Tutorial on Part Equations

see also:  Conditional Equations

The following tutorial, provided courtesy of Mel Boss, is intended to explain the basics of using Part Equations in I-DEAS. The following cases are addressed:

Use Equations in I-DEAS to control mathematical relationships among variables (dimensions). Keeping units consistent is essential (and often challenging). All calculations in I-DEAS are performed in SI (metric) units where Meters, Kilograms and Newtons are the standard units.

Here are three rules:

1. Don't use |units| designations where they ARE NOT required.
2. Always use |units| designations where they ARE required.
3. Units to the left of "=" MUST match units to the right.

The following examples demonstrate some basics.

Example 1 - Area Calculation

Figure 1A - Example 1

Figure 1B - Example 1: Area as the product of width and height

Example 1 is a simple AREA calculation. Note that no "|units|" designations are required. Area, in this case, is the Dependent Variable. The Independent Variables "HeightSectn1" and "WidthSectn1" are dimensions on the Section and are expressed in inches; therefore, the result (in x in) is in**2 (sq.in.). To the Right of "=" matches to the Left.

Example 2 - Independent/Dependent Relations

"Area" in this case is an Independent Variable. Assign a value to it, and the Dependent Variable, "HeightSectn1" is calculated. Note, if your model file is not set to SI units (meters, kilograms, Newtons), the value for "Area" MUST have |units| designated. If YOU do not assign |units| to a scalar value such as "Area," I-DEAS assumes meters. Set the Dependent Variable to "From Equation" in the list area with the "->" button. Width and height variables are readily exchanged. (Hint: To safely test an expression, select "Apply." If the solution looks wrong, you can make adjustments. "OK" dismisses the form.

Figure 2 - Example 2: Area and width control the dependent variable for height

Example 3 - Multiple Sections

Although, at first this case looks complicated, it is very similar to the previous example. Here, we designate area to be equal across three sections. Thus, "Area" is an Independent Variable, and its units are designated as |in sq|.

Figure 3A - Example 3: Equal area maintained among sections

Since Area=Area2, Ma ster Series assumes "Area2" to have the same units (Rule #3 - left = right). "HeightSection1," "RadiusSectn2" and "WidthSectn3" are Dependent Variables driven by "Area" (Hint: the "Value" column in the list area of the table shows the calculated value of the variables in the units of YOUR choice. This value is for YOUR information. You may want to change the units of the resultant from "none" to be consistent with your model file).

Figure 3B - Example 3: A "|units|" designation is required

Example 4 - Keeping Units Straight

This case is EXACTLY like the previous case except for the introduction of the variable "Line_for_Area," a linear dimension for a line at Section 2, that I use to control "Area." If you "Drag" on the dimension, the dependent variables at Sections 1, 2 and 3 change.

Figure 4A - Example 4: "Drag" line to change area dynamically

I use this example to demonstrate 2 things: 1)area, volume, density (and others) can be represented in terms of a linear dimension to enable dynamic change rather easily - "Drag" (ie. a very powerful capability); 2) Always remember Rule #3 - left side = right side.

I use a constant to preserve Rule #3. Simply multiply the variable "Line_for_Area" by 1|in|. In other words... |in| * |in| = |in sq|.

If we were to do the same exercise with Density, the constant's units would need to be #/in**4 ( eg. #/in**3 = |in| * |#/in**4| ).

Figure 4B - Example 4: Area value is dynamically changed by "Dragging" on the dimension for the line at the center section

Figure 4C - Example 4: The three sections are "Lofted" to produce a smooth transition that maintains constant area

Example 5 - Conditional Relations and Inequalities

Figure 5A - Example 5: A Conditional Expression controls this geometry in a way
such that the outer rectangle is a square when the circle radius is greater than .4 inches

Figure 5B - Example 5: Spaces are included in the above expression.

This expression and the two that follow are functionally equivalent. Spaces don't affect the result; HOWEVER, you are limited to 80 total characters!

Figure 5C - Example 5: Spaces are removed from the above expression.

Figure 5D - Example 5: Finally, the expression is simplified to "If-Then-Else."

HINTS: I-DEAS Smart View is an excellent source o n the subject of equations. Look it up. Print it. Study it. Be aware, however, that I have noted a few inacuaracies and exclusions...

Unlike ordinary equalities (like the first four examples), Conditional Expressions require that "|units|" be designated as shown. The best advise is to "Apply" rather than "OK" in the Equations Form to test the results.

The 80 character limit can cause problems when the variable names are long and the expression is verbose (Figure 5B), and it is not documented in MS3 Smart View.

The entire Conditional Expression must be on ONE line (I-DEAS Smart View is misleading in their examples).

Figure 5E - Example 5: The Conditional Expressoin

Example 6 - Trigonometric Functions

In trig functions, the units for "|deg|" MUST be specified. Again, the best advise is to "Apply" prior to "OK" to test your equation, and set the "Value " to degrees as shown in the following example.

Figure 6A- Example 6: A right triangle is fully constrained.

Figure 6B- Example 6: "|deg|" is REQUIRED in trig functions