Wednesday, December 22, 2010

ProE - to create involutes using a datum curve from equations

The easiest way is to create the involutes using a datum curve from equations.
Assuming a cylindrical coordinate system your equations will be:
z=0
theta=(180/pi)*tan(t*alpha_max)-t*alpha_max+90
r=DBASE/(2*cos(t*alpha_max))
Where:
DBASE = m*z/cos(alpha) - base circle diameter
m - gear module
z - number of teeth
alpha_max - max roll angle (at tip circle)
alpha_max=acos(dbase/da)

This curve will give you one side of the tooth. To create the other side you will mirror this curve about the tooth center plane.

To create the tooth center plane you need first to determine the 1/2 center angle at the base circle (or 1/2 tooth thk. at base circle):

/*tooth half center opening at base circle
gamma=((pi/2+2*x*tan(alpha))/z+tan(alpha)-alpha*pi/180)*180/ pi
where: z - number of teeth
x - profile shift
alpha - pressure angle (20deg. typical)

Create the tooth center plane at this angle relative to the csys used to create the involute.

Mirror the involute curve about the previous plane. Now you should the both sides of the tooth. To complete the tooth profile refer to the basic rach information provided in the ISO 53 standard (or the corresponding AGMA standard).

Copy -Rotate the final tooth profile with a rotaion angle about the "z" axis equal to 360/z. Pattern this feature (360/z increment, z-1 copies)
You can use the ciurves to create cuts/protrusions for the crown

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