CAM Design – Part 2, Focus on the CAM Richard Lindeke ME 3230 ME 3230 11/14/2018

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) ME 3230 11/14/2018

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 ME 3230 11/14/2018

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 ME 3230 11/14/2018

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! ME 3230 11/14/2018

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 ME 3230 11/14/2018

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 ME 3230 11/14/2018

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 ME 3230 11/14/2018

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) ME 3230 11/14/2018

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 ME 3230 11/14/2018

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() ME 3230 11/14/2018

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 ME 3230 11/14/2018

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  ME 3230 11/14/2018

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 … ME 3230 11/14/2018

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) pi+1=(xi+1, yi+1) ME 3230 11/14/2018

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 ME 3230 11/14/2018

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: ME 3230 11/14/2018

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 ME 3230 11/14/2018

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 ME 3230 11/14/2018

A similar Development for Flat Face Followers: 11/14/2018

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 ME 3230 11/14/2018

Continuing (for point of follower contact with CAM): ME 3230 11/14/2018

Radius of Curvature of CAM and Model for determining Base radius: ME 3230 11/14/2018

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; 8.15;8.20;8.38 To be “graded” #8.24 – due next Monday ME 3230 11/14/2018