1、ANSOFT MAXWELL 2D/3DFIELD CALCULATOR-Examples-IntroductionThis 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
2、 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 a
3、nd meaningful from a Maxwells 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 ent
4、ities;- 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
5、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 mech
6、anics 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 Maxw
7、ell. 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 interfac
8、eThe 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. T
9、he 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 s
10、tack (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 st
11、ack 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 InterfaceStack sub-categories contain solut
12、ion 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 oper
13、ation 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 t
14、hat 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 on
15、ly; 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 situatio
16、ns 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
17、 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
18、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 coordinat
19、e 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) doesnt change if the (local) coordinate system i
20、s 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 ExamplesExample ES1: Calculate the charge density distribution and total electric charge on the sur
21、face of an objectDescription: 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 o
22、f 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 vec
23、tor to the surface of interest, equal to the surface charge density)- Geom - Surface (select the surface of interest) - OK- Plotb) 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- Norm
24、al- - EvalExample ES2: Calculate the Maxwell stress distribution on the surface of an objectDescription: 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 met
25、hod for calculation the force is quite sensitive to mesh.The Maxwell electric stress vector has the following expression for objects without electrostrictive effects:21EnDTnEwhere the unit vector n is the normal vector to the surface of interest. The sequence of calculator commands necessary to impl
26、ement 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 (cr
27、eates 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- PlotIf an integration of the Maxwell stress is to be performed over the surface of interest, then
28、 the Plot command above should be replaced with the following sequence:- Normal- - EvalNote: 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 calcu
29、lations hold true in general for any instance where a volume distribution of force density is equivalent to a surface distribution of stress (tension): dSTvfFnwhere 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
30、 above results for the electrostatic case hold for magnetostatic applications if the electric field quantities are replaced with corresponding magnetic quantities.Current flow ExamplesExample CF1: Calculate the resistance of a conduction path between two terminalsDescription: Assume a given conducto
31、r 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
32、of the DC resistance is:CDsAdRwhere 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 t
33、he 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
34、2DCIPR dVJJEPVThe 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- - EvalThe resistance can now be easily calculated from power
35、and the square of the current.There is another way to calculate the resistance which makes use of the well known Ohms law.IURDCAssuming 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
36、 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.Ex
37、ample CF2: Export the field solution to a uniform gridDescription: 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 s
38、olution 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. Howeve
39、r, 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 vect
40、or 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)- OKFig. CF2 Define the size of the export region (box) and spacing withinMinimum, maximum The radiation resistance is given by the fol
41、lowing formula:2rmsavIPRdSHjdSHESav *0*1Re2e1 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 is needed in the above formula. The sequence of calculator commands necessary for
42、 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- - EvalNote: The integration surface above must be an open surface (radiation surface) if a sym
43、metry 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 vectorDescription: Same as in Example AC1.
44、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- CrossTo plot the real part of the Poynting vector the following commands should be added to the above sequence:- Cmplx - Real- Num - Scalar
45、 (0.5) OK- Geom - Surface(select the surface of interest) - OK- PlotA 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 solidDescription: Consider (as example) the device in Fig. AC3.a) full
46、 model b) quarter modelFig. AC3 Geometry of inductor modelAssume that the induced current through the surface marked with an arrow in the quarter model is to be calculated. Please note that there is an expected net current flow through the market surface, due to the symmetry of the problem. As a gen
47、eral recommendation, the surface that is going to be used in the process of integrating the current density should exist prior to initiating the respective post-processing. In some cases this also means that the geometry needs to be created in such a way so that the particular post-processing task i
48、s made possible. Once the object containing the integration surface exists, after the solution was calculated, while in the post-processor use the Geometry/Create/Faces List command to create the integration surface necessary for the calculation. Make sure that the object with expected induced curre
49、nts has non-zero conductivity and that the eddy-effect calculation was turned on.Assuming now that all of the above was taken care of, the sequence of calculator commands necessary to obtain separately the real part and the imaginary part of the induced current is described below:For the real part of the induced current:- Qty - J- Cmplx - Real- Geom - Surface (select the previously defined integration surface) OK- Normal- - EvalFor the imaginary part of the induced current:- Qty - J- Cm
