Issues of Gear Design Using 3D Solid Modeling Systems

By Charles Cooper
Gear Technology Magazine

More and more gear shops are wrestling with the issue of whether or not solid modeling is right for their gear design work. The Q & A Page of The Gear Industry Home Page^TM has had numerous questions asking how to model gears in solid modeling applications such as AutoCAD, Solidworks and Pro/Engineer. Given the problems people have been having, we are presenting the step-by-step process for modeling gears in Pro/Engineer, but first we thought it would be a good idea to explore the question of whether or not you should even try to design gears using Pro/Engineer or any other 3D solid modeling program.

"From a design point of view, we've gotten along for hundreds of years without solid modeling-we don't need it!" These are the words of Gulliver Silvagi, a product design engineer with Ford, but they reflect the general opinion among gear designers as to the utility of 3-D solid modeling programs like Pro/Engineer, Solidworks and Autocad. Such programs have their uses in both design and manufacturing processes but initial gear design is not one of them. The issue really comes down to the way gear design programs work versus the way 3D solid modeling programs work, and how they each model gears.

Gear Design Software
Dedicated gear design software is mathematical in nature. It has to be in order to properly model the involute curve and the tooth profile generated from that curve. Decicated gear design programs do the calculations necessary to create the true geometry of the gear tooth. This used to be a tedious and time-consuming operation, often taking the gear designer 50 hours or more to perform the calculations. These programs do the same calculations in seconds and so produce a true involute tooth profile quickly and easily.

However, due to their graphical nature, CAD/CAM systems can not do this. "They are graphical modeling tools and there is a finite number of calculations they can perform, a finite number of points they can plot along the involute curve," said Universal Technical Systems President Jack Marathe. "Because of this, the best they can do on their own is approximate the involute tooth profile."

Pat O'Donnell, President of Performance Gear Systems and a consultant who works extensively with Pro/Engineer said, "Pro/Engineer is a great CAD/CAM system, but it was not written to design gears. That's not what it does."

CAD systems approximate shapes such as the involute tooth profile by defining points along a curve and then simply connecting those points with straight lines. The more points you can plot, the smaller the lines are that draw the curve. While they can plot many of the points along the curve, coming close to the involute profile, there is always an error due to the need for the software to approximate using points and lines.

Another area where the mathematical model used by gear design software is preferable is in the design of the gear itself. Taking a helical gear and designing it in Pro/Engineer as an example, one sees that the method of constructing the three dimensional solid model provides a good approximation, but not a precise duplication, of the true geometry of the gear being designed.

Frank DeSimone, the Product Line Manager for Geometry at PTC, the makers of Pro/Engineer, explains that "a helical gear is nothing more than a constant cross-section [of a spur gear] rotated by a helix angle as the profile is swept across the gear width. Since a profile (sketch) is changing in rotary position as it is being swept, it naturally translates into a Pro/Engineer feature, the Variable Section Sweep." According to O'Donnell, this means that there is a cut at the center of the gear's face width and that the two resulting halves are rotated in accordance with the helix angle, slanting the teeth into the characteristic helical shape, transforming the spur gear into a helical. Because the spur gear design was based on the involute tooth design which was, itself, only an approximation of the true involute geometry, this model of a helical gear can only be as good and as accurate as the original approximation.

Gear ratings
Dedicated gear design programs allow you to make a gear that is within the AGMA or ISO quality rating you are designing for. In fact, the standards are already incorporated into many gear design programs. According to Robert Errichello, President of GearTech, a gear design consulting firm, "For rating gears, for bending fatigue and pitting, you want software that will allow you to stick to industrial quality codes. That way you can compare the gear you just designed to the accepted industry standards." Solid modeling programs can't do that for you and so force the designer to go back to the AGMA and/or ISO calculations to get the standards.

Strengths of 3-D Solid Modeling
One shouldn't believe that three dimensional solid modeling programs don't have a place in the gear industry. They clearly do, but not as gear design tools. According to Errichello, the place for solid modeling is in system design and analysis. "System dynamics analysis is helped by 3D solid modeling." This is especially true when trying to find the torsional natural frequencies of a particular system as well as in the aerospace industry where gears are very thin and light-weight and have problems with resonance.

For applications like these, where precise tooth profiles are not as necessary as in the gear design itself, solid modeling programs are very useful. Silvagi adds that solid modeling is a good downstream tool, good for defining tool paths for EDMs, lasers and other systems that can draw data from a CAD system. Solid modeling is also the basis for stereolithography and other rapid prototyping systems.

These abilities and applications make modern CAD/CAM systems such as Pro/Engineer very powerful engineering design tools with a great deal to offer the designer. All of this flexibility is made possible by a process called parametric modeling.

Parametric Modeling
Prior to the introduction of parametric modeling, most programs created engineering models via 2-D drawings, 3-D wireframes or 3-D surface models. In each case, full product descriptions, down to the proper dimensioning scheme and tolerances, were impossible. This changed with the introduction of parametric modeling.

Parametric modeling allows the design engineer to let the characteristic parameters of a product drive the design of that product. In the case of gear designers, key dimensions that would describe the gear being designed such as diametral pitch, pressure angle, root radius, web thickness, etc. could be used as the parameters to define the gear. But, the parameters do not have to be geometric. They can also capture key process information such as case hardening specifications, quality grades, metallurgical properties and even load classifications for the gear being designed.

Programs like Pro/Engineer use these parameters, in conjunction with the program's features, to generate the shape of the gear and to add in all the essential information to create a product model. In creating a tooth profile, for example, the parametric dimensional information drives the shape of the tooth and non-geometric parametric information specifies things like the required case hardening depth or the nondestructive test requirements.

Since many gears are similar in many respects, Pro/Engineer can capture the differences within a family of parts very easily. For instance, two gears may be identical except for the web thickness and material. With a single product model, both gears are completely described because Pro/Engineer models the baseline design ("generic") and iterations on that design ("instances") via a spreadsheet. Differentiating parameters are characterized in the spreadsheet.

While all of these features and abilities are very useful to the designer, they do not deal with the question of the complexity of the calculations needed to define a gear tooth nor the tendency toward approximation inherent in CAD/CAM programs. Clearly, something more is needed.

The Synthesis of Gear Design Software and CAD: One Solution.
Given the limitations imposed by most gear design software on visual rendering and by CAD systems on the accuracy of the models, what is the gear designer to do? Most gear design software on the market today will export DXF files or X-Y coordinates that can be used by mainstream CAD/CAM software to draw the part.

There are also programs that act as bridges between the gear design application and the CAD/CAM system. One such product is DesignLink by UTS. Developed in conjunction with Jerand Technical Services, DesignLink bridges the gap between UTS gear design and engineering programs that run on its TK Solver platform and PTC's Pro/Engineer. "The combination of the mathematical modeling power of TK Solver and 3D graphical modeling power of Pro/Engineer provides a whole new capability for Pro/Engineer users," said Jerand President Bob Monat. "It's a new paradigm, with a unique productivity-boosting capability."

The geometry of the gear is designed with TK Solver and UTS gear software. This includes optimizing the design to increase both the life of the gear and the horsepower rating, reduce noise and cost, and so on. For plastic or powdered metal gears, the UTS software also helps you design molds by adjusting for shrinkage (plastic gears) or growth (powdered metal gears) when the gears come out of the mold.

DesignLink transfers the numeric information from TK Solver to Pro/Engineer, which reads the data as parameters of the model. This includes the number of teeth, face width, outside diameter, helix angle, pitch, pressure angle and coordinates of the tooth profiles for all the teeth. Once the transfer is complete, the 3D model is easily rendered. Since they are changeable parameters in the solid model, users may control the size of the Pro/Engineer model according to the number of points on the tooth profiles. Fewer points may lower precision somewhat, but that will not be a problem unless you are designing tooling such as a mold cavity.

According to Marathe, this combination of gear design and solid modeling software is the only way to accurately model gears in a 3D solid modeling environment. "Gear design involves complex mathematical calculations to get the geometry correct. It is not as simple as drawing an involute and a fillet and joining a few curves together. Accurate calculation of gear profile coordinates makes it easy to use CAD/CAM systems to make molds and other tooling for plastic and powdered metal gears. The whole job then becomes automated."