Machinery's Handbook, 31st Edition
CAMS AND CAM DESIGN 2385 Calculation of Contact Stresses.— When a roller follower is loaded against a cam, the com- pressive stress developed at the surface of contact may be calculated from (22) for a steel roller against a steel cam. For a steel roller on a cast iron cam, use 1850 instead of 2290 in Equation (22). S c = maximum calculated compressive stress, psi F n = normal load, lb b = width of cam, inch R c = radius of curvature of cam surface, inch r f = radius of roller follower, inch The plus sign in (21) is used in calculating the maximum compressive stress when the roller is in contact with the convex portion of the cam profile and the minus sign is used when the roller is in contact with the concave portion. When the roller is in contact with the straight (flat) portion of the cam profile, R c = ∞ and 1/ R c = 0. In practice, the greatest compressive stress is most apt to occur when the roller is in contact with that part of the cam profile which is convex and has the smallest radius of curvature. Example: Given the previous cam example, the radius of the roller r f = 0.25 in., the con vex radius of the cam R c = (2.26 − 0.25) in., the width of contact b = 0.3 in., and the normal load F n = 110 lbs. Find the maximum surface compressive stress. From (21), . . . S 2290 03 110 025 1 201 1 93,000 psi c = + = a k This calculated stress should be less than the allowable stress for the material selected from Table 2. Cam Materials: In considering materials for cams it is difficult to select any single mate rial as being the best for every application. Often the choice is based on custom or the machinability of the material rather than its strength. However, the failure of a cam or roller is commonly due to fatigue, so that an important factor to be considered is the limit ing wear load, which depends on the surface endurance limits of the materials used and the relative hardnesses of the mating surfaces. Table 2. Cam Materials Cam Materials for Use with Roller of Hardened Steel Maximum Allowable Compressive Stress, psi Gray-iron casting, ASTM A48-48, Class 20, 160–190 BHN, phosphate coated 58,000 Gray-iron casting, ASTM A339-51T, Grade 20, 140–160 BHN 51,000 Nodular-iron casting, ASTM A339-51T, Grade 80-60-03, 207–241 BHN 72,000 Gray-iron casting, ASTM A48-48, Class 30, 200–220 BHN 65,000 Gray-iron casting, ASTM A48-48, Class 35, 225–225 BHN 78,000 Gray-iron casting, ASTM A48-48, Class 30, heat-treated (Austempered), 225–300 BHN 90,000 SAE 1020 steel, 130–150 BHN 82,000 SAE 4150 steel, heat-treated to 270–300 BHN, phosphate-coated 20,000 SAE 4150 steel, heat-treated to 270–300 BHN 188,000 SAE 1020 steel, carburized to 0.045 in. depth of case, 50–58 RC 226,000 SAE 1340 steel, induction hardened to 45–55 RC 198,000 SAE 4340 steel, induction hardened to 50–55 RC 226,000 Based on United Shoe Machinery Corp. data by Guy J. Talbourdet. S b F r R ! 2290 1 1 c n f c = c m
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