CAM Design – Part 2, Focus on the CAM

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CAM Design Part 2, Focus on the CAM

• Richard Lindeke
• ME 3230

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Ideas

• The CAM profile is a series of Tangent Points
  that allow the follower to move as specified by
  the computed transition analyses
• The CAM is designed based on a Base Circle
• Design rule of thumb the base circle radius
  should be 2-3 times maximum lift value
• This size controls the size of the CAM system and
  hence its cost
• too small of a base radius can lead to follower
  bridging of Hollows or cancave regions about
  the profile
• An ideal CAM has only Convex surfaces (but this
  is dictated by the follow travel and base circle
  size)

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Roller Follower Design follows this development
procedure

• Notice Base Circle
• Notice Prime Circle
• The path of the roller center about the CAM at
  initial dwell
• rpc rb ro
• The principle here is that while in reality the
  CAM rotates we model the CAM by inverting the
  motion to the follower about the fixed CAM
• We draw the follower at radial offsets from the
  CAM center based on the designed follower paths
  for raises and returns
• These radial markers are laid out at angles that
  are reversed to the rotation of the actual CAM in
  practice

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Consideration of Pressure Angle

• The pressure angle ? is the angle between the
  direction of follower travel (Radial from CAM)
  and a normal to the CAM Surface curve
• For a given force of the follower roller, the
  force normal to the travel of the follow (drag
  along the CAM) is proportional to the Sine of
  Pressure angle, high normal force leads to
  increased stem wear

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Consideration of Pressure Angle

• Highest ? occurs at Pitch Points on the CAM
  surface (which correspond to inflection points of
  the follower displacement curves)
• As a rule of thumb, ? should be limited to values
  of ?30?
• In cases of excessive ?, the base circle diameter
  should be increased or follower displacement
  profiles changed
• Think about multi-valve engines!

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Using a flat follower -- why

• Pressure Angle at all location is 0 degrees
• Notice Cam follower offset
• From a kinematics perspective it is unimportant
• From a Machine Design view it is critical as it
  determines bending moments on the follower stem
• During design, the follower dictates that the CAM
  surface must be convex to avoid bridging thus
  forcing larger base diameters compared to roller
  or cylindrical followers

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Flat Follower How?

• Again, as with roller followers, we sketch the
  base circle (rule of thumb as starting point!)
• Layoff radial lines from 0? then using follow
  path data, layoff lines equal to the computed
  values
• Draw lines perpendicular to these segments to
  represent the follower face

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Leads to this Tentative CAM

• A 10-15-6 rise over 60? starting at 60? to 0.75
• A harmonic return over 60? starting at 280?

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Check the Flat Faces intersections
If face intersections require a negative angle
increment (as with I45 to I56 seen here) it means
that it will be not possible to generate or
operate the CAM. We must use a larger base
circle than the 2.25 radial size chosen (3 times
rise)
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To solve this Problem

• Increase base circle size until the three face
  follower lines (at 100?, 110? and 120?) intersect
• This leads to a CUSP in the CAM surface

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Analytical Determination of CAM Profiles

• We will focus on an Offset Radial Roller Follower
  Design
• Step 1 (of course) Determine the follower
  positions as a function of CAM angle
• Step 2 determine (chose) base and follower radii
  and the follower offset
• Step 3 determine successive positions of the
  roller center (or cylinder center!)
• R r0 rb f(?)

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Follower Center Location (by Components)

• Looking at the position of the roller center at
  the radial Angle ?
• The series of Center Positions with the circles
  so centered will form the envelope to define the
  CAM profile as a series of

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Getting the Tangent Positions

• Uses a 3-position approach to model the CAM
  surface
• This is most accurate and simplest computational
  approach
• Begins with the computation of the CAM center of
  and radius of curvature as a function of CAM
  angle ?
• Radius of Curvature (?) determines if the surface
  is Concave (-?) or convex (?) 0 indicates a
  CUSP
• Contact stresses between CAM and Follower are
  functions of ?

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Radius of Curvature is given by

• We the solution follows from differentiation of
  our models for the x-comp. and y-comp of the of
  the CAM contact points not often known! So

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We will get at ? and Center of Curvature
indirectly!

• We can approximate the CAM CenCur as the same
  point as the center of curvature of the Prime
  Circle defining the location of the Center of the
  cylindrical follower
• We will use 3 consecutive ones to find pc
• pi-1 (xi-1, yi-1)
• pi (xi, yi)
• pi1(xi1, yi1)

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Leads to
The sign of the radius of curvature is found by
taking the Cross Product
If the Cross product is positive CAM is convex,
negative then CAM is Concave
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We use this Center of Curvature to Approximate
the CAM Profile

• First the angle ? (the slope orientation angle
  from the center of curvature to the center
  follower center) is found

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Finding Coordinate of the appropriate tangent
points on the CAM Surface

• If ? indicates CONVEX surface
• If ? indicates CONCAVE surface

These Xi Yi values become the coordinates for
CAM machining on a CNC machine
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Finding Pressure Angle (analytically)

• The nominal value of the pressure angle is given
  by
• Here ? is the pressure angle (between the outward
  normal to the CAM surface at contact point and
  the follower velocity direction (as we saw
  earlier)
• The other angle are the Slope Orientation angle
  and the Cam angle

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A similar Development for Flat Face Followers
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A similar Development for Flat Face Followers

• Radial displacement
• t is the distance from follower axis to the point
  of contact
• Minimum and Maximum values for t set the minimum
  length of the follower face

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Continuing (for point of follower contact with
CAM)
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Radius of Curvature of CAM and Model for
determining Base radius
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Chapter Eight Continues

• Develops graphical and analytical modeling
  techniques for CAM
• With oscillating Roller/Cylindrical followers
• With oscillating Flat Face followers too
• Please study these methods as well
• Homework
• For practice 8.7 8.12 8.158.208.38
• To be graded 8.24 due next Monday