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Involute curve in bevel gear teeth

  1. Jun 12, 2013 #1

    I have always wonder about this. I understand the concept of bevel gear, but never quite see how the involute profile would function in a bevel gear.

    assuming that there is a tooth(either of the driving or driven gear) located at the center between two gears ( where it has the greatest contact with another tooth)

    say it is involute and still appear so to you when you look straight down, perpendicular to the face of the teeth (so your line of sight align with the teeth's face normal, and about 45 degree to the axis of the gears).

    now, if we rotate the gear such that the teeth are no longer in the center, it will no longer be involute relative to you, or more importantly to the tooth of another gear that it is in contact with, so wouldn't this create interference or causes the driven gear to not move at constant speed (say the driving gear is moving at constant speed).

    thank you
  2. jcsd
  3. Jun 13, 2013 #2
    Or am I not understanding involute profile? I thought involute profile only works when the teeth face are on the same plane as they are in spur gears.
  4. Jun 30, 2013 #3


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    Think of a bevel gear as having a vanishing point. The pitch circle of a spur gear is actually a cylindrical surface of fixed diameter. But the pitch surface of a bevel gear is a cone with it's apex at the vanishing point.

    Now consider that, centred on the axis of the pitch cone, is another cone that is perpendicular to the surface of the pitch cone. It is in that section that the bevel gear has an involute profile. That involute tooth profile is projected over the surface of the bevel gear but with straight lines always passing through the vanishing point.

    When two bevel gears are engaged they share one vanishing point. Their pitch cone surfaces are in contact so are parallel, the sections perpendicular to their surface are co-planar at any point of contact. It is in that plane that the bevel gear profile is involute.

    While spur gears are specified by diameter of root, base, pitch and tip circles, a bevel gear is specified by the angle of root, base, pitch and tip cone surfaces.
  5. Jun 30, 2013 #4

    center of the axis of the pitch cone? the middle point of the axis of the cone?

    are you describing the line of contact when their apex are connected together?

    I apologize for my poor reading skills in English. I just want to make sure I'm not misunderstanding you.
  6. Jun 30, 2013 #5


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    The pitch surface of a bevel gear is the pitch cone.

    The involute profile appears on the surface of the back cone.

    The pitch cone and the back cone are perpendicular at their intersection. The back cones of two coupled bevel gears are coplanar at the point of contact. The tooth profiles of coupled bevel gears are designed on the surface of the back cones.
  7. Jul 4, 2013 #6
    so the involute profile is projected on the back cone?
  8. Jul 4, 2013 #7


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    To design a bevel gear of a particular module, generate the profile for a spur gear of that module and then trace that profile onto the back cone surface of the bevel gear.

    The working surface for a (straight cut) bevel gear is then generated by straight lines from that back cone profile to the vanishing point.

    If you look at the back cone contact of two meshed bevel gears, it will look like the contact between two spur gears cut in the same module and system.

    Now you can “see how the involute profile would function in a bevel gear”.
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