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Sonotrode Calculator help page

This is the help / documentation for the Power ultrasonics Sonotrode Calculator, version 0.1 (October 2004)


  1. Introduction
  2. Analyses
  3. Menus
  4. Entering and reading data
  5. Proposed developments
  6. Formulae
  7. Disclaimer
  8. Linking to the Calculator
  9. Licensing the Calculator
  10. Further information / Links
  11. Version history


  1. I click on the menus and nothing happens
  2. I can't see the image
  3. Why does the image disappear when I click on a menu?
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Introduction / aims

This online calculator automates some simple calculations relating to the design of ultrasonic components - notably sonotrodes (horns) and boosters (interstage horns). The intention is not to provide a comprehensive solution to the design of ultrasonics components (I don't believe that would be a practical proposition anyway) but rather to offer a starting point for new designs and an educational tool for newcomers to ultrasonics.

A complete, successful sonotrode design will still require expert advice, perhaps finite element analysis (FEA) and most likely a series of prototypes - see the disclaimer.

While accepting these limitations I plan to develop the calculator to be as useful as possible, with more shapes and not-so-simple calculations to come (more details). If you'd like to request development in any particular direction please contact me.

During development the calculator is available to all free of charge, but at some stage I may apply restrictions to advanced analysis options, requiring registration and / or payment of a subscription charge.

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This version of the calculator provides 3 analysis options:

Show properties
This displays the material properties used for the calculations (Young's Modulus, Density and Poisson's Ratio), plus some derived properties (sound velocity for axial and radial-mode vibrations and acoustic impedance).
Axial mode -> Calculate length
Given a frequency at which the sonotrode is to be resonant, calculates the length of the tuned section (a half wavelength).
Axial mode -> Calculate frequency
Given a sonotrode of known length, calculates it's resonant frequency.

Plans are afoot to add many more analyses to the calculator - see Proposed developments.

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Clears inputs and erases all options - start again from scratch
Allows you to select a setup file, restoring the calculator to the state it was in when you saved the file
Save As File
Allows you to save a setup file containing all information you have entered (analysis, shape, materials and inputs)
View Parameters
View / save a list of all information you have entered. Format is identical to that produced by "Save as File" above but the server delivers it as a text document. Use this option (then File -> Save As on your browser menu) if you are behind a corporate firewall and it blocks the file produced by "Save as File".
Offers some examples to run on the calculator and adapt to your needs.
Opens your browser's standard print dialogue, allowing you to print the page (subject to your computer setup).
Show Properties
Displays material properties and some derived properties such as sound velocity.
Axial mode
Calculations for axial-mode ultrasonic systems.
Radial mode
Calculations for axisymmetric vibrations of radial-mode ultrasonic systems.
Torsional mode
Calculations for torsional-mode ultrasonic systems.
Steel / Aluminium / Titanium etc.
Click on any material option, then narrow down your choice by selecting a sub-category and so on until you specify a unique material.
User defined
Choose this option if the material you want to use is not listed in the standard menus. You will need to provide it's elastic properties. See the links section for online resources giving material properties.
Rod / Stepped Sonotrode / Exponential Sonotrode etc.
Click on the shape that you wish to analyse (this section can be ignored if you choose "Show Properties" as your analysis).
After you have entered or changed inputs (eg. sonotrode diameter), click here to recalculate with the new value.
Turns off animation for the diagram (mode shape, amplitude and stress graphs).
Select slow, medium or fast animation cycle rate.
Brings up an information box (javascript alert) containing the calculator name, version number and release date.
Help Page
Brings up this page in a new window.
Shows formulae used in the calculations and assumptions on which they are based.
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Entering and reading data, units conversion


Depending on the analysis you select you will usually need to enter some numerical data about your analysis eg. to calculate the axial-mode tuned length of a rod sonotrode you will need to enter the working frequency and rod diameter. You enter data in the white text fields that appear on the left side of the calculator once the analysis, material and shapes have been selected.

Note that the calculator is designed to operate in several different units. A list of available units is shown just to the right of the input field. The units listed will be only those appropriate to the particular input (and if the input happens to be dimensionless there is no choice of units).

The calculator converts between different units automatically, so for example if you have a length specified as 125 mm and you change the unit selector to inches the value will change to 4.92125 in.

Note that this has implications when you first define an input value - you need to set your chosen units first and then enter the numerical value, which is a little counter-intuitive!

For your convenience, once you have chosen units for each input the calculator will remember your choices for the rest of the session.


After setting up your input data select Calculate -> Go from the menu to recalculate (perform the calculation). Your results will then be shown below the input data. The text fields used have a pale blue background and cannot be changed directly.

As for the inputs, you can choose units for the numerical results and the values will change accordingly. The values and units shown on the graph image will also be updated the next time you recalculate.

Unit conversion:

Finally towards the bottom left of the calculator a list of unit conversion factors is shown. These select menus are for information only - really just a compact way of displaying lists of data - and changing the value selected will make no difference to the calculator.

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Proposed developments

More Analyses:
In the initial release options are limited to axial-mode analysis (fixed length, unknown resonant frequency and fixed resonant frequency, unknown length). Radial-mode and torsional-mode analyses will be added once I can sort out the relevant formulae!
More Shapes:
In addition to straight and stepped sonotrodes I plan to add more shape options (notably the useful exponential sonotrode) for axial and torsional-mode analyses. Radial mode analysis will require a completely different set of shapes.
More Materials:
Additional materials will be added on request, or users can choose the "User defined material" and input their material properties directly. The links section lists online material property databases.
The mechanical parts of a complete ultrasonic system are commonly arranged in a "stack" - typically transducer, booster and sonotrode (aka converter, interstage and horn). The calculator can be developed to combine an arbitrary number of components with the output amplitude of one giving the input amplitude of the next.
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To view the formulae used in these calculations first select your analysis options and then click Help -> Formulae. This gives the formulas used and the assumptions behind them. I sadly decided to display these using images - I don't think there is yet enough MathML support out there!

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The formulae used here include some simplifying assumptions (eg. plane stress) that may not accurately represent a real-world sonotrode. Furthermore ultrasonic components in the real world are subject to many sources of variation that cannot be included here, eg. differences between nominal and actual material properties and the presence of other (unwanted) modes of vibration. Experts with specialist knowledge will be able to predict some of these problems and allow for others, possibly leading to a quite different design than the one that this program would suggest.

Therefore NO RESPONSIBILITY IS ACCEPTED FOR THE ACCURACY OF RESULTS PRODUCED BY THIS CALCULATOR, OR THEIR SUITABILITY FOR ANY PURPOSE. All users are strongly advised to verify both the input information and results, and to take expert advice on other issues that may affect the functioning of ultrasonic components.

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Linking to the Calculator

You're welcome to place a link to the calculator on your web site, subject only to the condition that you must not claim it as your own, place it inside a frame on your site or in any way claim or imply that you produced it. Some example links are shown below - to use any of these just cut and paste the code from the box on the right into your page. Alternatively feel free to adapt these or create your own link if you prefer.

Sonotrode Calculator from PowerUltrasonics
Sonotrode calculator graphic
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Licensing the Calculator

The calculator as seen here comprises two parts, available and licensed separately:

The calculator engine
The calculator engine is designed to be flexible - it can be applied to any mathematical calculation and is particularly useful where results can be displayed graphically. It uses the excellent "Template Toolkit 2" module by Andy Wardley (see the perl links section for more information). A perl program written as a TT2 plugin provides the special functions while various template files control the appearance of the calculator. The calculator engine is one part of a larger web site design / content management system that I plan to release as open source. When released, conditions of use will be as follows:
  • You may use the software without purchasing a licence provided certain copyright notices and links are left intact.
  • You may remove these copyright notices and links from the software after purchasing a licence for each web site on which it is to be used.
  • You may redistribute the software only as a complete package along with this licensing information.
If there's enough interest I may release an earlier draft version of the calculator engine alone - please contact me if you'd be interested.
The sonotrode calculation files
Because the calculator engine is generic (suitable for almost any calculations) it relies on separate files to define the specific menu options, inputs, outputs and calculations, as well as the graphics that will be drawn. This information is held as a set of data files that are read and executed as required by the calculator engine. These calculation files contain specialized knowledge of the application concerned and are therefore proprietary. You can purchase a licence to use these sonotrode calculations on your own site, with either the free or the licensed calculator engine.

Using the calculator for other applications

If you want a calculator to perform other calculations you can use the calculator engine either with or without my standard copyright notices (licensing fee applies to use without copyright notices). Then you can create the calculation files yourself using the sonotrode calculations as a model, or I will prepare them for you to your specifications (this work to be on a consultancy basis). In either case you would own the resulting proprietary calculation data files.

The following prices apply to licensing the calculator. These may change without notice - please contact me for a current quote:

Using the calculator engine complete with copyright notices and links (you may change colours, graphics etc. provided you don't obscure the copyright notices) Free
Using the calculator engine with copyright notices and links removed US$250 per web site
Using your own calculation files (non-ultrasonics applications) Free
Using my calculation files for sonotrode analysis, including one year's free upgrades US$250 per web site
Preparation of calculation files for a new application (consultancy) Quote on request
Installation of calculator with any of the above options on your web server (subject to server specifications) US$50

If you have any questions about licensing or other requests please ask.

Aside - a note about server-side programs

The calculator in its present form is a server-side application - all the important processing is done on the web server. This makes it ideal for cases where you want to offer a calculation service to your clients and web-site visitors without giving them full access to the program (unlike for example spreadsheets or Java applets). However this also means that it can't be installed on your desktop computer and run like other applications (at least not unless you're prepared to install a web server and perl first). I may develop a standalone version but it's not presently on the list of proposed developments. If you want to convince me there's a demand for this then please contact me!

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SVG (Scalable Vector Graphics):
Adobe SVG Viewer Download Area
Download SVG plugin for Microsoft Internet Explorer
Mozilla SVG project FAQ - How to use a plugin instead of Mozilla's native support
For Mozilla / Firefox browsers (in short: about:config, svg.enabled = false)
Instructions for installing Adobe SVG plugin
For Mozilla / Firefox browsers (in short: Install v6 plugin, copy NPSVG6.dll and to browser plugins folder)
Mozilla SVG Project
"The goal we're working towards with Mozilla's SVG implementation is SVG 1.1 Full. What exists now in the tree should be treated as a technology preview"
SVG Wiki home page
Huge repository of information on SVG provided by users and developers (a wiki is a community website built by its own readers)
Material property databases:
"The heart of MatWeb is a searchable database of material data sheets" Composition and property specifications for a huge database of materials.
Globalspec - The Engineering Search Engine
Searches other online databases to find the information you require (for material properties will often send you to Matweb).
Advanced materials site, includes many articles and datasheets relating to engineering materials
Conversion Factors, Material Properties and Constants
Page with many unit conversions and material properties for common materials by Walter A. Siegmund
Mechanical Material Properties
Page of material properties for many common materials by Hugh Jack
Perl home page
Perl is a scripting language widely used for programming on the World Wide Web. Arguably its greatest strength is the enormous number of modules and extensions for any conceivable application that users have written and generously shared with the rest of the Perl community.
Comprehensive Perl Archive Network
Searchable library of Perl modules and extensions.
ActivePerl Home Page
ActivePerl is a port of core Perl to Windows. It's the easiest way to use Perl on a Windows computer.
Template Toolkit module from Andy Wardley
The Template Toolkit is a set of Perl modules which collectively implement a template processing system.
Perl extension by Ronan Oger for generating Scalable Vector Graphics (SVG) documents.
Alternative browsers:
Official home page of Mozilla Firefox
"The new Firefox Preview Release empowers you to browse faster, more safely, and more efficiently than with any other browser. Join more than 3 million others and make the switch today."
Hot tip in Microsoft mag: drop the lost Explorer
SMH article by Graeme Philipson - July 27, 2004: "I have had enough of Internet Explorer. Microsoft's web browser is underfunctioned and has not been improved for years. It is shot full of security problems. It is slow and it is ugly. There is an alternative. It is called Firefox. I have been using it for a month and I can't envisage ever returning to Internet Explorer."
Why you should switch to Firefox now
ZDNet article by Robert Vamosi - 27 September 2004: "Recent flaws in the way Microsoft processes common Internet image files and a decision to offer IE updates only to Windows XP users lead to just one logical conclusion: bail on Microsoft Internet Explorer."

Problems / frequently asked questions:

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I click on the menus and nothing happens

The calculator requires that you have javascript turned on to operate the menus. If you are working on a company computer please ask your tech support staff how to enable javascript for this site. If this option isn't available to you, and you're using Microsoft Internet Explorer, you will need to "Enable Active Scripting" - an option to be found under Tools -> Internet Options -> Security -> Custom Level. And if that gets you concerned about the security of your computer (which it should!) then you could add to your "Trusted sites" zone, while leaving more restrictive security settings in place for the "Internet Zone". Or perhaps you should consider upgrading to a better browser, like Mozilla Firefox

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I can't see the image

The image uses the relatively new SVG (scalable vector graphics) format. If you don't see the image on the right side of the calculator (or the animation above) you will need to download a "Plugin" program to allow your browser to display this format. The SVG links section offers links to suitable plugins from Adobe and more information about the format.

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No image using Mozilla / Firefox

If in your browser the image above shows blue jumbled text and no animated circular "" you're probably using the built-in SVG support that comes standard with recent versions of Mozilla and Firefox. Unfortunately this lacks many useful functions including special fonts and animation, so is unable to show the images correctly, but the result may be usable. For full support including animation of the sonotrode's distorted shape the only solution I have found is to disable the built-in SVG engine and use the Adobe version 6.0 preview 1 plugin from July 2003. This is not a solution I find acceptable (Adobe describe this version as "pre-alpha") but it's the only one I've found that works - any other suggestions welcome. At the time of writing the current release version of the Adobe SVG plugin is 3.03 which works with MSIE but not with Firefox. If you wish to follow this solution (at your own risk) please see the SVG links section for instructions.

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Why does the image disappear when I click on a menu?

For most HTML elements the z-index property (or in its absence the order in which they are defined) dictates which one overlays the other. However for most browsers this doesn't work with embedded objects such as Flash animations and SVG graphics - they always appear on top of any positioned HTML elements. This makes it practically impossible to get menus to appear on top of such graphics (and menus hidden below the image are of very little use!) so until any other solution emerges I'm hiding the graphics whenever the menus are activated. If anyone can suggest a better solution I'd be happy to implement it.

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Version history:

Sonotrode calculations:

0.1b Improved separation of engine and application, created Sonotrode plugin
0.1c Added animation
0.1d Added version history

Calculator engine:

0.1a First release version
0.1b Improved separation of engine and application, improved css, fixed Mozilla menu problem
0.1c Added animation
0.1d Added version history, separated js, css files

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