Suggested Technique for Creating an Involute Gear
Procedure
Create default datum planes by selecting Insert, Datum Plane.
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Create a disk (Create, Protrusion, Extrude, Solid, Done, Both Sides, Done) sketched on DTM3 with the center at the intersection of DTM2 and DTM1. The depth of the disk will be blind.
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Next, create an angled datum plane by selecting Insert, Datum, Plane,Through, select A_1 (created from the protruded disk). Then select Angle, and select DTM2. Enter an angular dimension for the DTM 4 location.
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Sketch a datum curve on the front surface of the disk. The curve should be an arc with the center on A_1. The radius of the arc, arc length, and the angle between the endpoint of the arc and DTM4 should be dimensioned. The disk with this first datum curve is shown in Figure 1 below.
Figure 1
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Project the datum curve created in Step 4 to the back surface of the disk by selecting Insert, Datum, Curve, Projected, and Done. Select Select and Done from the PRJCRVTYP menu. Select the datum curve created in Step 4 to be projected, select the back surface of the disk to project the datum curve onto, select Along Dir and Done from the PROJ TYPE menu and DTM3 for direction reference. If necessary, flip the direction arrow to point in the direction of the back surface of the disk.
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These two curves will now be used as the spine and x-vector for a surface created using a variable section sweep. To create this feature, select Create, Surface, New, Advanced, Var Sec Swp, Done, NrmToOriginTraj, Done. Select the curve created on the front of the disk as the spine and the curve create on the back of the disk as the x-trajectory. In sketcher mode, create the sweep's section as a horizontal line just above the datum curves. Dimension this line vertically to A_1 and align the end points to the flat faces of the disk. Write the following sketcher relations to create the desired curve to this surface:
rbase = 2.0
todeg = 180/pi
a = 1.0
solve
a*todeg-atan(a)=trajpar*14.0
for a
sd4 = rbase*(1+a^2)^.5
PLEASE NOTE: The relations used in this example are for illustrative purposes only and should be modified to meet the requirements and design intent of the object being modeled.
The dimension sd4 refers to the distance between the axis and the sketched line.The value of 14.0 should be substituted with the number of degrees used for the length of the first datum curve and the 2.0 is the radius of the root circle for the gear. The variable a is used to solve for the dimension value and is set to 1.0 to initialize it so that it can be used to solve the equation. After regenerating, sd4 should snap to 2.0, the radius of the root circle. Regenerate the model and select Done. The involute surface created is shown below in Figure 2.
Figure 2
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Next, miror the involute surface about DTM4 by selecting Create, Surface, Transform, Mirror, Copy, Done. Create a cylindrical surface along A_1 with a radius slightly greater that the value for the radius of the root circle of the gear to connect the surface created in Step 6 with the mirror just created. Merge these 3 surfaces together. The resultant surface is shown below in Figure 3. The datum planes have been removed from this figure for clarity.
Figure 3
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Finally, transform rotate the merged surface about A_1 utilizing the same technique in Step 7 and pattern 360 degrees. Create a reference pattern of cuts, via Use Quilt, to create the teeth. For more information about surface transform, refer to Suggested Technique for Creating a Rotational Pattern Using a Surface Transform. Two adjacent cuts will create a single tooth. The completed involute gear is shown below in Figure4.
Figure 4
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