How to Draw Gear Teeth in Autocad TUTORIAL

The Anfractuous Curve, Drafting a Gear in CAD and Applications

By Nick Carter

Introduction:

Most of us reach a point in our projects where nosotros have to make use of gears. Gears can be bought set-made, they can exist milled using a special cutter and for those lucky enough to have access to a gear hobber, hobbed to perfect form. Sometimes though we don't accept the money for the milling cutters or gears, or in search of a project for our own edification seek to produce gears without the assistance of them. This commodity will explicate how to draw an involute gear using a graphical method in your CAD program that involves very piffling math, and a few ways of applying it to the industry of gears in your workshop.

The method I describe will allow you to graphically generate a very close approximation of the involute, to whatsoever precision yous desire, using a simple 2D CAD program and very piddling math. I don't desire to run though familiar territory so I would refer you to the Machinery's Handbook'due south chapter on gears and gearing which contains all the basic information and classification of the anfractuous gear which you volition need for this exercise. Some higher end CAD programs already have functions for generating the anfractuous tooth from input parameters, just where's the fun in that?

When we talk about gears, most of us are talking nigh the involute gear. An involute is best imagined by thinking of a spool of cord. Tie the end of the string to a pen, first with the pen against the edge of the spool and unwind the cord, keeping it taut. The pen will draw the anfractuous of that circle of the spool. Each tooth of an involute gear has the contour of that curve equally generated from the base circle of the gear to the exterior diameter of the gear.

Cartoon a Gear:

The easiest fashion to teach is to demonstrate, and then here are our parameters for drawing a:

16 Diametral Pitch (P), 20 Tooth (North), 14-1/2 Pressure level Angle (PA) anfractuous spur gear

• We need to compute the following data; a scientific reckoner is handy for figuring out the cosine of the pressure angle.
  ("/" Denotes segmentation, "*" denotes multiplication, the dedendum (d) is computed differently for other pressure level angles; run into Machinery'southward Handbook for the correct formula.)
  
• The Pitch Diameter (D) = Northward/P = 20/16 = i.25"
• The Pitch Radius (R) = D/2 = .625"
• The Base Circumvolve Diameter (DB) = D * COS (PA) = 1.25 * COS (14.five deg) = 1.210"
• The Base Circle Radius (RB) = DB/two = .605"
• The Addendum (a) = 1/P = 1/16 = .0625
• The Dedendum (d) = 1.157/P = one.157/16 = .0723" (rounding off at .0001")
• Outside Diameter (Do) = D+2*a = 1.375"
• Outside Radius (RO) = .625" (R) + .0625" (a) = .6875"
• Root Bore (DR) = D-2*d = 1.1054"                              (I had earlier used the letter "b" instead of "d", I recall this was a typo, making a note hither on ten/09/10 of the revision)
• Root Radius (RR) = .625" (R) - .0723" (d) = .5527"            (I had before used the letter of the alphabet "b" instead of "d", I think this was a typo, making a note here on 10/09/ten of the revision)

For our method we demand to compute the following every bit well:

1. Circumference of the Base circle, (CB) = Pi * (DB) = Pi * ane.210" = 3.8013"
2. 1/20th of the Base of operations Circumvolve Radius, (FCB) = .03025"
3. Number of times that FCB can be divided into CB, (NCB) = 125.6628
4. 360 degrees divided by NCB, (ACB) = two.86 degrees
5. Gear Tooth Spacing (GT) = 360/N = 18 degrees
6. The 1/20th of the Base Circumvolve Radius (FCB) is an arbitrary segmentation, which yields a very close approximation; y'all can use any fraction you think will yield a skillful result. At present we have all our pertinent data, let's become drawing!
   

Note: Click on whatever cartoon to download a .dxf file of that drawing.

Open up your CAD plan and draw concentric circles of the Pitch Diameter (D), Base of operations Circle diameter (DB), Outside Bore (Practise), and Root Bore (DR). Add a circle of .25" diameter for the bore of the gear. Make sure the circle centers are at x=0, y=0.
1) Draw a line from the circle center (0,0) to the base circumvolve perpendicular to your grid. In other words at 0, 90, 180 or 270 degrees. I chose 270 degrees. 2) Depict a line i/20th of the Base Circumvolve Radius (RB) long (FCB = .03025") at a correct angle from the end of that line. This line is now tangent to the base circle. It will be very hard to come across unless you zoom in on the intersection of the base circle and the lines. three) Radially copy the two lines (center at 0,0), make 14 copies at ii.86 degrees apart (ACB), for a total of 15 line pairs. Depending on the diameter of the gear you may need more or less lines, smaller gears need more, larger gears may demand a smaller fraction of RB (base circumvolve radius). 4) Number each gear up of lines, starting with 0 for the start 1, going to 14 Drawing shows the ii lines, and the copies of the line laid out and numbered.
5) Extend the tangent line for each re-create so information technology's length is the 1/20th of the base circumvolve radius (FCB) times the number that you accept next to that tangent line (0 x FCB, ane x FCB, two x FCB…14 x FCB) extend them from the tangent bespeak. Virtually CAD programs volition make this very easy, providing that yous started the line from tangent point, usually you only change the length parameter for each line, in Autosketch there is a brandish showing the line information and retyping the length extends the line from its start betoken. Brand certain yous zoom in on the drawing so you extend the correct line. Cartoon shows the tangent lines extended, and the length of tangent #fourteen, which is .4235" or FCB x 14
half dozen) Starting at tangent line #0, draw a line from the cease of tangent #0 to then end of tangent #1, from the end of tangent #1 to tangent #two, tangent #two to tangent #3 then on. You should at present have a very close approximation of the anfractuous curve starting at the base circle and extending by the annex circumvolve. Trim the involute curve to Do, the outside diameter of the gear. Drawing shows the anfractuous drawn along the ends of the tangent lines.
7) Erase all the tangent lines, leaving the involute curve generated past the process. Brand a line that goes from the intersection of the involute curve and the pitch diameter circumvolve (D) to the center of the gear. Note that this will not be the same as the line going from the commencement of the involute at the base circle (DB) to the center. 8) Draw a 2d line � of the Gear tooth spacing (GT) radially from the beginning line; normally this is best accomplished by radially copying the line from the first. 4.5 degrees is � of the gear tooth spacing (GT=eighteen degrees). 9) Now mirror a copy of the anfractuous curve around this 2d line, make sure yous leave the original curve, thus copying the other side of the anfractuous 9 degrees (one/2 GT) from the pitch circle (D) intersection with the involute. Cartoon shows steps 7 - 9
10) Erase the radial lines, leaving the ii involute curves. Draw a line from the start of each involute at the base circle to the eye of the gear. Trim those lines to the Root Diameter (DR) circle.
11) Erase all the circles except the Root Diameter (DR) circumvolve. Draw a curve from the outside tip of one involute to the other, which has a eye at 0,0 (the center of the gear) thus drawing the outside of the tooth (the curve has the radius of RO). Yous now have a completed gear tooth. 12) Radially copy the completed gear tooth 19 times around the Root Bore (DR) circle, spacing the copies 18 degrees autonomously (GT), making twenty gear teeth (T) in full. 13) Erase the Root Diameter (DR) circumvolve and make a curve (or direct line) between ends of two teeth which has a middle at 0,0 (the middle of the gear). Purists volition note that I have omitted the pocket-size fillet more often than not drawn at the bottom of the root. I did not depict information technology because I will be milling this gear on my CNC milling machine and the endmill will provide a fillet automatically. fourteen) Radially copy that bend or line around the gear as yous did with the gear teeth. You now have a completed involute gear.

An Application:

Milling a gear from apartment stock with CNC If we want to manufactory this gear out of a flat plate on a CNC milling machine we need to figure out what bore endmill will generate a minimum radius that won't interfere with the gear. If you are lucky enough to have admission to a laser or h2o abrasive jet automobile then you don't have to worry about this. We tin do this graphically by drawing two meshing gears and either inserting a circumvolve of the bore of an endmill in the molar gullet - information technology should be apparent whether information technology interferes with the gear teeth (call up that nosotros are concerned with the fillet the endmill produces, not the endmill itself, it can overlap the other gear'southward tooth), or by inquiring in the cad programme to the length of the root arc. In this example a one/xvi" endmill will not interfere with the gear teeth meshing.

A rule of thumb that seems to work is to use an endmill with a bore not larger than: DR * Pi / 2T = i.1054 * PI / 40 = .0868"
A 1/16" endmill is .0625" so information technology should piece of work, I take not tested this rule of thumb for all possible gears and so revert to graphical analysis if you accept any doubts. The drawing is imported into a CAM program and the g-code generated to manufacturing plant the gear profile.

The gears milled with the method seem nearly perfect and mesh perfectly in spite of the small steps that make upwardly the approximate anfractuous.

Another Application, "Approximate Hobbing":

In his excellent article on "Spur Gears and Pinions" (HSM April 1999, Vol. 12, #two pp. viii-fifteen), John A. Cooper outlines a method for forming a gear with a cutting tool that is a circular rack of the same pitch equally the gear. Office of his method entails cutting the individual teeth, and then lowering the cutter by half the circular pitch (CP) while keeping information technology engaged with the blank, thus rotating the blank while keeping the teeth in mesh and taking a 2d serial of cuts, generating a good approximation of the anfractuous.

Using what we have learned through cartoon the gear allows us to expand on the procedure and shows the relation between the rotation of the gear and the movement of the rack like cutter. On the lathe you lot make a cutter out of tool steel that is a round rack of the aforementioned pitch equally the gear, for the gear in the previous practice the rack has xiv.five caste sides, the same as an pinnacle thread, so grind a tool flake the same for as for an acme thread. The grooves are pi/P (CP) autonomously, or three.1415/sixteen (CP=.1963"), cutting flutes are milled and the cutter hardened. You lot then brand a gear blank of the desired size (same as the drawing instance, Practice = 1.375") and mount it on a dividing head, chuck the cutter yous accept fabricated in the factory, and bring it down and so the middle of the cutter is aligned with the midpoint on the gear. Take a cut(s) to the full molar depth, across the width of the bare. Rotate the bare 1/8th of the gear tooth spacing (GT/8, 18 deg./8, two.25 degrees), rather than leaving the gear in mesh with the cutter. Move the cutter in the direction of rotation by 1/8 x CP (1/eight * pi/P, .0245") Take another cut to full depth, echo the process until you lot take fabricated eight passes. Retract the cutter against the direction of rotation by pi/P (.1963") and begin the process over again until all the teeth are cut.

While this method is ho-hum (unless you have a CNC milling motorcar and fourth centrality) if you practice eight passes, you can certainly get away with two or four passes and make a perfectly serviceable gear. Information technology does lend itself particularly to making worm gears of almost perfect form.

Yous actually don't need to depict the gear for this method, but afterward cartoon the gear you will accept a better understanding of how the method works, and how far the blank needs to be rotated and the cutter moved.

Final thoughts

Some other utilise of this method: Printed newspaper patterns (on label stock, particularly) could be used to grind unmarried point grade tools for use in a fly cutter or on your shaper, for sawing wooden gears by hand with a jewelers saw or plasma cutting large gears from steel plate.

I'thousand certain the crafty reader will find many other uses for this technique. This method can besides be used with traditional drafting techniques, pencil and newspaper, simply it will take a much longer time. The original example of this method was taken from "Analysis and Design of Mechanisms" for drafting one tooth and copying each tooth as yous rotate a tracing around the circle.

I love manual drafting but at that place are and so many cheap and free CAD programs available now that it would be a expert time to upgrade if you are yet using dividers and a t-square.

For those of y'all with a love of mathematics and computer programming there is some other way of generating the anfractuous curve using polar coordinates, which lends itself to the generation of the curve in various programming languages or with spreadsheet and CAD macros. A quick search on the Internet using the term "Polar Involute" will return many pages dealing with that method.

If y'all are making meshing gears that have a big ratio (say a 10 tooth gear and a 48 molar gear) and y'all draw them in mesh (separated betwixt centers by half the pitch diameter of each gear), yous will notice that the larger gear undercuts the teeth of the smaller gear, thus producing interference. There are strategies for dealing with this such as increasing the center altitude (thus backfire), stubbing the larger gear's teeth, undercutting the smaller gear'south teeth, etc, some further research on your part volition allow you to deal with this problem should it occur.

I hope this leaves you with a amend agreement of the geometry of an involute curve and a practical method of drawing gears for your projects.

• References: Analysis and Design of Mechanisms, Deane Lent, Prentice Hall, Inc.1961
• Machinery's Handbook, 27th ed., Industrial Press, 2004
• "Spur Gears and Pinions", John A. Cooper, HSM April 1999, Vol. 12, #2

Copyright Nicholas Carter, 2007

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How to Draw Gear Teeth in Autocad TUTORIAL

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