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  • Ath

    User Guide - 4.5.0

  • ATH 4

    Advanced Transition Horn, version 4

    Marcel Batík

    All rights reserved, Copyright © 2020

    www.at-horns.eu

    2

  • 1. Introduction

    Ath4 is a freeware acoustic horn shape generator. State-of-the-art geometries are employed for a high performace horns and waveguides.

    Software Requirements

    • Windows operating system (tested on Windows 7/10)

    • Gmsh SDK version 4.3 (freeware)

    Optional software tools

    • STL viewer, 3D CAD

    • ABEC 3 + VACS (available at http://www.randteam.de, BEM analysis of the horn acoustics)

    Setup procedure

    1. Download zip file from http://www.at-horns.eu and extract its contents to an arbitrary destination on your hard drive. This will be the directory from where you will run the ath program via a command line.

    2. Download Gmsh Software Development Kit (SDK) archive from http://gmsh.info. You may need to look into the archive for older binary versions and find the one currently required (see Software Requirements above). The only file really required is the gmsh-4.3.dll. Extract this file to the same directory as the ath4 program in the previous step.

    3. To run the tool, first you need to start a command line window, i.e. to run a program cmd.exe (typically found in the directory C:\Windows\System32). A convenient way of starting the command line for Ath4 is to create a shortcut icon to cmd.exe and set the "Start in" property to the Ath directory. After this shortcut is launched it takes you right to the program directory and you are set to run the tool. If this reminds you the old MS-DOS times, you are right - this is still the way Ath4 operates.

    Workflow overview

    1. To desing a new horn from scratch, first a horn definition file must be prepared. Most easily an existing (demo) file can be adapted. This file will store the complete description of your horn geometry and all the related parameters - more on this in chapter 2.

    2. The program ath.exe is executed from the command line with a horn definition file name as its parameter. Output is stored in a dedicated directory speficied in the definition file, with all the files requested (STL, ABEC project, ASCII coordnate files, etc.).

    3. Once satisfied with the basic geometry (after inspecting the shape in STL viewer or CAD), open the generated ABEC project and run a BEM simulation which will predict the acoustical behaviour of the device. Repeat steps 1 - 3 until fully satisfied with the results.

    4. Make the physical horn based on the STL file or the coordinate files (for CAD) and enjoy.

    3

    http://www.randteam.de/ http://gmsh.info/ http://www.at-horns.eu/

  • 2. Horn definition file

    The definiton file is an ordinary ASCII text file created and edited with a plain text editor, such as the default Notepad or Notepad++1. The structure is simple and the only syntactical entity is an item. Items are specified one per line in the following format:

    Item_Identifier = Item_Value

    There are several types of item values that will be referenced further:

    Value Type Description r Floating point (a "real") number. Use dot "." as the decimal point. r[] Vector of real numbers. Values are separated by commas "," or vertical bars "|". i Integer number (i.e. a whole number, without a decimal part). i[] Vector of integer numbers. Values separated by commas "," or vertical bars "|". b Logical type, can be any one of these constants: yes, true, 1, no, false, 0 s Text string. Must be enclosed in quotes if containing spaces (e.g. "two words").

    All the identifiers and keywords are case sensitive (i.e. "cone" is not the same as "Cone"). Comments can be used anywhere in the file - everything from a semicolon ";" to the end of the line is ignored. Empty lines are also ignored.

    The definition file is composed of several logical sections, although the order of individual items can be completely arbitrary. All the available items are described in detail on the following pages. Some items can be omitted - in that case the default values will be used (if any).

    Horn Geometry Section

    These are the items for the horn geometry - overal shape and size.

    Mesh / STL Settings Section

    The term "mesh" denotes a discretized horn surface description for the purpose of subsequent finite element analysis. Mesh setting strongly affects not only the output shape quality and resolution but also the performance of a BEM analysis. In general, the finer the mesh the higher quality of the results to higer frequencies, but be aware that a too fine mesh will greatly increase computation times. With the default values the BEM analysis works well to about 10 kHz in most situations.

    ABEC Project Setting Section

    The tool can generate a complete ABEC project, including the mesh file, ready for a BEM analysis. Once the BEM project is generated you can modify it freely on the level of the individual ABEC script files.

    Output Section

    This section specifies the output of the program - what types of files and where should be generated.

    1 Freeware available at https://notepad-plus-plus.org/

    4

  • 2.1 Overview on horn geometry

    The basic principle employed in the tool is simple and powerfull at the same time - it uses a selected type of profile curve and connects a compression driver exit (or whatever is used as a horn driver) to a horn mouth by this particular type of curve around the horn. The mouth can be of virtually any shape. To achieve that there's the concept of a guiding curve, which is a 2D curve that the horn surface goes through at some distance from the throat (see Fig.1). Shape of this curve thus defines the overal shape of the horn interior surface. Together with another parameter, the total length of the horn, the horn is defined completely. Of course there are more parameters to be set but this is the basic principle.

    Fig 1. - Horn geometry overview

    At this point two different profile curve types can be used: OS+SE (oblate-spheroidal profile terminated by a superellipse additive) or cone+SE (straight wall terminated by a superellipse additive). More on the details of mathematics involved can be found in Appendix A.

    Although the shape of a guiding curve in general could be completely arbitrary, two basic types are implemented in the tool at the moment: superellipse2 or superformula3 (the later alone giving a huge number of shapes possible).

    For the mouth outline shape, there are also two possibilities implemented: 1) It can be determined by the actual shape of the guiding curve, or 2) specified independently to force it being a rectangle or a circle.

    Of course a pure OS waveguide (as an example of a strictly axisymmetric device) can still be generated by this machinery - just use a circle for the guiding curve (circle being a special case of superellipse).

    In the following text the terms width, height and length (or depth interchangeably) of the horn geomtery will be used in the intuitive sense if looking at the horn from the perspective of a listener.

    2 https://en.wikipedia.org/wiki/Superellipse 3 https://en.wikipedia.org/wiki/Superformula

    5

  • 2.2 Definiton file summary 2.2.1 Horn Geometry

    Identifier Value Throat.Diameter r Throat diameter [mm]. Throat.Profile s OS | cone

    The initial horn profile: oblate spheroidal or conical. Default: OS

    Throat.Angle r Throat entry angle, measured from horn axis [deg]. Sets the tangent angle for the horn walls at the throat entrance. This is mainly used with an OS profile to perfectly match the exit angle of a driver. For a conical profile this item has no meaning since the cone angle is determined by the guiding curve. Default: 0

    Throat.Ext.Length r Length of an optional throat extension [mm]. Default: 0 (i.e. no extension)

    Throat.Ext.Profile s cone | b-cubic Throat extension profile: conical or cubic Bezier. For a conical extension, the item Throat.Angle defines the angle. Default: cone (the only available at the moment)

    Length i The total length (depth) of the horn [mm]. This is the basic parameter of the horn geometry.

    GCurve s SE | SF Shape of the guiding curve: SE=superellipse, SF=superformula

    GCurve.Dist r Distance of the guiding curve from the throat: If set between 0 and 1, it is taken as a fractional part of the total horn length. If set > 1, it is taken as an absolute distance [mm].

    GCurve.SE.Exp r Exponent of a superellipse for GCurve=SE. GCurve.SF r[] Superformula definition for GCurve=SF.

    Array of six numbers corresponding to the common SF parameters: a, b, m, n1, n2, n3. The scale (size) of the curve si determined by GCurve.XDim (or GCurve.Angle) and GCurve.VertScale.

    GCurve.XDim r Defines the size of the guiding curve. See Fig. XXX. Either .XDim or .Angle must be set for GCurve.

    GCurve.Angle r Defines the size of the guiding curve. See Fig. XXX. Either .XDim or .Angle must be set for GCurve.

    GCurve.VertScale r Vertical to horizontal ratio for the guiding curve. This is the basic parameter to control the overal shape. For GCurve=SE it simply sets the semi-axes ratio. Default: 1

    GCurve.Rot r Optional rotation of the guiding curve in anti-clockwise direction [deg]. Default: 0

    Term.s r The "s" parameter of the termination additive - see Appendix A. Default: 0.7

    Ter m.q r The "q" parameter of the termination additive - see Appendix A. Default: 0.995

    6

  • Term.n r The "n

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