Figure 1: Solid Edge provides Goal Seek, a handy and efficient tool for simplifying problems like changing a pulley diameter or increasing tension using a familiar free-body diagram approach.
Engineers are constantly faced with solving problems — it’s what they are paid to do. The faster a formidable solution or the more challenging the problem solved, the more successful that person will become. Depending on the problem or the tools, finding an answer is often easier said than done. While many formulas and methods for attacking problems are in the public domain, engineers often need to solve problems from the ground up. In many cases, the answer to the question at hand is not spelled out in a book.
Each engineering discipline has its own unique challenges that often fall into some common classification. For example, mechanical engineers are generally tasked with designing power transmissions, building structural frames, and other things that are easily solved using free-body diagrams and known engineering calculations. Costly alternative solutions involve doing calculations by hand or in spreadsheets and in some cases constructing and testing physical prototypes. It is difficult to iterate through or optimize these calculations while changes are being made.
A common example is determining the location of a set of pulleys for a power transmission application. While it’s not too hard to lay the components out, a simple change of a pulley diameter or an increase in the tension may cause problems. Usually belts are purchased in fixed lengths.
Figure 2: This fulcrum-and-lever example looks simple, but where will the fulcrumneed to be placed in order to lift 286 pounds? Goal Seek solves it fast.
Solid Edge software provides a handy tool, called Goal Seek, to simplify such problem solving with a familiar free-body diagram approach. Users simply sketch the system in 2D, add some dimensions and any defining constraints, and the system solves for the desired parameter. Solid Edge also supports parameters based on complex equations and the results can directly drive 3D geometry.
Current methods range from brute-force evaluations with calculators, spreadsheets, or in some cases, licensed add-on applications that are supposed to work with the MCAD application. In any case, without an integrated solution like Solid Edge’s Goal Seek, arriving at a solution is prone to problems such as mismatched units of measure. Goal Seek addresses these issues and lets designers focus on solving problems as opposed to double checking answers.
The Problem with Problem Solving
Take the pulley system in Figure 1 (above) and try to determine where the tension pulley must be placed in terms of the x and y dimensions to obtain a standard belt length of 25 in. (635mm). A complex equation based on a plethora of trig operations is needed to generate a sufficient formula to solve this variable. Using an MCAD system with a parametric 2D solver still requires the user to determine the desired belt length by increasing (solving for) x. 2D solvers typically treat the circumference as a driven value. A specific set of equations could be established to enable this, but a completely different set would be needed if another variable needs to be controlled, such as the y variable. A two-pulley system is simple, but attempting to solve this problem for a system with four or more pulleys is quite complex. Do the math to see why (closed book, no notes).
Now that you get the point, let’s back up a bit and start with something easier. A classic demonstration example is a lever with a force applied to one end to lift the other. Sliding the fulcrum along the lever varies the amount of force while sacrificing lift. A simple free-body diagram in Figure 2 illustrates this concept. Applying a force of 100 pounds to one side will lift a 200-pound load. This is simple to compute, but where will the fulcrum need to be placed in order to lift 286 pounds? The equation has to be simple if the 120-in. length changes.
Figure 3: The GUI shows how the tool snaps to the answer from the initial image on the left to the results on the right. Notice the simple approach Goal Seek uses to help capture the input values.
The amount of work in rearranging equations increases with every question. The chance for error also gets greater. The fulcrum-and-lever example is simple, but it illustrates the need to be able to attack a problem from different angles.
Other common problems that require varying an input parameter to obtain a desired result are determining beam dimensions based on loads, optimizing areas by varying some boundary parameters, finding critical angles in four-bar linkages, finding pulley locations for constant belt lengths, computing balance point, calculating maximum, and many other similar practical examples.
The Answers with Goal Seek
Goal Seek automates engineering calculations by eliminating the need to rearrange equations and, in many cases, removes the need to even develop equations. The system works by mimicking the simplicity of familiar free-body diagrams but uses a 2D parametric sketch solver to compute the geometry of the diagram. Users simply dimension the geometry, establish any interrelated equations, and then let Goal Seek find the unknown parameter. The heart of the system stores certain measurements such as area and perimeter so the solver can use them to compute the free-body diagrams. This capability greatly reduces the need for developing complex equations such as capturing circumferences or areas.
Finding the area of a triangle simply requires plugging in the base and height into the equation: area = ½ (base x height) and out pops the answer. However, if a specific area is desired, but the height can vary, one will have to rearrange the equation and solve for height. Goal Seek in Solid Edge solves for any variable regardless of the equation (or free-body diagram).
Once the free-body diagram is drawn and dimensioned, Goal Seek finds a specific value for a desired variable by adjusting the value of another variable. Goal Seek shows you the effects on the free-body diagram during the process to give a visual indication of what’s happening. The solve process uses optimized algorithms to arrive at a solution fast — assuming a solution exists. If not, Solid Edge warns the user that the request can’t be geometrically (and mathematically) solved. In the previous pulley example, if the user sets a belt length that is too short (let’s exaggerate by setting it to 100mm), Solid Edge will warn the user that attempting to find a valid x dimension can’t be achieved.
Let’s take a close look at how Goal Seek can be used to solve the pulley example. After drawing the geometry using typical sketch and relationship tools, the area is measured and saved. During this process, the perimeter (belt length) is also captured. Goal Seek guides the user through all required steps by basically asking for you the goal and what can be changed. Here the belt length is to be set to 635mm while adjusting x until that length is satisfied. Goal Seek quickly snaps to the answer as seen in the change from the initial image on the left to the results on the right (see Figure 3, page 26). The user interface spans the top of both. Notice the simplistic approach that Goal Seek uses to help the user capture the input values.
Goal Seek can help engineers in many other areas. The examples above are for problem solving on 2D geometry, but this 2D geometry can be used to drive actual 3D models. Initial calculations used to determine critical fit and position between parts are available throughout the design process. Should the “final” design need to accommodate a greater load, store more fluid, or transmit power faster, Goal Seek can easily handle the calculations and ultimately drive the 3D geometry. Figure 4 shows an excerpt of a complete 3D assembly of the pulleys and belt being driven from a 2D sketch, which was sized using Goal Seek.
Figure 4: Goal Seek takes care of calculations and can then drive the 3D geometry.
An Integrated Calculation
The solution offered by Solid Edge is unique in the industry as it is integrated into the 2D and 3D solve process and works directly with the Variable Table, an internal table that lists all dimensions and allows equations to be established between them. Other MCAD solutions often rely on add-on “calculators” that are licensed from third parties and aren’t built into the solve process.
The competitive landscape for product development means products must be designed better and faster. Having to manually calculate basic parameters to solve fit and position problems is counterproductive and subject to error. The desktop computer is a powerful “calculator” and when coupled with an MCAD system, provides tremendous leverage. Using a familiar 2D free-body diagram approach that is integrated with 3D modeling, Goal Seek provides engineers with a powerful, fast, and simple tool to solve complex problems.
Siemens PLM Software
Kris Kasprzak is director of Solid Edge Marketing for Siemens PLM Software. Send comments about this article to DE-Editors@deskeng.com.