Machine Design

Math software quickly solves for design characteristics

The mathematics for motor models used at our company amount to three pages of linear and nonlinear equations.

The Optimization-parameters window lets users select variables, such as cost, that the software will adjust to a minimum, or user preferred value. It can also find maximum values. The feature lets TK Solver users add bounds and constraints to math models.

Function wizards make it easier to program TK Solver functions, such as this fluid properties example.

At one time, we used GW Basic to crunch through them. But each equation had to be individually rewritten to solve for a different variable. And each variable solved for had to be isolated.

But the math program TK Solver makes it a matter of simply entering equations in any order, without isolating variables, and without tedious and time-consuming coding. What's even better is the backsolving feature.

Backsolving is one way to play "what if" with the equations. It lets us instantly swap inputs and outputs to quickly optimize designs. We can enter performance criteria needed for new motors into the software model and solve for the design parameters that produce the needed results. Inputs could be voltage, torque, and speed at two different points. The solution could be armature resistance, brush-top voltage, torque constant, or frictional-torque loss.

No two motor designs are alike. One might be used in an office printer while another goes into an ATM. So the list of equations gets run frequently. The declarative structure of the software makes it easy to use. I can solve, for example, Amps = Volts/Ohms or the other two variables without rewriting the equation.

The Solution Optimizer, another feature, let us set preferences and limits for solving TK models. The Optimizer comes in the software's Premium Edition and works like this: First create a TK model, a series of equations, and make sure it solves correctly. Then select a target variable the one you want to minimize, maximize, or set to a specific value. Set the decision variables, the ones with input values that can change. Insert these variables and their constraints into the Optimizer screen. Hit the Solve button.

MathLook, another feature, has been updated in V5 to work as users type in equations. It takes any rule in a TK model and displays it in 2D math notation. It's an easy way to check an equation's correctness. Users can also place these images in any MS Office document, so it's useful for documentation.

Also new is a group of "function wizards," one for each of TK's 100-plus built-in functions. Instead of coding functions from scratch, pick the function to be included in a model, input the values, and TK creates the expression.

Plotting in TK has come a long way in recent years with, for example, colors and legends. But the basic functions are the same: put in the labels, pick the X and Y-axis lists, and plot.

The Report Wizard, new in TK 5, takes users through a series of screens to generate print reports. Users select models, set up pages (with a company logo if you like), and select objects to be included, such as variables, tables, plots and Math-Look images. Users can print the report or save it in Adobe PDF or RTF file formats. Another capability links TK models with Excel spreadsheets and creates stand-alone collaborative models in the Premium version.

Over the years I've written more than 400 TK models, from a one-rule model that calculates the load on a bearing, to complete motor designs with more than 300 rules. TK's objectbased interface and declarative structure make it easy to use and reuse code, and to combine models anyway we need to.

The software lets us spend less time on complex calculations and more on core business. For instance, we can arrive at a design in 30 to 60 min. Previously, it took a day or two.

The $399 program (Premium version $599) comes from
Universal Technical Systems Inc.
202 West State St., Suite 700
Rockford, IL 61101
Joseph Gardner

Joseph Gardner is a design engineering manager with Hansen Corp., Princeton, Ind.

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