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Mathcad

Automating Engineering Calculations
Software for predictive engineering cuts costs in product design

08/03/2009 by Sandy Joung of PTC

CAD software has evolved to make the basic mathematics of product design transparent to users. But design also requires frequent ad-hoc calculations for everything from converting units to testing probability models. These vital calculations were - and often still are - done with calculators or manually on paper.


Bidirectional integration between Mathcad and Pro/Engineer lets dimensions and parameters from the CAD model drive a Mathcad analysis. Here, results from these calculations have returned to Pro/Engineer to update the model geometry.

This manual approach suits organizations with simple product-development processes and relatively obvious market demands. But today’s typical company faces evermore- challenging competitors, increasing product complexity and the number of globally dispersed teams even while budgets tighten. Spreadsheets or manual engineering calculations cannot scale to meet these demands.

A more-efficient approach is to automate and capture ad-hoc calculations with engineering calculation software such as Mathcad, which simultaneously performs and documents calculations using standard math notation. The program has been around for over 20 years. Its direct competitors are Matlab and Mathematica, however these programs use their own syntax (programming language) to compute results. Also, the math, text, and graphics are not integrated into one worksheet.

Mathcad users can easily insert equations into the user interface, via typing or selecting functions in the UI, as they would appear in a textbook, and the software dynamically calculates the result. Engineers can combine live math, text, graphs, and images to comprehensively document their design assumptions and calculations. This practice documents the original designer’s specific intent in a form that’s traceable, testable, and — most important — reusable.

For example, users can easily share calculations, which are readily understood by anyone who can read and understand mathematical equations. Compare this to spreadsheets and their complex web of cells and abbreviations for calculation functions, or to other math applications that require special programming languages. If you don’t know the programming language, you can’t see the basic assumptions and equations used to calculate results.

Mathcad also lets users cut-and-paste equations from one worksheet to another. This cuts time recreating calculations and makes it easier for companies to develop standardized templates of approved calculations and share best practices. The software generates annotations explaining where equations were copied from (or users can add notes). In addition, the integration between Mathcad and Windchill lets users easily capture, search, and reuse engineering calculations and design knowledge on an enterprise-wide scale.

The software performs complex calculations in a fraction of the time it takes traditional methods such as calculators, which often require complex programming for advanced functions. Users can also set up matrices, arrays, and programs to perform iterative calculations much faster. These capabilities reduce or prevent designer error and helps companies deliver better-quality products in shorter time frames.


A worksheet in Mathcad combines natural math notation and diagrams, letting engineers fully document analyses and calculations.

For example, consider the case of a designer building a new shock absorber. First, an existing product model is opened from a CAD file repository such as Windchill. The original designer’s detailed assumptions and decisions are readily available in a Mathcad worksheet, which resembles a Word document if the worksheet is stored and associated with the CAD model. Calculations and notes documented in the worksheet might show, for instance, that a shock absorber was originally intended for a certain axle size and later changed to fit a different size. The designer can thereby determine where the original engineer’s design compromises might affect the new design — for example, in axle clearance or vibration threshold. This information can help avoid a lot of wheel-spinning.

Automating the capture of engineering calculations also helps ensure that design requirements are met. The software handles calculations involving factors such as weight, volume, strength, and stress that are too difficult or time consuming to do manually, to predict the behavior of a component or material before it goes for a complete analysis.

Mathcad has a direct, bidirectional integration with Pro/Engineer that lets users make calculations on the exact geometries of a CAD model. The software then updates the results in the CAD model. This lets designers tighten assumptions passed to analysis software, saving the costs of unnecessary testing. (Examples of assumptions include dimensions, tolerances, range of testing loads, and range of testing temperature.)

In fact, engineering calculation software proves useful in all stages of product design:

In concept design and planning, the software lets users perform calculations to test functional performance, instead of just drawing geometries and hoping the design will meet the requirements. In the building of a refrigeration unit, for instance, a designer can use the software to see if the piping will fit inside the refrigerator casing. Likewise, a cell-phone designer might check the basic fit of the printed-circuit board, speaker, or microphone. This is different from CAD, which lets users draw the dimensions and geometries but doesn’t tell how the design will perform unless users run analysis or calculations via some other method.

Requirements definition typically involves the whole design team including the design engineer, project manager, marketing, as well as the customer via video conference. Engineers can use Mathcad here for “scratch pad math” and preliminary design optimization to explore alternatives that might arise in the meeting. For example, a design engineer might calculate the impact of changing the material or part thickness on the amount of material needed, cost of the part, and other physical properties such as strength. The software lets users easily change the design input parameters and see the results or impact instantly. This helps designers fully exploit the spontaneity of the meeting to raise and resolve important issues.

Design modeling often begins with a search for previous parts or assemblies for reuse. In the shock-absorber example, designers might retrieve the current-generation model from the CAD library along with the axle or other assemblies that makes use of the shock absorber. If the files contain engineering calculations, designers are likely to gain a precise knowledge of the conditions surrounding the original designer’s work because they can see and understand the initial analysis.

Analysis can benefit from the use of engineering-calculation software because it supports pre and post-processing tasks for FEA and other tools. As a preprocessor, the software helps with basic sizing and the testing of top-level assumptions by giving first-order approximations of performance using simplified geometries, surface areas, volumes, and the like. The insight gained helps engineers avoid wasting time on a misdirected analysis project. A full FEA simulation can take several hours, so it’s helpful to make it as meaningful as possible.

As a tool for post-processing, the software helps designers sanity-check analysis results by running simplified tests that will deliver numbers in the same range as the FEA outputs. For instance, to sanity-check the shock absorber’s stress test, the designer can use Mathcad to place a virtual box around the shock and then put a load on the box. The software can’t perform the same detailed, computationally intensive deformation testing as a full-blown FEA tool, but it does deliver results within range of the FEA tests.

Finally, the software supports quality assurance by helping users check that the product will meet manufacturing specifications. Again, the software can’t perform extensive testing, but in a matter of seconds it can answer and clearly document simple conditional statements: Does the model meet a certain safety requirement for maximum load or weight, load before failure, or adequate insulation for electrical parts? The software even tells whether a design meets certain Six Sigma requirements. Tests that raise a flag help catch quality problems early in the cycle before the model had been passed directly to manufacturing, where solving even a small problem can quickly become quite costly.

Mathcad offers a broad range of over 700 functions. Other useful capabilities include support for matrices, differential equations, IEEE-adherent math, which ensures that designs conform to standards for math definitions and formulas (for example, the definition of the operation 0/0), and other commonly used engineering equations. The software also provides extensions for data analysis, signal processing, and other disciplines. The use of a file format based on XML and support for standards-based data-exchange interfaces lets the software work with a range of CAD and CAE applications, as well as other engineering calculation software and Open DataBase Connectivity (ODBC)-compliant databases.

 

Article edited by Leslie Gordon, Sr Editor, Machine Design

Article reprinted by permission of Penton Media, publisher of Machine Design