my gear ill a help and legal

MyGEARillaHelpAndLegal 4/7/2009 of 11

You, Too, Can Draw Gears

Why MyGEARilla1? MyGEARilla draws spur gears inside AutoCAD2 with complete size and feature control. More than that, MyGEARilla brings some of the problems of involute spur gear study within common reach. Professor Faydor L. Litvin cites four gear analysis challenges in the pages of Dudley's Gear Handbook. MyGEARilla simplifies two of those four: 3

• Determination of tooth surfaces generated by cutting • Avoidance of tooth undercutting

MyGEARilla assists in 2D modeling the involute spur gear4 tooth form by graphically simulating the hobbing5 process. A drawn "cutter", optionally changeable, forms the basis for the "pseudo hobbing". The resulting measureable tooth form consists of a GENERATED involute and fillet, not an abstract calculated one and which some analysts use downstream in CNC, FEA -- and as a foundation for solids modeling. A screen report documents all vital data including automatic measurements of the circular tooth thickness, the outside diameter, the root diameter and, where it normally exists on small tooth numbers, the exact point where the root fillet intersects with the involute profile. MyGEARilla was briefly described in Manufacturing Engineering, July, 1995, p. 28. While it was designed for AutoCAD Release 13, this version accomodates releases 2004 and 2005. Drawing gears on the computer is vastly different than on a drawing boardi.

1 Formerly HobMaster. 2 MyGEARilla is written in AutoCAD’s powerful programming language AutoLISP, enhanced with Visual LISP (VLISP). 3 Dudley's Gear Handbook, second edition, p. 1.1. 4 Also Involute Stub Tooth Gears, Metric Gears and Splines – plus generated toothed pulleys. 5 That goes for rack cutting and generating grinder machines as well.


In short, after the gear is drawn, all gear tooth elements can be verified from within AutoCAD's editor.

Pondering a special gear? Perhaps that means a special cutter. Go ahead and draw that cutter tooth with your own special proportions and substitute it for MyGEARilla's polyline standard tooth. Then check the results before ordering that cutter. Standard Hob and Shaper Cutter on left:

Unusual tooth numbers? Not that you'd like to but I've successfully ran with tooth numbers as low as 3 and as high as 5,000. Pressure angles are simply decimal numbers to MyGEARilla, so you can ignore the traditional 14 1/2 and 20 degree limits. A plastics molder reports this as a feature he uses to compensate for shrinkage. Preparing To Run MyGEARilla. I suggest starting within a new drawing (say Drawing1.dwg), one with no other entities present. Then load MyGEARillaXX.vlx from the Tools, Load Application pulldown menu. From there and during that editing session, you can then run MyGEARilla by typing MyGEAR at the command line. Please note that all 3 AutoCAD files within the ZIP distribution file (MyGEARillaxx.VLX, MyGEARilla.DCL, and MyGEARillaDialog.sld) must be present on AutoCAD’s search path. Inputs Needed When You Run MyGEARilla. Inputs are, for the most part, self explanatory. A dialog box form, is pictured to your right: Teeth. How many teeth in the pinion or gear? This field will accept a whole number, any integer greater than 2. Pressure Angle, Degrees. Any decimal number is acceptable. It should go without saying, within practical limits

Figure 1


Diametral pitch. Any number in the range of 0.001 through 400. If you're interested in Module (MOD) or Circular Pitch (CP) gears, you must first convert their values to diametral pitch (DP).

DP = 25.4 / MOD DP = Pi / CP

Arc Or Circular Tooth Thickness. A decimal value. C.T.T. is the key to varying your gear size and how it meshes with its mate. As the hobbing machine operator must infeed the hob to reduce size and outfeed it to increase size, there is a parallel with MyGEARilla. An increase in the C.T.T., just like a hob outfeed, means a larger gear. Standard Fine or Standard Course. If your cutter is standard, select the appropriate dialog button for Course or Fine. MyGEARilla uses this input to calculate and draw the standard cutter. It decides on the cutter’s addendum (the gear’s dedendum) proportion based upon the following table.

If you wish to customize the cutter proportions, select the Pause option and draw your own cutter tooth. If you choose this way, onscreen rules adjacent to the default cutter drawing, must be followed. Outside Diameter. This will decide the actual gear addendum at times. When using low tooth numbers, and if you wish the involute flanks to converge to a sharp point, simply enter a much larger6 value than MyGEARilla suggests. As an added calculation feature, MyGEARilla reports the diameter of convergenceii. When using large tooth numbers, good convergence is not possible with the standard cutter. In such cases, you will see (refer to p 8) choppy results near the tooth’s top. To solve this, try increasing the cutter dedendum. Flutes Or Gashes. This is automatically selected by MyGEARilla. For the actual number, get the cutter and count the flutes. If 6 Okay, there are limits. Actually, you won’t be allowed to enter a value larger than (teeth + 4) / DP

Cutter Addendum (gear dedendum)

Fine Course (1.2/DP) + 0.002 1.25/DP


you don't have one, ask your hob supplier. A word to the wise: Be realistic. MyGEARilla is designed to simulate conditions on a real machine. On a real generating machine, a 12 flute cutter will produce a 9 tooth gear with involute and the trochoid (undercut) curve profiles that look exactly as pictured above. You can see that the involute curves are actually a series of flats when viewed close. Sure, you can cheat with MyGEARilla and select more flutes in order to achieve a smoother drawn appearance. However, that runs the risk of certain AutoCAD limitations when running MyGEARilla. You may find that some 75, or so, flutes can be successfully run on your machine but that may depend on the number of gear teeth (the more teeth, the more computer resources are needed), your operating system, and the machine’s memory configuration. Be patient because this will slow things down.

Noteworthy: MyGEARilla checks each of these flats for perpendicularity to the tangent of the gear’s base diameteriii. This guarantees the entire involute is as true as can possibly be generated by the cutter you selected. This way, it can accurately report the topmost diameter (usually the O.D.) and the bottommost diameter (usually the undercut) even on gears with large numbers of teeth. As a visual bonus, it draws arrowheads to those exact points.

For a cosmetically smooth involute curve it is easier, inside AutoCAD, to simply select the polyline tooth, then use the Pedit command’s Fit or Spline option. For other types of machines -- rack cutting and generating grinder machines – you’ll need to translate their scheme of axial cutting edge advancement, into MyGEARilla’s needed input for “Flutes”. MyGEARilla’s basis is a hobbing machine which creates a single gear tooth space for each complete hob revolution. As an example, a 1 diametral pitch hob with 12 flutes (or gashes) advances the cutting edges 3.1416 inches for each revolution, 0.262 inches for each flute. Gear Center. This will always be located at AutoCAD’s 0,0 coordinate. The Drawing Begins. MyGEARilla now starts things off with a drawing of some basic arcs, the cutter tooth surrounded by another closed outline, and a sample tooth drawing showing a few possible modifications. The Pause Option. If you selected the Pause option, MyGEARilla will completely stop and allow you to use your basic AutoCAD skills to create the special cutter outline. If you elect to pause, the following screen greets you.


You may make some modifications to the already-drawn cutter (the innermost closed polyline within the red boundary) or replace it with one of your own drawings. Restrictions apply and those instructions are located adjacent to the boundary outline.

Please pay special attention to step 9 as you may need your handiwork for another MyGEARilla run. If you happen to forget to copy to a different drawing, not all is lost. Your

cutter drawing remains inside your current drawing in the form of a block named OriginalCutr. It stays there until your next launch of MyGEARilla which does its routine

purging work. Resume with the MyGEAR command. The drawing. It's nearly complete now - and you have to make one more decision. Display how many teeth? By now MyGEARilla has drawn 1 tooth which points upward but it can draw as many as the total number in your gear. Most folks choose 1 tooth since it gives them all they need for the moment. No big penalty here. I chose 3 for the sample below but if you want more after MyGEARilla is through, use AutoCAD's ARRAY command. The end result -- the gear tooth drawing and the report -- follows:


A word about arc tooth thickness. You will sometimes note a slight difference between your input and the measured value. Reason? MyGEARilla a well-known approximation formula. If you need a result closer to your intent, try again once or twice with different C.T.T. inputs. You'll get the feel of it. Modifyingiv the standard cutter tooth or creating your own. Let’s say you want to use a topping hob, add a tip radius, a protuberance, or an addendum ramp. As shown, modifying the left side is all that’s needed. Modifications below the pitch line, however, must be symmetrical7. Go ahead, but please follow the on-screen tips. When you're through, it has to be one enclosed polyline. At right is a user-modified topping cutter. Please note the restrictions.

7 Radius both tip corners, for example.


Drawing a full radius cutter tip is easy. Seeing its results, even easier.


Figure 2, Choppy results at tooth tip

The tooth above first appears to be one with a converged O.D. However, MyGEARilla detects that the involute actually ends at the topmost indicator and gives an actual diameter measurement of 9.7431. Let’s look close and see if we can see what MyGEARilla sees:

Aha! There’s a step at the arrowhead’s point. The amount isn’t much, only 0.0001”, but in cases like these, you’ll appreciate the distinction. The cure? Simply lengthen the cutter’s addendum (pause MyGEARilla and modify the drawn cutter).


Below, a tooth drawn with the use of the stock-drawn modified cutter.

Comments and criticism? I welcome both since it is impossible for me to test all the blends of data which MyGEARilla allows. You and your shared experiences - some, disturbing at times - continue to be my best resourcev. Keep them coming. And don't forget to keep me posted on your good ones as well. The Legal Stuff and Contact Information Permission to use, copy, and distribute this software for any non-commerial, non-profit purpose and without fee is hereby granted, provided that both the credit to the author (that’s me) and the copyright notice appears in the running program’s dialog box (see Figure 1 on Page 2), and that both the above copyright notice and this permission notice also appears in all supporting documentation. Leonard R. Miller Rt 4 Box 183B Camden, Ar, 71701 [email protected]


i The following is from The Internal Gear (1949), The Fellows Gear Shaper Co., p 81. I have fond memories of using several of their gear shaper machines in the early 1970’s. Sadly, Fellows is now out of business and I dedicate this facsimile to all who worked and thrived at that Springfield, Vermont facility for some 100 years.

ii MyGEARilla uses iteration to establish converging involutes.

Ro Outside Radius Rp Pitch Radius Rb Base Radius � Pressure Angle t Circular Tooth Thickness, user


iii To check for yourself, first extend the base circle radius (Rb) to the left, approx. 9 o’clock. Also, change its linetype to continuous from hidden. Finally, draw a line perp to the involute flat, then to tan of the Rb. When complete, the line will normally be drawn near to, though not exactly, the mid point of that flat. Exceptions are at the O.D. and the Root Dia. Here, those flats are frequently truncated yet your drawn line will still appear, although not affixed to the flat. That’s okay as long as the tangent attachment to the Rb equals its neighbor’s angular property. See the drawing below which illustrates the equiangular characteristic of construction lines when drawn from the gear’s center:

iv Modifying the standard cutter involves the following steps. Explode the polyline into conventional lines. Then, make the required changes. Then, re-select the new lines (and arcs) using Pedit, Multiple. Finally, the Pedit option Join, accepting the default fuzz distance of 0.0000…. Voilà, It’s a polyline once again. v Credits to the following for their contributions in reporting several verifiable errors: James Ackerman, David Kenna, E. J. Kutkowski, Madeleine Lentz, and Nathaniel Wilkerson. vi That’s a spam-guarded email address. Get rid of the 3’s before you use it.

my gear ill a help and legal

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