When modeling components in CAD there is always a tradeoff between accuracy and speed. More exact models generally take more time to model, contain more features and are slower to regenerate. Not a great problem when you only have a few of them but when you have hundreds or may be thousands of them, overmodeling will slow you, and your workmates down.
Gears is a case in point. The various methods I have seen involve creating the involute curve from an equation and using it to create a cut which is them patterned around the axis. To do this takes around 3-10 features per tooth which when multiplied by 20-40 teeth and multiplied again by 20-30 or more gears can start adding up to a lot of features very quickly. Another by-product is that some construction methods end up with datums for Africa.
What I wanted was a method of creating a tooth with a single feature that was fully parametric and possessed sufficient accuracy for our purposes. To do this I approximated the involute curve with two radii. One radius runs from the base circle to the PCD and the second radius runs from the PCD to the OD.
To minimise the errors associated with this construction the geometric locations of three sketch points where the true involute intercepts the base circle, PCD and OD were mathematically calculated. Also the ends of the two arcs were forced to be normal to the sketched pressure angle construction line which in turn forced the approximating radii to specific values removing any requirement to guess them. The lower pair radii are mirrored in the sketch about the rotational patterning datum plane-on-the-fly.
The critical relations to drive the sketch are
PCD = teeth*module
OD = PCD+2*module
base_circle = PCD*cos(pressure_angle)
base_intercept = (PCD/2*sin(pressure_angle)/PI()/base_circle)*360
d15 = (sqrt(od^2-base_circle^2)/2-PCD/2* sin(pressure_angle))/PI()/base_circle*360
d10 = 90/teeth
dedendum_dia = PCD-2.4*module-.1
root_fillet = .3*module
increment = 360/teeth
start = increment/4
Note: I also offset the first tooth/cut from the reference plane by
Gears is a case in point. The various methods I have seen involve creating the involute curve from an equation and using it to create a cut which is them patterned around the axis. To do this takes around 3-10 features per tooth which when multiplied by 20-40 teeth and multiplied again by 20-30 or more gears can start adding up to a lot of features very quickly. Another by-product is that some construction methods end up with datums for Africa.
What I wanted was a method of creating a tooth with a single feature that was fully parametric and possessed sufficient accuracy for our purposes. To do this I approximated the involute curve with two radii. One radius runs from the base circle to the PCD and the second radius runs from the PCD to the OD.
To minimise the errors associated with this construction the geometric locations of three sketch points where the true involute intercepts the base circle, PCD and OD were mathematically calculated. Also the ends of the two arcs were forced to be normal to the sketched pressure angle construction line which in turn forced the approximating radii to specific values removing any requirement to guess them. The lower pair radii are mirrored in the sketch about the rotational patterning datum plane-on-the-fly.
The critical relations to drive the sketch are
PCD = teeth*module
OD = PCD+2*module
base_circle = PCD*cos(pressure_angle)
base_intercept = (PCD/2*sin(pressure_angle)/PI()/base_circle)*360
d15 = (sqrt(od^2-base_circle^2)/2-PCD/2* sin(pressure_angle))/PI()/base_circle*360
d10 = 90/teeth
dedendum_dia = PCD-2.4*module-.1
root_fillet = .3*module
increment = 360/teeth
start = increment/4
Note: I also offset the first tooth/cut from the reference plane by