CatWorks

On a pictures above are some examples of my early works in Catia...

...and above are more recent works, when models became better structured, flexible, more parametric and intelligent...

...and some gears in catia, elements of tractors' manual transmission, with lots of applied knowledge.

On the left picture above is archetype model of a gear, and on the right side are gears all derived from it (File -> SaveAs...)

The main model of spur gear consists of more then 100 relations/formulas, it allows user to change usual gear parameters, it has few checks and rules and is completely made in Catia. Units are in mm and parameters calculations are made according to ISO/European standard.

I didn't use Excel table to import profile points from file, neither third-party gear-profile generating/calculating software, like KISSSoft, MITCalc, Camnetics Geartrax or GearGN, nor it is imported STEP/IGES/DXF file, it is a pure Catia's CATPart model, approx. 370KB of size and you can generate any spur gear-pair from it by changing number of teeths, module, profile shift, etc.

Involute profile is very close to true involute, it's not approximated by a piece of circle arc or something. It's obtained analitically and mathematically as close to true involute curve as it was possible - it's a spline passing through 6 calculated points, because larger number of points would unecessarily complicate calculations, and Catia isn't C++ or Basic, or any programming language. All calculations are implemented in formulas within Catia itself.

Archetype gear model in Catia is not yet finished completely the way I wanted it to, it needs to include more accurate gear tooth root profile and to include check for a minimally allowed number of teeth in order for tooth not to be undercut, or if it's undercut, it needs to show the exact profile anyway. Implementing mathematics of trochoid in formulas should allow to have more precise transition from involute's end at base circle to root diameter of gear, especially in case when base circle diameter is above, ie. when it's larger then root circle diameter (d_b>d_f).

Whenever this case occurs with particular combinations of parameters it is impossible to approximate transition between base circle dia. and root circle dia. with plain radii-and people do this often which is wrong (or because is easier that way), they use the radii of the tool tip to approximate this transition.

But this will often produce selfintersecting sketch, even when model looks truly like a real gear.

And then this model become unuseful, although it seemed completely parametric at first look, because you get errors during its regeneration when you change some parameters.

This simply happens because the envelope of consecutive positions of the tip of tool that generates root of gear tooth (rounded tip of gear rack) doesn't describe circle arc during its rolling without sliding , it describes trochoidal shape in a root of gear tooth. I will cite next few words:

"I have seen some cad

drawings of gears that did look real --- from the base circle

up.Below the base circle is another matter. Most if not all

of the cad drawings of gears I've seen have had some kind of

arbitrary lines and radii below the base circle. They com-

pletly ignored the effects of the trochoidal shape of a gener-

ated root radius and of the undercut in the smaller numbers of

teeth." -GearGN's author quoted

General idea was to make pure sample gear model in Catia which would enable deriving any kind of gear pair from it (external spur or helical), in Catia's native file format, model that would regenerate fast and reliably and wouldn't include reworking, importing bunch of points from other file formats, slow regenerating, etc.