Finite element simulation of a
hypothetical five-tooth pinion engaging a ten-tooth gear. Virtual testing
of this non-standard, 43-degree pressure angle gear set is the most
cost-effective way to quantifiy its potential performance. To view an
animation, visit www.integra-engineering.com
When applied to gearing and gear set designs, standardized calculation methods such as those based on ANSI/AGMA standards are not meant to model or simulate gear behavior for analysis. Their intent is to determine load ratings that are safe. They were made that way on purpose, i.e., to each convey a simple procedure for calculating a rating that the whole world of engineers can agree is safe in almost all situations.
Sometimes, these standardization committees would like to include a given parameter with a new set of equations. However, since they also realize that the general population of engineers might easily misinterpret or possibly abuse that parameter, the parameter will be omitted in favor of factoring an existing one. Basically, standardized calculation methods provide a "cookbook" procedure for use of rating equations primarily meant to ensure certification and/or approval of the standard gear sets recognized by inclusion.
For evaluation of non-standard de-signs, engineers use FEA to simulate events and analyze a product's behavior and thereby predict its performance. They understand that real-world modeling requires nonlinear and dynamic capabilities that may supercede many of the simplifications and idealizations of standardized calculation methods.
Consider, for instance, use of multiple pressure angles, or the angle of attack between intermeshing gear teeth. Engineers generally employ a symmetrical involute gear tooth model when designing gears because it allows an almost infinite range of gear sizes. This is limited to a single pressure angle, such that standard tooling can be used to cut and manufacture these different size gears. Standardized calculation methods, therefore, assume the use of a single pressure angle. Using non-standard asymmetric teeth with multiple pressure angles requires FEA. Such gearing is now used for aerospace equipment.
When two gears contact, dynamics are
caused by manufacturing tolerances that spoil the perfect involute shapes
of the teeth. Standardized calculation methods assign a compensation
factor, but FEA permits duplication of the actual profile error, as shown
by the profile error plot. Using Mechanical Event Simulation from ALGOR
Inc., engineers can then simulate these dynamics.
For many applications, of course, integration of the two approaches—FEA and standardized calculation methods—would combine the best of both worlds. Integra Engineering Inc., for example, performs mechanical and structural engineering consulting for leading OEMs who require cost-effective, state-of-the-art simulation and analysis. Using 3D CAD packages like Solid Edge, and FEA packages such as ALGOR's Accupak for nonlinear transient dynamics, the company offers sophisticated design solutions with mechanical event simulation, or MES. However, because dedicated routines for gear design are not available in the major commercial FEA packages, achieving these simulations has required the following procedure:
Lay out geometric gear boundaries to estimate the
gear system required.
Use MathCad-based AGMA rating formulae for iterating
Draw, obtain, and/or refine gearing geometry of all
teeth and wheels.
a. Convert symmetrical portions to a DXF or IGES format.
b. Or, extrude 2D profiles of constant width designs
within ALGOR's SuperDraw program.
Using Solid Edge, generate geometry of a repeating
part of the system.
Import into ALGOR for automatic mesh generation or
Complete model and process using ALGOR's Mechanical Event Simulation (MES).
Integrating standardized software whose output is a CAD solid model could facilitate this procedure. Instead of seven steps, there would be three:
Generate gear system design and geometry with a
standardized calculation package such as KISSsoft (see side story).
Import Solid Edge file generated by KISSsoft into
ALGOR for FEA or MES analysis.
Complete the model and process using MES.
For gear designers, life suddenly be-comes much easier. Rather than employing off-the-shelf gear programs to generate a multitude of numbers that must then be converted into gearing geometry and IGES files, a standardized calculation software package like KISSsoft will perform all of these steps quite easily.
Ultimately, however, it is the engineer who must interpret the final results, evaluate their impact, and render a judgment. Calculation and integration—without evaluation—can only go so far.