INTERNATIONALLY KNOWN MAKER OF HIGH-PRECISION TOOLS USES FEA TO SHORTEN DESIGN PHASE

Harold Lawson, Jr., of Moore Special Tool Co., Inc.

Moore Special Tool Co., Inc., of Bridgeport, Connecticut, is an internationally-known manufacturer of high-precision Jig Grinders, Aspheric Generators, Universal Coordinate Measuring Machines, and Metrology products.

After Moore began using the CADKEY 3-D design and drafting software for some of their engineering work, they looked for other computer-aided engineering tools, most notably finite element analysis (FEA). "While we were looking for FEA software, one of our major concerns was how the FEA programs would interact with the CAD software that we had already invested in," recalls Harold Lawson of Moore. "We needed a system that would be CADKEY-compatible. Not only did Algor's FEA System have, at the time we purchased it, individual modules available that could convert our CADKEY files, but their CAD program, Superdraw II, had Import and Export commands incorporated into it that let us transfer CADKEY files directly to and from their system. They also offer training courses throughout the US. This was another definite plus, since it meant that we could learn how to use the software quickly and begin applying it to Moore's designs right away."

Equally important for Moore in their decision to use Algor's FEA System was the fact that Algor's computer analysis is so much faster than the physical testing that Moore had been using.

As Lawson explains, "Before we began using Algor's FEA, the method of testing a design was to go through the whole process of fabricating the part and trying it out - but that still didn't tell us how manufacturing tolerances would affect it. That is, I wouldn't know what would happen if I ran plus or minus 10 or 15 percent unless I were to go through the trouble of making parts that were 10 to 15 percent off the actual specifications and test them, too. Unfortunately, that requires the use of a lot of personnel and manufacturing time." Application of FEA at Moore will mean a substantial time savings in their prototype cycle by enabling them to come much closer to the optimal design the first time around.

"Since we have very close tolerances, prototype testing created a real bottleneck in the design process. Whereas most manufacturers are not worried about millionths of an inch, we are."

The Problem

One part that Lawson has analyzed with Algor is a classic shrink-fit problem involving a plain, thin ring gear having an inner diameter of approximately six inches, and measuring 13/16 inch high with a cross-section of 0.180 inch. This gear is shrink-fitted 1/3 of the way down from the top of a thick, slightly cone-shaped cylinder. The contact pressure between the inside of the gear and the outside of the cylinder has to be high enough to maintain a friction torque; but if the interference fit is too high, the gear and cylinder will deform. Moreover, the higher the interference fit, the more the cylinder ID will deform. Moor's design goal was to minimize the deformation of the inside cylinder while still producing the required torque transmission between the cylinder and gear. Lawson also wanted to know the tolerances and how they would affect the torque transmission capacity of the gear.

"We could have just looked up this shrink fit in the ASME Handbook and used their rules. But there was a problem: in the case when a thin ring gear is being shrink-fitted onto a thick, hollow shaft, the Handbook doesn't provide a way to determine the minimum amount of interference fit required; there really isn't one," Lawson relates. He could have attempted to figure it out using the torque and contact pressure of the two surfaces, but this still left yet another question: how much would the inside of the thick cylinder deform due to the pressure from the ring gear? Says Lawson, "The answer to a question like this is critical to us - is it 20 or 40 millionths of an inch?"

"Furthermore," he continues, "how much material do I have to leave so that the toolmakers (who hand-fit and hand-assemble these parts) can do an accurate job?" Moore uses CNC griders, lathes and milling machines to manufacture their parts; but for hand-fitted parts in general, a hand-lapping and hand-scraping process is employed to remove material from two adjoining surfaces to create a perfect match. The materials from which the gear and cylinder will be fabricated are two types of steel: 4140 and 4150. Both these substances withstand Moore's heat-treating very well.

FEA Analysis

The Algor FEA System was an indispensable tool that Lawson used to help him design the shrink-fitted gear. He began by creating the outline geometry of the model in Superdraw II which, he says, "does everything you want it to do." Although it was only necessary to model a "pie-section" of the gear/cylinder interface due to its symmetry about the center axis and the uniformity of the loading conditions, Lawson chose to model the full 360 degrees for documentation and display purposes. To create the full model, Lawson had a choice of generating the mesh using either Superdraw II or Algor's mesh generators. He chose the latter method, linking the outline of the model through MSHGEN and into RADGENBR, which automatically generated 64 "pie-sections" of four elements each, creating a total of 256 brick elements.

With AEdit, Algor's preprocessing editor, Lawson set boundary conditions on the model and applied loads. He constrained several nodes in the direction of the Z-axis to hold the gear fixed in space. "You have to hold at least one node totally fixed, or two of the nodes translationally fixed," he explains. "Otherwise, the model is free to move around anywhere in space. Then, when you apply the loads, they won't affect the geometry of the model - they'll just be pushing it around in space." A uniform internal pressure of 281 psi was also applied to each of the element faces on the inner diameter of the gear with AEdit.

"Calculating the resulting displacements from the applied loads was easy, using Algor's processor," comments Lawson. "All I had to do was enter the file name and specify which options I wanted the processor to use. Their program did the rest, using the model that I had specified." The results of Algor's analysis indicated that a radial displacement of approximately 0.0008 inch had occurred. Knowing this, Lawson could then work backwards. When the displacement of 0.0008 inch is reached, the contact pressure required to hold the gear in place would be produced.

To verify the model, checking boundary conditions and ensuring that displacements had occurred, Lawson used CPLOT. To view the original and displaced models in 3-D after verification, he used TDraw.

Lawson's analysis confirmed that Moore could use this gear on the cylinder and that it would handle the 90 foot-pounds of torque to which it would be subjected. "That torque will be transmitted by the outside ring to the inner ring, and won't slip," he points out. The Algor program also determined that the stresses, according to the von Mises criterion, were 2500 psi - very low for the type 4140 steel that would be used. It turned out that the interference fit was 0.0015 inch. Lawson says, "I spoke with the designer, who said the 0.0015 inch interference fit was within safety and manufacturing factors - and, in fact, was quite good. This means that we could relax manufacturing tolerances from those that had originally been anticipated, so they wouldn't be ridiculously high."

FEA was used to analyze the fit between the gear and cylinder pictured.

Future of FEA at Moore

"In the future, when we have more expertise in using Algor's FEA System, we plan to use larger models created with CADKEY and then converted into Algor's format through SuperDraw II's Files:Import command," Lawson relates. "In particular, I would like to use Algor to analyze displacements from castings, some of which are simply due to gravity. We would like to predict the bowing due to gravity or nonuniform loading of rolling members on the castings under consideration."

According to Lawson, another area where Moore plans to apply FEA is their 3-point support method for the Jig Grinders, Aspheric Generators, and Universal Coordinate Measuring Machines. "Three points of support are sufficient to prevent rocking," he notes. "However if the support points do not form an equilateral triangle and the loads are not evenly distributed, determining the best configuration can be tricky. We'd like to use Algor's FEA to help us with these support problems."

Lawson concludes, "After using Algor on the ring gear and finding out not only how much it shortened the design phase, but also how much more information it could provide for us, we intend to use FEA as a tool whenever possible."