculator commands is: · Qty -> H · Geom -> Line (choose the closed polygonal line around the conductor) OK · Tangent · · Eval The value should be reasonably close to the value of the corresponding current. The match between the two can be used as a measure of the global accuracy of the calculation in the general region where the closed line was placed. Example MS2: Calculate the magnetic flux through a surface Description: Assume the case of a magnetostatic application. To calculate the magnetic flux through an already existing surface the sequence of calculator commands is: · Qty -> B · Geom -> Surface… (specify the integration surface) OK · Normal · · Eval The result is positive or negative depending on the orientation of the B vector with respect to the normal to the surface of integration. The above operation corresponds to the following mathematical formula for the magnetic flux: Example MS3: Calculate components of the Lorentz force Description: Assume a distribution of magnetic field surrounding conductors with applied DC currents. The calculation of the components of the Lorentz force has the following steps in the field calculator. · Qty -> J · Qty -> B · Cross · Scalar -> ScalarX · Geom -> Volume … (specify the volume of interest) OK · · Eval The above example shows the process for calculating the X component of the Lorentz force. Similar steps should be performed for all components of interest. Example MS4: Calculate the distribution of relative permeability in nonlinear material Description: Assume a non-linear magnetostatic problem. To plot the relative permeability distribution inside a non-linear material the following steps should be taken: · Qty -> B · Scal? -> ScalarX · Qty -> H · Scal? -> ScalarX · Const -> Mu0 · * (multiply) · / (divide) · Smooth · Geom -> Surface… (specify the geometry of interest) OK · Plot As an example of distribution of relative permeability please take a look at plot in Fig. MS 4. Fig. MS4 Distribution of relative permeability (saturation) Note: The above sequence of commands makes use of one single field component (X component). Please note that any spatial component can be used for the purpose of calculating relative permeability in non-linear soft magnetic materials. The result would still be the same if we used the Y component or the Z component. The “smoothing” also used in the sequence is also recommended particularly in cases where the mesh density is not very high. Frequency domain (AC) Examples Example AC1: Calculate the radiation resistance of a circular loop Description: Assume a circular loop of radius 0.02 m with an applied current excitation at 1.5 GHz; The radiation resistance is given by the following formula: where S is the outer surface of the region (preferably spherical), placed conveniently far away from the source of radiation. Assuming that a half symmetry model is used, no ½ is needed in the above formula. The sequence of calculator commands necessary for the calculation of the average power is as follows: - Qty -> H · Curl · Num -> Complex (0 , -12) OK · * · Qty -> H · Cmplx -> Conj · Cross · Cmplx -> Real · Geom -> Surface…(select the surface of interest) -> OK · Normal · · Eval Note: The integration surface above must be an open surface (radiation surface) if a symmetry model is used. Surfaces of existing objects cannot be used since they are always closed. Therefore the necessary integration surface must be created in the example above using Geometry/Create/Faces List command. Example AC2: Calculate/Plot the Poynting vector Description: Same as in Example AC1. To obtain the Poynting vector the following sequence of calculator commands is necessary: - Qty -> H · Curl · Num -> Complex (0 , -12) OK · * · Qty -> H · Cmplx -> Conj · Cross To plot the real part of the Poynting vector the following commands should be added to the above sequence: ….. · Cmplx -> Real · Num -> Scalar (0.5) OK · Geom -> Surface…(select the surface of interest) -> OK · Plot A plot similar to the one in Fig. AC2 is obtained. Fig. AC2 Distribution of the real part of the Poynting vector Example AC3: Calculate total induced current in a solid Description: Consider (as example) the device in Fig. AC3. a) full model b) quarter model Fig. AC3 Geometry of indu