Drawing a Spur Gear Profile in AUTOCAD Stan Beebe

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Erik Beasley
7 years ago
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1 Drawing a Spur Gear Profile in AUTOCAD Stan Beebe This describes the process by which an involute gear tooth is designed and drawn in AUTOCAD. A module of 0.2mm is chosen for convenience. Also, a 40 tooth gear will be chosen for example, the process is similar for the pinion. Figure 1 below shows a few of the properties of a gear tooth, I apologize for the poor drawing. Definitions: P = pitch = 1 / module N = number of teeth D = pitch diameter B = base diameter A = addendum Dd = dedendum C = clearance f = pressure angle a = angle between teeth Figure 1 Determine the pitch diameter: D = N / P = N * module = 40 * 0.2mm = 8mm Determine the base diameter: Choose a pressure angle, typically between 14.5 and 25. A value of 20 will be used for this example. B = D * cos(f) = 8mm * cos(20 ) = mm For convenience of later calculations, the base radius is found to be mm. Determine Addendum and Dedendum: A = 1.0 / P = module = 0.2mm

2 Dd = 1.25 / P = 1.25 * module = 0.25mm Note: the value used for the dedendum above (1.25) can be chosen from various standards, 1.25 and 1.35 are common. Determine Clearance: C = Dd - A = = 0.05mm Determine angle between teeth: a = 360 / 40 = 9 Since the teeth are on a circular gear the point of contact that allows constant angular velocity follows an involute path as shown below in Figure 2: Figure 2 Imagine a string unwrapping from the circle, i.e. the purple line is the radius of the green arc being and it is equal to the length of the blue arc.

3 So in this manner, the teeth profiles are drawn. The tricky part is the length of the involute radius (purple line in Figure 2). However, this is easily remedied by forming a chart of discrete involute radii for various angles formed by the tangent normal (red radius line in Fig. 2, about 270 in this instance). So the length of the purple line is equal to the length of the blue arc. Thus we need only find the arc lengths for a discrete set of angles described above. The length of the blue arc is: radius * angle (in radians). About five degree (5*2p / 360 radians) increments seems to produce adequate resolution, more can be used if desired. Since the teeth are drawn about the base diameter, the base radius is used for the calculation. A sample is shown below for the first 5 increment: Arc length = base radius * 5 * 2p / 360 = mm * = mm Continue these calculations for 10,15,20,25, etc. Results are tabulated in Table 1 below. Angle (deg) Arc Length (mm) Table 2 All one has to do now is draw these in a CAD program as illustrated below in Figure 3. For AUTOCAD do the following: Before starting I like to make a couple layers, in this case I ve added four additional layers of different colors to make things easier to see. Draw the base circle, mm radius. Draw a vertical line from the center outward past the circle. In a new layer, draw a tangent line, in my case to the right, a little more than a radius in length. Create polar array of this tangent line about the center of the circle at increments that you used to calculate the involute radius (5 in my case) and about 10 of them should be enough (hence the ten 5 calculations shown in Table 2).

4 So this is what mine looks like after the array of 10 items, 5 between items: (Exported from AUTOCAD) Now just make each of the arrayed lines the appropriate length. From the chart we see that the first line (0 line, horizontal above) is mm long. Just delete it. As for the others, use the lengthen command: Type lengthen, then t for total, then input the appropriate segment length, i.e for the second segment. Then click on the segment that you want to alter. Be sure to click towards the end of the segment you want truncated. Repeat the command for each consecutive segment. It may be helpful to draw in the addendum circle at this point so you know when you ve truncated enough segments. You ll know you ve done enough when the segment you just truncated stick above the addendum circle. The radius of the addendum circle is the pitch circle radius plus the addendum, 4.2mm in our case. It should look like this: Notice that the last three were not necessary, as they are past the addendum circle. Now connect the endpoints of the involute radii with a spline curve using default tangents. I do this in another layer. Pick the intersection of the vertical line and the base circle as one of the points. It should look something like this:

5 Now in order to mirror the segment to produce the other side of a tooth, we will need to know its intersection with the pitch circle in order to determine tooth thickness. Turn off the layer that contains the involute radii lines for clarity. Draw in the pitch circle and draw a line from the center to the intersection of the pitch circle and the tooth profile line (blue line above above). Make a polar array this new line by 1/4th the tooth angle, a, you only need one, so I choose 2 elements, 2.25 between elements. In order to use decimal angle values, make sure to set Format> Units> Angle to the proper number of decimal points. Mirror the tooth profile about this line. It should look like this:

6 Now, you are nearly complete. Just truncate the tooth at the addendum circle with a straight line. In order to complete the gear with one array, a complete tooth must the drawn, we do not have the bottom defined yet. Array the tooth using 2 elements, 9 between elements to make another reference tooth. Draw a straight line between the bottoms of the profiles. Add fillets to these corners if you wish. I believe you can use half the clearance (0.025mm) as the fillet radius. Here s what mine looks like: Now, just delete the unneeded parts and you are one array away from completing your gear. Mine looks like this:

7 Now array the remaining 39 teeth and PRESTO, you should have one of these: All you have to do now is export it as a stereo-lithography file into Pro-Manufacturer, produce some g-code, clamp some brass into your micro-cnc mill, put in that endmill, and cut the sucker out. If you have any questions about any of this, feel free to me at stanbeebe@hotmail.com.

Drawing an Approximate Representation of an Involute Spur Gear Tooth Project Description

Drawing an Approximate Representation of an Involute Spur Gear Tooth Project Description Create a solid model and a working drawing of the 24 pitch gears specified below. It is only necessary to create